array(1) { [0]=> object(Apache_Solr_Document)#24 (3) { ["_documentBoost":protected]=> bool(false) ["_fields":protected]=> array(6) { ["content_id"]=> array(1) { [0]=> string(14) "DIRECTORY_3423" } ["content_title"]=> array(1) { [0]=> string(21) "MARIO ROSOLINO ABUNDO" } ["description"]=> array(1) { [0]=> string(110903) "

 

Nato a Pescara il 9/5/1957, nel Luglio del 1979 si laurea in Matematica cum laude presso l'Università degli Studi di L'Aquila. Nell' a.a 79/80 è assistente volontario del corso di Istituzioni di Matematiche presso la Facoltà di Scienze M.F.N. dell' Università di L'Aquila. Negli anni accademici 79/80, 80/81, 81/82, 82/83 è borsista dell'Istituto Nazionale di Alta Matematica (I.N.D.A.M.).  Nell' a.a. 83/84 è professore incaricato di Matematica presso un Liceo Scientifico romano.  Nell' anno 1983 vince il concorso libero a ricercatore universitario di Analisi Matematica (sottosettore Calcolo delle Probabilità) presso l'Università di Roma Tor Vergata e l' 8 ottobre 1984 entra in servizio presso la facoltà di Scienze M.F.N. del suddetto Ateneo. A decorrere dall' 8/10/87 risulta confermato nel ruolo dei ricercatori universitari per il gruppo A02B, successivamente MAT/06. Nel novembre 2004 si trasferisce alla Facoltà di Ingegneria dell'Università di Roma Tor Vergata, dove tuttora presta servizio.  Dal 31 dicembre  2018 e' Professore Associato in Probabilita' e Statistica Matematica (MAT/06) presso il Dipartimento di Matematica dell'Universita' Tor Vergata. 

Attività scientifica Svolge attività di referee per varie riviste internazionali. Fa parte dell’ Editorial Advisory Board di TOAMJ (The Open Appl. Math. Journal). E’ Mathematical Reviewer per MathSciNet. E’ stato coordinatore (dal 1998 al 2000) di un progetto dal titolo: "Metodi stocastici per sistemi biologici cooperativi", finanziato dal Comitato Nazionale per le Scienze Matematiche del CNR.  La produzione scientifica di Mario Abundo ha riguardato inizialmente le proprietà ergodiche e statistiche di mappe sull'intervallo ([1], [2], [3], [4], [5]) e sul cubo n-dimensionale unitario ([7]), con riguardo alle misure invarianti, all'entropia topologica e metrica, agli esponenti caratteristici e teoremi limite centrali, con qualche escursione alla probabilità quantistica ([8]). Successivamente, egli si è occupato di generazione di vettori pseudocasuali e di successioni generate da sistemi dinamici instabili ([11]); di applicazioni di metodi e tecniche della teoria dei processi stocastici alla meccanica statistica, tra cui il metodo del simulated annealing, e di statistica applicata a modelli biomatematici, modellizzando sistemi di interesse biologico ([6], [9], [10], [12], [13]) (dinamica di popolazioni, sistemi preda-predatore, crescita tumorale, interazioni virus-sistema immunitario) per mezzo di equazioni differenziali stocastiche con particolare riguardo all'aspetto computazionale (simulazione numerica e stima dei parametri del modello). Si è poi occupato di modellizzazione e simulazione stocastica di sistemi biologici cooperativi (folding proteico) ([14], [16], [17], [23]) ed è stato coordinatore (dal 1998 al 2000) di un progetto dal titolo: "Metodi stocastici per sistemi biologici cooperativi", finanziato dal Comitato Nazionale per le Scienze Matematiche del CNR.  Inoltre, si è occupato di processi di Markov e loro approssimazione di diffusione ([15], [18], [36]); di proprietà delle soluzioni di equazioni differenziali stocastiche associate a modelli di evoluzione, di problemi di uscita e ottenibilità della frontiera, di proprietà ergodiche e di reversibilità della misura stazionaria di un processo di diffusione ([19]). Più recentemente, ha affrontato lo studio di vari problemi di primo passaggio (diretti e inversi) di processi di diffusione e processi di diffusione con salti attraverso frontiere, costanti o dipendenti dal tempo, deterministiche o stocastiche ([20], [22], [26], [31]); questi problemi hanno applicazioni in Biologia, in Ingegneria, Economia e in Finanza Matematica. Si è occupato di probabilità condizionali di attraversamento del moto Browniano su frontiere lineari a tratti ([24]), e su una frontiera curva mediante approssimazione poligonale della frontiera ([21]); di teoremi di confronto di soluzioni di equazioni differenziali stocastiche ([25]); del rischio di ottenibilità di stati minimali da parte di un processo diffusivo con salti ([27]); di proprietà di funzionali di processi di diffusione unidimensionali ([28], [29], [30], [33]); di diffusioni asimmetriche unidimensionali ([32], [37]); della media temporale di un processo di diffusione con salti ([34]) e di tempi di primo passaggio per processi integrali ([42]); del tempo di primo attraversamento tra una diffusione e un processo di Poisson composto ([35]); di diffusioni unidimensionali con salti aleatori in corrispondenza di una barriera ([38]); dell’area di primo passaggio per processi di diffusioni unidimensionali con e senza salti ([39], [40], Preprint [2]); di problemi inversi di primo passaggio per diffusioni con stato iniziale aleatorio ([41], [44]]); di risultati asintotici sulla probabilità di uscita per processi governati da una rate function di tipo integrale ([43]). Attività didattica Dall' a.a. 1984/85 al 2000/01 svolge corsi di esercitazioni di Analisi Matematica I e II, di Istituzioni di Matematiche I e II e di Calcolo delle Probabilità e Statistica Matematica presso l' Università di Roma Tor Vergata. Assiste inoltre alla preparazione di tesi e partecipa a sedute di laurea in qualità di relatore e controrelatore. Negli a.a. 91/92, 92/93, 93/94, 94/95, 95/96, 96/97, 97/98, 98/99, 99/00, 2001/02, 2002/03, 2003/04, 2004/05, 2005/06, 2006/07, 2007/08, 2008/09, 2009/10, 2010/11, 2011/12 tiene la supplenza del corso di Analisi Matematica I e nell' a.a. 2000/01 le supplenze dei corsi di Analisi Matematica 2 e Analisi Matematica 3, presso la Facoltà di Ingegneria dell' Università di Roma Tor Vergata. Nell' a.a 93/94 tiene la supplenza di Calcolo delle Probabilità presso la Facoltà di Ingegneria dell' Università di L' Aquila. Negli a.a. 98/99, 99/00 e 2000/01 tiene la supplenza del corso di Metodi Probabilistici, Statistici e Processi Stocastici presso la Facoltà di Scienze dell’ Università della Tuscia in Viterbo. Negli a.a. 2001/02, 2002/03, 2003/04, 2004/05, tiene per affidamento il corso di Probabilità 2 per il corso di laurea in Matematica dell’ Università di Roma Tor Vergata. Lo stesso corso tiene per supplenza negli a.a. 2005/06 , 2006/07, 2007/08. Negli a.a. 2008/09, 2009/10, tiene per supplenza il corso di Probabilità 1 per la laurea triennale in Matematica dell’ Università di Roma Tor Vergata. Negli a.a. 2001/02, 2002/03, 2003/04, tiene la supplenza di Calcolo delle Probabilità e Statistica presso la Facoltà di Ingegneria dell' Università di Roma Tor Vergata. Negli a.a. 2004/05, 2005/06, 2006/07, 2007/08, 2008/09, 2009/10, 2011/12 tiene per affidamento il corso di Calcolo delle Probabilità e Statistica per la laurea triennale in Ingegneria dell' Università di Roma Tor Vergata. Negli a.a. 2008/09, 2009/10, 2010/11 tiene per supplenza il corso di Equazioni differenziali stocastiche per la laurea magistrale in Ingegneria Matematica dell' Università di Roma Tor Vergata. Negli a.a. 2008/09, 2009/10, 2010/11, 2011/12 svolge la seconda parte del corso di Complementi di Probabilità e Statistica, per la laurea magistrale in Ingegneria Informatica dell' Università di Roma Tor Vergata. Nel 2000 è stato membro di commissione di un concorso a ricercatore universitario per il settore disciplinare A02B (Probabilità e Statistica Matematica), presso l’Università di Napoli Federico II. Nel 2003 è stato membro di commissione di un concorso a ricercatore universitario per il settore disciplinare MAT/06 (Probabilità e Statistica Matematica), presso l’Università di Genova. E' autore del testo universitario: Esercizi e temi d’esame di Calcolo delle Probabilità e Statistica, Aracne Editrice, Roma, II edizione, 2006 (ISBN 88-548-0493-2),. E’ autore del Testo universitario: Esercizi e problemi di Analisi Matematica 1. Con brevi richiami di teoria. Aracne Editrice, Roma, 2007 (ISBN 978-88-548-1300-7), nonchè di numerosi articoli divulgativi e di didattica della Matematica, Partecipazione a Convegni e Congressi - Mathematical Problems from Physics of fluids Roma, Accademia Nazionale dei Lincei, giugno 1985. - Seminari di Fisica e Matematica, Università di Roma "La Sapienza" e "Tor Vergata", Dicembre 1986- Aprile 1987.  - Anno di Probabilità quantistica Roma, Università "Tor Vergata", Ottobre 1986-Luglio 1987.  - Educational Computing in Mathematics Roma, Università "La Sapienza", 4-6 giugno 1987.  - III Soviet-Italian Symposium on Statistical Mechanics Como, Villa Olmo, 27/6-5/7/87.  - Processi Stocastici in Biostatistica Gargnano, 27/9-3/10/87.  - Dinamica non lineare Bologna, Dip. di Fisica 30/5-3/6/88.  - Fractals in Nature and in Mathematics Roma, Ist. Enciclopedia Ital. 16,17/5/88.  - XVII Conference on Stochastic Processes and Their Applications Roma, 27/6-1/7/88.  - Venice-1 /Symposium on Applied and Industrial Mathematics Venezia, 1-6/10/89.  - Computer Simulations, Statistical methods and Applications Portofino, 21-24/5/90.  - XIV Convegno A.M.A.S.E.S. Pescara, 13-16/9/90 .  - Convegno congiunto progetti 40 % "Modelli probabilistici e Statistica Matematica" e " Processi  Stocastici e Calcolo Stocastico" Maiori, 4-6/10/90 .  - Convegno Annuale ISCS (Italian Society for Computer Simulation) Roma, 14/12/1990. - European Simulation Multiconference Copenhagen, 17-19 June 1991.  - XI European Meeting on Cybernetics and Systems Research Vienna, April 1992. - I Simposio Italo-Russo di Probabilita' e Statistica Matematica e Incontro del Gruppo Nazionale  40 % Processi Stocastici e Calcolo Stocastico Coppito, L'Aquila, 27-30 aprile 1992.  - II International Conference on Biomathematics Repubblica di S. Marino, 5-7 October 1992.  - Stochastic Processes in Biological Modeling Torino, 11-12 June 1993. - XII European Meeting on Cybernetics and System Research Vienna, April 1994.  - XV Congresso Unione Matematica Italiana. Padova, 11-16 settembre 1995. - XIII European Meeting on Cybernetics and Systems Research Vienna, April 1996.  - Convegno Mathesis: Il fascino discreto della Matematica L' Aquila, Aprile 1996.  - Convegno congiunto progetti 40 % " ProcessiStocastici e Calcolo Stocastico" .Cremona settembre 1996  - Convegno Annuale ISCS (Italian Society for Computer Simulation) Roma, dicembre 1996.  - Special functions and their applications in Probability and Statistics Workshop, Pugnochiuso, 18-21 giugno 1997. - XXI Convegno annuale A.M.A.S.E.S. Roma, 10-13 settembre 1997. - XIV European Meeting on Cybernetics and Systems Research Vienna, April 1998. - Convegno Nazionale: Processi stocastici e applicazioni. Padova, settembre 1998 - Congresso nazionale Mathesis , L’ Aquila ottobre 1998 - Convegno Annuale ISCS (Italian Society for Computer Simulation) Roma, giugno 1999 - XVI Congresso Unione Matematica Italiana. Napoli, settembre 1999. - XV European Meeting on Cybernetics and Systems Research Vienna, April 2000. - XXV Convegno annuale A.M.A.S.E.S. Firenze, settembre 2001. - XVI European Meeting on Cybernetics and Systems Research, Vienna, April 2002. - XVII European Meeting on Cybernetics and Systems Research, Vienna, April 2004. - BIOCOMP 2005, Vietri, Dicembre 2005. - XVIII European Meeting on Cybernetics and Systems Research. Vienna, April 2006. - Session chairman at Eurocast 2007: XI European Conference on Computer aided System theory, Las Palmas (Gran Canaria), February 2007. - BIOCOMP 2007, Vietri, Settembre 2007. - IXX European Meeting on Cybernetics and Systems Research. Vienna, March 2008. - SPA Berlin 2009: 33rd Conference on Stochastic Processes and Their Applications, July 2009. - XX European Meeting on Cybernetics and Systems Research. Vienna, April 2010. - Eurocast 2011: XIII European Conference on Computer aided System theory, Las Palmas (Gran Canaria), February 2011. - BIOCOMP 2012, Vietri, Giugno 2012.

FULL LIST OF PUBBLICATIONS OF MARIO ABUNDO Journals/Collections 44. M. Abundo: The double-barrier inverse first-passage problem for Wiener process with random  starting point (2012). Available online 12 September 2012. doi: 10.1016/j.spl.2012.09.006 Printed version will appear in vol. 83 (2013), 168-176. 43. M. Abundo, C. Macci, G. Stabile: Asymptotic results for exit probabilities of stochastic processes governed by an integral type rate function.  Probab. Math. Statis. Vol. 32, (1), (2012), 25-39. 42. M. Abundo: First-passage time of a stochastic integral process trough a linear boundary.        International Journal of Applied  Mathematics (IJAM), vol. 25, No 1, (2012),  41-49. 41. M. Abundo: An inverse first-passage problem for one-dimensional diffusions with random  starting point.  Statistics and Probability Letters, 82 (1) (2012), 7-14;  doi.org/10.1016/j.spl.2011.09.005  40. M. Abundo: On the first-passage area of a one-dimensional jump-diffusion process. Methodol. Comput. Appl.  Probab. Online First, April 2011: DOI: 10.1007/s11009-011-9223-1. 39. M. Abundo and M. Abundo: The first-passage area of an emptying Brownian queue.       International Journal of Applied  Mathematics (IJAM), vol. 24, No 2, (2011), 259-266. 38. M. Abundo: First passage problems for one-dimensional diffusions with random jumps from  a boundary.  Stochastic Anal. Appl. 29 (1)  (2011), 121- 145. 37. M. Abundo: First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes. Open Systems & Information Dynamics  Vol. 16, No. 4  (2009), 325-350. 36. M. Abundo: On the Continuous Diffusion Approximation of Some Discrete Markov Chains.   The Open Applied Mathematics Journal, 2009, 3, 7-13. 35. M. Abundo: On the First Hitting Time of a One-dimensional Diffusion and a Compound  Poisson Process. Methodol. Comput. Appl.  Probab. (2010)  12:473–490    (Online First, 2008: DOI10.1007/s11009-008-9115-1). 34. M. Abundo:  On the distribution of the time average of a  jump-diffusion process        International Journal of Applied  Mathematics (IJAM), vol. 21, No. 3 (2008), 447-454.  33. M. Abundo: Some Remarks on the maximum of a one-dimensional diffusion process.  Probab.  Math.  Statis. Vol. 28 (1) (2008), 107-120. 32. M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions      Lecture Notes in Computer Science, Computer Aided Systems Theory – EUROCAST 2007,  vol. 4739, pp. 179-186, Springer Berlin/ Heidelberg, 2007. 31. M. Abundo: Limit at zero of the first-passage time density and the inverse problem for one- dimensional diffusions Stochastic Anal. Appl., 24 (2006), 1119-1145. 30. M. Abundo: The arc-sine law for the first instant at which a diffusion process equals the ultimate value of a functional Int. J. Pure Appl. Math., 30 (1), 13-22 (2006). 29. M. Abundo: Qualitative behaviour of the first-passage-time density of a one-dimensional diffusion over a moving boundary Scientiae Mathematicae Japonicae, 64, No. 2 (2006), 199-  216, : e-2006, 641-658.  28. M. Abundo: Stopping a stochastic integral process as close as possible to the ultimate value of  a functional Scientiae Mathematicae Japonicae , 60 No. 3 (2004), 475-479, : e-2004, (10) 417- 421.  27. M. Abundo: On the risk of extinction for a population subject to a random markov evolution with jumps Open Sys. & Information Dyn. 11, 105-121 (2004). 26. M. Abundo: On the first-passage time of diffusion processes over a one-sided stochastic  boundary Stochastic Analysis and Applications vol. 21, No. 1, 1-23 (2003). 25. M. Abundo: Some comparison results of solutions of diffusion and jump-diffusion equations.  Advances and Applications in Statistics vol. 2 (1), 51-78 (2002).  24. M. Abundo: Some conditional crossing results of Brownian motion over a piecewise-linear  boundary Statistics and Probability Letters, vol. 58 (2), 131-145 (2002).  23. M. Abundo, L. Accardi, N. Rosato, L. Stella: Analysing protein energy data by a stochastic  model for cooperative interactions: comparison and characterization of cooperativity  J. Math. Biol. 44, 341-359 (2002). 22. M. Abundo: On first-passage-times for one-dimensional jump-diffusion processes.  Probab. Math. Statis., vol 20, Fasc. 2, 399-423 (2000). 21. M. Abundo: Some results about boundary crossing for Brownian motion. Ricerche di  Matematica vol. L, (2), 283-301 (2001). 20. M. Abundo: On first-crossing times of one-dimensional diffusions over two time-dependent  boundaries. Stochastic Analysis and Applications. , 18 (2), 179-200 (2000). 19. M. Abundo: On some properties of one-dimensional diffusion processes on an interval Probab. Math. Statis., vol 17, Fasc. 2 (1997), pp. 235-268. 18. M. Abundo, P. Baldi, L. Caramellino : A diffusion approximation which models hierarchic interactions in cooperative biological systems Open Systems & Information  Dynamics 5: 1-23, (1998). 17. M. Abundo, L. Accardi, N. Rosato, L. Stella: A stochastic model for the  cooperative relaxation of proteins, based on a hierarchy of bonds between aminoacidic  residues Math. Models and Meth. in Appl. Sci., vol. 8, No. 2 (1998) 327-358. 16. M. Abundo, L. Accardi, N. Rosato, G. Mei, A. Finazzi Agrò : A stochastic model for the sigmoidal behaviour of cooperative biological systems  Biophysical Chemistry 58 (1996) 313-323.  15. M. Abundo, L. Caramellino : Some remarks about a Markov chain which models  cooperative biological systems Open Systems & Information Dynamics Vol. 3 No 3 (1995) 325-343.  14. M. Abundo, L. Accardi, N. Rosato : A Markovian model for cooperative interactions  in proteins Math. Models and Meth. in Appl. Sci. Vol. 5, No. 6 (1995) 835-863.  13. M. Abundo, C. Rossi : Some scenario Analyses for HIV epidemic Statistica Applicata, vol. 6, n. 2, 121-136 (1994).  12. M. Abundo, C. Rossi: A stochastic model of the impact of genetic variability of HIV on  the immune system in infected patients In Modeling the AIDS Epidemic E. H. Kaplan and M.L. Brandeau (Editors), 481-498, Raven Press, New York, 1994.  11. M. Abundo, L. Accardi, A. Auricchio : Hyperbolic automorphisms of Tori and pseudo-random sequences Calcolo vol. 29, 213-240 (1992). 10. M. Abundo, C. Rossi, O. Rubiu : Estimation of parameters for a stochastic model of  tumoral cells treated with anticancer agents J. Exp. Clin. Cancer Res., 12, 2, 81-90 (1993).  9. M. Abundo : A stochastic model for predator-prey systems: basic properties,stability  and computer simulation J. Math. Biol. 29: 495-511 (1991). 8. M. Abundo, L. Accardi : Squeezing corrections to the Bloch equations Il Nuovo Cimento vol. 106 B, n. 2, 187-194 (1991). 7. M. Abundo, G. Mele : Absolutely continuous invariant measures for expanding maps of a  d-dimensional unit cube in Rd and their entropy. Note di Matematica vol X, n.2. 217-233  (1990).  6. M. Abundo, C. Rossi : Numerical Simulations of a stochastic model for cancerous cells submitted to chemoterapy J. Math. Biol. (1989) 27: 81,90. 5. M. Abundo : An almost sure invariance principle for the maps Sa(x)=ax(1-x) in the interval [0,1] Le Matematiche, Vol. XLII (1987)- Fasc. I-II, 11-18 .  4. M. Abundo : Entropy and characteristic exponents for the quadratic map on the unit interval  Note di Matematica vol. VII (1987), 47-54. 3. M. Abundo : A remark about topological and measure entropy for a class of maps of the interval [0,1] Rendiconti del Circolo Matematico di Palermo Serie II, Tomo XXXV (1986),  456-465.  2. M. Abundo, B. Tirozzi : A central limit theorem for expanding maps of the interval [0,1]  Boll. Un. Mat. Ital. (6) 4-A (1985), 237-244. 1. M. Abundo, B. Tirozzi : The central limit theorem for a class of maps of the interval [0,1]  Boll. Un. Mat. Ital. (6) 3-B (1984), 25-37.  Proceedings of conferences with referee 14. M. Abundo, M. Abundo: On the first-passage area of an emptying Brownian queue. in: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, Moreno-Diaz R. jr.,  Moreno-Diaz R. eds.) Extended Abstracts of the 13th International Conference on Computer  Aided System Theory, EUROCAST 2011, IUCTC Universidad de Las Palmas de Gran Canaria,  ISBN: 978-84-693-9560-8,  70-71  13.  M. Abundo On First-passage Problems for one-dimensional diffusions with random jump reflection at a boundary. In: R. Trappl (Ed.) Cybernetics and Systems 2010 , pp 163-168, Austrian Society for Cybernetics Studies,Vienna,  2010.  12.  P. Abundo, N. Rosato and M. Abundo A Stochastic Model for Infective Events in Operating Room Caused by Air Contamination.In: Proceedings of BIOCOMP 2007, CP1028, Collective Dynamics: Topics on Competition and Cooperation in the Biosciences (L.M. Ricciardi, A. Buonocore, and E. Pirozzi eds.), American Insitute of Physics, 2008, pp. 198-209. 11. M. Abundo:  On First-passage Problems for Asymmetric Diffusions.               In: R. Trappl (Ed.) Cybernetics and Systems  2008 , pp 238-243, Austrian Society for  Cybernetics Studies,Vienna,  2008.  10. M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions in: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, Moreno-Diaz R. jr.,  Moreno-Diaz R. eds.) Extended Abstracts of the 11th International Conference on Computer  Aided System Theory, EUROCAST 2007, IUCTC Universidad de Las Palmas de Gran Canaria,  ISBN: 978-84-690-3603-7,  66-67  9. M. Abundo: The inverse first-passage time problem for one-dimensional diffusions In: R. Trappl (Ed.) Cybernetics and Systems 2006 , pp 226-231, World Scientific, 2006. 8. M. Abundo: Extinction risk for a population driven by a jump-diffusion equation In: R. Trappl (Ed.) Cybernetics and Systems 2004 , pp 169-175, World Scientific, 2004. 7. M. Abundo: On comparison of solutions of diffusion and jump-diffusion equations  In: R. Trappl (Ed.) Cybernetics and Systems 2002 , pp 307-312, Austrian Society for  Cybernetics Studies, Vienna, 2002. 6. M. Abundo: On boundary up-crossing for Brownian motion. In: R. Trappl (Ed.) Cybernetics  and Systems 2000 , pp 295-300, Austrian Society for Cybernetics Studies, Vienna, 2000. 5. M. Abundo: Some remarks on first-crossing-time problem for one-dimensional diffusion processes. In: R. Trappl (Ed.) Cybernetics and Systems '98 , pp 384-389, Austrian Society  for Cybernetics Studies, Vienna, 1998. 4. M. Abundo: Diffusion approximation of discrete Markov chains with Binomial-like  transition probabilities In: R. Trappl (Ed.) Cybernetics and Systems '96 ,  pp 508-513, Austrian Society for Cybernetics Studies, Vienna, 1996. 3. M. Abundo: Analysis of noise in cooperative systems in Biology In: R. Trappl (Ed.) Cybernetics and Systems '94, pp 823-830, World Scientific, 1994.  2. M. Abundo: A stochastic model for protein aggregation In: Topics on Biomathematics, I. Barbieri et Al. (Editors), 113-118, World Scientific, 1993. 1. M. Abundo: On the non-exit problem for some stochastic dynamical systems  In: R. Trappl (Ed.) Cybernetics and Systems Research '92 , 837-844, World Scientific, 1992. Technical reports 5. M. Abundo: Sequencing DNA fragments by using a simulated annealing algorithm  Technical Report Centro Matematico V. Volterra N.46, July 90. 4. M. Abundo: The simulated annealing algorithm viewed as an iterated function system  Technical Report Centro Matematico V. Volterra N.45, July 90.  3. M. Abundo: Proprietà di trasformazioni sull' intervallo [0,1] Technical Report Dipartimento di Matematica II Università di Roma (1986) .  2. M. Abundo, S. Ghinami, B. Tirozzi: 1/f noise for a stochastic dynamic of a one dimensional  lattice spin system Technical Report Dipartimento di Matematica II Università di Roma,  (1985). 1. M. Abundo: Equivalenza tra l'ensemble canonico e l'ensemble di Gibbs per opportuni campi di Gibbs Estratto della Tesi di Laurea, 1979.  Preprints 1. M. Abundo: On first-hitting time to a linear boundary for perturbed Brownian motion.  Preprint 2012. 2. M. Abundo: The first-crossing area of a diffusion process with jumps over a constant barrier. Preprint 2012. Books 1. M. Abundo: Esercizi e temi d’esame di Calcolo delle Probabilità e Statistica. Aracne Editrice, Roma, II edizione, 2006 (ISBN 88-548-0493-2). 2. M. Abundo: Esercizi e problemi di Analisi Matematica 1. Con brevi richiami di teoria.  Aracne Editrice, Roma, 2007 (ISBN 978-88-548-1300-7)

 

 

Mario Abundo was born in Pescara on May, 9, 1957; in July 1979 he graduated cum laude in Mathematics at the University of L'Aquila. In the academic year 79/80 is voluntary assistant of the course Istituzioni di Mathematiche, Faculty of Science of the University of L'Aquila. In the academic years 79/80, 80/81, 81/82, 82/83 is fellow of the Istituto nazionale di Alta Matematica (INDAM). In the academic year 83/84 is Professor of Mathematics at a High School in Rome. In the year 1983 he wins the open competition for assistant professor of Mathematics (subsector Probability) at the University of Rome Tor Vergata  and in October 8, 1984 enters the service at the Faculty of Science of that University. With effect from 08/10/87 he is confirmed in the role  of Ricercatore universitario for the group A02B, successively MAT/06. In November 2004 he moves to the Faculty of Engineering, University of Rome Tor Vergata, where he  is still serving.

By 31 december  2018 he is Professore Associato in Probabilita' e Statistica Matematica (MAT/06) at the Department of Mathematics, Universita' Tor Vergata. 

 SCIENTIFIC ACTIVITY He is referee for several international journals. He belongs to the Editorial Advisory Board of The Open Appl. Math. Journal (TOAMJ). He is Mathematical Reviewer for MathSciNet. He was the coordinator (from 1998 to 2000) of a project entitled "Stochastic methods for cooperative biological systems", funded by the National Committee for Mathematical Sciences of the National Research Council (CNR). The scientific production of Mario Abundo in the first period mainly concerns the ergodic and statistical properties of maps on the interval ([1], [2], [3], [4], [5])  and on the n-dimensional unit cube ([7]), with regard to the invariant measures, topological and metric entropy, the characteristic exponents and central limit theorems,  with an excursion to the quantum probability ([8]).       Subsequently, he has dealt with generation of pseudo-random vectors and sequences generated by unstable dynamic systems ([11]); with application of methods and  techniques of stochastic processes to statistical mechanics, including the method of simulated annealing; with stochastic models for the evolution of biological systems ([6], [9], [10], [12], [13]) (population dynamics, predator-prey systems, tumor growth, virus-immune system interactions ) obtained in terms of stochastic differential equations, with particular regard to the computational aspect (numerical simulation and estimation of parameters of the model). Then, he worked on modeling and stochastic simulation of cooperative biological systems (protein folding) ([14], [16], [17], [23]) and he was coordinator  (from 1998 to 2000) of a project entitled: "Stochastic methods for cooperative biological systems", funded by the Comitato Nazionale per le Scienze Matematiche of the  Consiglio Nazionale delle Ricerche (CNR). In addition, he worked on Markov processes and their diffusion approximations ([15], [18], [36]), on the properties of solutions of stochastic differential equations  associated to evolution models, on exit problems and attainability of boundaries, on ergodic properties and reversibility of the stationary measure of a  diffusion process ([19]). More recently, he approached the study of various problems (direct and inverse) concerning the first passage of diffusion processes with jumps through constant or  time-dependent, deterministic or stochastic boundaries ([20], [22], [26], [31]); these problems have applications in Biology, Engineering, Economics and Financial  Mathematics. He has worked on the conditional crossing probability of Brownian motion over piecewise linear boundaries ([24]), and on a curve boundary, by using a polygonal approximation of the boundary ([21]); he worked on comparison theorems for solutions of stochastic differential equations ([25]); on the risk  of attaining minimal states by a diffusion process with jumps ([27]); on property of functionals of one-dimensional diffusion processes ([28], [29], [30], [33]);  on asymmetric one-dimensional diffusions ([32], [37]); on the time average of a diffusion process with jumps ([34]) and on first passage times for integral processes  ([42]); on the first hitting time of a diffusion and a compound Poisson process ([35]); on one-dimensional diffusions with random jumps in correspondence of a  barrier ([38]); on the first passage area of one-dimensional diffusions with and without jumps ([39], [40], Preprint [2]); on single or double barrier inverse  first-passage problems for one-dimensional diffusions with random initial state ([41], [44]]); on the asymptotic exit probability for processes governed by a rate  function of integral type ([43]). TEACHING ACTIVITY From the academic year 1984/85 to 2000/01 M. Abundo offers courses of Exercises of Mathematical Analysis, Foundations of Mathematics, and of Probability and Mathematical Statistics, at the University of Rome, Tor Vergata. He also assists in the preparation of thesis and he participates in meetings degree as supervisor. In the academic years 91/92, 92/93, 93/94, 94/95, 95/96, 96/97, 97/98, 98/99, 99/00, 2001/02, 2002/03, 2003/04, 2004 / 05, 2005/06, 2006/07, 2007/08, 2008/09, 2009/10, 2010/11, 2011/12, he holds the "supplenza" of Analisi Matematica I and in the year 2000/01 he holds the "supplenza" of Analisi Matematica 2 and 3 at the Faculty of  Engineering, the University of Rome, Tor Vergata. In the academic year 93/94 he holds the "supplenza" of Calcolo delle Probabilita', at the Faculty of Engineering, University of L 'Aquila. In the academic years 98/99, 99/00 and 2000/01 he holds the "supplenza" of Metodi Probabilistici, Statistici e Processi Stocastici, at the Faculty of Sciences of  University of Tuscia in Viterbo. In the academic years 2001/02, 2002/03, 2003/04, 2004/05, he holds the load of Probabilita' 2 for the degree in Mathematics at the University of Rome, Tor Vergata.  The same teaching he holds as "supplenza" in the academic years 2005/06, 2006/07, 2007/08. In the academic years 2008/09, 2009/10, he holds the "supplenza" of Probabilita' 1 for the degree in Mathematics at the University of Rome, Tor Vergata. In the academic years 2001/02, 2002/03, 2003/04, he holds the "supplenza" of Calcolo delle Probabilita' e Statistica at the Faculty of Engineering, the University of Rome,  Tor Vergata. In the academic years 2004/05, 2005/06, 2006/07, 2007/08, 2008/09, 2009/10, 2011/12 he holds the load of Calcolo delle Probabilita' e Statistica for the degree  in Engineering at the University of Rome, Tor Vergata. In the academic years 2008/09, 2009/10, 2010/11 he holds the "supplenza" of Equazioni differenziali stocastiche for the Laurea Magistrale in  Mathematical Engineering at the University of Rome, Tor Vergata. In the academic years 2008/09, 2009/10, 2010/11, 2011/12 he holds the second part of the course of  Complementi di Probabilita'e Statistica for the Laurea Magistrale in Computer Engineering at the University of Rome, Tor Vergata. In the year 2000 he was a member of the commission of a competition for university researchers, for the subject area A02B (Probability and Mathematical Statistics) at  the University of Naples Federico II. In 2003 he was a member of the commission of a competition for university researchers, for the subject area MAT/06 (Probability and Mathematical Statistics) at the  University of Genoa. He is the author of the teaching book for University: Esercizi e temi d'esame di Calcolo delle Probabilita' e Statistica, Aracne Editrice, Rome, second edition,  2006 (ISBN 88-548-0493-2). He is the author of the teaching book for University: Esercizi e Problemi di Analisi Matematica 1. Con brevi richiami di Teoria. Aracne Editrice, Rome, 2007  (ISBN 978-88-548-1300-7), as well as of several divulgative articles and articles on teaching of Mathematics. Participation to Conferences and Congresses  - Mathematical Problems from Physics of fluids Rome, Accademia Nazionale dei Lincei, June 1985. - Seminar of Physics and Mathematics, University of Rome "La Sapienza" and "Tor Vergata", December 1986 -    April 1987.  - Year of Quantum Probability Rome University "Tor Vergata", October 1986-July 1987.  - Educational Computing in Mathematics Rome University "La Sapienza", 4-6 June 1987.  - III Soviet-Italian Symposium on Statistical Mechanics Como, Villa Olmo, 27/6-5/7/87.  - Stochastic Processes in Biostatistics Gargnano, 27/9-3/10/87.  - Nonlinear Dynamics Bologna, Dept. of Physics 30/5-3/6/88.  - Fractals in Nature and Mathematics in Rome, Encyclopedia Ist Ital 16.17 / 5/88. - XVII Conference on Stochastic Processes and Their Applications Rome, 27/6-1/7/88.  - Venice-1 / Symposium on Applied and Industrial Mathematics Venice, 1-6/10/89.  - Computer Simulations, Statistical methods and Applications Portofino, 21-24/5/90.  - XIV Conference A.M.A.S.E.S. Pescara, 13-16/9/90.  - Joint Meeting projects 40% "Probabilistic models and Mathematical Statistics" and "Processes    Stochastic and Stochastic Calculation "Maiori, 4-6/10/90.  - Annual Meeting ISCS (Italian Society for Computer Simulation) Rome, 14/12/1990.  - European Simulation Multiconference, Copenhagen, 17-19 June 1991. - XI European Meeting on Cybernetics and Systems Research, Vienna, April 1992.  - The Italo-Russian Symposium of Probability 'and Mathematical Statistics and the National Group Meeting    40% Stochastic Processes and Stochastic Calculation Coppito, L'Aquila, 27-30 April 1992. - II International Conference on Biomathematics Republic of S. Marino, 5-7 October 1992. - Stochastic Processes in Biological Modeling Turin, 11-12 June 1993. - XII European Meeting on Cybernetics and Systems Research, Vienna, April 1994. - Fifteenth Congress of the Italian Mathematical Union. Padua, 11-16 September 1995. - XIII European Meeting on Cybernetics and Systems Research, Vienna, April 1996. - Conference Mathesis: The Discreet Charm of Mathematics L 'Aquila, April 1996. - Joint Meeting projects 40% "ProcessiStocastici and Stochastic Calculation." Cremona September 1996 - Annual Meeting ISCS (Italian Society for Computer Simulation) Rome, December 1996. - Special functions and Their applications in Probability and Statistics Workshop,    Pugnochiuso, 18-21 June 1997. - XXI Annual Conference A.M.A.S.E.S. Rome, 10-13 September 1997. - XIV European Meeting on Cybernetics and Systems Research, Vienna, April 1998. - National Conference: Stochastic processes and applications. Padua, September 1998 - National Congress Mathesis, L 'Aquila October 1998 - Annual Meeting ISCS (Italian Society for Computer Simulation) Rome, June 1999 - XVIth Congress of the Italian Mathematical Union. Naples, September 1999. - XV European Meeting on Cybernetics and Systems Research, Vienna, April 2000. - Twenty-fifth Annual Meeting A.M.A.S.E.S. Florence, September 2001. - XVI European Meeting on Cybernetics and Systems Research, Vienna, April 2002. - XVII European Meeting on Cybernetics and Systems Research, Vienna, April 2004. - BIOCOMP 2005, Vietri, December 2005. - XVIII European Meeting on Cybernetics and Systems Research. Vienna, April 2006. - Session chairman at Eurocast 2007: XI European Conference on Computer-aided System Theory,    Las Palmas (Gran Canaria), February 2007. - BIOCOMP 2007, Vietri, September 2007. - IXX European Meeting on Cybernetics and Systems Research. Vienna, March 2008. - SPA Berlin 2009: 33rd Conference on Stochastic Processes and Their Applications, July 2009. - XX European Meeting on Cybernetics and Systems Research. Vienna, April 2010. - Eurocast 2011: XIII European Conference on Computer-aided System Theory,    Las Palmas (Gran Canaria), February 2011. - BIOCOMP 2012, Vietri, June 2012. FULL LIST OF PUBLICATIONS OF MARIO ABUNDO Journals / Collections 44. M. Abundo: The double-barrier reverse first-passage problem for the Wiener process with random        starting point (2012). Available online 12 September 2012. doi: 10.1016/j.spl.2012.09.006  Printed version will Appear in vol. 83 (2013), 168-176. 43. M. Abundo, C. Macci, G. Stable: Asymptotic results for exit probabilities of stochastic        processes Governed by an integral type rate function.        Probab. Math. Statis. Vol 32, (1), (2012), 25-39. 42. M. Abundo: First-passage time of a stochastic integral process trough a linear boundary. International Journal of Applied Mathematics (Ijam), vol. 25, No 1, (2012), 41-49. 41. M. Abundo: An inverse first-passage problem for one-dimensional diffusions with random       starting point. Statistics and Probability Letters, 82 (1) (2012), 7-14;       doi.org/10.1016/j.spl.2011.09.005 40. M. Abundo: On the first-passage area of ??a one-dimensional jump-diffusion process.       Methodol. Comput. Appl. Probab. Online First, April 2011: DOI: 10.1007/s11009-011-9223-1. 39. M. Abundo and M. Abundo: The first-passage area of ??an emptying Brownian queue. International Journal of Applied Mathematics (Ijam), vol. 24, No 2, (2011), 259-266. 38. M. Abundo: First passage problems for one-dimensional diffusions with random jumps from        a boundary. Stochastic Anal. Appl. 29 (1) (2011), 121 - 145. 37. M. Abundo: First-Passage Problems for Diffusions Asymmetric and Skew-diffusion        Processes. Open Systems & Information Dynamics Vol 16, No. 4 (2009), 325-350. 36. M. Abundo: On the Continuous Diffusion Approximation of Some Discrete Markov Chains.        The Open Applied Mathematics Journal, 2009, 3, 7-13. 35. M. Abundo: On the First Hitting Time of a One-dimensional Diffusion and a Compound        Poisson Process. Methodol. Comput. Appl. Probab. (2010) 12:473-490        (Online First, 2008: DOI10.1007/s11009-008-9115-1). 34. M. Abundo: On the distribution of the time average of a jump-diffusion process International Journal of Applied Mathematics (Ijam), vol. 21, No. 3 (2008), 447-454. 33. M. Abundo: Some Remarks on the maximum of a one-dimensional diffusion process.        Probab. Math. Statis. Vol 28 (1) (2008), 107-120. 32. M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions Lecture Notes in Computer Science, Computer Aided Systems Theory - EUROCAST 2007,        vol. 4739, pp. 179-186, Springer Berlin / Heidelberg, 2007. 31. M. Abundo: Limit at zero of the first-passage time density and the inverse problem for one-        dimensional diffusions Stochastic Anal. Appl., 24 (2006), 1119-1145. 30. M. Abundo: The arc-sine law for the first instant alla quale a diffusion process equals the         ultimate value of a functional Int J. Pure Appl. Math., 30 (1), 13-22 (2006). 29. M. Abundo: Qualitative behavior of the first-passage-time density of a one-dimensional        diffusion over a moving boundary Scientiae Mathematicae Japonicae, 64, No. 2 (2006), 199 -        216: E-2006, 641-658. 28. M. Abundo: Stopping a stochastic integral process as close as possible to the ultimate value of        a functional Scientiae Mathematicae Japonicae, 60 No. 3 (2004), 475-479,       : E-2004, (10) 417 - 421. 27. M. Abundo: On the risk of extinction for a population subject to a markov random evolution         with jumps Open Sys. & Information Dyn. 11, 105-121 (2004). 26. M. Abundo: On the first-passage time of diffusion processes over a one-sided stochastic         boundary Stochastic Analysis and Applications vol. 21, No. 1, 1-23 (2003). 25. M. Abundo: Some comparison results of solutions of diffusion and jump-diffusion equations.        Advances and Applications in Statistics vol. 2 (1), 51-78 (2002). 24. M. Abundo: Some conditional crossing results of Brownian motion over a piecewise-linear        boundary Statistics and Probability Letters, vol. 58 (2), 131-145 (2002). 23. M. Abundo, L. Accardi, N. Rosato, L. Stella: Analysing protein energy data by a stochastic        model for cooperative interactions: comparison and characterization of cooperativity        J. Math. Biol. 44, 341-359 (2002). 22. M. Abundo: On first-passage-times for one-dimensional jump-diffusion processes.       Probab. Math. Statis., Vol 20, Issue. 2, 399-423 (2000). 21. M. Abundo: Some results about boundary crossing for Brownian motion. Research       Mathematics vol. L, (2), 283-301 (2001). 20. M. Abundo: On first-crossing times of one-dimensional diffusions over two time-dependent       boundaries. Stochastic Analysis and Applications. , 18 (2), 179-200 (2000). 19. M. Abundo: On some properties of one-dimensional diffusion processes        on an interval Probab. Math. Statis., Vol 17, Issue. 2 (1997), pp. 235-268. 18. M. Abundo, P. Baldi, L. Caramellino: A diffusion approximation Which models       hierarchic cooperative interactions in biological systems Open Systems & Information       Dynamics 5: 1-23, (1998). 17. M. Abundo, L. Accardi, N. Rosato, L. Stella: A stochastic model for the       cooperative relaxation of proteins, based on a hierarchy of bonds between aminoacidic       residues Math. Models and Meth. in Appl. Sci, vol. 8, No. 2 (1998) 327-358. 16. M. Abundo, L. Accardi, N. Rosato, G. Mei, A. Finazzi Agro:       A stochastic model for the sigmoidal behavior of cooperative biological systems       Biophysical Chemistry 58 (1996) 313-323. 15. M. Abundo, L. Caramellino: Some remarks about a Markov chain Which models     cooperative biological systems Open Systems & Information Dynamics      Vol 3 No 3 (1995) 325-343. 14. M. Abundo, L. Accardi, N. Rosé: A Markovian model for cooperative interactions       proteins in Math. Models and Meth. in Appl. Sci Vol 5, No. 6 (1995) 835-863. 13. M. Abundo, C. Rossi: Scenario Analyses for Some HIV epidemic       Applied Statistics, vol. 6, n. 2, 121-136 (1994). 12. M. Abundo, C. Rossi: A stochastic model of the impact of genetic variability of HIV on        the immune system in infected patients In Modeling the AIDS Epidemic        E. H. Kaplan and M.L. Brandeau (Editors), 481-498, Raven Press, New York, 1994. 11. M. Abundo, L. Accardi, A. Auricchio: Hyperbolic automorphisms of Tori and        pseudo-random sequences Calculation vol. 29, 213-240 (1992). 10. M. Abundo, C. Rossi, O. Rubiu: Estimation of parameters for a stochastic model of       tumoral cells treated with anticancer agents J. Exp Clin. Cancer Res, 12, 2, 81-90 (1993). 9. M. Abundo: A stochastic model for predator-prey systems: basic properties, stability        and computer simulation J. Math. Biol. 29: 495-511 (1991). 8. M. Abundo, L. Accardi: Squeezing corrections to the Bloch equations       Il Nuovo Cimento vol. B 106, no. 2, 187-194 (1991). 7. M. Abundo, G. Apples: Absolutely continuous invariant Measures for expanding maps of a        d-dimensional unit cube in Rd and Their entropy. Notes in Mathematics vol X, 2. 217-233       (1990). 6. M. Abundo, C. Rossi: Numerical Simulations of a stochastic model for cancerous cells       Submitted to J. chemoterapy Math. Biol. (1989) 27: 81.90. 5. M. Abundo: An almost sure invariance principle for the maps Sa (x) = ax (1-x) in the interval       [0,1] The Mathematics, Vol XLII (1987) - Issue. I-II, 11-18. 4. M. Abundo: Entropy and characteristic exponents for the quadratic map on the unit interval       Notes in Mathematics vol. VII (1987), 47-54. 3. M. Abundo: A remark about topological and measure entropy for a class of maps of the       interval [0,1] Proceedings of the Mathematical Circle of Palermo Series II, Volume XXXV (1986),       456-465. 2. M. Abundo, B. Tirozzi: A central limit theorem for expanding maps of the interval [0,1]       A Bull. Mat. Ital. (6) 4-A (1985), 237-244. 1. M. Abundo, B. Tirozzi: The central limit theorem for a class of maps of the interval [0,1]       A Bull. Mat. Ital. (6) 3-B (1984), 25-37. Proceedings of conferences with referee 14. M. Abundo, M. Abundo: On the first-passage area of ??an emptying Brownian queue.        in: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, R. Moreno-Diaz jr.,        R. Moreno-Diaz eds.) Extended Abstracts of the 13th International Conference on Computer        Aided System Theory, EUROCAST 2011, IUCTC Universidad de Las Palmas de Gran Canaria,        ISBN: 978-84-693-9560-8, 70-71 13. M. Abundo On First-Passage Problems for one-dimensional diffusions with random jump reflection at a boundary.  In: R. Trappl (Ed.) Cybernetics and Systems 2010, pp. 163-168, Austrian Society for Cybernetics Studies, Vienna, 2010. 12. P. Abundo, N. Rosato and M. Abundo A Stochastic Model for Infective Events in Operating Room Caused by Air Contamination.  In: Proceedings of BIOCOMP 2007, CP1028, Collective Dynamics: Topics on Competition and Cooperation in the Biosciences (LM Ricciardi, A. Buonocore, and E. Pirozzi eds.) American Institute of Physics, 2008, p. 198-209. 11. M. Abundo: On First-Passage Problems for Asymmetric diffusions. In: R. Trappl (Ed.) Cybernetics and Systems 2008, pp. 238-243, Austrian Society for        Cybernetics Studies, Vienna, 2008. 10. M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions        in: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, R. Moreno-Diaz jr.,       R. Moreno-Diaz eds.) Extended Abstracts of the 11th International Conference on Computer       Aided System Theory, EUROCAST 2007, IUCTC Universidad de Las Palmas de Gran Canaria,       ISBN: 978-84-690-3603-7, 66-67 9. M. Abundo: The inverse first-passage time problem for one-dimensional diffusions       In: R. Trappl (Ed.) Cybernetics and Systems 2006, pp. 226-231, World Scientific, 2006. 8. M. Abundo: Extinction risk for a population driven by a jump-diffusion equation        In: R. Trappl (Ed.) Cybernetics and Systems 2004, pp. 169-175, World Scientific, 2004. 7. M. Abundo: On comparison of solutions of diffusion and jump-diffusion equations       In: R. Trappl (Ed.) Cybernetics and Systems 2002, pp. 307-312, Austrian Society for       Cybernetics Studies, Vienna, 2002. 6. M. Abundo: On boundary-crossing up for Brownian motion. In: R. Trappl (Ed.) Cybernetics       and Systems 2000, pp. 295-300, Austrian Society for Cybernetics Studies, Vienna, 2000. 5. M. Abundo: Some remarks on first-crossing-time problem for one-dimensional diffusion        processes. In: R. Trappl (Ed.) Cybernetics and Systems '98, pp. 384-389, Austrian Society        for Cybernetics Studies, Vienna, 1998. 4. M. Abundo: Diffusion approximation of discrete Markov chains with Binomial-like        transition probabilities In: R. Trappl (Ed.) Cybernetics and Systems '96,        pp. 508-513, Austrian Society for Cybernetics Studies, Vienna, 1996. 3. M. Abundo: Analysis of noise in cooperative systems in Biology        In: R. Trappl (Ed.) Cybernetics and Systems '94, pp. 823-830, World Scientific, 1994. 2. M. Abundo: A stochastic model for protein aggregation        In: Topics on Biomathematics, I. Barbieri et al (Editors), 113-118, World Scientific, 1993. 1. M. Abundo: On the non-exit problem for some stochastic dynamical systems        In: R. Trappl (Ed.) Cybernetics and Systems Research '92, 837-844, World Scientific, 1992. Technical reports 5. M. Abundo: Sequencing DNA fragments by using a simulated annealing algorithm       Technical Report Center Mathematician V. Volterra 46, July 90. 4. M. Abundo: The simulated annealing algorithm viewed as an Iterated Function System      Technical Report Center Mathematician V. Volterra Ranked # 45, July 90. 3. M. Abundo: Properties of transformations on 'interval [0,1]       Technical Report Department of Mathematics, University of Rome (1986). 2. M. Abundo, S. Ghinami, B. Tirozzi: 1 / f noise for a stochastic dynamic of a one dimensional        lattice spin systems Technical Report Department of Mathematics, University of Rome,       (1985). 1. M. Abundo: Equivalence between the ensemble and the canonical ensemble of Gibbs appropriate        Gibbs fields Retrieved Thesis, 1979. Preprints 1. M. Abundo: On first-hitting time to a linear boundary for perturbed Brownian motion.     Preprint 2012. 2. M. Abundo: The first-crossing area of ??a diffusion process with jumps over a constant barrier.     Preprint 2012. Books 1. M. Abundo: Esercizi e temi d'esame di Calcolo delle Probabilita' e Statistica.                         Aracne Editrice, Rome, second edition, 2006 (ISBN 88-548-0493-2). 2. M. Abundo: Esercizi e Problemi di Analisi matematica 1. Con brevi richiami di Teoria.                         Aracne Editrice, Rome, 2007 (ISBN 978-88-548-1300-7)

 

By 31 december  2018 he is Professore Associato in Probabilita' e Statistica Matematica (MAT/06) at the Department of Matemathics, Universita' Tor Vergata. 

a:78:{i:0;a:14:{s:9:"citazione";s:179:"Abundo, M. (2019). An inverse first-passage problem revisited: the case of fractional Brownian motion, and time-changed Brownian motion. STOCHASTIC ANALYSIS AND APPLICATIONS, 1-9.";s:4:"data";s:4:"2019";s:2:"id";s:20:"PUBBLICAZIONE_351434";s:6:"handle";s:11:"2108/214937";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:116:"An inverse first-passage problem revisited: the case of fractional Brownian motion, and time-changed Brownian motion";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:29:"10.1080/07362994.2019.1608834";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:1;a:14:{s:9:"citazione";s:139:"Abundo, M., & Pirozzi, E. (2019). On the Fractional Riemann-Liouville Integral of Gauss-Markov processes and applications. [Working paper].";s:4:"data";s:4:"2019";s:2:"id";s:20:"PUBBLICAZIONE_351436";s:6:"handle";s:11:"2108/214939";s:9:"metadata1";s:5:"Altro";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:88:"On the Fractional Riemann-Liouville Integral of Gauss-Markov processes and applications.";s:9:"metadata6";s:21:"Abundo, M; Pirozzi, E";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:2;a:14:{s:9:"citazione";s:181:"Abundo, M. (2018). Some Remarks on the Mean of the Running maximum of Integrated Gauss-Markov Processes and Their First-Passage Times.. In Lecture Notes Computer Science (pp.72-79).";s:4:"data";s:4:"2018";s:2:"id";s:20:"PUBBLICAZIONE_348755";s:6:"handle";s:11:"2108/212963";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:115:"Some Remarks on the Mean of the Running maximum of Integrated Gauss-Markov Processes and Their First-Passage Times.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:27:"10.1007/978-3-319-74727-9_9";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:3;a:14:{s:9:"citazione";s:130:"Abundo, M. (2018). The Randomized First-Hitting Problem of Continuously Time-Changed Brownian Motion. MATHEMATICS, 6(6)(91), 1-10.";s:4:"data";s:4:"2018";s:2:"id";s:20:"PUBBLICAZIONE_348757";s:6:"handle";s:11:"2108/212965";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:82:"The Randomized First-Hitting Problem of Continuously Time-Changed Brownian Motion.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:23:"doi:10.3390/math6060091";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:4;a:14:{s:9:"citazione";s:156:"Abundo, M. (2018). The arctangent law for a certain random time related to one-dimensional diffusions. STOCHASTIC ANALYSIS AND APPLICATIONS, 36(1), 181-187.";s:4:"data";s:4:"2018";s:2:"id";s:20:"PUBBLICAZIONE_348748";s:6:"handle";s:11:"2108/212957";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:83:"The arctangent law for a certain random time related to one-dimensional diffusions.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:29:"10.1080/07362994.2017.1387565";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:5;a:14:{s:9:"citazione";s:180:"Abundo, M., & Furia, S. (2018). Joint Distribution of First-Passage Time and First-Passage Area of Certain Lèvy Processes. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 1-20.";s:4:"data";s:4:"2018";s:2:"id";s:20:"PUBBLICAZIONE_348759";s:6:"handle";s:11:"2108/212967";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";s:69:"First-passage time; First-passage area; Jump-diffusion; Lévy process";s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";s:737:"Let be X(t) = x − μt + σBt − Nt a Lévy process starting from x > 0, where μ ≥ 0, σ ≥ 0, Bt is a standard BM, and Nt is a homogeneous Poisson process with intensity > 0, starting from zero. We study the joint distribution of the first-passage time below zero, τ(x), and the first-passage area, A(x), swept out by X till the time τ(x). In particular, we establish differential-difference equations with outer conditions for the Laplace transforms of τ(x) and A(x), and for their joint moments. In a special case (μ = σ = 0), we show an algorithm to find recursively the moments E[τ(x)mA(x)n], for any integers m and n; moreover, we obtain the expected value of the time average of X till the time τ(x).";s:9:"metadata5";s:92:"Joint Distribution of First-Passage Time and First-Passage Area of Certain Lèvy Processes.";s:9:"metadata6";s:19:"Abundo, M; Furia, S";s:9:"metadata7";s:25:"10.1007/s11009-018-9677-5";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:6;a:14:{s:9:"citazione";s:141:"Abundo, M., & Pirozzi, E. (2018). Integrated Stationary Ornstein-Uhlenbeck Process, and Double Integral Processes. PHYSICA. A, 494, 265-275.";s:4:"data";s:4:"2018";s:2:"id";s:20:"PUBBLICAZIONE_348750";s:6:"handle";s:11:"2108/212959";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:81:"Integrated Stationary Ornstein-Uhlenbeck Process, and Double Integral Processes.";s:9:"metadata6";s:21:"Abundo, M; Pirozzi, E";s:9:"metadata7";s:27:"10.1016/j.physa.2017.12.043";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:7;a:14:{s:9:"citazione";s:181:"Abundo, M. (2017). On the joint distribution of first-passage time and first-passage area of drifted Brownian motion. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 19, 985-996.";s:4:"data";s:4:"2017";s:2:"id";s:20:"PUBBLICAZIONE_333203";s:6:"handle";s:11:"2108/200169";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:98:"On the joint distribution of first-passage time and first-passage area of drifted Brownian motion";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:8;a:14:{s:9:"citazione";s:190:"Abundo, M. (2017). The mean of the running maximum of an integrated Gauss-Markov process and the connection with its first-passage time. STOCHASTIC ANALYSIS AND APPLICATIONS, 35(3), 499-510.";s:4:"data";s:4:"2017";s:2:"id";s:20:"PUBBLICAZIONE_333201";s:6:"handle";s:11:"2108/200166";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:117:"The mean of the running maximum of an integrated Gauss-Markov process and the connection with its first-passage time.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:29:"10.1080/07362994.2016.1273784";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:9;a:14:{s:9:"citazione";s:158:"Abundo, M. (2015). Some Remarks on First-passage Times for Integrated Gauss-Markov Processes.. Paper presented at EUROCAST 2015, LAS PALMAS DE GRAN CANARIA.";s:4:"data";s:4:"2015";s:2:"id";s:20:"PUBBLICAZIONE_231712";s:6:"handle";s:11:"2108/113518";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:75:"Some Remarks on First-passage Times for Integrated Gauss-Markov Processes.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:10;a:14:{s:9:"citazione";s:131:"Abundo, M.R. (2014). On first-hitting time of a linear boundary by perturbed brownian motion. THE OPEN MATHEMATICS JOURNAL, 7, 6-8.";s:4:"data";s:4:"2014";s:2:"id";s:20:"PUBBLICAZIONE_236670";s:6:"handle";s:11:"2108/117815";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:71:"On first-hitting time of a linear boundary by perturbed brownian motion";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";s:27:"10.2174/1874117701407010006";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:11;a:14:{s:9:"citazione";s:167:"Abundo, M.R. (2014). One-dimensional reflected diffusions with two boundaries and an inverse first- hitting problem. STOCHASTIC ANALYSIS AND APPLICATIONS, 32, 975-991.";s:4:"data";s:4:"2014";s:2:"id";s:20:"PUBBLICAZIONE_205109";s:6:"handle";s:10:"2108/97449";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:95:"One-dimensional reflected diffusions with two boundaries and an inverse first- hitting problem.";s:9:"metadata6";s:11:"Abundo, M R";s:9:"metadata7";s:28:"10.1080/07362994.2014.959595";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:12;a:14:{s:9:"citazione";s:176:"Abundo, M. (2013). Investigating the distribution of the first-crossing area of a diffusion process with jumps over a threshold. THE OPEN APPLIED MATHEMATICS JOURNAL, 7, 18-28.";s:4:"data";s:4:"2013";s:2:"id";s:20:"PUBBLICAZIONE_183361";s:6:"handle";s:10:"2108/89075";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:108:"Investigating the distribution of the first-crossing area of a diffusion process with jumps over a threshold";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:13;a:14:{s:9:"citazione";s:151:"Abundo, M. (2013). On the first-passage area of a one-dimensional jump-diffusion process. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 15, 85-103.";s:4:"data";s:4:"2013";s:2:"id";s:19:"PUBBLICAZIONE_37003";s:6:"handle";s:9:"2108/9263";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:69:"On the First-Passage Area of a One-Dimensional Jump-Diffusion Process";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1007/s11009-011-9223-1";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:14;a:14:{s:9:"citazione";s:127:"Abundo, M. (2013). On the representation of an integrated Gauss-Markov process. SCIENTIAE MATHEMATICAE JAPONICAE, 26, 719-723.";s:4:"data";s:4:"2013";s:2:"id";s:20:"PUBBLICAZIONE_186783";s:6:"handle";s:10:"2108/89068";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:60:"On the representation of an integrated Gauss-Markov process";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:15;a:14:{s:9:"citazione";s:264:"Abundo, M. (2013). Some Remarks on the First-Crossing Area of a Diffusion Process with Jumps over a Constant Barrier.. In Lecture Notes in Computer Science, Computer Aided Systems Theory. EUROCAST 2013, Part I. vol. 8111 (pp. 20-27). Berlin/ Heidelberg : Springer.";s:4:"data";s:4:"2013";s:2:"id";s:20:"PUBBLICAZIONE_186782";s:6:"handle";s:10:"2108/89067";s:9:"metadata1";s:19:"Contributo in libro";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:98:"Some Remarks on the First-Crossing Area of a Diffusion Process with Jumps over a Constant Barrier.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:29:"DOI 10.1007/978-3-642-53856-8";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:16;a:14:{s:9:"citazione";s:146:"Abundo, M. (2013). Some randomized first-passage problems for one-dimensional diffusion processes. SCIENTIAE MATHEMATICAE JAPONICAE, 76(1), 33-46.";s:4:"data";s:4:"2013";s:2:"id";s:20:"PUBBLICAZIONE_183566";s:6:"handle";s:10:"2108/89074";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:78:"Some randomized first-passage problems for one-dimensional diffusion processes";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:17;a:14:{s:9:"citazione";s:164:"Abundo, M. (2013). The double-barrier inverse first-passage problem for Wiener process with random starting point. STATISTICS & PROBABILITY LETTERS, 83(1), 168-176.";s:4:"data";s:4:"2013";s:2:"id";s:20:"PUBBLICAZIONE_183669";s:6:"handle";s:10:"2108/89072";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:94:"The double-barrier inverse first-passage problem for Wiener process with random starting point";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1016/j.spl.2012.09.006";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:18;a:14:{s:9:"citazione";s:180:"Abundo, M.R. (2013). Solving an Inverse First-Passage-Time Problem for Wiener Process Subject to Random Jumps from a Boundary. STOCHASTIC ANALYSIS AND APPLICATIONS, 31(4), 695-707.";s:4:"data";s:4:"2013";s:2:"id";s:20:"PUBBLICAZIONE_183345";s:6:"handle";s:10:"2108/89069";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:104:"Solving an Inverse First-Passage-Time Problem for Wiener Process Subject to Random Jumps from a Boundary";s:9:"metadata6";s:11:"Abundo, M R";s:9:"metadata7";s:28:"10.1080/07362994.2013.800358";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:19;a:14:{s:9:"citazione";s:157:"Abundo, M. (2012). An inverse first-passage problem for one-dimensional diffusions with random starting point. STATISTICS & PROBABILITY LETTERS, 82(1), 7-14.";s:4:"data";s:4:"2012";s:2:"id";s:20:"PUBBLICAZIONE_186802";s:6:"handle";s:10:"2108/89070";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:91:"An inverse first-passage problem for one-dimensional diffusions with random starting point.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:33:"doi.org/10.1016/j.spl.2011.09.005";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:20;a:14:{s:9:"citazione";s:181:"Abundo, M. (2012). An inverse first-passage problem for one-dimensional diffusions with random starting point (vol 82, pg 7, 2012). STATISTICS & PROBABILITY LETTERS, 82(3), 705-705.";s:4:"data";s:4:"2012";s:2:"id";s:20:"PUBBLICAZIONE_186893";s:6:"handle";s:10:"2108/89211";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:35:"Settore MAT/05 - Analisi Matematica";s:9:"metadata4";N;s:9:"metadata5";s:111:"An inverse first-passage problem for one-dimensional diffusions with random starting point (vol 82, pg 7, 2012)";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1016/j.spl.2011.11.020";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:21;a:14:{s:9:"citazione";s:170:"Abundo, M. (2012). First-passage time of a stochastic integral process through a linear boundary. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 25(1), 41-49.";s:4:"data";s:4:"2012";s:2:"id";s:20:"PUBBLICAZIONE_184029";s:6:"handle";s:10:"2108/89071";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:77:"First-passage time of a stochastic integral process through a linear boundary";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:22;a:14:{s:9:"citazione";s:209:"Abundo, M., Macci, C., & Stabile, G. (2012). Asymptotic results for exit probabilities of stochastic processes governed by an integral type rate function. PROBABILITY AND MATHEMATICAL STATISTICS, 32(1), 25-39.";s:4:"data";s:4:"2012";s:2:"id";s:20:"PUBBLICAZIONE_178120";s:6:"handle";s:10:"2108/86408";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:108:"Asymptotic results for exit probabilities of stochastic processes governed by an integral type rate function";s:9:"metadata6";s:31:"Abundo, M; Macci, C; Stabile, G";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:23;a:14:{s:9:"citazione";s:161:"Abundo, M. (2011). First passage problems for one-dimensional diffusions with random jumps from a boundary. STOCHASTIC ANALYSIS AND APPLICATIONS, 29(1), 121-145.";s:4:"data";s:4:"2011";s:2:"id";s:19:"PUBBLICAZIONE_32652";s:6:"handle";s:9:"2108/8574";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:87:"First passage problems for one-dimensional diffusions with random jumps from a boundary";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:28:"10.1080/07362994.2011.532037";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:24;a:14:{s:9:"citazione";s:201:"Abundo, M. (2011). On the first-passage area of an emptying Brownian queue. In Extended Abstracts of the 13th International Conference on Computer Aided System Theory, EUROCAST 2011 (pp.70-71).";s:4:"data";s:4:"2011";s:2:"id";s:19:"PUBBLICAZIONE_33996";s:6:"handle";s:9:"2108/8582";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:55:"On the first-passage area of an emptying Brownian queue";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:25;a:14:{s:9:"citazione";s:137:"Abundo, M. (2011). The first-passage area of an emptying Brownian queue. IAENG INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS, 24, 259-266.";s:4:"data";s:4:"2011";s:2:"id";s:19:"PUBBLICAZIONE_32577";s:6:"handle";s:9:"2108/8495";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:52:"The first-passage area of an emptying Brownian queue";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:26;a:14:{s:9:"citazione";s:220:"Abundo, M. (2010). On First-passage Problems for one-dimensional diffusions with random jump reflection at a boundary. In Cybernetics and Systems 2010 (pp.163-168). Vienna : Austrian Society for Cybernetics Studies.";s:4:"data";s:4:"2010";s:2:"id";s:19:"PUBBLICAZIONE_34041";s:6:"handle";s:9:"2108/8580";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:103:"On First-passage Problems for one-dimensional diffusions with random jump reflection at a boundary";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:27;a:14:{s:9:"citazione";s:174:"Abundo, M. (2010). On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 12(3), 473-490.";s:4:"data";s:4:"2010";s:2:"id";s:19:"PUBBLICAZIONE_32698";s:6:"handle";s:9:"2108/8576";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:88:"On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1007/s11009-008-9115-1";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:28;a:14:{s:9:"citazione";s:150:"Abundo, M. (2009). First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes. OPEN SYSTEMS & INFORMATION DYNAMICS, 16(4), 325-350.";s:4:"data";s:4:"2009";s:2:"id";s:19:"PUBBLICAZIONE_32735";s:6:"handle";s:9:"2108/8578";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:77:"First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1142/S1230161209000256";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:29;a:14:{s:9:"citazione";s:139:"Abundo, M. (2009). On the Continuous Diffusion Approximation of Some Discrete Markov Chains. THE OPEN APPLIED MATHEMATICS JOURNAL, 3, 7-13.";s:4:"data";s:4:"2009";s:2:"id";s:19:"PUBBLICAZIONE_32770";s:6:"handle";s:9:"2108/8735";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:72:"On the Continuous Diffusion Approximation of Some Discrete Markov Chains";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:30;a:14:{s:9:"citazione";s:129:"Abundo, M. (2008). On First-passage Problems for Asymmetric Diffusions.. Paper presented at Cybernetics and Systems 2008, Vienna.";s:4:"data";s:4:"2008";s:2:"id";s:19:"PUBBLICAZIONE_36496";s:6:"handle";s:9:"2108/9404";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:52:"On First-passage Problems for Asymmetric Diffusions.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:31;a:14:{s:9:"citazione";s:150:"Abundo, M. (2008). On the distribution of the time average of a jump-diffusion process. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS, 21(3), 447-454.";s:4:"data";s:4:"2008";s:2:"id";s:19:"PUBBLICAZIONE_32905";s:6:"handle";s:9:"2108/8584";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:68:"On the distribution of the time average of a jump-diffusion process";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:32;a:14:{s:9:"citazione";s:153:"Abundo, M. (2008). Some Remarks on the maximum of a one-dimensional diffusion process. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 28(1), 107-120.";s:4:"data";s:4:"2008";s:2:"id";s:19:"PUBBLICAZIONE_35758";s:6:"handle";s:9:"2108/8978";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:67:"Some Remarks on the maximum of a one-dimensional diffusion process.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:33;a:14:{s:9:"citazione";s:182:"Abundo, M. (2007). On first-passage problems for asymmetric one-dimensional diffusions. In COMPUTER AIDED SYSTEMS THEORY- EUROCAST 2007 (pp.179-186). BERLIN : SPRINGER-VERLAG BERLIN.";s:4:"data";s:4:"2007";s:2:"id";s:19:"PUBBLICAZIONE_13953";s:6:"handle";s:10:"2108/23394";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:67:"On first-passage problems for asymmetric one-dimensional diffusions";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1007/978-3-540-75867-9";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:34;a:14:{s:9:"citazione";s:97:"Abundo, M. (2006). Esercizi e temi d’esame di calcolo delle probabilità e statistica.. ARACNE.";s:4:"data";s:4:"2006";s:2:"id";s:19:"PUBBLICAZIONE_34397";s:6:"handle";s:9:"2108/8686";s:9:"metadata1";s:10:"Monografia";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:69:"Esercizi e temi d’esame di calcolo delle probabilità e statistica.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:35;a:14:{s:9:"citazione";s:178:"Abundo, M. (2006). Limit at zero of the first-passage time density and the inverse problem for one-dimensional diffusions. STOCHASTIC ANALYSIS AND APPLICATIONS, 24(6), 1119-1145.";s:4:"data";s:4:"2006";s:2:"id";s:18:"PUBBLICAZIONE_2501";s:6:"handle";s:10:"2108/23403";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:102:"Limit at zero of the first-passage time density and the inverse problem for one-dimensional diffusions";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1080/07362990600958804";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:36;a:14:{s:9:"citazione";s:186:"Abundo, M. (2006). Qualitative behaviour of the first-passage-time density of a one-dimensional diffusion over a moving boundary. SCIENTIAE MATHEMATICAE JAPONICAE, 64(2), 199-216.";s:4:"data";s:4:"2006";s:2:"id";s:19:"PUBBLICAZIONE_35773";s:6:"handle";s:9:"2108/9005";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:116:"Qualitative behaviour of the first-passage-time density of a one-dimensional diffusion over a moving boundary";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:37;a:14:{s:9:"citazione";s:206:"Abundo, M. (2006). The arc-sine law for the first instant at which a diffusion process equals the ultimate value of a functional. INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS, 30(1), 13-22.";s:4:"data";s:4:"2006";s:2:"id";s:19:"PUBBLICAZIONE_35771";s:6:"handle";s:9:"2108/9003";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:117:"The arc-sine law for the first instant at which a diffusion process equals the ultimate value of a functional";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1007/s11009-011-9223-1";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:38;a:14:{s:9:"citazione";s:155:"Abundo, M.R. (2006). The inverse first-passage time problem for one-dimensional diffusions. In Cybernetics and Systems 2006 (pp.226-231). World Scientific.";s:4:"data";s:4:"2006";s:2:"id";s:19:"PUBBLICAZIONE_36498";s:6:"handle";s:9:"2108/9409";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:69:"The inverse first-passage time problem for one-dimensional diffusions";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:39;a:14:{s:9:"citazione";s:162:"Abundo M. (2004). On the risk of extinction for a population subject to a random Markov evolution with jumps. OPEN SYSTEMS & INFORMATION DYNAMICS, 11(2), 105-121.";s:4:"data";s:4:"2004";s:2:"id";s:18:"PUBBLICAZIONE_2603";s:6:"handle";s:10:"2108/23406";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:90:"On the risk of extinction for a population subject to a random Markov evolution with jumps";s:9:"metadata6";s:9:"Abundo M.";s:9:"metadata7";s:34:"10.1023/B:OPSY.0000034190.48550.25";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:40;a:14:{s:9:"citazione";s:176:"Abundo, M. (2004). Stopping a stochastic integral process as close as possible to the ultimate value of a functional. SCIENTIAE MATHEMATICAE JAPONICAE, 60(3), 475-479.";s:4:"data";s:4:"2004";s:2:"id";s:19:"PUBBLICAZIONE_35776";s:6:"handle";s:9:"2108/9007";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:106:"Stopping a stochastic integral process as close as possible to the ultimate value of a functional";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:41;a:14:{s:9:"citazione";s:154:"Abundo, M.R. (2004). Extinction risk for a population driven by a jump-diffusion equation. In Cybernetics and Systems 2004 (pp.169-175). World Scientific.";s:4:"data";s:4:"2004";s:2:"id";s:19:"PUBBLICAZIONE_36501";s:6:"handle";s:9:"2108/9410";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:68:"Extinction risk for a population driven by a jump-diffusion equation";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:42;a:14:{s:9:"citazione";s:156:"Abundo, M. (2003). On the first-passage time of a diffusion process over a one-sided stochastic boundary. STOCHASTIC ANALYSIS AND APPLICATIONS, 21(1), 1-23.";s:4:"data";s:4:"2003";s:2:"id";s:18:"PUBBLICAZIONE_1574";s:6:"handle";s:10:"2108/23409";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:85:"On the first-passage time of a diffusion process over a one-sided stochastic boundary";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:21:"10.1081/SAP-120017530";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:43;a:14:{s:9:"citazione";s:152:"Abundo, M. (2002). Some comparison results of solutions of diffusion and jump-diffusion equations. ADVANCES AND APPLICATIONS IN STATISTICS, 2(1), 51-78.";s:4:"data";s:4:"2002";s:2:"id";s:19:"PUBBLICAZIONE_35779";s:6:"handle";s:9:"2108/9083";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:79:"Some comparison results of solutions of diffusion and jump-diffusion equations.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:44;a:14:{s:9:"citazione";s:155:"Abundo, M. (2002). Some conditional crossing results of Brownian motion over a piecewise-linear boundary. STATISTICS & PROBABILITY LETTERS, 58(2), 131-145.";s:4:"data";s:4:"2002";s:2:"id";s:19:"PUBBLICAZIONE_15951";s:6:"handle";s:10:"2108/23385";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:85:"Some conditional crossing results of Brownian motion over a piecewise-linear boundary";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:29:"10.1016/S0167-7152(02)00108-6";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:45;a:14:{s:9:"citazione";s:238:"Abundo, M., Accardi, L., Rosato, N., & Stella, L. (2002). Analysing protein energy data by a stochastic model for cooperative interactions: Comparison and characterization of cooperativity. JOURNAL OF MATHEMATICAL BIOLOGY, 44(4), 341-359.";s:4:"data";s:4:"2002";s:2:"id";s:19:"PUBBLICAZIONE_14772";s:6:"handle";s:10:"2108/23390";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:130:"Analysing protein energy data by a stochastic model for cooperative interactions: Comparison and characterization of cooperativity";s:9:"metadata6";s:43:"Abundo, M; Accardi, L; Rosato, N; Stella, L";s:9:"metadata7";s:21:"10.1007/s002850100133";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:46;a:14:{s:9:"citazione";s:130:"Abundo, M.R. (2002). On comparison of solutions of diffusion and jump-diffusion equations. Paper presented at EMCSR 2002, Vienna.";s:4:"data";s:4:"2002";s:2:"id";s:19:"PUBBLICAZIONE_36503";s:6:"handle";s:9:"2108/9411";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:69:"On comparison of solutions of diffusion and jump-diffusion equations";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:47;a:14:{s:9:"citazione";s:115:"Abundo, M. (2001). Some results about boundary crossing for Brownian motion. RICERCHE DI MATEMATICA, L(2), 283-301.";s:4:"data";s:4:"2001";s:2:"id";s:19:"PUBBLICAZIONE_35940";s:6:"handle";s:9:"2108/9132";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:56:"Some results about boundary crossing for Brownian motion";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:48;a:14:{s:9:"citazione";s:162:"Abundo, M. (2000). On first-crossing times of one-dimensional diffusions over two time-dependent boundaries. STOCHASTIC ANALYSIS AND APPLICATIONS, 18(2), 179-200.";s:4:"data";s:4:"2000";s:2:"id";s:19:"PUBBLICAZIONE_13662";s:6:"handle";s:10:"2108/23741";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:88:"On first-crossing times of one-dimensional diffusions over two time-dependent boundaries";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:25:"10.1080/07362990008809663";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:49;a:14:{s:9:"citazione";s:145:"Abundo, M. (2000). On first-passage-times for one-dimensional jump-diffusion processes. PROBABILITY AND MATHEMATICAL STATISTICS, 20(2), 399-423.";s:4:"data";s:4:"2000";s:2:"id";s:19:"PUBBLICAZIONE_35783";s:6:"handle";s:9:"2108/9084";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:69:"On first-passage-times for one-dimensional jump-diffusion processes.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:50;a:14:{s:9:"citazione";s:105:"Abundo, M.R. (2000). On boundary up-crossing for Brownian motion.. Paper presented at EMCSR 2000, Vienna.";s:4:"data";s:4:"2000";s:2:"id";s:19:"PUBBLICAZIONE_36505";s:6:"handle";s:9:"2108/9412";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:44:"On boundary up-crossing for Brownian motion.";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:51;a:14:{s:9:"citazione";s:134:"Accardi, L., & Abundo, M. (1999). A stochastic model for the cooperative behaviour of biological systems. AMINO ACIDS, 17(1), 120-121.";s:4:"data";s:4:"1999";s:2:"id";s:20:"PUBBLICAZIONE_168541";s:6:"handle";s:10:"2108/81387";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:70:"A stochastic model for the cooperative behaviour of biological systems";s:9:"metadata6";s:21:"Accardi, L; Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:52;a:14:{s:9:"citazione";s:254:"Abundo, M., Accardi, L., Stella, L., & Rosato, N. (1998). A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acid residues. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 8(2), 327-358.";s:4:"data";s:4:"1998";s:2:"id";s:20:"PUBBLICAZIONE_168340";s:6:"handle";s:10:"2108/81328";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:127:"A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acid residues";s:9:"metadata6";s:43:"Abundo, M; Accardi, L; Stella, L; Rosato, N";s:9:"metadata7";s:25:"10.1142/S0218202598000147";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:53;a:14:{s:9:"citazione";s:256:"Abundo, M., Accardi, L., Stella, L., & Rosato, N. (1998). A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acidic residues. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 8(2), 327-358.";s:4:"data";s:4:"1998";s:2:"id";s:19:"PUBBLICAZIONE_10613";s:6:"handle";s:10:"2108/23401";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:129:"A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acidic residues";s:9:"metadata6";s:43:"Abundo, M; Accardi, L; Stella, L; Rosato, N";s:9:"metadata7";s:25:"10.1142/S0218202598000147";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:54;a:14:{s:9:"citazione";s:195:"Abundo, M., Baldi, P., & Caramellino, L. (1998). A diffusion approximation which models hierarchic interactions in cooperative biological systems. OPEN SYSTEMS & INFORMATION DYNAMICS, 5(1), 1-23.";s:4:"data";s:4:"1998";s:2:"id";s:18:"PUBBLICAZIONE_7432";s:6:"handle";s:10:"2108/23402";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:96:"A diffusion approximation which models hierarchic interactions in cooperative biological systems";s:9:"metadata6";s:36:"Abundo, M ; Baldi,P ; Caramellino, L";s:9:"metadata7";s:23:"10.1023/A:1009658417365";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:55;a:14:{s:9:"citazione";s:208:"Abundo, M.R. (1998). Some remarks on first-crossing-time problem for one-dimensional diffusion processes.. In Cybernetics andSystems '98 (pp.384-389). Vienna : Austrian Society for Cybernetics Studies.";s:4:"data";s:4:"1998";s:2:"id";s:19:"PUBBLICAZIONE_36509";s:6:"handle";s:9:"2108/9413";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:91:"Some remarks on first-crossing-time problem for one-dimensional diffusion processes.";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:56;a:14:{s:9:"citazione";s:166:"Abundo, M. (1997). On some properties of one-dimensional diffusion processes on an interval. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 17(2), 235-268.";s:4:"data";s:4:"1997";s:2:"id";s:19:"PUBBLICAZIONE_36398";s:6:"handle";s:9:"2108/9226";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:79:"On some properties of one-dimensional diffusion processes on an interval";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:57;a:14:{s:9:"citazione";s:194:"Abundo, M., Accardi, L., Finazzi Agro', A., Mei, G., & Rosato, N. (1996). A stochastic model for the sigmoidal behaviour of cooperative biological systems. BIOPHYSICAL CHEMISTRY, 58(3), 313-323.";s:4:"data";s:4:"1996";s:2:"id";s:19:"PUBBLICAZIONE_21098";s:6:"handle";s:10:"2108/23195";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:80:"A stochastic model for the sigmoidal behaviour of cooperative biological systems";s:9:"metadata6";s:62:"Abundo, M ; Accardi, L ; Finazzi Agro', A ; Mei, G ; Rosato, N";s:9:"metadata7";s:28:"10.1016/0301-4622(95)00111-5";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:58;a:14:{s:9:"citazione";s:194:"Abundo, M., Accardi, L., Finazzi Agrò, A., Mei, G., & Rosato, N. (1996). A stochastic model for the sigmoidal behaviour of cooperative biological systems. BIOPHYSICAL CHEMISTRY, 58(3), 313-323.";s:4:"data";s:4:"1996";s:2:"id";s:20:"PUBBLICAZIONE_166727";s:6:"handle";s:10:"2108/80187";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:80:"A stochastic model for the sigmoidal behaviour of cooperative biological systems";s:9:"metadata6";s:58:"Abundo, M; Accardi, L; Finazzi Agrò, A; Mei, G; Rosato, N";s:9:"metadata7";s:28:"10.1016/0301-4622(95)00111-5";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:59;a:14:{s:9:"citazione";s:223:"Abundo, M.R. (1996). Diffusion approximation of discrete Markov chains with Binomial-like transition probabilities. In Cybernetics and Systems '96 (pp.508-513). Vienna : Austrian Society for Cybernetics Studies.";s:4:"data";s:4:"1996";s:2:"id";s:19:"PUBBLICAZIONE_36513";s:6:"handle";s:9:"2108/9414";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:105:"Diffusion approximation of discrete Markov chains with Binomial-like transition probabilities";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:60;a:14:{s:9:"citazione";s:162:"Abundo, M., & Caramellino, L. (1995). Some remarks on a Markov chain modelling cooperative biological systems. OPEN SYSTEMS & INFORMATION DYNAMICS, 3(3), 325-343.";s:4:"data";s:4:"1995";s:2:"id";s:18:"PUBBLICAZIONE_5884";s:6:"handle";s:10:"2108/23404";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:71:"Some remarks on a Markov chain modelling cooperative biological systems";s:9:"metadata6";s:25:"Abundo, M; Caramellino, L";s:9:"metadata7";s:18:"10.1007/BF02228996";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:61;a:14:{s:9:"citazione";s:173:"Abundo, M., Accardi, L., & Rosato, N. (1995). A Markovian model for cooperative interactions in proteins. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 5(6), 835-863.";s:4:"data";s:4:"1995";s:2:"id";s:19:"PUBBLICAZIONE_12994";s:6:"handle";s:10:"2108/23399";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:58:"A Markovian model for cooperative interactions in proteins";s:9:"metadata6";s:32:"Abundo, M; Accardi, L; Rosato, N";s:9:"metadata7";s:25:"10.1142/S0218202595000462";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:62;a:14:{s:9:"citazione";s:243:"Abundo, M., & Rossi, C. (1994). A stochastic model of the impact of genetic variability of HIV on the immune system in infected patients. In MODELING THE AIDS EPIDEMIC: PLANNING, POLICY, AND PREDICTION (pp.481-498). PHILADELPHIA : RAVEN PRESS.";s:4:"data";s:4:"1994";s:2:"id";s:19:"PUBBLICAZIONE_11234";s:6:"handle";s:10:"2108/23400";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:104:"A stochastic model of the impact of genetic variability of HIV on the immune system in infected patients";s:9:"metadata6";s:19:"Abundo, M; Rossi, C";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:63;a:14:{s:9:"citazione";s:109:"Abundo, M., & Rossi, C. (1994). Some scenario Analyses for HIV epidemic. STATISTICA APPLICATA, 6(2), 121-136.";s:4:"data";s:4:"1994";s:2:"id";s:19:"PUBBLICAZIONE_36400";s:6:"handle";s:9:"2108/9225";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:39:"Some scenario Analyses for HIV epidemic";s:9:"metadata6";s:19:"Abundo, M; Rossi, C";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:64;a:14:{s:9:"citazione";s:135:"Abundo, M.R. (1994). Analysis of noise in cooperative systems in Biology. In Cybernetics nd Systems '94 (pp.823-830). World Scientific.";s:4:"data";s:4:"1994";s:2:"id";s:19:"PUBBLICAZIONE_36516";s:6:"handle";s:9:"2108/9415";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:51:"Analysis of noise in cooperative systems in Biology";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:65;a:14:{s:9:"citazione";s:201:"Abundo M, Rossi C, & Rubiu O (1993). Estimation of parameters for a stochastic model of tumoral cells treated with anticancer agents. JOURNAL OF EXPERIMENTAL & CLINICAL CANCER RESEARCH, 12(2), 81-90.";s:4:"data";s:4:"1993";s:2:"id";s:19:"PUBBLICAZIONE_20232";s:6:"handle";s:10:"2108/23384";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:95:"Estimation of parameters for a stochastic model of tumoral cells treated with anticancer agents";s:9:"metadata6";s:26:"Abundo M; Rossi C; Rubiu O";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:66;a:14:{s:9:"citazione";s:124:"Abundo, M.R. (1993). A stochastic model for protein aggregation. In Topics on Biomathematics (pp.113-118). World Scientific.";s:4:"data";s:4:"1993";s:2:"id";s:19:"PUBBLICAZIONE_36519";s:6:"handle";s:9:"2108/9416";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:42:"A stochastic model for protein aggregation";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:67;a:14:{s:9:"citazione";s:153:"Abundo M, Accardi L, & Auricchio A (1992). Hyperbolic automorphisms of tori and pseudo-random sequences. CALCOLO, 29(2009/04/03 00:00:00.000), 213-240.";s:4:"data";s:4:"1992";s:2:"id";s:18:"PUBBLICAZIONE_5251";s:6:"handle";s:10:"2108/23055";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:60:"Hyperbolic automorphisms of tori and pseudo-random sequences";s:9:"metadata6";s:32:"Abundo M; Accardi L; Auricchio A";s:9:"metadata7";s:18:"10.1007/BF02576183";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:68;a:14:{s:9:"citazione";s:155:"Abundo, M.R. (1992). On the non-exit problem for some stochastic dynamical systems. In Cybernetics and Systems Research '92 (pp.837-844). World Scientific.";s:4:"data";s:4:"1992";s:2:"id";s:19:"PUBBLICAZIONE_36522";s:6:"handle";s:9:"2108/9417";s:9:"metadata1";s:21:"Intervento a convegno";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:61:"On the non-exit problem for some stochastic dynamical systems";s:9:"metadata6";s:10:"Abundo, MR";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:69;a:14:{s:9:"citazione";s:166:"Abundo, M. (1991). A stochastic model for predator-prey systems: basic properties, stability and computer simulation. JOURNAL OF MATHEMATICAL BIOLOGY, 29(6), 495-511.";s:4:"data";s:4:"1991";s:2:"id";s:19:"PUBBLICAZIONE_15950";s:6:"handle";s:10:"2108/23388";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:98:"A stochastic model for predator-prey systems: basic properties, stability and computer simulation.";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:18:"10.1007/BF00164048";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:70;a:14:{s:9:"citazione";s:228:"Abundo, M., & Accardi, L. (1991). Squeezing corrections to the Bloch equations. IL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. B, GENERAL PHYSICS, RELATIVITY, ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS, 106(2), 187-194.";s:4:"data";s:4:"1991";s:2:"id";s:19:"PUBBLICAZIONE_36402";s:6:"handle";s:9:"2108/9237";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:44:"Squeezing corrections to the Bloch equations";s:9:"metadata6";s:21:"Abundo, M; Accardi, L";s:9:"metadata7";s:18:"10.1007/BF02827333";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:71;a:14:{s:9:"citazione";s:180:"Abundo, M., & Mele, G. (1990). Absolutely continuous invariant measures for expanding maps of a d-dimensional unit cube in Rd and their entropy. NOTE DI MATEMATICA, 10(2), 217-233.";s:4:"data";s:4:"1990";s:2:"id";s:19:"PUBBLICAZIONE_36404";s:6:"handle";s:9:"2108/9228";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:112:"Absolutely continuous invariant measures for expanding maps of a d-dimensional unit cube in Rd and their entropy";s:9:"metadata6";s:18:"Abundo, M; Mele, G";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:72;a:14:{s:9:"citazione";s:166:"Abundo, M., & Rossi, C. (1989). Numerical Simulations of a stochastic model for cancerous cells submitted to chemotherapy. JOURNAL OF MATHEMATICAL BIOLOGY, 27, 81-90.";s:4:"data";s:4:"1989";s:2:"id";s:19:"PUBBLICAZIONE_36436";s:6:"handle";s:9:"2108/9243";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:89:"Numerical Simulations of a stochastic model for cancerous cells submitted to chemotherapy";s:9:"metadata6";s:19:"Abundo, M; Rossi, C";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:73;a:14:{s:9:"citazione";s:120:"Abundo, M. (1987). An almost sure invariance principle for the maps Sa(x)=ax(1-x) in the interval [0,1], 42(1-2), 11-18.";s:4:"data";s:4:"1987";s:2:"id";s:19:"PUBBLICAZIONE_36437";s:6:"handle";s:9:"2108/9285";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:84:"An almost sure invariance principle for the maps Sa(x)=ax(1-x) in the interval [0,1]";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:74;a:14:{s:9:"citazione";s:132:"Abundo, M. (1987). Entropy and characteristic exponents for the quadratic map on the unit interval. NOTE DI MATEMATICA, 7(1), 47-54.";s:4:"data";s:4:"1987";s:2:"id";s:19:"PUBBLICAZIONE_36438";s:6:"handle";s:9:"2108/9303";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:79:"Entropy and characteristic exponents for the quadratic map on the unit interval";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";s:24:"10.1285/i15900932v7n1p47";s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:75;a:14:{s:9:"citazione";s:176:"Abundo, M. (1986). A remark about topological and measure entropy for a class of maps of the interval [0,1]. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 35 (S. II), 456-465.";s:4:"data";s:4:"1986";s:2:"id";s:19:"PUBBLICAZIONE_36439";s:6:"handle";s:9:"2108/9287";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:89:"A remark about topological and measure entropy for a class of maps of the interval [0,1]";s:9:"metadata6";s:9:"Abundo, M";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:76;a:14:{s:9:"citazione";s:163:"Abundo, M., & Tirozzi, B. (1985). A central limit theorem for expanding maps of the interval [0,1]. BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B, 6(4-A), 237-244.";s:4:"data";s:4:"1985";s:2:"id";s:19:"PUBBLICAZIONE_36440";s:6:"handle";s:9:"2108/9289";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:64:"A central limit theorem for expanding maps of the interval [0,1]";s:9:"metadata6";s:21:"Abundo, M; Tirozzi, B";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}i:77;a:14:{s:9:"citazione";s:167:"Abundo, M.R., & Tirozzi, B. (1984). The central limit theorem for a class of maps of the interval [0,1]. BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B, 6(3-B), 25-37.";s:4:"data";s:4:"1984";s:2:"id";s:19:"PUBBLICAZIONE_36441";s:6:"handle";s:9:"2108/9304";s:9:"metadata1";s:19:"Articolo su rivista";s:9:"metadata2";N;s:9:"metadata3";s:53:"Settore MAT/06 - Probabilita' e Statistica Matematica";s:9:"metadata4";N;s:9:"metadata5";s:68:"The central limit theorem for a class of maps of the interval [0,1]";s:9:"metadata6";s:22:"Abundo, MR; Tirozzi, B";s:9:"metadata7";N;s:9:"metadata8";N;s:9:"metadata9";N;s:10:"metadata10";N;}}" } ["meta_keywords"]=> array(1) { [0]=> string(1) "," } ["reserved"]=> array(1) { [0]=> string(1) "0" } ["auth_ip"]=> array(1) { [0]=> string(1) "0" } } ["_fieldBoosts":protected]=> array(6) { ["content_id"]=> bool(false) ["content_title"]=> bool(false) ["description"]=> bool(false) ["meta_keywords"]=> bool(false) ["reserved"]=> bool(false) ["auth_ip"]=> bool(false) } } }