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Multiple Object Tracking (MOT) focuses on modeling the relationship of detected objects among consecutive frames and merge them into different trajectories. MOT remains a challenging task as noisy and confusing detection results often…
Based on the Distributed Convolutional Neural Network(DisCNN), a straightforward object detection method is proposed. The modules of the output vector of a DisCNN with respect to a specific positive class are positively monotonic with the…
We give a simple proof of the existence of response solutions in some quasi-periodically forced systems with a degenerate fixed points. The same questions were answered in \cite{ss18} using two versions of KAM theory. Our method is based on…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
Implicit surface representations, such as signed-distance functions, combined with deep learning have led to impressive models which can represent detailed shapes of objects with arbitrary topology. Since a continuous function is learned,…
Deep neural networks are composed of layers of parametrised linear operations intertwined with non linear activations. In basic models, such as the multi-layer perceptron, a linear layer operates on a simple input vector embedding of the…
This paper proposes a method for automatically monitoring and analyzing the evolution of complex geographic objects. The objects are modeled as a spatiotemporal graph, which separates filiation relations, spatial relations, and…
This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…
We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
Developing deep learning models that effectively learn object-centric representations, akin to human cognition, remains a challenging task. Existing approaches facilitate object discovery by representing objects as fixed-size vectors,…
It has recently been shown that one-dimensional Ising problems can have degenerate, disordered ground states (GSs) over a finite range of coupling onstants, ie, without `fine tuning'. The disorder is however of a special kind, consisting of…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
An effective way to model the complex real world is to view the world as a composition of basic components of objects and transformations. Although humans through development understand the compositionality of the real world, it is…
Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a…
We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping…
Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation…