Tootfinder

Complete characterization of symmetric Kubo-Ando operator means satisfying Moln\'ar's weak associativity
Graeme W. Milton, Aaron Welters
https://arxiv.org/abs/2405.20108 <…

Complete characterization of symmetric Kubo-Ando operator means satisfying Molnár's weak associativity
We provide a complete characterization of a subclass of means of positive operators in the class of symmetric Kubo-Ando means that was first introduced and studied in L. Molnár, ``Characterizations of certain means of positive operators," Linear Algebra Appl. 567 (2019) 143-166. In Theorem 6 of that paper, he gives a characterization of this subclass (which we call the Molnár class of means) in terms of the operator monotone functions representing the means, which includes the geometric mean.…

Cluster Monomials in Graph Laurent Phenomenon Algebras
Guilherme Zeus Dantas e Moura, Ramanuja Charyulu Telekicherla Kandalam, Dora Woodruff
https://arxiv.org/abs/2404.16153

Cluster Monomials in Graph Laurent Phenomenon Algebras
Laurent Phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Linear Laurent Phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent Phenomenon algebras whose structure is given by the data of a directed graph. The main result of this paper is that the cluster monomials of a linear Laurent Phenomenon algebra form a linear basis, conjectured by Lam and Pylyavskyy an…

Non-holomorphic modular forms from zeta generators
Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Oliver Schlotterer, Leila Schneps, Bram Verbeek
https://arxiv.org/abs/2403.14816

Non-holomorphic modular forms from zeta generators
We study non-holomorphic modular forms built from iterated integrals of holomorphic modular forms for SL$(2,\mathbb Z)$ known as equivariant iterated Eisenstein integrals. A special subclass of them furnishes an equivalent description of the modular graph forms appearing in the low-energy expansion of string amplitudes at genus one. Notably the Fourier expansion of modular graph forms contains single-valued multiple zeta values. We deduce the appearance of products and higher-depth instances of…

Regular Typed Unification
Jo\~ao Barbosa, M\'ario Florido, V\'itor Santos Costa
https://arxiv.org/abs/2404.16406 https://arxi…

Regular Typed Unification
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a homogeneous collection of values, but instead, to partition it in a way that is similar to data types in programming languages. We first define the new unification algorithm which is based on constraint generation and constraint solving, and then prove its main pro…

This https://arxiv.org/abs/2308.11842 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csMA_…

${\rm E}(3)$-Equivariant Actor-Critic Methods for Cooperative Multi-Agent Reinforcement Learning
Identification and analysis of symmetrical patterns in the natural world have led to significant discoveries across various scientific fields, such as the formulation of gravitational laws in physics and advancements in the study of chemical structures. In this paper, we focus on exploiting Euclidean symmetries inherent in certain cooperative multi-agent reinforcement learning (MARL) problems and prevalent in many applications. We begin by formally characterizing a subclass of Markov games with…

Homotopy type of shellable $q$-complexes and their homology groups
Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa, Hugues Verdure, Glen Wilson
https://arxiv.org/abs/2403.07102

Homotopy type of shellable $q$-complexes and their homology groups
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to $q$-matroid complexes and determines singular homology groups for a subclass of these $q$-simplicial complexes. In this paper, we determine the homotopy type of shellable $q$-simplicial complexes. Moreover, we establish the shell…

Moduli difference of inverse logarithmic coefficients of univalent functions
Vasudevarao Allu, Amal Shaji
https://arxiv.org/abs/2403.10031 https://<…

Moduli difference of inverse logarithmic coefficients of univalent functions
Let $f$ be analytic in the unit disk and $\mathcal{S}$ be the subclass of normalized univalent functions with $f(0) = 0$, and $f'(0) = 1$. Let $F$ be the inverse function of $f$, given by $F(w)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on some disk $|w|\le r_0(f)$. The inverse logarithmic coefficients $Γ_n$, $n \in \mathbb{N}$, of $f$ are defined by the equation $ \log(F(w)/w)=2\sum_{n=1}^{\infty}Γ_{n}w^{n},\,|w|<1/4.$ In this paper, we find the sharp upper and lower bounds for…

Cluster Monomials in Graph Laurent Phenomenon Algebras
Guilherme Zeus Dantas e Moura, Ramanuja Charyulu Telekicherla Kandalam, Dora Woodruff
https://arxiv.org/abs/2404.16153

Cluster Monomials in Graph Laurent Phenomenon Algebras
Laurent Phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Linear Laurent Phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent Phenomenon algebras whose structure is given by the data of a directed graph. The main result of this paper is that the cluster monomials of a linear Laurent Phenomenon algebra form a linear basis, conjectured by Lam and Pylyavskyy an…

Exact objectives of random linear programs and mean widths of random polyhedrons
Mihailo Stojnic
https://arxiv.org/abs/2403.03637 https://

Exact objectives of random linear programs and mean widths of random polyhedrons
We consider \emph{random linear programs} (rlps) as a subclass of \emph{random optimization problems} (rops) and study their typical behavior. Our particular focus is on appropriate linear objectives which connect the rlps to the mean widths of random polyhedrons/polytopes. Utilizing the powerful machinery of \emph{random duality theory} (RDT) \cite{StojnicRegRndDlt10}, we obtain, in a large dimensional context, the exact characterizations of the program's objectives. In particular, for any $α…

Nilpotent symplectic alternating algebras II
Layla Sorkatti, Gunnar Traustason
https://arxiv.org/abs/2404.11038 https://arxiv.org/pdf…

Nilpotent symplectic alternating algebras II
In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension $10$ over any field. It is known that symplectic alternating algebras over $\mbox{GF}(3)$ correspond to a special rich class $\mathcal{C}$ of $2$-Engel $3$-groups of exponent $27$ and under this correspondence we will see that the nilpotent algebras correspond to a subclass of $\mathcal{C}$ that are those groups in $\mathcal{C…

This https://arxiv.org/abs/2303.15898 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Markov Chains with an Aggregator and their Applications
We study the properties of a subclass of stochastic processes called discrete-time nonlinear Markov chains with an aggregator. In these chains, the next period's distribution of the process depends on both the current state of the process and on a real-valued function of the current distribution of the process. For these chains, we provide conditions for the uniqueness of an invariant distribution and a simple method to find the unique invariant distribution, which do not rely on contraction ar…

White Dwarf Merger Remnants: The DAQ Subclass
Mukremin Kilic, Pierre Bergeron, Simon Blouin, Gracyn Jewett, Warren R. Brown, Adam Moss
https://arxiv.org/abs/2403.08878

White Dwarf Merger Remnants: The DAQ Subclass
Four years after the discovery of a unique DAQ white dwarf with a hydrogen-dominated and carbon-rich atmosphere, we report the discovery of four new DAQ white dwarfs, including two that were not recognized properly in the literature. We find all five DAQs in a relatively narrow mass and temperature range of $M=1.14-1.19~M_{\odot}$ and $T_{\rm eff}=13,000-17,000$ K. In addition, at least two show photometric variations due to rapid rotation with $\approx10$ min periods. All five are also kinemat…

This https://arxiv.org/abs/2104.06812 has been replaced.
link: https://scholar.google.com/scholar?q=a

On eigenmeasures under Fourier transform
Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $\RR^d$. In particular, we classify all periodic eigenmeasures on $\RR$, which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on $\RR$ with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and pr…

This https://arxiv.org/abs/2401.01777 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Carleman estimates for third order operators of KdV and non KdV-type and applications
In this paper we study a class of variable coefficient third order partial differential operators on $\mathbb{R}^{n+1}$, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of $\mathbb{R}^{n+1}$. A discussion of possible applications in the context of dispersive equations is provided.

Main $\mathbf{Q}$-eigenvalues of quasi-threshold graphs
\'Atila Jones, Vilmar Trevisan, Cybele T. M. Vinagre
https://arxiv.org/abs/2404.09396 https://<…

Main $\mathbf{Q}$-eigenvalues of quasi-threshold graphs
In this note, we present a structural description of certain connected cographs having $k \geq 2$ main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are quasi-threshold graphs with two main $\mathbf{Q}$-eigenvalues. In addition, we describe all the quasi-threshold graphs belonging to the subclass of generalized core-satellite graphs with $k \geq 2$ main $\mathbf{Q}$-eigenvalues.

Switching Classes: Characterization and Computation
Dhanyamol Antony, Yixin Cao, Sagartanu Pal, R. B. Sandeep
https://arxiv.org/abs/2403.04263 https://

Switching Classes: Characterization and Computation
In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that are closed under switching. We characterize the maximum subclass for many important classes $\mathcal{G}$, and prove that it is finite when $\mathcal{G}$ is minor-closed and omits at least one graph. For several graph classes, we develop polynomial-time algorit…

Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure
Haesung Lee, Gerald Trutnau
https://arxiv.org/abs/2404.14902 https…

Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure
We show weak existence and uniqueness in law for a general class of stochastic differential equations in $\mathbb{R}^d$, $d\ge 1$, with prescribed sub-invariant measure $\widehatμ$. The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate and discontinuous, and locally unbounded, respectively. Uniqueness in law is obtained via $L^1(\mathbb{R}^d,\widehatμ)$-uniqueness in a subclass of continuous Markov processes, namely right processes that hav…

On Koebe radius and coefficients estimate for univalent harmonic mappings
Mikhail Borovikov
https://arxiv.org/abs/2403.05526 https://…

On Koebe radius and coefficients estimate for univalent harmonic mappings
The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk $\mathbb D=\{z\in\mathbb C : |z|<1\}$ is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary.

This https://arxiv.org/abs/2210.11521 has been replaced.
link: https://scholar.google.com/scholar?q=a

Decomposable context-specific models
We introduce a family of discrete context-specific models, which we call decomposable. We construct this family from the subclass of staged tree models known as CStree models. We give an algebraic and combinatorial characterization of all context-specific independence relations that hold in a decomposable context-specific model, which yields a Markov basis. We prove that the moralization operation applied to the graphical representation of a context-specific model does not affect the implied in…

This https://arxiv.org/abs/2401.16579 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

On Channel Simulation with Causal Rejection Samplers
One-shot channel simulation has recently emerged as a promising alternative to quantization and entropy coding in machine-learning-based lossy data compression schemes. However, while there are several potential applications of channel simulation - lossy compression with realism constraints or differential privacy, to name a few - little is known about its fundamental limitations. In this paper, we restrict our attention to a subclass of channel simulation protocols called causal rejection samp…

This https://arxiv.org/abs/2309.07488 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Long-Term Mean-Variance Optimization Under Mean-Reverting Equity Returns
This paper studies the mean-variance optimal portfolio choice of an investor pre-committed to a deterministic investment policy in continuous time in a market with mean-reversion in the risk-free rate and the equity risk-premium. In the tradition of Markowitz, optimal policies are restricted to a subclass of factor exposures in which losses cannot exceed initial capital and it is shown that the optimal policy is characterized by an Euler-Lagrange equation derived by the method of Calculus of Va…

This https://arxiv.org/abs/2307.03482 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite Elements with Switch Detection for Numerical Optimal Control of Nonsmooth Dynamical Systems with Set-Valued Heaviside Step Functions
This paper develops high-accuracy methods for numerically solving optimal control problems subject to nonsmooth differential equations with set-valued step functions. A notable subclass of these systems are Filippov systems. The set-valued step functions are here written as the solution map of a linear program. Using the optimality conditions of this problem we rewrite the initial nonsmooth system into a equivalent dynamic complementarity systems (DCS). We extend the Finite Elements with Switch…

A Nearly Finitary Matroid that is not $k$-Nearly Finitary
Patrick Tam
https://arxiv.org/abs/2404.04721 https://arxiv.org/pdf/2404.047…

A Nearly Finitary Matroid that is not $k$-Nearly Finitary
The class of $k$-nearly finitary matroids for some natural number $k$ is a subclass of the class of nearly finitary matroids. A natural question is whether this inclusion is proper. We answer this question affirmatively by constructing a nearly finitary matroid that is not $k$-nearly finitary for any $k \in \mathbb{N}$.

This https://arxiv.org/abs/2108.05555 has been replaced.
link: https://scholar.google.com/scholar?q=a

Longitudinal Network Models and Permutation-Uniform Markov Chains
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the same parameter, improving data reduction. Further we show that the permutation-uniform subclass of these chains permit interpretation as an independent, identically distributed sequence on the same state space. We then apply these ideas to temporal exponential r…

Semibrick-cosilting correspondence
Ramin Ebrahimi, Alireza Nasr-Isfahani
https://arxiv.org/abs/2403.11168 https://arxiv.org/pdf/2403.…

Semibrick-cosilting correspondence
Let $Λ$ be a finite dimensional algebra. In this paper we show that there is a natural bijection between cosilting modules in Mod$Λ$ and semibricks in Mod$Λ$ satisfying some condition. Also this bijection restricts to a bijection between all semibricks in mod$Λ$ and a certain subclass of cosilting modules. These bijections are generalizations of Asai's correspondence [7] between support $τ^-$-tilting modules and right finite semibricks.

This https://arxiv.org/abs/2310.19190 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Renewal structure of the Tree Builder Random Walk
In this paper, we study a class of random walks that build their own tree. At each step, the walker attaches a random number of leaves to its current position. The model can be seen as a subclass of the Random Walk in Changing Environments (RWCE) introduced by G. Amir, I. Benjamini, O. Gurel-Gurevich and G. Kozma. We develop a renewal framework for the process analogous to that established by A-S. Sznitman and M. Zerner in the context of RWRE. This provides a more robust foundation for analyzin…

This https://arxiv.org/abs/2403.18113 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$\ell_1$ spreading models and the FPP for Cesàro mean nonexpansive maps
Let $K$ be a nonempty subset of a Banach space $X$. A mapping $T\colon K\to K$ is called $\mathfrak{cm}$-nonexpansive if for any sequence $(u_i)_{i=1}^\infty$ and $y$ in $K$, $\limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} \big(T u_{i+k} - Ty\big)\|\leq \limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} (u_{i+k} - y)\|$ for all $n\in\mathbb{N}$. As a subclass of the class of nonexpansive maps, its FPP is well-established in a wide variety of…