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We consider a complex of pseudo-differential operators associated with an overdetermined system of operators defined on the torus. We characterize the global solvability of this complex when the system has constant coefficients.…
The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones---two…
A "wireless fingerprint" which exploits hardware imperfections unique to each device is a potentially powerful tool for wireless security. Such a fingerprint should be able to distinguish between devices sending the same message, and should…
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
Signed Graph Neural Networks (SGNNs) have been shown to be effective in analyzing complex patterns in real-world situations where positive and negative links coexist. However, SGNN models suffer from poor explainability, which limit their…
We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…
Methods for learning feature representations for Offline Handwritten Signature Verification have been successfully proposed in recent literature, using Deep Convolutional Neural Networks to learn representations from signature pixels. Such…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
Full waveform inversion (FWI) aims at estimating subsurface medium properties from measured seismic data. It is usually cast as a non-linear least-squares problem that incorporates uncertainties in the measurements. In exploration…
In this paper, we show that if a set in bivariate metric semigroups-valued bounded variation spaces is pointwise totally bounded and joint equivariated then it is precompact. These spaces include bounded Jordan variation spaces, bounded…
We consider systems of strict multivariate polynomial inequalities over the reals. All polynomial coefficients are parameters ranging over the reals, where for each coefficient we prescribe its sign. We are interested in the existence of…
We consider the approximation of Poisson type problems where the source is given by a singular measure and the domain is a convex polygonal or polyhedral domain. First, we prove the well-posedness of the Poisson problem when the source…
Reconfiguration problems involve determining whether two given configurations can be transformed into each other under specific rules. The Token Sliding problem asks whether, given two different set of tokens on vertices of a graph $G$, we…
Resolvent degree is an invariant measuring the complexity of algebraic and geometric phenomena, including the complexity of finite groups. To date, the resolvent degree of a finite simple group $G$ has only been investigated when $G$ is a…
Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number…
We present a construction of graph-directed invariant sets of weak contractions in the sense of Matkowski-Rus on semi-metric spaces. We follow the approach by Bessenyei and P\'enzes, which applies the Kuratowski noncompactness measure…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
For real toric surfaces and conjugation invariant point conditions with all conjugate pairs on the boundary divisors, we prove that the signed count of real curves of arbitrary genus in the linear system through the given points is…