相关论文: Two classes of ODE models with switch-like behavio…

The paper concerns a continuous model governed by a ODE system originated by a discrete duopoly model with bounded rationality, based on constant conjectural variation. The ultimately boundedness of the solutions (existence of an absorbing…

Deep neural networks have been successful in diverse discriminative classification tasks, although, they are poorly calibrated often assigning high probability to misclassified predictions. Potential consequences could lead to…

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…

We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…

We consider a system of ODE in a Fr\'echet space with unconditional Schauder basis. The right side of the ODE is a discontinuous function. Under certain monotonicity conditions we prove an existence theorem for the corresponding initial…

Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…

In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…

Symbiotic solitons (SS) and quantum droplets (QD) are self-trapped localized modes emerging in binary Bose-gas mixtures with intra-component repulsion and inter-component attraction. We have shown that two-dimensional SS can be stabilized…

If a partition of a lattice in R^d is selfsimilar, it is called lattice substitution system (LSS). Such sets represent nonperiodic, but highly ordered structures. An important property of such structures is, whether they are model sets or…

Low frequency quasi-localized modes of amorphous glasses appear to exhibit universal density of states, depending on the frequencies as $D(\omega) \sim \omega^4$. To date various models of glass formers with short range binary interaction,…

We study the critical behavior of Boolean variables on scale-free networks with competing interactions (Ising spin glasses). Our analytical results for the disorder-network-decay-exponent phase diagram are verified using Monte Carlo…

We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the…

The present article considers stability of the solutions to nonlinear and nonautonomous compartmental systems governed by ordinary differential equations (ODEs). In particular, compartmental systems with a right-hand side that can be…

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

Recent years have witnessed significant progress in the development of machine learning models across a wide range of fields, fueled by increased computational resources, large-scale datasets, and the rise of deep learning architectures.…

We study the robustness of Transformer language models under semantic out-of-distribution (OOD) shifts, where training and test data lie in disjoint latent spaces. Using Wasserstein-1 distance and Gevrey-class smoothness, we derive…

We confirm the presence of a mean-field Bose glass in 2D quasicrystalline Bose-Hubbard models. We focus on two models where the aperiodic component is present in different parts of the problem. First, we consider a 2D generalisation of the…

This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…

Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…

While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into…