In this work we investigate how future actions are influenced by the previous ones, in the specif... more In this work we investigate how future actions are influenced by the previous ones, in the specific contexts of scientific collaborations and friendships on social networks. We are not interested in modeling the process of link formation between the agents themselves, we instead describe the activity of the agents, providing a model for the formation of the bipartite network of actions and their features. Therefore we only require to know the chronological order in which the actions are performed, and not the order in which the agents are observed. Moreover, the total number of possible features is not specified a priori but is allowed to increase along time, and new actions can independently show some new entry features or exhibit some of the old ones. The choice of the old features is driven by a degree-fitness method. With this term we mean that the probability that a new action shows one of the old features does not solely depend on the "popularity" of that feature (i....
We consider an urn model with multiple drawing and random time-dependent addition matrix. The mod... more We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has general random entries. For the proportion of balls of a given color, we prove almost sure convergence results and fluctuation theorems (through CLTs in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution). Asymptotic confidence intervals are given for the limit proportion, whose distribution is generally unknown.
Twitter is among the most used online platforms for the political communications, due to the conc... more Twitter is among the most used online platforms for the political communications, due to the concision of its messages (which is particularly suitable for political slogans) and the quick diffusion of messages. Especially when the argument stimulate the emotionality of users, the content on Twitter is shared with extreme speed and thus studying the tweet sentiment if of utmost importance to predict the evolution of the discussions and the register of the relative narratives. In this article, we present a model able to reproduce the dynamics of the sentiments of tweets related to specific topics and periods and to provide a prediction of the sentiment of the future posts based on the observed past. The model is a recent variant of the P\'olya urn, introduced and studied in arXiv:1906.10951 and arXiv:2010.06373, which is characterized by a "local" reinforcement, i.e. a reinforcement mechanism mainly based on the most recent observations, and by a random persistent fluctu...
We consider a model of N two-colors urns in which the reinforcement of each urn depends also on t... more We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter α in [0,1]; in particular, for α=0 the N urns behave as N independent Polya's urns. As shown in [9], for α>0 urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter α. In particular the standard scaling t^-1/2 appears only for α>1/2. For α≥ 1/2 we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.
Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random... more Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species Sampling Sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, a class of generalized species sampling sequences that are conditionally identically distributed is introduced and studied: the Generalized Ottawa sequences (GOS). This class contains a '`randomly reinforced" version of the Pólya urn and of the Blackwell-MacQueen urn scheme. For the empirical means and the predictive means of a GOS, we prove two convergence results toward suitable mixtures of Gaussian distributions. The first one is in the sense of stable convergence and the second one in the sense of almost sure conditional convergence. In the last part of the paper we study the length of the partition induced by a GOS at time ...
We consider a random trial-based telegraph process, which describes a motion on the real line wit... more We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical P\'olya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with non-zero mean), and (ii) the case of P\'olya trials and intertimes having first Gamma and then exponential distributions with constant rates.
Let (Xn) be an exchangeable sequence of indicators and π the probability distribution of lim sup ... more Let (Xn) be an exchangeable sequence of indicators and π the probability distribution of lim sup n Xn, where Xn = 1 n P n i=1 X i. Then, Cn = √ n˘Xn − E(X n+1 | X 1 ,. .. , Xn)c onverges stably (in particular, in distribution) provided π does not have a singular continuous part. Moreover, Cn P → 0 in case π is absolutely continuous with respect to Lebesgue measure, and √ n Cn converges a.s. under a mild Lipschitz condition on the density of π. Results of this type are useful in Bayesian statistics where π is the prior distribution. Related results are also obtained for the case where the Xn take values in an arbitrary measurable space.
For a two-colors, randomly reinforced urn, we prove a result of almost sure conditional convergen... more For a two-colors, randomly reinforced urn, we prove a result of almost sure conditional convergence toward a Gaussian kernel.
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting... more We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are correlated, forcing their convergence to the same, possibly random, limit. Random walks of this form have been introduced in the context of urn models and in stochastic approximation. We also propose an application to opinion dynamics in a random network evolving via preferential attachment. We study, in particular, random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. Under certain conditions, synchronization is faster than convergence.
In this work we are interested in identifying clusters of ‘‘positional equivalent’ ’ actors, i.e.... more In this work we are interested in identifying clusters of ‘‘positional equivalent’ ’ actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. We develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Moreover, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We valida...
Let (Xn) be a sequence of random variables (with values in a separable metric space) and (Nn) a s... more Let (Xn) be a sequence of random variables (with values in a separable metric space) and (Nn) a sequence of random indices. Conditions for X Nn to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well.
We consider a model of N two-colors urns in which the reinforcement of each urn depends also on t... more We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter α ∈ [0, 1]; in particular, for α = 0 the N urns behave as N independent Pólya's urns. As shown in [9], for α > 0 urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter α. In particular the standard scaling t −1/2 appears only for α > 1/2. For α ≥ 1/2 we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.
Abstract. Let (Xn) be a sequence of random variables (with values in a separable metric space) an... more Abstract. Let (Xn) be a sequence of random variables (with values in a separable metric space) and (Nn) a sequence of random indices. Conditions for XNn to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well. 1.
Randomly evolving systems composed by elements which interact among each other have always been o... more Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement that recently has been introduced in [Crimaldi et al. (2016)]. Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such interacting stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network.
Rich get richer rule comforts previously often chosen actions. What is happening to the evolution... more Rich get richer rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual non-linear reinforcement. We show how these systems can naturally be considered as models for coordination games, technological or opinion dynamics.
Journal of Financial Regulation and Compliance, 2021
Purpose A difference is noted by comparing the net loans to the non-financial sector in the two s... more Purpose A difference is noted by comparing the net loans to the non-financial sector in the two sets of institutions. The post-global financial crisis (GFC), literature agrees on a reduced lending pace by financial institutions (FIs) as a result of stricter capital regulations. At the same time, an increasing volume of outstanding loans, directed even to advanced countries, characterize the balance sheet of several multilateral development banks (MDBs). Design/methodology/approach This paper observes how a different degree of banking regulation might have shaped the economic response to the GFC by FIs and MDBs. Findings The authors indicate that MDBs’ financing, with a coherent objective of countercyclical support to the economies hit by the GFC, seems to have filled a market gap caused by the FIs’ pro-cyclical lending reduction. Originality/value While a controversial issue is whether Basel standards should be imposed on MDBs, a harmonization amongst MDBs of their transparency and ...
We introduce the Generalized Rescaled Polya (GRP) urn. In particular, the GRP urn provides three ... more We introduce the Generalized Rescaled Polya (GRP) urn. In particular, the GRP urn provides three different generative models for a chi-squared test of goodness of fit for the long-term probabilities of correlated data, generated by means of a reinforcement mechanism. Beside this statistical application, we point out that the GRP urn is a simple variant of the standard Eggenberger-Polya urn, that, with suitable choices of the parameters, shows "local" reinforcement, almost sure convergence of the empirical mean to a deterministic limit and different asymptotic behaviours of the predictive mean.
We present a new network model accounting for homophily and triadic closure in the evolution of s... more We present a new network model accounting for homophily and triadic closure in the evolution of social networks. In particular, in our model, each node is characterized by a number of features and the probability of a link between two nodes depends on common features. The bipartite network of the actors and features evolves according to a dynamics that depends on three parame-ters that respectively regulate the preferential attachment in the transmission of the features to the nodes, the number of new features per node, and the power-law behavior of the total number of observed features. We provide theoretical results and statistical estimators for the parameters of the model. We validate our approach by means of simulations and an empirical analysis of a network of scientifc collaborations.
Tradizionalmente, gli studi dose-risposta sono esperimenti di tipo binario volti a stimare un det... more Tradizionalmente, gli studi dose-risposta sono esperimenti di tipo binario volti a stimare un determinato “quantile” di interesse di una curva di risposta. In questo lavoro si considera il caso in cui la risposta osservata sia una generica variabile aleatoria reale, non necessariamente dicotomica, e lo scopo dell’esperimento consiste nello stimare la dose target associata ad una preassegnata risposta media. Ripercorrendo i risultati di Giovagnoli e Pintacuda (1998) e Baldi Antognini et al (2006), viene proposta ed analizzata un’estensione randomizzata dell’algoritmo up-and-down, fornendo inoltre una procedura di stima della risposta media basata sul metodo di massima verosimiglianza.
In this work we investigate how future actions are influenced by the previous ones, in the specif... more In this work we investigate how future actions are influenced by the previous ones, in the specific contexts of scientific collaborations and friendships on social networks. We are not interested in modeling the process of link formation between the agents themselves, we instead describe the activity of the agents, providing a model for the formation of the bipartite network of actions and their features. Therefore we only require to know the chronological order in which the actions are performed, and not the order in which the agents are observed. Moreover, the total number of possible features is not specified a priori but is allowed to increase along time, and new actions can independently show some new entry features or exhibit some of the old ones. The choice of the old features is driven by a degree-fitness method. With this term we mean that the probability that a new action shows one of the old features does not solely depend on the "popularity" of that feature (i....
We consider an urn model with multiple drawing and random time-dependent addition matrix. The mod... more We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has general random entries. For the proportion of balls of a given color, we prove almost sure convergence results and fluctuation theorems (through CLTs in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution). Asymptotic confidence intervals are given for the limit proportion, whose distribution is generally unknown.
Twitter is among the most used online platforms for the political communications, due to the conc... more Twitter is among the most used online platforms for the political communications, due to the concision of its messages (which is particularly suitable for political slogans) and the quick diffusion of messages. Especially when the argument stimulate the emotionality of users, the content on Twitter is shared with extreme speed and thus studying the tweet sentiment if of utmost importance to predict the evolution of the discussions and the register of the relative narratives. In this article, we present a model able to reproduce the dynamics of the sentiments of tweets related to specific topics and periods and to provide a prediction of the sentiment of the future posts based on the observed past. The model is a recent variant of the P\'olya urn, introduced and studied in arXiv:1906.10951 and arXiv:2010.06373, which is characterized by a "local" reinforcement, i.e. a reinforcement mechanism mainly based on the most recent observations, and by a random persistent fluctu...
We consider a model of N two-colors urns in which the reinforcement of each urn depends also on t... more We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter α in [0,1]; in particular, for α=0 the N urns behave as N independent Polya's urns. As shown in [9], for α>0 urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter α. In particular the standard scaling t^-1/2 appears only for α>1/2. For α≥ 1/2 we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.
Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random... more Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species Sampling Sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, a class of generalized species sampling sequences that are conditionally identically distributed is introduced and studied: the Generalized Ottawa sequences (GOS). This class contains a '`randomly reinforced" version of the Pólya urn and of the Blackwell-MacQueen urn scheme. For the empirical means and the predictive means of a GOS, we prove two convergence results toward suitable mixtures of Gaussian distributions. The first one is in the sense of stable convergence and the second one in the sense of almost sure conditional convergence. In the last part of the paper we study the length of the partition induced by a GOS at time ...
We consider a random trial-based telegraph process, which describes a motion on the real line wit... more We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical P\'olya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with non-zero mean), and (ii) the case of P\'olya trials and intertimes having first Gamma and then exponential distributions with constant rates.
Let (Xn) be an exchangeable sequence of indicators and π the probability distribution of lim sup ... more Let (Xn) be an exchangeable sequence of indicators and π the probability distribution of lim sup n Xn, where Xn = 1 n P n i=1 X i. Then, Cn = √ n˘Xn − E(X n+1 | X 1 ,. .. , Xn)c onverges stably (in particular, in distribution) provided π does not have a singular continuous part. Moreover, Cn P → 0 in case π is absolutely continuous with respect to Lebesgue measure, and √ n Cn converges a.s. under a mild Lipschitz condition on the density of π. Results of this type are useful in Bayesian statistics where π is the prior distribution. Related results are also obtained for the case where the Xn take values in an arbitrary measurable space.
For a two-colors, randomly reinforced urn, we prove a result of almost sure conditional convergen... more For a two-colors, randomly reinforced urn, we prove a result of almost sure conditional convergence toward a Gaussian kernel.
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting... more We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are correlated, forcing their convergence to the same, possibly random, limit. Random walks of this form have been introduced in the context of urn models and in stochastic approximation. We also propose an application to opinion dynamics in a random network evolving via preferential attachment. We study, in particular, random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. Under certain conditions, synchronization is faster than convergence.
In this work we are interested in identifying clusters of ‘‘positional equivalent’ ’ actors, i.e.... more In this work we are interested in identifying clusters of ‘‘positional equivalent’ ’ actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. We develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Moreover, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We valida...
Let (Xn) be a sequence of random variables (with values in a separable metric space) and (Nn) a s... more Let (Xn) be a sequence of random variables (with values in a separable metric space) and (Nn) a sequence of random indices. Conditions for X Nn to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well.
We consider a model of N two-colors urns in which the reinforcement of each urn depends also on t... more We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter α ∈ [0, 1]; in particular, for α = 0 the N urns behave as N independent Pólya's urns. As shown in [9], for α > 0 urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter α. In particular the standard scaling t −1/2 appears only for α > 1/2. For α ≥ 1/2 we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.
Abstract. Let (Xn) be a sequence of random variables (with values in a separable metric space) an... more Abstract. Let (Xn) be a sequence of random variables (with values in a separable metric space) and (Nn) a sequence of random indices. Conditions for XNn to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well. 1.
Randomly evolving systems composed by elements which interact among each other have always been o... more Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement that recently has been introduced in [Crimaldi et al. (2016)]. Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such interacting stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network.
Rich get richer rule comforts previously often chosen actions. What is happening to the evolution... more Rich get richer rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual non-linear reinforcement. We show how these systems can naturally be considered as models for coordination games, technological or opinion dynamics.
Journal of Financial Regulation and Compliance, 2021
Purpose A difference is noted by comparing the net loans to the non-financial sector in the two s... more Purpose A difference is noted by comparing the net loans to the non-financial sector in the two sets of institutions. The post-global financial crisis (GFC), literature agrees on a reduced lending pace by financial institutions (FIs) as a result of stricter capital regulations. At the same time, an increasing volume of outstanding loans, directed even to advanced countries, characterize the balance sheet of several multilateral development banks (MDBs). Design/methodology/approach This paper observes how a different degree of banking regulation might have shaped the economic response to the GFC by FIs and MDBs. Findings The authors indicate that MDBs’ financing, with a coherent objective of countercyclical support to the economies hit by the GFC, seems to have filled a market gap caused by the FIs’ pro-cyclical lending reduction. Originality/value While a controversial issue is whether Basel standards should be imposed on MDBs, a harmonization amongst MDBs of their transparency and ...
We introduce the Generalized Rescaled Polya (GRP) urn. In particular, the GRP urn provides three ... more We introduce the Generalized Rescaled Polya (GRP) urn. In particular, the GRP urn provides three different generative models for a chi-squared test of goodness of fit for the long-term probabilities of correlated data, generated by means of a reinforcement mechanism. Beside this statistical application, we point out that the GRP urn is a simple variant of the standard Eggenberger-Polya urn, that, with suitable choices of the parameters, shows "local" reinforcement, almost sure convergence of the empirical mean to a deterministic limit and different asymptotic behaviours of the predictive mean.
We present a new network model accounting for homophily and triadic closure in the evolution of s... more We present a new network model accounting for homophily and triadic closure in the evolution of social networks. In particular, in our model, each node is characterized by a number of features and the probability of a link between two nodes depends on common features. The bipartite network of the actors and features evolves according to a dynamics that depends on three parame-ters that respectively regulate the preferential attachment in the transmission of the features to the nodes, the number of new features per node, and the power-law behavior of the total number of observed features. We provide theoretical results and statistical estimators for the parameters of the model. We validate our approach by means of simulations and an empirical analysis of a network of scientifc collaborations.
Tradizionalmente, gli studi dose-risposta sono esperimenti di tipo binario volti a stimare un det... more Tradizionalmente, gli studi dose-risposta sono esperimenti di tipo binario volti a stimare un determinato “quantile” di interesse di una curva di risposta. In questo lavoro si considera il caso in cui la risposta osservata sia una generica variabile aleatoria reale, non necessariamente dicotomica, e lo scopo dell’esperimento consiste nello stimare la dose target associata ad una preassegnata risposta media. Ripercorrendo i risultati di Giovagnoli e Pintacuda (1998) e Baldi Antognini et al (2006), viene proposta ed analizzata un’estensione randomizzata dell’algoritmo up-and-down, fornendo inoltre una procedura di stima della risposta media basata sul metodo di massima verosimiglianza.
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Papers by Irene Crimaldi