Tootfinder

A Characterization of Weighted Homogeneous Polynomials via the Discriminant
David Bradley-Williams, Pablo Cubides Kovacsics, Immanuel Halupczok
https://arxiv.org/abs/2403.05324

A Characterization of Weighted Homogeneous Polynomials via the Discriminant
If a bivariate polynomial is weighted homogeneous, then its discriminant is a monomial. Over fields of characteristic $0$, we show that if one adds another simple condition, this becomes an equivalence. We also give a third equivalent condition which is stated geometrically.

On the Weights of Root Subgroups of Affine Toric Varieties
Immanuel van Santen
https://arxiv.org/abs/2403.14389 https://arxiv.org/pdf…

On the Weights of Root Subgroups of Affine Toric Varieties
Let $X$ be an affine toric variety and let $D(X)$ be the set of weights of all root subgroups. It is known that $D(X)$ together with its embedding into the character group determines $X$ as a toric variety. In this article we prove that $X$ is already determined by the abstract set $D(X)$ together with some additional combinatorial data.

Feature selection in linear SVMs via hard cardinality constraint: a scalable SDP decomposition approach
Immanuel Bomze, Federico D'Onofrio, Laura Palagi, Bo Peng
https://arxiv.org/abs/2404.10099

Feature selection in linear SVMs via hard cardinality constraint: a scalable SDP decomposition approach
In this paper, we study the embedded feature selection problem in linear Support Vector Machines (SVMs), in which a cardinality constraint is employed, leading to a fully explainable selection model. The problem is NP-hard due to the presence of the cardinality constraint, even though the original linear SVM amounts to a problem solvable in polynomial time. To handle the hard problem, we first introduce two mixed-integer formulations for which novel SDP relaxations are proposed. Exploiting the …

Derivation of Yudovich solutions of Incompressible Euler from the Vlasov-Poisson system
Immanuel Ben-Porat, Mikaela Iacobelli, Alexandre Rege
https://arxiv.org/abs/2403.14080

Derivation of Yudovich solutions of Incompressible Euler from the Vlasov-Poisson system
We derive the two dimensional incompressible Euler equation as a quasineutral limit of the Vlasov-Poisson equation using a modulated energy approach. We propose a strategy which enables to treat solutions where the gradient of the velocity is merely $\mathrm{BMO}$, in accordance to the celebrated Yudovich theorem.

Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems
Daniel Adler, David Wei, Melissa Will, Kritsana Srakaew, Suchita Agrawal, Pascal Weckesser, Roderich Moessner, Frank Pollmann, Immanuel Bloch, Johannes Zeiher
https://arxiv.org/abs/2404.14896

Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems
The relaxation behaviour of isolated quantum systems taken out of equilibrium is among the most intriguing questions in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. However, kinetic constraints in the Hamiltonian can lead to a breakdown of this fundamental paradigm due to a fragmentation of the underlying Hilbert space into dynamically decoupled subsectors in which therma…

Derivation of Yudovich solutions of Incompressible Euler from the Vlasov-Poisson system
Immanuel Ben-Porat, Mikaela Iacobelli, Alexandre Rege
https://arxiv.org/abs/2403.14080

Derivation of Yudovich solutions of Incompressible Euler from the Vlasov-Poisson system
We derive the two dimensional incompressible Euler equation as a quasineutral limit of the Vlasov-Poisson equation using a modulated energy approach. We propose a strategy which enables to treat solutions where the gradient of the velocity is merely $\mathrm{BMO}$, in accordance to the celebrated Yudovich theorem.

Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems
Daniel Adler, David Wei, Melissa Will, Kritsana Srakaew, Suchita Agrawal, Pascal Weckesser, Roderich Moessner, Frank Pollmann, Immanuel Bloch, Johannes Zeiher
https://arxiv.org/abs/2404.14896

Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems
The relaxation behaviour of isolated quantum systems taken out of equilibrium is among the most intriguing questions in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. However, kinetic constraints in the Hamiltonian can lead to a breakdown of this fundamental paradigm due to a fragmentation of the underlying Hilbert space into dynamically decoupled subsectors in which therma…