Statistical mechanics of temporal association in neural networks with transmission delays

We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the determination dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations

Oscillations, metastability and phase transitions in brain and models of cognition

Neuroscience is being practiced in many different forms and at many different organizational levels of the Nervous System. Which of these levels and associated conceptual frameworks is most informative for elucidating the association of neural processes with processes of Cognition is an empirical question and subject to pragmatic validation. In this essay, I select the framework of Dynamic System Theory. Several investigators have applied in recent years tools and concepts of this theory to interpretation of observational data, and for designing neuronal models of cognitive functions. I will first trace the essentials of conceptual development and hypotheses separately for discerning observational tests and criteria for functional realism and conceptual plausibility of the alternatives they offer. I will then show that the statistical mechanics of phase transitions in brain activity, and some of its models, provides a new and possibly revealing perspective on brain events in cognition

Cultural Neuroeconomics of Intertemporal Choice

According to theories of cultural neuroscience, Westerners and Easterners may have distinct styles of cognition (e.g., different allocation of attention). Previous research has shown that Westerners and Easterners tend to utilize analytical and holistic cognitive styles, respectively. On the other hand, little is known regarding the cultural differences in neuroeconomic behavior. For instance, economic decisions may be affected by cultural differences in neurocomputational processing underlying attention; however, this area of neuroeconomics has been largely understudied. In the present paper, we attempt to bridge this gap by considering the links between the theory of cultural neuroscience and neuroeconomic theory\ud of the role of attention in intertemporal choice. We predict that (i) Westerners are more impulsive and inconsistent in intertemporal choice in comparison to Easterners, and (ii) Westerners more steeply discount delayed monetary losses than Easterners. We examine these predictions by utilizing a novel temporal discounting model based on Tsallis' statistics (i.e. a q-exponential model). Our preliminary analysis of temporal discounting of gains and losses by Americans and Japanese confirmed the predictions from the cultural neuroeconomic theory. Future study directions, employing computational modeling via neural networks, are briefly outlined and discussed

Graphs in machine learning: an introduction

Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper, we give an introduction to some methods relying on graphs for learning. This includes both unsupervised and supervised methods. Unsupervised learning algorithms usually aim at visualising graphs in latent spaces and/or clustering the nodes. Both focus on extracting knowledge from graph topologies. While most existing techniques are only applicable to static graphs, where edges do not evolve through time, recent developments have shown that they could be extended to deal with evolving networks. In a supervised context, one generally aims at inferring labels or numerical values attached to nodes using both the graph and, when they are available, node characteristics. Balancing the two sources of information can be challenging, especially as they can disagree locally or globally. In both contexts, supervised and un-supervised, data can be relational (augmented with one or several global graphs) as described above, or graph valued. In this latter case, each object of interest is given as a full graph (possibly completed by other characteristics). In this context, natural tasks include graph clustering (as in producing clusters of graphs rather than clusters of nodes in a single graph), graph classification, etc. 1 Real networks One of the first practical studies on graphs can be dated back to the original work of Moreno [51] in the 30s. Since then, there has been a growing interest in graph analysis associated with strong developments in the modelling and the processing of these data. Graphs are now used in many scientific fields. In Biology [54, 2, 7], for instance, metabolic networks can describe pathways of biochemical reactions [41], while in social sciences networks are used to represent relation ties between actors [66, 56, 36, 34]. Other examples include powergrids [71] and the web [75]. Recently, networks have also been considered in other areas such as geography [22] and history [59, 39]. In machine learning, networks are seen as powerful tools to model problems in order to extract information from data and for prediction purposes. This is the object of this paper. For more complete surveys, we refer to [28, 62, 49, 45]. In this section, we introduce notations and highlight properties shared by most real networks. In Section 2, we then consider methods aiming at extracting information from a unique network. We will particularly focus on clustering methods where the goal is to find clusters of vertices. Finally, in Section 3, techniques that take a series of networks into account, where each network i