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A study of dependency features of spike trains through copulas [article]

Pietro Verzelli, Laura Sacerdote
2019 arXiv   pre-print
A study of dependency features of spike trains through copulas Pietro  ... 
arXiv:1903.08460v1 fatcat:eesaf4e46vcsrdcbqb52dmf3iu

Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere

Pietro Verzelli, Cesare Alippi, Lorenzo Livi
2019 Scientific Reports  
Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which critically affect their behavior. Results show that their performance is usually maximized in a narrow region of hyper-parameter space called edge of criticality. Finding such a region requires searching in hyper-parameter space in a sensible way:
more » ... ter configurations marginally outside such a region might yield networks exhibiting fully developed chaos, hence producing unreliable computations. The performance gain due to optimizing hyper-parameters can be studied by considering the memory-nonlinearity trade-off, i.e., the fact that increasing the nonlinear behavior of the network degrades its ability to remember past inputs, and vice-versa. In this paper, we propose a model of ESNs that eliminates critical dependence on hyper-parameters, resulting in networks that provably cannot enter a chaotic regime and, at the same time, denotes nonlinear behavior in phase space characterized by a large memory of past inputs, comparable to the one of linear networks. Our contribution is supported by experiments corroborating our theoretical findings, showing that the proposed model displays dynamics that are rich-enough to approximate many common nonlinear systems used for benchmarking.
doi:10.1038/s41598-019-50158-4 pmid:31554855 pmcid:PMC6761167 fatcat:5xow22avvnbwjntdxv5vjhwkkm

Learn to Synchronize, Synchronize to Learn [article]

Pietro Verzelli and Cesare Alippi and Lorenzo Livi
2021 arXiv   pre-print
In recent years, the machine learning community has seen a continuous growing interest in research aimed at investigating dynamical aspects of both training procedures and machine learning models. Of particular interest among recurrent neural networks we have the Reservoir Computing (RC) paradigm characterized by conceptual simplicity and a fast training scheme. Yet, the guiding principles under which RC operates are only partially understood. In this work, we analyze the role played by
more » ... zed Synchronization (GS) when training a RC to solve a generic task. In particular, we show how GS allows the reservoir to correctly encode the system generating the input signal into its dynamics. We also discuss necessary and sufficient conditions for the learning to be feasible in this approach. Moreover, we explore the role that ergodicity plays in this process, showing how its presence allows the learning outcome to apply to multiple input trajectories. Finally, we show that satisfaction of the GS can be measured by means of the Mutual False Nearest Neighbors index, which makes effective to practitioners theoretical derivations.
arXiv:2010.02860v3 fatcat:62gmvogyajcoxgr572t7pt4bie

Input-to-State Representation in linear reservoirs dynamics [article]

Pietro Verzelli and Cesare Alippi and Lorenzo Livi and Peter Tino
2021 arXiv   pre-print
Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them appealing for analytical studies by a large community of researchers with backgrounds spanning from dynamical systems to neuroscience. However, even in the simple linear case, the working principle of these networks is not fully understood and their design is
more » ... ly driven by heuristics. A novel analysis of the dynamics of such networks is proposed, which allows the investigator to express the state evolution using the controllability matrix. Such a matrix encodes salient characteristics of the network dynamics; in particular, its rank represents an input-indepedent measure of the memory capacity of the network. Using the proposed approach, it is possible to compare different reservoir architectures and explain why a cyclic topology achieves favourable results as verified by practitioners.
arXiv:2003.10585v3 fatcat:qeucvlukb5epdlmemwihro3oqa

Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere [article]

Pietro Verzelli and Cesare Alippi and Lorenzo Livi
2019 arXiv   pre-print
Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which critically affect their behaviour. Results show that their performance is usually maximized in a narrow region of hyper-parameter space called edge of chaos. Finding such a region requires searching in hyper-parameter space in a sensible way: hyper-parameter
more » ... onfigurations marginally outside such a region might yield networks exhibiting fully developed chaos, hence producing unreliable computations. The performance gain due to optimizing hyper-parameters can be studied by considering the memory--nonlinearity trade-off, i.e., the fact that increasing the nonlinear behavior of the network degrades its ability to remember past inputs, and vice-versa. In this paper, we propose a model of ESNs that eliminates critical dependence on hyper-parameters, resulting in networks that provably cannot enter a chaotic regime and, at the same time, denotes nonlinear behaviour in phase space characterised by a large memory of past inputs, comparable to the one of linear networks. Our contribution is supported by experiments corroborating our theoretical findings, showing that the proposed model displays dynamics that are rich-enough to approximate many common nonlinear systems used for benchmarking.
arXiv:1903.11691v1 fatcat:ivpomppg4zdvjooprb6msdqlua

A characterization of the Edge of Criticality in Binary Echo State Networks [article]

Pietro Verzelli, Lorenzo Livi, Cesare Alippi
2018 pre-print
Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to be effective in solving tasks when configured on a region in (hyper-)parameter space called Edge of Criticality (EoC), where the system is maximally sensitive to perturbations hence affecting its behaviour. In this paper, we propose binary ESNs, which are
more » ... hitecturally equivalent to standard ESNs but consider binary activation functions and binary recurrent weights. For these networks, we derive a closed-form expression for the EoC in the autonomous case and perform simulations in order to assess their behavior in the case of noisy neurons and in the presence of a signal. We propose a theoretical explanation for the fact that the variance of the input plays a major role in characterizing the EoC.
doi:10.1109/mlsp.2018.8516959 arXiv:1810.01742v1 fatcat:5gchmfuqvzggfmyov6gwcet6my

Page 187 of American Architect and Architecture Vol. 87, Issue 1537 [page]

1905 American Architect and Architecture  
A pair of magnificent bronze doors were cast for the Triumphal Arch of the Castel Nuovo at Naples, erected by Pietro di Martino for Alfonzo of Aragon to commemorate his entry into the city in 1443.  ...  The left-hand doors are by Tiburzio Verzelli da Camerino, of somewhat later date, but corresponding gener- ally in design, and those on the right by Antonio Calcagni, each having employed several assistants  ... 

Bollettino Della Deputazione Di Storia Patria Per L'Umbria N. 108/2 (2011)

Jaitner-Hahner Ursula, Matteini Federica, Gackenholz Puxeddu Marianne, Gallo Carrabba Angelo, Giusti Sr. Chiara Emmanuela osc Umiker Sr. Monica Benedetta osc, Bruzzone Gian Luigi, Angeletti Vittorio, Bartoli Marta, Prosperi Gianluca, Bettoni Fabio, Mari Paolo, Neri Lusanna Enrica
2012 Zenodo  
Sul sinodo di Pietro Orsini: Coletti 2007 Conc.  ...  informazioni che a quello scopo gli erano state trasmesse 127 : Ill.mo et R.mo signor mio oss.mo, il cardinale Orsino arrivò qui martedì su le ventun' hora, con un gran caldo, del quale il cardinale di Verzelli  ... 
doi:10.5281/zenodo.800674 fatcat:samrzm5jcbcptkz7sze2d6tv4a

The Catafalque of Paul V: Architecture, Sculpture and Iconography

Arianna Packard
2017
Pietro a' quella di S.  ...  Pietro trasportato a S.  ...  "Verzelli e filo di ferro." 541 Ibid., 68. "Pittori terra d'ombra giesso Colla penelli Cartoni." 542 Ibid., 68. "letti locandi carbone candele e corde grosse per le statue."543 Berendsen 1959, 68.  ... 
doi:10.7916/d8bc45st fatcat:uvoi4gwn3zg5zlft3gi3feg5ce

Edizione a cura di Luca BELLONE «QuadRi» Quaderni di RiCOGNIZIONI

De L'albicante
unpublished
Sono in Verzelli forse altretanti et in Casal, che non riescon fora: così passando questi pochi giorni, ne stavan tutti lieti ai bei soggiorni. 786 [c. 20v] 174.  ...  Il cavalier Giovan Pietro Cicogna (fine XV sec. -1560), nobile milanese, illustre ufficiale al servizio dell'esercito imperiale. 205 Cfr.  ...  Pietro Gioffredo, nella Storia delle Alpi marittime, lo nomina anche fra gli ufficiali che si distinsero maggiormente nel contrastare la spedizione degli imperiali in Provenza. 8, 5 -Segue il colonnello  ... 
fatcat:rhkogyxuwrh3ja2c733a342hdy

GIORNALE LIGUSTICO D I ARCHEOLOGIA, STORIA E LETTERATURA

Lucio Settimio, Valerio Fiacco, Nonio Capro, Marcello, Asconio Lucrezio, Pediano, Quintiliano
unpublished
Pietro di Oneglia.  ...  Pietro Fran.° Buttigella a dimandare Mad."  ... 
fatcat:qnimrjqyv5arhihmq6nltd7pxu

LA CONGIURA DEL FIESCO

E Corte, D Toscana
unpublished
Di là anderìa alla uolta di Verzelli per recognoscere un po' quelle cose.  ...  E t anchora s intende in le parti del Sig.r Pietro Luigi farsi genti, et m axim e in P ia cenza. Pertanto m è parso darne notitia a V.  ... 
fatcat:hejggeyxlncftceksdt5atlj6y

DONNE GUERRA POLITICA

Esperienze Memorie, Della Resistenza, Dianella Gagliani, Elda Guerra, Laura Mariani, Fiorenza Tarozzi, Donne, Politica Esperienze E Memorie Della Resistenza, Dianella Gagliani, Elda Guerra, Laura Mariani, Fiorenza
2000 unpublished
Gelsomina Bonora, mondina di San Pietro in Casale, nome di battaglia Gilera per la sua velocità in bicicletta: «La vita nella lotta partigiana l'ho finita così.  ...  nella Repubblica di Montefiorino e sottoposta a ripetute operazioni belliche resterà ai margini della Resistenza e della sua memoria (Monica Casini), a differenza della pianura delle mondine (Angela Verzelli  ... 
fatcat:nf4pj75k5zh6xgkezhlwnzd3nq

The Cassa Integrazione Guadagni, unemployment welfare and industrial conflict in post-war Italy, 1941-1987

Niccolò Serri, Apollo-University Of Cambridge Repository, Apollo-University Of Cambridge Repository, Pedro Ramos Pinto
2019
As argued by Pietro Causarano, two of the distinctive characteristics of Fordist manufacturing, large-scale dimension and technocratic management, were never dominant in the Italian industrial apparatus  ...  Verzelli alle Camere Confederali del Lavoro, ai Comitati Regionali CGIL, alle Federazioni Nazionali di Categoria, Circolare 3092, oggetto: pensioni, assegni familiari, indennità di disoccupazione, Roma  ... 
doi:10.17863/cam.37529 fatcat:a7l77natrbh5dcr6difcka53si

UNIVERSITÀ DI BOLOGNA Dipartimento di Scienze della Terra e Geologico-Ambientali DOTTORATO IN SCIENZE DELLA TERRA XIX CICLO La valorizzazione del patrimonio geologico Un'esperienza di ricerca sui geositi tra Emilia-Romagna e Baviera

William Cavazza, Dott, Stefano Mariani, Gaspare Gian, Zuffa, Dott Ssa Maria, Angela Cazzoli, Dott Ssa, Maria Carla, Centineo Dott, Marabini
2004 Cina   unpublished
Pietro Zangheri alle operazioni di campagna, un elenco, revisionato da Ruggieri, è presente anche nel catalogo dell'omonima collezione veronese (Zangheri, 1969 Lg. 0°44'40'', Lt.44°20'28'', q. 50 ."  ...  Il lavoro svolto Le attività aperte alla cittadinanza sono state precedute da alcuni incontri con la Dott.ssa Vanna Verzelli (Sindaco di Fontanelice) e alcuni assessori comunali per verificare la fattibilità  ... 
fatcat:jnrusx32dvbnvpe3fhvj5xcwdq