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Using projection between Euclidian spaces of different dimensions, the signal compression and decompression become straightforward. This encoding/decoding technique requires no preassigned measuring matrix as in compressed sensing.…
For iterative learning control (ILC), one of the basic problems left to address is how to solve the contradiction between convergence conditions for the output tracking error and for the input signal (or error). This problem is considered…
Detecting anomalous edges in dynamic graphs is an important task in many applications over evolving triple-based data, such as social networks, transaction management, and epidemiology. A major challenge with this task is the absence of…
Designing effective graph neural networks (GNNs) with message passing has two fundamental challenges, i.e., determining optimal message-passing pathways and designing local aggregators. Previous methods of designing optimal pathways are…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
This paper is concerned with a translation invariant network of identical quantum stochastic systems subjected to external quantum noise. Each node of the network is directly coupled to a finite number of its neighbours. This network is…
While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision. Existing equivariant methods often sacrifice the efficiency and flexibility that make Transformers so effective through…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
We tackle the problem of modeling sequential visual phenomena. Given examples of a phenomena that can be divided into discrete time steps, we aim to take an input from any such time and realize this input at all other time steps in the…
Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is…
We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called…
The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but…
The conception of the conformal phase transiton (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is introduced and elaborated. The main features of such a phase transition are established. In…