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We present and analyse numerical methods with operator splitting procedures, applied to an epidemic model which takes into account the space-dependence of the infection. We derive conditions on the time step, under which the numerical methods preserve the non-negativity and monotonicity properties of the exact solution. Our results are illustrated by numerical experiments.

In this paper we present some extensions of the classical SIR model with non-symmetric spatial dependence. SIR-type models usually describe the epidemic in a population, which is split into three categories, namely the susceptibles (S), the infected (I) and the recovered (R). The proposed model yields a system of partial integro-differential equations. Two methods handling the integrals of the equations are presented. We give numerical examples which show that the discrete models preserve the basic qualitative properties of the original biological process, and these results are supported by the oretical theorems.

Il campo di prigionia di Padula, in Italia, operativo durante la prima guerra mondiale in una grande certosa e caserma, è stato oggetto di numerosi studi italiani, cechi e slovacchi, in quanto era uno dei più grandi campi italiani e fungeva da centro per la creazione della Legione Cecoslovacca. Tuttavia, migliaia dei suoi detenuti erano ungheresi, la cui vita è stata a malapena discussa. Questo articolo si propone di presentare la vita dei prigionieri di guerra ungheresi tenuti a Padula. Con l'ausilio di fonti ad esse pertinenti, quali lettere e memorie, è possibile approfondire quattro aspetti: religione, salute, lamentele e lavoro. Un altro scopo dello studio è quello di offrire un elenco dei prigionieri ungheresi.

The representations of heroes and the heroic acts point to social values, norms, and morality of the present, creating a bridge between the past and a potential future. In this paper, a cross-cultural explorative study of heroes is presented aiming to explore general tendencies and possible patterns related to the different social contexts. Participants were reached from seven countries via social media (N = 974) for corpus construction. We asked by their choice of hero, national hero, and desired heroic action in their respective countries. A thematic analysis was conducted. Results show that there is a high rate of no choice, while among the chosen the prototypical hero is a lone moral man acting in the private (family) or public sphere (political actors). Both spheres offer the naturalization of the hero. There is a dialogical frame between the exceptional and the ordinary. Chosen heroes are dominantly contemporary males’ family members or political figures. While the purpose attributed to the personal hero is to maintain stability, the purpose attributed to the heroic actions of the public sphere is to obtain change. Similarities and differences between the seven subcorpuses are also described.

This paper reports the development of the Multiple Threat and Prejudice Questionnaire (MTPQ), a complex, multidimensional measure that assesses both identity threat on different dimensions of identification and the psychological distancing of outgroups relevant to each dimension. While mainstream approaches to prejudice focus on target groups and/or develop unidimensional measures, we present an instrument measuring the subjective perception of threat to different identity dimensions, which provides the condition to distance the other and to construct prejudice reinforcing and stabilizing self-boundaries. The present study confirmed the hypothetical factor structure based on data from 1482 participants.

This study was aimed at testing if exposure to a narrative about a heroic helper, can increment responsibility—taking about past ingroup wrongdoings and reduce prejudice and intergroup hostility in the present. We used the narrative of a Hungarian hero in an experiment who acted for targets of the Holocaust in Hungary, and measured if this narrative might increase collective responsibility for the Holocaust, decrease Hungarians’ hostile attitudes towards the Jewish minority, and this effect could be expanded to ongoing conflicts with other minorities. We used an experimental group (N = 99) exposed to the narrative, and a control group (N = 101) that was not. Both groups completed a test-battery measuring national identification, empathy, responsibility-taking, and prejudice. Data were analyzed with SPSS, and open-ended questions were content—analyzed by four independent coders. Results show that learning about a heroic helper increased acceptance of responsibility for the Holocaust and empathic abilities, whereas these effects were not generalized to current intergroup relations.

We investigate local-density dependent Markov processes on a class of large graphs sampled from a graphon, where the transition rates of the vertices are influenced by the states of their neighbors. We show that as the average degree converges to infinity, the evolution of the process in the transient regime converges to the solution of a set of non-local integro-partial differential equations. We also provide rigorous derivation for the epidemic threshold in the case of the Susceptible-Infected-Susceptible (SIS) process on such graphons.

In this article a mathematical model describing the possible events that could have lead to the ecological catastrophe of Easter Island is extended in a way that instead of the originally spatially discrete model (the domain is split into several regions) now a spatially continuous one is considered (the number of each population is observed at each point of the domain). In other words, the original system of ordinary differential equations is transformed into a system of partial differential equations, and then the effect of the diffusion of the trees is observed, i.e. whether it stabilizes the system like in the original case, or not. It turned out that because the linearized system can be written in a pretty similar form to the matrix of the two dimensional case which was examined in a previous article [10], the same theorems can be said about this system, meaning that the increase of the diffusion of the trees actually stabilizes the system in this case too.

A number of theories have been constructed to explain the ecological collapse of the Easter Island. Basener and his co-authors proposed a mathematical model in the form of a system of ordinary differential equations. This system describes the change of the number of people, rats and trees in some subregions of the island. The movement of the human and rat populations was described by some diffusion parameters. They showed that the increase of the diffusion parameters of people and rats makes the system unstable. In the present paper we introduce a diffusion parameter for the tree population and show that this parameter has a stabilizing effect. Thus, it behaves oppositely to the other two diffusion parameters from the stability point of view. The results are demonstrated with some numerical calculations of the stability region.

There is a broad consensus about the fundamental role of thehippocampal system (hippocampus and its adjacent areas) in theencoding and retrieval of episodic memories. This paper presents afunctional model of this system. Although memory is not asingle-unit cognitive function, we took the view that the wholesystem of the smooth, interrelated memory processes may have acommon basis. That is why we follow the Ockham's razor principleand minimize the size or complexity of our model assumption set.The fundamental assumption is the requirement of solving the socalled ``homunculus fallacy'', which addresses the issue ofinterpreting the input. Generative autoassociators seem to offer aresolution of the paradox. Learning to represent and to recallinformation, in these generative networks, imply maximization ofinformation transfer, sparse representation and noveltyrecognition. A connectionist architecture, which integrates theseaspects as model constraints, is derived. Numerical studiesdemonstrate the novelty recognition and noise filtering propertiesof the architecture. Finally, we conclude that the derivedconnectionist architecture can be related to the neurobiologicalsubstrate.

It has been suggested that sensory information processing makes use of a factorial code. It has been shown that the major components of the hippocampal-entorhinal loop can be derived by conjecturing that the task of this loop is forming and encoding independent components (ICs), one type of factorial codes. However, continuously changing environment poses additional requirements on the coding that can be (partially) satisfied by extending the analysis to the temporal domain and performing IC analysis on concatenated inputs of time slices. We use computer simulations to decide whether IC analysis on temporal sequences can produce place fields in labyrinths or not.

For interacting agents in time-critical applications, learning whether a subtask can be scheduled reliably is an important issue. The identification of sub-problems of this nature may promote e.g., planning, scheduling and segmenting in Markov decision processes. We define a subtask to be schedulable if its execution time has a small variance. We present an algorithm for finding such subtasks.

Independent subspace analysis (ISA) that deals with multi-dimensional independent sources, is a generalization of independent component analysis (ICA). However, all known ISA algorithms may become ineffective when the sources possess temporal structure. The innovation process instead of the original mixtures has been proposed to solve ICA problems with temporal dependencies. Here we show that this strategy can be applied to ISA as well. We demonstrate the idea on a mixture of 3D processes and also on a mixture of facial pictures used as two-dimensional deterministic sources. ISA on innovations was able to find the original subspaces, while plain ISA was not.

We present a prototype of a recently proposed two stage model of the entorhinal–hippocampal loop. Our aim is to form a general computational model of the sensory neocortex. The model — grounded on pure information theoretic principles — accounts for the most characteristic features of long-term memory (LTM), performs bottom-up novelty detection, and supports noise filtering. Noise filtering can also serve to correct the temporal ordering of information processing. Surprisingly, as we examine the temporal characteristics of the model, the emergent dynamics can be interpreted as perceptual priming, a fundamental type of implicit memory. In the model's framework, computational results support the hypothesis of a strong correlation between perceptual priming and repetition suppression and this correlation is a direct consequence of the temporal ordering in forming the LTM. We also argue that our prototype offers a relatively simple and coherent explanation of priming and its relation to a general model of information processing by the brain.

We subseribe to the idea that the brain employs generative networks. In turn, we conclude that channel capacity constraints form the main obstacle for effective information transfer in the brain. Robust and fast information flow processing methods warranting efficient information transfer, e.g. grouping of inputs and information maximization principles need to be applied. For this reason, indepent component analyses on groups of patterns were conducted using (a) model labyrinth, (b) movies on highway traffic and (c) mixed acoustical signals. We found that in all cases ‘familiar’ inputs give rise to cumulated firing histograms close to exponential distributions, whereas ‘novel’ information are better deseribed by broad, sometimes truncated Gaussian distributions. It can be shown that upon minimization of mutual information between processing channels, noise can reveal itself locally. Therefore, we conjecture that novelty - as opposed to noise - can be recognized by means of the statistics of neuronal firing in brain areas.