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The talk describes recent progress in understanding the behaviour of the stress tensor and its correlation functions at a critical point of a generic quenched random system. The topics covered include:(i) the stress tensor in random systems…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
In randomly connected networks of pulse-coupled elements a time-dependent input signal can be buffered over a short time. We studied the signal buffering properties in simulated networks as a function of the networks state, characterized by…
In this paper a periodic parameter switching scheme is applied to the Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show numerically, via computer graphic simulations, that the obtained synthesized attractor…
The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and…
The fidelity of operations on a solid-state quantum processor is fundamentally bounded by environmental decoherence. Characterizing environmental fluctuations is challenging because the acquisition time of nonadaptive experimental protocols…
Neuromorphic chips embody computational principles operating in the nervous system, into microelectronic devices. In this domain it is important to identify computational primitives that theory and experiments suggest as generic and…
Take a centered random walk S_n and consider the sequence of its partial sums A_n = S_1 + ... + S_n. Suppose S_1 is in the domain of normal attraction of an \alpha-stable law with 1 < \alpha <= 2. Assuming that S_1 is either…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
This paper presents a set of results relating to the occupation time $\alpha(t)$ of a process $X(\cdot)$. The first set of results concerns exact characterizations of $\alpha(t)$ for $t\geq0$, e.g., in terms of its transform up to an…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We…
We study numerically the relaxation of a driven elastic string in a two dimensional pinning landscape. The relaxation of the string, initially flat, is governed by a growing length $L(t)$ separating the short steady-state equilibrated…
Stress time series from the PLC effect typically exhibit stick-slips of upload and download type. These data contain strong short-term correlations of a nonlinear type. We investigate whether there are also long term correlations, i.e. the…
The human lifespan retrieval curve describes the proportion of recalled memories from each year of life. It exhibits a reminiscence bump - a tendency for aged people to better recall memories formed during their young adulthood than from…
The scaling behavior of fluctuation for a download network which we have investigated a few years ago based upon Zhang's Encophysics web page has been presented. A power law scaling, namely $\sigma \sim < f> ^ \alpha $ exists between the…
Length Generalization is the essential capacity of autonomous agents to perform tasks in longer contexts than those encountered during training. To systematically study this feat, we test how well models can approximate the next token…
We develop a framework for collective frequency selection and attractor formation by means of delay plasticity. Specifically, we consider adaptive axonal delays (AADs), motivated by activity-dependent myelination in the brain which…
The relaxation time approximation (RTA) is a well known method of describing the time evolution of a statistical ensemble by linking distributions of the variables of interest at different stages of their temporal evolution. We show that if…