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Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…
Elementary algebraic constraints on the form of an autocorrelation function C(tw+t,tw)=<A(tw+t)A(tw)> rule out some two-time scalings found in the literature as possible long-time asymptotic forms. The same argument leads to the realization…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
The article discusses a generalization of model of economic growth with constant pace, which takes into account the effects of dynamic memory. Memory means that endogenous or exogenous variable at a given time depends not only on their…
The design of machines and algorithms capable of learning in a dynamically changing environment has become an increasingly topical problem with the increase of the size and heterogeneity of data available to learning systems. As a…
Breakthroughs in deep learning and memory networks have made major advances in natural language understanding. Language is sequential and information carried through the sequence can be captured through memory networks. Learning the…
Various features of the development of individual living species, including individual humans, are programmed. Is death also programmed, and if yes, how is it implemented and what can be the underlying mechanism providing the inevitability…
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…
Tensor-power (TP) recurrent model is a family of non-linear dynamical systems, of which the recurrence relation consists of a p-fold (a.k.a., degree-p) tensor product. Despite such the model frequently appears in the advanced recurrent…
Continual Learning (CL) algorithms incrementally learn a predictor or representation across multiple sequentially observed tasks. Designing CL algorithms that perform reliably and avoid so-called catastrophic forgetting has proven a…
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…
Task incremental learning aims to enable a system to maintain its performance on previously learned tasks while learning new tasks, solving the problem of catastrophic forgetting. One promising approach is to build an individual network or…
The prevailing assumption of an exponential decay in large language model (LLM) reliability with sequence length, predicated on independent per-token error probabilities, posits an inherent limitation for long autoregressive outputs. Our…
Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been…
For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable…
We consider the predecessor problem on the ultra-wide word RAM model of computation, which extends the word RAM model with 'ultrawords' consisting of $w^2$ bits [TAMC, 2015]. The model supports arithmetic and boolean operations on…
Typical neural networks with external memory do not effectively separate capacity for episodic and working memory as is required for reasoning in humans. Applying knowledge gained from psychological studies, we designed a new model called…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
Neural networks powered with external memory simulate computer behaviors. These models, which use the memory to store data for a neural controller, can learn algorithms and other complex tasks. In this paper, we introduce a new memory to…
This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…