- Madalina Deaconu (Inria & Institut Élie Cartan de Lorraine)
Title: A stroll within hitting times to achieve strong approximation
Abstract: Based on hitting times construction, we introduce new numerical methods for the path approximation of a class of stochastic processes. The approach constructs jointly the sequences of exit times and corresponding exit positions of well-chosen domains. We discuss also convergence theorems and present numerical results that permit to illustrate the efficiency and accuracy of the method.
Priscilla (Cindy) Greenwood (University of British Columbia)
Title: Environmental Noise and Population Extinction
Abstract: An Allee equation for population size has environmental noise modelled by a random parameter following an Ornstein-Uhlenbeck process. We gain insight from a combined bifurcation-diagram and sample path plots. Then we compute distributions of first passage times.
- Sonja Grün (Jülich Research Centre - RWTH Aachen University)
Title: Overview of the detection of significant spatio-temporal spike patterns
Abstract: In the last 14 years Laura Sacerdote supported my work on spike time coordination by students she send me to Juelich. Our hypothesis is that cell assembly activity is expressed by coordinated spiking of simultaneously recorded spike trains from many neurons. Assuming a synfire chain as a model of the cell assembly activity, we expect to find spatio-temporal spike patterns when the assembly is activated. Here I give a short overview of statistical tools we developed with her students for the detection and significance evaluation of spatio-temporal spike patterns.
- Samuel Herrmann (Université de Bourgogne)
Title: When Rejection Becomes Constructive: The Exact Simulation Method
Abstract: By systematically rejecting unsuitable proposals, we eventually arrive at one that fits—assuming we're patient and the pool of options is diverse enough. This deceptively simple idea underlies a class of random variable simulation techniques known as rejection methods. These methods are particularly powerful for simulating quantities such as first passage times, exit times, and more.
- Lubomir Kostal (Czech Academy of Sciences)
Title: Neuronal information transmission: from finite-size effects to source-channel coding
Abstract: Shannon's information theory provides a valuable framework for analyzing neural coding and information transmission. However, Shannon limits are only achievable asymptotically, as the complexity of encoding and decoding — as well as the associated delays — grow without bound, a scenario unlikely in biological systems. In this talk, we explore the finite-size effects and decoding errors that arise in realistically constrained neural populations. We then show that it may be possible to match the statistics of the input (stimulus) and neuronal noise in such a way that uncoded transmission becomes exactly optimal in the Shannon sense. Because uncoded transmission is entirely analog, avoiding both source discretization and block coding. We thus hypothesize that it may represent a viable strategy for information transmission in real neural systems.
Isaac Meilijson (Tel Aviv University)
Title: How variable can a mean-zero Martingale be, with given final variance?
Abstract: Tight upper bounds are presented for the expected maximum (Dubins and Schwarz), maximal absolute value (Dubins and Schwarz), diameter (Dubins, Gilat, Meilijson), local time at any point (Gilat, Meilijson, Sacerdote) and number of upcrossings of any interval (Gilat, Meilijson, Sacerdote). The bounds are attained for stopped Standard Brownian Motion, at explicitly determined stopping times.
- Goran Peskir (The University of Manchester)
Title: The Dubins constants for Walsh's spider process
Abstract: A long-standing open problem of L. E. Dubins seeks to determine the maximal expected range of Walsh's spider process on n edges per root of the expected stopping time. The solution is known for n=1 (1988) and n=2 (2009). In this talk I will address the case n>2.
Shigeru Shinomoto (ATR Institute International)
Title: Functional Connectivity Falls Short of Monosynaptic Truth
Abstract: Information processing in the brain is thought to result from
the coordination of large-scale neuronal activity, but this occurs on a
fine neural circuit. Here, we investigate their relationship. First, we
estimate monosynaptic connectivity by applying an advanced analysis
method to spike trains recorded with high-density microelectrodes and
confirm that the estimated neuronal wiring is largely consistent with
neuroanatomical and neurophysiological evidence. Second, we simulate
calcium imaging signals from the same dataset and confirm that the
estimated functional connectivity is influenced by shared inputs and
population synchronization on slower timescales. Notably, even with
unrealistically fast calcium dynamics, the functional connectivity is
only partially consistent with the monosynaptic connectivity. These
findings suggest the complementary roles for monosynaptic and functional
connectivity: the former provides circuit-level specificity, while the
latter reflects emergent system-wide patterns of activity.
Tatyana Turova (Lund University)
Title: Critical Long-Range Geometric Random Graphs.
Abstract: We derive the weak limit of the properly rescaled size of the largest connected component when the number of vertices in the graph goes to infinity. We discuss possible different scalings of the largest connected component depending on the decay with distance of the connecting probabilities.