Tootfinder

The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q
Xue-Bin Liang
https://arxiv.org/abs/2403.08727 https://

The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q
For any positive integer $q\geq 2$ and any real number $δ\in(0,1)$, let $α_q(n,δn)$ denote the maximum size of a subset of $\mathbb{Z}_q^n$ with minimum Hamming distance at least $δn$, where $\mathbb{Z}_q=\{0,1,\dotsc,q-1\}$ and $n\in\mathbb{N}$. The asymptotic rate function is defined by $ R_q(δ) = \limsup_{n\rightarrow\infty}\frac{1}{n}\log_qα_q(n,δn). $ The famous $q$-ary asymptotic Gilbert-Varshamov bound, obtained in the 1950s, states that \[ R_q(δ) \geq 1 - δ\log_q(q-1)-δ\log_q\…

On arithmetic nature of $q$-analogue of the generalized Stieltjes constants
Tapas Chatterjee, Sonam Garg
https://arxiv.org/abs/2404.08025 https://

On arithmetic nature of $q$-analogue of the generalized Stieltjes constants
In this article, our aim is to extend the research conducted by Kurokawa and Wakayama in 2003, particularly focusing on the $q$-analogue of the Hurwitz zeta function. Our specific emphasis lies in exploring the coefficients in the Laurent series expansion of a $q$-analogue of the Hurwitz zeta function around $s=1$. We establish the closed-form expressions for the first two coefficients in the Laurent series of the $q$-Hurwitz zeta function. Additionally, utilizing the reflection formula for the…

On arithmetic nature of $q$-analogue of the generalized Stieltjes constants
Tapas Chatterjee, Sonam Garg
https://arxiv.org/abs/2404.08025 https://

On arithmetic nature of $q$-analogue of the generalized Stieltjes constants
In this article, our aim is to extend the research conducted by Kurokawa and Wakayama in 2003, particularly focusing on the $q$-analogue of the Hurwitz zeta function. Our specific emphasis lies in exploring the coefficients in the Laurent series expansion of a $q$-analogue of the Hurwitz zeta function around $s=1$. We establish the closed-form expressions for the first two coefficients in the Laurent series of the $q$-Hurwitz zeta function. Additionally, utilizing the reflection formula for the…

This https://arxiv.org/abs/2312.17122 has been replaced.
link: https://scholar.google.com/scholar?q=a

Large Language Model for Causal Decision Making
Large Language Models (LLMs) have shown their success in language understanding and reasoning on general topics. However, their capability to perform inference based on user-specified structured data and knowledge in corpus-rare concepts, such as causal decision-making is still limited. In this work, we explore the possibility of fine-tuning an open-sourced LLM into LLM4Causal, which can identify the causal task, execute a corresponding function, and interpret its numerical results based on use…

This https://arxiv.org/abs/2206.00207 has been replaced.
link: https://scholar.google.com/scholar?q=a

Statistical and Computational Complexities of BFGS Quasi-Newton Method for Generalized Linear Models
The gradient descent (GD) method has been used widely to solve parameter estimation in generalized linear models (GLMs), a generalization of linear models when the link function can be non-linear. In GLMs with a polynomial link function, it has been shown that in the high signal-to-noise ratio (SNR) regime, due to the problem's strong convexity and smoothness, GD converges linearly and reaches the final desired accuracy in a logarithmic number of iterations. In contrast, in the low SNR setting,…

This https://arxiv.org/abs/2310.04947 has been replaced.
link: https://scholar.google.com/scholar?q=a

OTFS based Joint Radar and Communication: Signal Analysis using the Ambiguity Function
Orthogonal time frequency space (OTFS) modulation has recently been identified as a suitable waveform for joint radar and communication systems. Focusing on the effect of data modulation on the radar sensing performance, we derive the ambiguity function (AF) of the OTFS waveform and characterize the radar global accuracy. We evaluate the behavior of the AF with respect to the distribution of the modulated data and derive an accurate approximation for the mean and variance of the AF, thus, appro…

This https://arxiv.org/abs/2212.07625 has been replaced.
link: https://scholar.google.com/scholar?q=a

Isoparametric functions on Finsler space forms
In this paper, we prove that transnormal functions are isoparametric functions on a Finsler space form $(N(c),F)$ under certain conditions, which generalize Theorem B in [5]. Further more, we obtain a local isoparametric function constructed by a distance function and give a global isoparametric function on a standard Finsler sphere.

Fractional distortion in hyperbolic groups
Pallavi Dani, Timothy Riley
https://arxiv.org/abs/2403.08645 https://arxiv.org/pdf/2403.08…

Fractional distortion in hyperbolic groups
For all integers $p>q>0$ and $k >0$, and all non-elementary torsion-free hyperbolic groups $H$, we construct a hyperbolic group $G$ in which $H$ is a subgroup, such that the distortion function of $H$ in $G$ grows like $\exp^k(n^{p/q})$. Here, $\exp^k$ denotes the $k$-fold-iterated exponential function.

This https://arxiv.org/abs/2303.04137 has been replaced.
link: https://scholar.google.com/scholar?q=a

Diffusion Policy: Visuomotor Policy Learning via Action Diffusion
This paper introduces Diffusion Policy, a new way of generating robot behavior by representing a robot's visuomotor policy as a conditional denoising diffusion process. We benchmark Diffusion Policy across 12 different tasks from 4 different robot manipulation benchmarks and find that it consistently outperforms existing state-of-the-art robot learning methods with an average improvement of 46.9%. Diffusion Policy learns the gradient of the action-distribution score function and iteratively opt…

This https://arxiv.org/abs/2402.01092 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Dynamical Model of Neural Scaling Laws
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. Th…

This https://arxiv.org/abs/2310.06689 has been replaced.
link: https://scholar.google.com/scholar?q=a

Approximating Nash Equilibria in Normal-Form Games via Stochastic Optimization
We propose the first loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for approximating Nash equilibria, resulting in novel algorithms with provable guarantees. We complement our theoretical analysis with experiments demonstrating that stochastic gradient descent can outperform previous state-of-the-art approaches.

This https://arxiv.org/abs/2308.09582 has been replaced.
link: https://scholar.google.com/scholar?q=a

Agreement theorems for high dimensional expanders in the small soundness regime: the role of covers
Given a family $X$ of subsets of $[n]$ and an ensemble of local functions $\{f_s:s\toΣ\; | \; s\in X\}$, an agreement test is a randomized property tester that is supposed to test whether there is some global function $G:[n]\toΣ$ such that $f_s=G|_s$ for many sets $s$. A "classical" small-soundness agreement theorem is a list-decoding $(LD)$ statement, saying that \[\tag{$LD$} Agree(\{f_s\}) > \varepsilon \quad \Longrightarrow \quad \exists G^1,\dots, G^\ell,\quad P_s[f_s\overset{0.…

This https://arxiv.org/abs/2209.00081 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Semi-Algebraic Framework for Verification and Synthesis of Control Barrier Functions
Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This paper investigates the problems of verifying positive invariance of a semi-algebraic set as well as synthesizing sets that can be made positive invariant through Control Barrier Function (CBF)-based control. The key to our approach consists of mapping conditions for positive invariance to sum-of-sq…

This https://arxiv.org/abs/2312.06502 has been replaced.
link: https://scholar.google.com/scholar?q=a

On enforcing dyadic-type homogeneous binary function product constraints in MatBase
Homogeneous binary function products are often encountered in the sub-universes modeled by databases, from genealogical trees to sports, from education to healthcare, etc. Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility. The (Elementary) Mathematical Data Model provides 18 dyadic-type homogeneous binary function product constraint types. MatBase, an intelligent data and knowledge base management system prototype, allows …

This https://arxiv.org/abs/2104.15133 has been replaced.
link: https://scholar.google.com/scholar?q=a

Intermediate dimensions of infinitely generated attractors
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensions: a family of dimensions depending on a parameter $θ\in [0,1]$ which interpolate between the Hausdorff and box dimensions. Our main results are in the case when all the contractions are conformal. Under a natural separation condition we prove that the intermediate dimensions of the limit set are the maximum of the…

This https://arxiv.org/abs/2208.07540 has been replaced.
link: https://scholar.google.com/scholar?q=a

Large-Scale Minimization of the Pseudospectral Abscissa
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control system that has optimization parameters. We describe a subspace procedure to cope with the setting when the matrix-valued function is of large size. The proposed subspace procedure solves a sequence of reduced problems obtained by restricting the matrix-valued f…

This https://arxiv.org/abs/2305.04656 has been replaced.
link: https://scholar.google.com/scholar?q=a

Preservation theorems for Tarski's relation algebra
We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question whether they are generated by a finite set of operations. We obtain several positive and negative results along these lines. Specifically, the homomorphism-safe fragment is finitely generated (both over finite and over arbitrary structures). The function-preserving fragment is not finitely generated (and, in fact, not expressible …

This https://arxiv.org/abs/2206.00347 has been replaced.
link: https://scholar.google.com/scholar?q=a

Comparative statics with adjustment costs and the le Chatelier principle
We develop a theory of monotone comparative statics for models with adjustment costs. We show that comparative-statics conclusions may be drawn under the usual ordinal complementarity assumptions on the objective function, assuming very little about costs: only a mild monotonicity condition is required. We use this insight to prove a general le Chatelier principle: under the ordinal complementarity assumptions, if short-run adjustment is subject to a monotone cost, then the long-run response to…

This https://arxiv.org/abs/2310.04947 has been replaced.
link: https://scholar.google.com/scholar?q=a

OTFS based Joint Radar and Communication: Signal Analysis using the Ambiguity Function
Orthogonal time frequency space (OTFS) modulation has recently been identified as a suitable waveform for joint radar and communication systems. Focusing on the effect of data modulation on the radar sensing performance, we derive the ambiguity function (AF) of the OTFS waveform and characterize the radar global accuracy. We evaluate the behavior of the AF with respect to the distribution of the modulated data and derive an accurate approximation for the mean and variance of the AF, thus, appro…

Algebraic identities among $q$- analogue of Euler double zeta values
Tapas Chatterjee, Sonam Garg
https://arxiv.org/abs/2404.07688 https://

Algebraic identities among $q$- analogue of Euler double zeta values
In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant. Using a $q$-analogue of the Nielsen Reflexion Formula for $q>1$, we investigate identities involving different versions of $q$-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of $ζ_q(s_1, s_2)$ as $s_1$…

Fractional distortion in hyperbolic groups
Pallavi Dani, Timothy Riley
https://arxiv.org/abs/2403.08645 https://arxiv.org/pdf/2403.08…

Fractional distortion in hyperbolic groups
For all integers $p>q>0$ and $k >0$, and all non-elementary torsion-free hyperbolic groups $H$, we construct a hyperbolic group $G$ in which $H$ is a subgroup, such that the distortion function of $H$ in $G$ grows like $\exp^k(n^{p/q})$. Here, $\exp^k$ denotes the $k$-fold-iterated exponential function.

This https://arxiv.org/abs/2312.10409 has been replaced.
link: https://scholar.google.com/scholar?q=a

Density density correlation functions of chiral Luttinger liquids with a point contact impurity
The density density correlation function (most singular parts) of chiral Luttinger liquids forming the fractional quantum Hall effect (FQHE) edge is systematically derived in presence of a point-contact junction acting as a localised scalar impurity and is shown to be expressible as compact analytical functions with second order poles and involving the bare scale-independent reflection and transmission coefficients. The results are validated on comparison with standard fermionic perturbation th…

This https://arxiv.org/abs/2402.01092 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Dynamical Model of Neural Scaling Laws
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. Th…

This https://arxiv.org/abs/1709.03385 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Recursive Stopping Time Structure of the $3x+1$ Function
The $3x + 1$ problem concerns iteration of the map $T:\mathbb{Z}\rightarrow\mathbb{Z}$ given by \begin{align*} T(x)=\left\{\begin{array}{lcr}\;\;\;\;\displaystyle{\frac{x}{2}} & \mbox{if $x\equiv 0\ (\text{mod}\ 2)$},\\ \\\displaystyle{\frac{3x+1}{2}} & \mbox{if $x\equiv 1\ (\text{mod}\ 2)$}.\end{array}\right. \end{align*} The $3x+1$ Conjecture states that every $x\geq1$ has some iterate $T^s(x)=1$. The least $s\in\mathbb{N}$ such that $T^s(x)

This https://arxiv.org/abs/2201.02323 has been replaced.
link: https://scholar.google.com/scholar?q=a

Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks
We study distributed algorithms for finding a Nash equilibrium (NE) in a class of non-cooperative convex games under partial information. Specifically, each agent has access only to its own smooth local cost function and can receive information from its neighbors in a time-varying directed communication network. To this end, we propose a distributed gradient play algorithm to compute a NE by utilizing local information exchange among the players. In this algorithm, every agent performs a gradie…

This https://arxiv.org/abs/2111.05030 has been replaced.
link: https://scholar.google.com/scholar?q=a

A central limit theorem for the variation of the sum of digits
We prove a Central Limit Theorem for probability measures defined via the variation of the sum-of-digits function, in base $b\ge 2$. For $r\ge 0$ and $d \in \mathbb{Z}$, we consider $μ^{(r)}(d)$ as the density of integers $n\in \mathbb{N}$ for which the sum of digits increases by $d$ when we add $r$ to $n$. We give a probabilistic interpretation of $μ^{(r)}$ on the probability space given by the group of $b$-adic integers equipped with the normalized Haar measure. We split the base-$b$ expans…

This https://arxiv.org/abs/2402.04689 has been replaced.
link: https://scholar.google.com/scholar?q=a

Stein Boltzmann Sampling: A Variational Approach for Global Optimization
In this paper, we introduce a new flow-based method for global optimization of Lipschitz functions, called Stein Boltzmann Sampling (SBS). Our method samples from the Boltzmann distribution that becomes asymptotically uniform over the set of the minimizers of the function to be optimized. Candidate solutions are sampled via the \emph{Stein Variational Gradient Descent} algorithm. We prove the asymptotic convergence of our method, introduce two SBS variants, and provide a detailed comparison wit…

Algebraic identities among $q$- analogue of Euler double zeta values
Tapas Chatterjee, Sonam Garg
https://arxiv.org/abs/2404.07688 https://

Algebraic identities among $q$- analogue of Euler double zeta values
In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant. Using a $q$-analogue of the Nielsen Reflexion Formula for $q>1$, we investigate identities involving different versions of $q$-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of $ζ_q(s_1, s_2)$ as $s_1$…

This https://arxiv.org/abs/1610.07914 has been replaced.
link: https://scholar.google.com/scholar?q=a

The ACPATH Metric: Precise Estimation of the Number of Acyclic Paths in C-like Languages
NPATH is a metric introduced by Brian A. Nejmeh in [13] that is aimed at overcoming some important limitations of McCabe's cyclomatic complexity. Despite the fact that the declared NPATH objective is to count the number of acyclic execution paths through a function, the definition given for the C language in [13] fails to do so even for very simple programs. We show that counting the number of acyclic paths in CFG is unfeasible in general. Then we define a new metric for C-like languages, calle…

This https://arxiv.org/abs/2201.09754 has been replaced.
link: https://scholar.google.com/scholar?q=a

Deep Reinforcement Learning with Spiking Q-learning
With the help of special neuromorphic hardware, spiking neural networks (SNNs) are expected to realize artificial intelligence (AI) with less energy consumption. It provides a promising energy-efficient way for realistic control tasks by combining SNNs with deep reinforcement learning (RL). There are only a few existing SNN-based RL methods at present. Most of them either lack generalization ability or employ Artificial Neural Networks (ANNs) to estimate value function in training. The former n…

This https://arxiv.org/abs/2207.11611 has been replaced.
link: https://scholar.google.com/scholar?q=a

Assouad type dimensions of infinitely generated self-conformal sets
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of sets. Under natural separation conditions, we prove a formula for the Assouad dimension and prove sharp bounds for the Assouad spectrum in terms of the Hausdorff dimension of the limit set and dimensions of the set of fixed points of the contractions. The Asso…

This https://arxiv.org/abs/2211.11974 has been replaced.
link: https://scholar.google.com/scholar?q=a

Green function in metric measure spaces
We study existence and uniqueness of Green functions for the Cheeger $Q$-Laplacian in metric measure spaces that are Ahlfors $Q$-regular and support a $Q$-Poincaré inequality with $Q>1$. We prove uniqueness of Green functions both in the case of relatively compact domains, and in the global (unbounded) case. We also prove existence of global Green functions in unbounded spaces, complementing the existing results in relatively compact domains proved recently in [BBL20].

This https://arxiv.org/abs/2112.00994 has been replaced.
link: https://scholar.google.com/scholar?q=a

Transforming Radical Differential Equations to Algebraic Differential Equations
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations among them by means of a rational change of variables. The solutions of the given equation and its transformation correspond one-to-one. This work can be seen as a generalization of previous work on reparametrization of ODEs and PDEs with radical c…

This https://arxiv.org/abs/2203.07007 has been replaced.
link: https://scholar.google.com/scholar?q=a

On pseudoeffective cones of projective bundles and volume function
In this article, we compute the pseudo-effective cones of various projective bundles $\mathbb{P}_X(E)$ over higher dimensional varieties $X$ under some assumptions on $X$ as well as on the vector bundle $E$. We also compute the volume function on fibre product $\mathbb{P}(E)\times_C\mathbb{P}(F)$ of two projective bundles over a smooth irreducible complex projective curve $C$. In particular, we show that the volume function on the fiber product of two ruled surfaces is of polynomial type.

This https://arxiv.org/abs/2210.03203 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Aemulus Project VI: Emulation of beyond-standard galaxy clustering statistics to improve cosmological constraints
There is untapped cosmological information in galaxy redshift surveys in the non-linear regime. In this work, we use the AEMULUS suite of cosmological $N$-body simulations to construct Gaussian process emulators of galaxy clustering statistics at small scales ($0.1-50 \: h^{-1}\,\mathrm{Mpc}$) in order to constrain cosmological and galaxy bias parameters. In addition to standard statistics -- the projected correlation function $w_\mathrm{p}(r_\mathrm{p})$, the redshift-space monopole of the cor…

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
Miguel Aguilar-Janita, Silvio Franz, Victor Martin-Mayor, Javier Moreno-Gordo, Giorgio Parisi, Federico Ricci-Tersenghi, Juan J. Ruiz-Lorenzo
https://arxiv.org/abs/2403.08503…

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can an…

This https://arxiv.org/abs/2210.16109 has been replaced.
link: https://scholar.google.com/scholar?q=a

Electron-hole asymmetry of quantum collective excitations in high-$T_c$ copper oxides
We carry out a systematic study of collective spin- and charge excitations for the canonical single-band Hubbard, $t$-$J$-$U$, and $t$-$J$ models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. Recently developed variational wave function approach, combined with the expansion in inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron-hole asymmetry of magnetic excitations, with a robust param…

Computational data on ${\mathfrak S}_n$-extensions of $\mathbb Q$
Gunter Malle
https://arxiv.org/abs/2403.09146 https://arxiv.org/pdf…

Computational data on ${\mathfrak S}_n$-extensions of $\mathbb Q$
We discuss computational results on field extensions $K/{\mathbb Q}$ of degree $n\le11$ with Galois group of the Galois closure isomorphic to the full symmetric group ${\mathfrak S}_n$. More precisely, we present statistics on the number of such extensions as a function of the field discriminant and compare them to the known predictions by Bhargava and the author. We also investigate the numbers of fields with equal discriminant and tabulate class numbers and class groups to compare them agains…

This https://arxiv.org/abs/2307.00521 has been replaced.
link: https://scholar.google.com/scholar?q=a

zkFi: Privacy-Preserving and Regulation Compliant Transactions using Zero Knowledge Proofs
We propose a middleware solution designed to facilitate seamless integration of privacy using zero-knowledge proofs within various multi-chain protocols, encompassing domains such as DeFi, gaming, social networks, DAOs, e-commerce, and the metaverse. Our design achieves two divergent goals. zkFi aims to preserve consumer privacy while achieving regulation compliance through zero-knowledge proofs. These ends are simultaneously achievable. zkFi protocol is designed to function as a plug-and-play …

This https://arxiv.org/abs/2201.02323 has been replaced.
link: https://scholar.google.com/scholar?q=a

Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks
We study distributed algorithms for finding a Nash equilibrium (NE) in a class of non-cooperative convex games under partial information. Specifically, each agent has access only to its own smooth local cost function and can receive information from its neighbors in a time-varying directed communication network. To this end, we propose a distributed gradient play algorithm to compute a NE by utilizing local information exchange among the players. In this algorithm, every agent performs a gradie…

This https://arxiv.org/abs/2403.02165 has been replaced.
link: https://scholar.google.com/scholar?q=a

Two Splits, Three Ways: Advances in Double Splitting Quenches
In this work we introduce a method for calculating holographic duals of BCFTs with more than two boundaries. We apply it to calculating the dynamics of entanglement entropy in a 1+1d CFT that is instantaneously split into multiple segments and calculate the entanglement entropy as a function of time for the case of two splits, showing that our approach reproduces earlier results for the double split case. Our manuscript lays the groundwork for future calculations of the entanglement entropy for…

The Overlap Gap Property limits limit swapping in QAOA
Mark Xin Hong Goh
https://arxiv.org/abs/2404.06087 https://arxiv.org/pdf/2404.…

The Overlap Gap Property limits limit swapping in QAOA
The Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm designed for combinatorial optimization problem. We show that under the assumption that the Overlap Gap Property (OGP) in the solution space for the Max-$q$-XORSAT is a monotonic increasing function, the swapping of limits in QAOA leads to suboptimal results limited by the OGP. Furthermore, since the performance of QAOA for the pure $q$-spin model matches asymptotically for Max-$q$-XORSAT on large-girth regular hypergr…

This https://arxiv.org/abs/2212.11325 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bent functions and strongly regular graphs
The family of bent functions is a known class of Boolean functions, which have a great importance in cryptography. The Cayley graph defined on $\mathbb{Z}_{2}^{n}$ by the support of a bent function is a strongly regular graph $srg(v,kλ,μ)$, with $λ=μ$. In this note we list the parameters of such Cayley graphs. Moreover, it is given a condition on $(n,m)$-bent functions $F=(f_1,\ldots,f_m)$, involving the support of their components $f_i$, and their $n$-ary symmetric differences.

Quark Counting, Drell-Yan West, and the Pion Wave Function
Mary Alberg, Gerald A. Miller
https://arxiv.org/abs/2403.03356 https://arx…

Quark Counting, Drell-Yan West, and the Pion Wave Function
The relation between the pion's quark distribution function, $q(x)$, its light-front wave function, and the elastic charge form factor, $F(Δ^2)$ is explored. The square of the leading-twist pion wave function at a special probe scale, $ζ_H$, is determined using models and Poincare covariance from realistic results for $q(x)$. This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship be…

This https://arxiv.org/abs/1704.04370 has been replaced.
link: https://scholar.google.com/scholar?q=a

Fast Similarity Sketching
We consider the $\textit{Similarity Sketching}$ problem: Given a universe $[u] = \{0,\ldots, u-1\}$ we want a random function $S$ mapping subsets $A\subseteq [u]$ into vectors $S(A)$ of size $t$, such that similarity is preserved. More precisely: Given sets $A,B\subseteq [u]$, define $X_i = [S(A)[i] = S(B)[i]]$ and $X = \sum_{i\in [t]} X_i$. We want to have $E[X] = t\cdot J(A,B)$, where $J(A,B) = |A\cap B|/|A\cup B|$ and furthermore to have strong concentration guarantees (i…

This https://arxiv.org/abs/2002.11339 has been replaced.
link: https://scholar.google.com/scholar?q=a

Generalized maps between diffeological spaces
By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological spaces and asymptotic maps is enriched over the category of diffeological spaces, and inherits completeness and cocompleteness. In particular, the set of asymptotic functions on a Euclidean open set include Schwartz distributions and form a Colombeau type smooth differential algebra over Robinson's field of asymptotic…

This https://arxiv.org/abs/2208.06473 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Dynamic Principal Agent Problem with One-sided Commitment
In this paper we consider a principal agent problem where the agent is allowed to quit, by incurring a cost. When the current agent quits the job, the principal will hire a new one, possibly with a different type. We characterize the principal's dynamic value function, which could be discontinuous at the boundary, as the (unique) minimal solution of an infinite dimensional system of HJB equations, parametrized by the agent's type. This dynamic problem is time consistent in certain sense. Some…

This https://arxiv.org/abs/2107.05772 has been replaced.
link: https://scholar.google.com/scholar?q=a

On λ-backbone coloring of cliques with tree backbones in linear time
A $λ$-backbone coloring of a graph $G$ with its subgraph (also called a backbone) $H$ is a function $c \colon V(G) \rightarrow \{1,\dots, k\}$ ensuring that $c$ is a proper coloring of $G$ and for each $\{u,v\} \in E(H)$ it holds that $|c(u) - c(v)| \ge λ$. In this paper we propose a way to color cliques with tree and forest backbones in linear time that the largest color does not exceed $\max\{n, 2 λ\} + Δ(H)^2 \lceil\log{n} \rceil$. This result improves on the previously existin…

This https://arxiv.org/abs/2209.07848 has been replaced.
link: https://scholar.google.com/scholar?q=a

Boundedness of bundle diffeomorphism groups over a circle
In this paper we study boundedness of bundle diffeomorphism groups over a circle. For a fiber bundle $π: M \to S^1$ with fiber $N$ and structure group $Γ$ and $r \in {\Bbb Z}_{\geq 0} \cup \{ \infty \}$ we distinguish an integer $k = k(π, r) \in {\Bbb Z}_{\geq 0}$ and construct a function $\widehatν : {\rm Diff}_π(M)_0 \to {\Bbb R}_k$. When $k \geq 1$, it is shown that the bundle diffeomorphism group ${\rm Diff}_π(M)_0$ is uniformly perfect and $clb_π\,{\rm Diff}^r_π(M)_0 \leq k+3$, if …

This https://arxiv.org/abs/2110.01673 has been replaced.
link: https://scholar.google.com/scholar?q=a

Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence
We introduce a recursive model-complete theory which completely axiomatizes the structure $Z_α=(Z, +, 0, 1, f)$ where $f : x \to \lfloorα x \rfloor $ is a unary function with $α$ a fixed transcendental number.When α$ is computable, our theory is recursively enumerable, and hence decidable as a result of completeness. Therefore, this result fits into the more general theme of adding traces of multiplication to integers without losing decidability.

This https://arxiv.org/abs/2310.19281 has been replaced.
initial toot: https://mastoxiv.page/@a…

Distinguishing Ion Dynamics from Muon diffusion in Muon Spin Relaxation
We propose a model to describe the fluctuations in the internal magnetic field due to ion dynamics observed in the muon spin relaxation ($μ$SR) by an Edwards-Anderson type autocorrelation function that separates the quasi-static and dynamic components of the correlation by a parameter $Q$ (where $0\le Q\le1$). Our Monte Carlo simulations for this model showed that the time evolution of muon spin polarization deviates significantly from the Kubo-Toyabe (KT) function. To further validate the mod…

This https://arxiv.org/abs/2209.13072 has been replaced.
link: https://scholar.google.com/scholar?q=a

General multiple Dirichlet series from perverse sheaves
We give an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb F_q(T)$, generalizing a set of axioms given by Diaconu and Pasol. The key axiom, relating the coefficients at prime powers to sums of the coefficients, formalizes an observation of Chinta. The existence of multiple Dirichlet series satisfying these axioms is proved by exhibiting the coefficients as trace functions of explicit perverse sheaves and using properties of perverse sheaves. The multiple…

This https://arxiv.org/abs/2305.17757 has been replaced.
link: https://scholar.google.com/scholar?q=a

Diversity-seeking Jump Games in Networks
Recently, strategic games inspired by Schelling's influential model of residential segregation have been studied in the TCS and AI literature. In these games, agents of k different types occupy the nodes of a network topology aiming to maximize their utility, which is a function of the fraction of same-type agents they are adjacent to in the network. As such, the agents exhibit similarity seeking strategic behavior. In this paper, we introduce a class of strategic jump games in which the agents…

This https://arxiv.org/abs/2207.09101 has been replaced.
link: https://scholar.google.com/scholar?q=a

Assessing quality of selection procedures: Lower bound of false positive rate as a function of inter-rater reliability
Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome; the applicant is either selected or not. This final outcome is not considered in IRR, which instead focuses on the ratings of the individual subjects or objects. We outline the connection between the ratings' measurement model (used for IRR) and a binary classif…

This https://arxiv.org/abs/2401.07968 has been replaced.
link: https://scholar.google.com/scholar?q=a

Characterizing the minimax rate of nonparametric regression under bounded convex constraints
We quantify the minimax rate for a nonparametric regression model over a convex function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where \[\varepsilon^{\ast} =\sup\{\varepsilon>0:n\varepsilon^2 \le \log M_{\mathcal{F}}^{\operatorname{loc}}(\varepsilon,c)\},\] where $M_{\mathcal{F}}^{\operatorname{loc}}(\cdot, c)$ is the local metric entropy of $\mathcal{F}$ and our loss function is the squared population $L_…

This https://arxiv.org/abs/2204.07484 has been replaced.
link: https://scholar.google.com/scholar?q=a

Operator semigroups in the mixed topology and the infinitesimal description of Markov processes
We define a class of not necessarily linear $C_0$-semigroups $(P_t)_{t\geq0}$ on $C_b(E)$ (more generally, on $C_κ(E):=\frac1κC_b(E)$, for some bounded function $κ$, which is the pointwise limit of a decreasing sequence of continuous functions) equipped with the mixed topology $τ_1^{\mathscr M}$ for a large class of topological state spaces $E$. If these semigroups are linear, classical theory of operator semigroups on locally convex spaces as well as the theory of bicontinuous semigroups a…

This https://arxiv.org/abs/2404.01201 has been replaced.
link: https://scholar.google.com/scholar?q=a

Search for gravitationally lensed interstellar transmissions
We consider interstellar light transmission facilitated by gravitational lensing. We study axially-symmetric lensing configurations where the transmitter, lens, and receiver are nearly aligned. With the transmitter positioned in the focal region of the lens, we investigate the caustic formed by a diffraction-limited beam of light emitted by the transmitter. We evaluated the impact of the lens's point spread function (PSF) on the received beam. We estimate the power delivered to a receiver at in…

This https://arxiv.org/abs/2005.07399 has been replaced.
link: https://scholar.google.com/scholar?q=a

Birkhoff-James orthogonality and applications : A survey
In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interest…

This https://arxiv.org/abs/2208.06473 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Dynamic Principal Agent Problem with One-sided Commitment
In this paper we consider a principal agent problem where the agent is allowed to quit, by incurring a cost. When the current agent quits the job, the principal will hire a new one, possibly with a different type. We characterize the principal's dynamic value function, which could be discontinuous at the boundary, as the (unique) minimal solution of an infinite dimensional system of HJB equations, parametrized by the agent's type. This dynamic problem is time consistent in certain sense. Some…

This https://arxiv.org/abs/2212.01917 has been replaced.
link: https://scholar.google.com/scholar?q=a

Möbius function of the subgroup lattice of a finite group and Euler Characteristic
The Möbius function of the subgroup lattice of a finite group has been introduced by Hall and applied to investigate several questions. In this paper, we consider the Möbius function defined on an order ideal related to the lattice of the subgroups of an irreducible subgroup $G$ of the general linear group $\mathrm{GL}(n,q)$ acting on the $n$-dimensional vector space $V=\mathbb{F}_q^n$, where $\mathbb{F}_q$ is the finite field with $q$ elements. We find a relation between this function and th…

Extending the Meijer $G$-function
Dmitrii Karp, Alexey Kuznetsov
https://arxiv.org/abs/2403.05708 https://arxiv.org/pdf/2403.05708

Extending the Meijer $G$-function
By replacing the Euler gamma function by the Barnes double gamma function in the definition of the Meijer $G$-function, we introduce a new family of special functions, which we call $K$-functions. This is a very general class of functions, which includes as special cases Meijer $G$-functions (thus also all hypergeometric functions ${}_p F_q$) as well as several new functions that appeared recently in the literature. Our goal is to define the $K$-function, study its analytic and transformation p…

The Overlap Gap Property limits limit swapping in QAOA
Mark Xin Hong Goh
https://arxiv.org/abs/2404.06087 https://arxiv.org/pdf/2404.…

The Overlap Gap Property limits limit swapping in QAOA
The Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm designed for combinatorial optimization problem. We show that under the assumption that the Overlap Gap Property (OGP) in the solution space for the Max-$q$-XORSAT is a monotonic increasing function, the swapping of limits in QAOA leads to suboptimal results limited by the OGP. Furthermore, since the performance of QAOA for the pure $q$-spin model matches asymptotically for Max-$q$-XORSAT on large-girth regular hypergr…

This https://arxiv.org/abs/2403.01565 has been replaced.
link: https://scholar.google.com/scholar?q=a

Strong survival and extinction for branching random walks via a new order for generating functions
We consider general discrete-time branching random walks on a countable set $X$. According to these processes, a particle at $x\in X$ generates a random number of children and places them at (some of) the sites of $X$, not necessarily independently nor with the same law at different starting vertices $x$.We introduce a new type of stochastic ordering of branching random walks, generalizing the germ order introduced by Hutchcroft in arXiv:2011.06402, which relies on the generating function of th…

Quark Counting, Drell-Yan West, and the Pion Wave Function
Mary Alberg, Gerald A. Miller
https://arxiv.org/abs/2403.03356 https://arx…

Quark Counting, Drell-Yan West, and the Pion Wave Function
The relation between the pion's quark distribution function, $q(x)$, its light-front wave function, and the elastic charge form factor, $F(Δ^2)$ is explored. The square of the leading-twist pion wave function at a special probe scale, $ζ_H$, is determined using models and Poincare covariance from realistic results for $q(x)$. This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship be…

This https://arxiv.org/abs/2312.10199 has been replaced.
link: https://scholar.google.com/scholar?q=a

Automatic nonlinear MPC approximation with closed-loop guarantees
Safety guarantees are vital in many control applications, such as robotics. Model predictive control (MPC) provides a constructive framework for controlling safety-critical systems, but is limited by its computational complexity. We address this problem by presenting a novel algorithm that automatically computes an explicit approximation to nonlinear MPC schemes while retaining closed-loop guarantees. Specifically, the problem can be reduced to a function approximation problem, which we then ta…

This https://arxiv.org/abs/2310.10486 has been replaced.
link: https://scholar.google.com/scholar?q=a

ManyQuadrupeds: Learning a Single Locomotion Policy for Diverse Quadruped Robots
Learning a locomotion policy for quadruped robots has traditionally been constrained to a specific robot morphology, mass, and size. The learning process must usually be repeated for every new robot, where hyperparameters and reward function weights must be re-tuned to maximize performance for each new system. Alternatively, attempting to train a single policy to accommodate different robot sizes, while maintaining the same degrees of freedom (DoF) and morphology, requires either complex learni…

This https://arxiv.org/abs/2310.19281 has been replaced.
initial toot: https://mastoxiv.page/@a…

Distinguishing Ion Dynamics from Muon diffusion in Muon Spin Relaxation
We propose a model to describe the fluctuations in the internal magnetic field due to ion dynamics observed in the muon spin relaxation ($μ$SR) by an Edwards-Anderson type autocorrelation function that separates the quasi-static and dynamic components of the correlation by a parameter $Q$ (where $0\le Q\le1$). Our Monte Carlo simulations for this model showed that the time evolution of muon spin polarization deviates significantly from the Kubo-Toyabe (KT) function. To further validate the mod…

This https://arxiv.org/abs/1811.10476 has been replaced.
link: https://scholar.google.com/scholar?q=a

Some differential equations for the Riemann $θ$-function on Jacobians
We prove some differential equations for the Riemann theta function associated to the Jacobian of a Riemann surface. The proof is based on some variants of a formula by Fay for the theta function, which are motivated by their analogues in Arakelov theory of Riemann surfaces.

This https://arxiv.org/abs/2310.19006 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Weisfeiler-Leman Dimension of Conjunctive Queries
The Weisfeiler-Leman (WL) dimension of a graph parameter $f$ is the minimum $k$ such that, if $G_1$ and $G_2$ are indistinguishable by the $k$-dimensional WL-algorithm then $f(G_1)=f(G_2)$. The WL-dimension of $f$ is $\infty$ if no such $k$ exists. We study the WL-dimension of graph parameters characterised by the number of answers from a fixed conjunctive query to the graph. Given a conjunctive query $φ$, we quantify the WL-dimension of the function that maps every graph $G$ to the number of …

Field-orientation-dependent magnetic phases in GdRu$_2$Si$_2$ probed with muon-spin spectroscopy
B. M. Huddart, A. Hern\'andez-Meli\'an, G. D. A. Wood, D. A. Mayoh, M. Gomil\v{s}ek, Z. Guguchia, C. Wang, S. J. Blundell, G. Balakrishnan, T. Lancaster
https://arxiv.org/abs/2403.09431…

Field-orientation-dependent magnetic phases in GdRu$_2$Si$_2$ probed with muon-spin spectroscopy
Centrosymmetric GdRu$_2$Si$_2$ exhibits a variety of multi-Q magnetic states as a function of temperature and applied magnetic field, including a square skyrmion-lattice phase. The material's behavior is strongly dependent on the direction of the applied field, with different phase diagrams resulting for fields applied parallel or perpendicular to the crystallographic $c$ axis. Here, we present the results of muon-spin relaxation ($μ^+$SR) measurements on single crystals of GdRu$_2$Si$_2$. Our…

This https://arxiv.org/abs/2310.02715 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Further results on covering codes with radius R and codimension tR + 1
The length function $\ell_q(r,R)$ is the smallest possible length $n$ of a $ q $-ary linear $[n,n-r]_qR$ code with codimension (redundancy) $r$ and covering radius $R$. Let $s_q(N,ρ)$ be the smallest size of a $ρ$-saturating set in the projective space $\mathrm{PG}(N,q)$. There is a one-to-one correspondence between $[n,n-r]_qR$ codes and $(R-1)$-saturating $n$-sets in $\mathrm{PG}(r-1,q)$ that implies $\ell_q(r,R)=s_q(r-1,R-1)$. In this work, for $R\ge3$, new asymptotic upper bounds on $\ell…

This https://arxiv.org/abs/2207.09101 has been replaced.
link: https://scholar.google.com/scholar?q=a

Assessing quality of selection procedures: Lower bound of false positive rate as a function of inter-rater reliability
Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome; the applicant is either selected or not. This final outcome is not considered in IRR, which instead focuses on the ratings of the individual subjects or objects. We outline the connection between the ratings' measurement model (used for IRR) and a binary classif…

This https://arxiv.org/abs/2402.16779 has been replaced.
link: https://scholar.google.com/scholar?q=a

One-loop quantization of Euclidean D3-branes in holographic backgrounds
In this note we analyze the semi-classical quantization of D3 branes in three different holographic backgrounds in type IIB string theory. The first background is Euclidean AdS$_5$ with $S^1\times S^3$ boundary accompanied with a twist to preserve supersymmetry. We work out the spectrum of fluctuations around the classical D3-brane configuration, compute its one-loop partition function, and match to the non-perturbative correction to the superconformal index of ${\cal N}=4$ SYM. We then study E…

This https://arxiv.org/abs/2403.08560 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Decoupling of the structure functions in momentum space based on the Laplace transformation
Using Laplace transform techniques, we describe the determination of the longitudinal structure function $F_{L}(x,Q^2)$, at the leading-order approximation in momentum space, from the structure function $F_{2}(x,Q^2)$ and its derivative with respect to ${\ln}Q^2$ in a kinematical region of low values of the Bjorken variable $x$. Since the $x$ dependence of $F_2(x,Q^2)$ and its evolution with $Q^2$ are determined much better by the data than $F_L(x,Q^2)$, this method provides both a direct check…

This https://arxiv.org/abs/2211.03464 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Survey on Quantum Reinforcement Learning
Quantum reinforcement learning is an emerging field at the intersection of quantum computing and machine learning. While we intend to provide a broad overview of the literature on quantum reinforcement learning - our interpretation of this term will be clarified below - we put particular emphasis on recent developments. With a focus on already available noisy intermediate-scale quantum devices, these include variational quantum circuits acting as function approximators in an otherwise classical…

This https://arxiv.org/abs/2208.13190 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exploiting higher-order derivatives in convex optimization methods
Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster convergence rates if the corresponding higher-order derivative is Lipschitz-continuous. Recently a series of lower iteration complexity bounds for such methods were proved, and a gap between upper an lower complexity bounds was revealed. Moreover, it was show…

This https://arxiv.org/abs/2305.12553 has been replaced.
link: https://scholar.google.com/scholar?q=a

Markov $α$-Potential Games
This paper proposes a new framework of Markov $α$-potential games to study Markov games. In this new framework, Markov games are shown to be Markov $α$-potential games, and the existence of an associated $α$-potential function is established. Any optimizer of an $α$-potential function is shown to be an $α$-stationary NE. Two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, are studied via this framework of Markov $α$-p…

This https://arxiv.org/abs/2310.02715 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Further results on covering codes with radius R and codimension tR + 1
The length function $\ell_q(r,R)$ is the smallest possible length $n$ of a $ q $-ary linear $[n,n-r]_qR$ code with codimension (redundancy) $r$ and covering radius $R$. Let $s_q(N,ρ)$ be the smallest size of a $ρ$-saturating set in the projective space $\mathrm{PG}(N,q)$. There is a one-to-one correspondence between $[n,n-r]_qR$ codes and $(R-1)$-saturating $n$-sets in $\mathrm{PG}(r-1,q)$ that implies $\ell_q(r,R)=s_q(r-1,R-1)$. In this work, for $R\ge3$, new asymptotic upper bounds on $\ell…

The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method
Thuan Quang Tran, Tuyen Trung Truong
https://arxiv.org/abs/2405.05834 https:/…

The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method
A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - was recently introduced by the second author. This method has good convergence guarantees, specially concerning finding roots of meromorphic functions. This paper explores using BNQN for the Riemann xi function. We show in particular that the Riemann hypothesis is equivalent to that all attractors of BNQN lie on the critical line. We also explain how an apparent relation between the basins of attraction of BNQN…

This https://arxiv.org/abs/2203.01707 has been replaced.
link: https://scholar.google.com/scholar?q=a

Testing Stationarity and Change Point Detection in Reinforcement Learning
We consider offline reinforcement learning (RL) methods in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the system transition and the reward function to be constant over time. However, the stationarity assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a consistent procedure to…

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, $q \equiv 1 \pmod 3$
Peter Beelen, Maria Montanucci, Lara Vicino
https://arxiv.org/abs/2404.18808

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, $q \equiv 1 \pmod 3$
In this article we continue the work started in arXiv:2303.00376v1, explicitly determining the Weierstrass semigroup at any place and the full automorphism group of a known $\mathbb{F}_{q^2}$-maximal function field $Y_3$ having the third largest genus, for $q \equiv 1 \pmod 3$. This function field arises as a Galois subfield of the Hermitian function field, and its uniqueness (with respect to the value of its genus) is a well-known open problem. Knowing the Weierstrass semigroups may provide a …

This https://arxiv.org/abs/2105.01473 has been replaced.
link: https://scholar.google.com/scholar?q=a

Equilibrium strategies in time-inconsistent stochastic control problems with constraints: necessary conditions
This paper is concerned with a time-inconsistent recursive stochastic control problems where the forward state process is constrained through an additional recursive utility system. By adapting the Ekeland variational principle, necessary conditions for equilibrium strategies are presented concerning a second-order Hamiltonian function defined by pairs of backward stochastic differential equations. At last, we consider a finite horizon state constrained investment-consumption problem with non-e…

Primitive normal Values of rational functions with one prescribed norm and trace over finite fields
Arpan Chandra Mazumder, Dhiren Kumar Basnet
https://arxiv.org/abs/2405.05298

Primitive normal Values of rational functions with one prescribed norm and trace over finite fields
Let $q, n, m \in \mathbb{N}$ be such that $q$ is a prime power and $a, b \in \mathbb{F}$. In this article we establish a sufficient condition for the existence of a primitive normal pair $(α, f(α)) \in \mathbb{F}_{q^m}$ over $\mathbb{F}$ with a prescribed primitive norm $a$ and a non-zero trace $b$ over $\mathbb{F}$ of $α$, where $f(x) \in \mathbb{F}_{q^m}(x)$ is a rational function of degree sum $n$ with some minor restrictions. Furthermore, for $q=7^k$, $m \geq 7$ and rational functions wi…

This https://arxiv.org/abs/2008.08359 has been replaced.
link: https://scholar.google.com/scholar?q=a

The central limit theorem for slow-fast systems with Lévy noise
We consider a slow-fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.

This https://arxiv.org/abs/2402.04705 has been replaced.
link: https://scholar.google.com/scholar?q=a

Decoherence rate in random Lindblad dynamics
Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is govern…

This https://arxiv.org/abs/2403.08727 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q
For any positive integer $q\geq 2$ and any real number $δ\in(0,1)$, let $α_q(n,δn)$ denote the maximum size of a subset of $\mathbb{Z}_q^n$ with minimum Hamming distance at least $δn$, where $\mathbb{Z}_q=\{0,1,\dotsc,q-1\}$ and $n\in\mathbb{N}$. The asymptotic rate function is defined by $ R_q(δ) = \limsup_{n\rightarrow\infty}\frac{1}{n}\log_qα_q(n,δn). $ The famous $q$-ary asymptotic Gilbert-Varshamov bound, obtained in the 1950s, states that \[ R_q(δ) \geq 1 - δ\log_q(q-1)-δ\log_q\…

This https://arxiv.org/abs/2208.14620 has been replaced.
link: https://scholar.google.com/scholar?q=a

Towards three-dimensional nucleon structures at the Electron-Ion Collider in China: A study of the Sivers function
Transverse momentum-dependent parton distribution functions (TMDs) provide three-dimensional imaging of the nucleon in the momentum space. With its fundamental importance in understanding the spin structure of the nucleon, the precise measurement of TMDs is considered as one of the main physics topics of the proposed Electron-Ion Collider in China (EicC). In this paper, we investigate the impact of future semi-inclusive deep inelastic scattering (SIDIS) data from EicC on the extraction of TMDs.…

This https://arxiv.org/abs/2402.04550 has been replaced.
link: https://scholar.google.com/scholar?q=a

Riemann-Lebesgue Forest for Regression
We propose a novel ensemble method called Riemann-Lebesgue Forest (RLF) for regression. The core idea in RLF is to mimic the way how a measurable function can be approximated by partitioning its range into a few intervals. With this idea in mind, we develop a new tree learner named Riemann-Lebesgue Tree (RLT) which has a chance to perform Lebesgue type cutting,i.e splitting the node from response $Y$ at certain non-terminal nodes. We show that the optimal Lebesgue type cutting results in larger…

This https://arxiv.org/abs/2309.05424 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cyclotomic function fields over finite fields with irreducible quadratic modulus
Let $\mathbb{F}_q$ be the finite field of order $q$ and $F=\mathbb{F}_q(x)$ the rational function field. In this paper, we give a characterization of the cyclotomic function fields $F(Λ_M)$ with modulus $M$, where $M \in \mathbb{F}_q[T]$ is a monic and irreducible polynomial of degree two. We also provide the full automorphism group of $F(Λ_M)$ in odd characteristic, extending results of \cite{MXY2016} where the automorphism group of $F(Λ_M)$ over $\mathbb{F}_q$ was computed.

This https://arxiv.org/abs/2307.02579 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

d-Fold Partition Diamonds
In this work we introduce new combinatorial objects called $d$--fold partition diamonds, which generalize both the classical partition function and the partition diamonds of Andrews, Paule and Riese, and we set $r_d(n)$ to be their counting function. We also consider the Schmidt type $d$--fold partition diamonds, which have counting function $s_d(n).$ Using partition analysis, we then find the generating function for both, and connect the generating functions $\sum_{n= 0}^\infty s_d(n)q^n$ to E…

This https://arxiv.org/abs/2403.01937 has been replaced.
link: https://scholar.google.com/scholar?q=a

Examining the critical phenomenon of pion parton distribution: Insights from the Moment Problem
A recent study by Wang {\it et al.}(arXiv:2309.01417) proposed a novel connection between the nature of the parton distribution function (PDF) and the characteristics of its moments. In this study, we apply these findings to analyze the evolution of the pion valence quark PDF, garnering valuable qualitative insights. Firstly, we validate the non-negativity and continuity of the PDF across a wide range of scales, indicating the logical consistency of our chosen evolution scheme. Subsequently, we…

An almost sharp quantitative version of the Duffin-Schaeffer conjecture
Dimitris Koukoulopoulos, James Maynard, Daodao Yang
https://arxiv.org/abs/2404.14628

An almost sharp quantitative version of the Duffin-Schaeffer conjecture
We prove a quantitative version of the Duffin-Schaeffer conjecture with an almost sharp error term. Precisely, let $ψ:\mathbb{N}\to[0,1/2]$ be a function such that the series $\sum_{q=1}^\infty φ(q)ψ(q)/q$ diverges. In addition, given $α\in\mathbb{R}$ and $Q\geqslant1$, let $N(α;Q)$ be the number of coprime pairs $(a,q)\in\mathbb{Z}\times\mathbb{N}$ with $q\leqslant Q$ and $|α-a/q|<ψ(q)/q$. Lastly, let $Ψ(Q)=\sum_{q\leqslant Q}2φ(q)ψ(q)/q$, which is the expected value of $N(…

Effective correlation and decorrelation for newforms, and weak subconvexity for $L$-functions
Nawapan Wattanawanichkul
https://arxiv.org/abs/2405.05249 htt…

Effective correlation and decorrelation for newforms, and weak subconvexity for $L$-functions
Let $f$ and $g$ be spectrally normalized holomorphic newforms of even weight $k \geq2$ on $Γ_0(q)$. If $f\neq g$, then assume that $q$ is squarefree. For a nice test function $ψ$ supported on $Γ_0(1)\backslash\mathbb{H}$, we establish the best known bounds (uniform in $k$, $q$, and $ψ$) for \[ \int_{Γ_0(q)\backslash\mathbb{H}}ψ(z)f(z)\overline{g(z)}y^{k}\frac{dxdy}{y^2}-\mathbf{1}_{f = g}\frac{3}π\int_{Γ_0(1)\backslash\mathbb{H}}ψ(z)\frac{dx dy}{y^2}.\] When $f=g$, our results yield an…

This https://arxiv.org/abs/2309.02325 has been replaced.
link: https://scholar.google.com/scholar?q=a

Monotone non-decreasing sequences of the Euler totient function
Let $M(x)$ denote the largest cardinality of a subset of $\{n \in \mathbf{N}: n \leq x\}$ on which the Euler totient function $φ(n)$ is non-decreasing. We show that $M(x) = (1+O(\frac{(\log\log x)^5}{\log x})) π(x)$ for all $x \geq 10$, answering questions of Erdős and Pollack--Pomerance--Treviño. A similar result is also obtained for the sum of divisors function $σ(n)$.

Balanced triple product $p$-adic $L$-functions and Stark points
Luca Dall'Ava, Aleksander Horawa
https://arxiv.org/abs/2403.05183 https://

Balanced triple product $p$-adic $L$-functions and Stark points
Let $E$ be an elliptic curve over $\mathbb{Q}$ and $\varrho_1, \varrho_2 \colon \mathrm{Gal}(H/\mathbb{Q}) \to \mathrm{GL}_2(L)$ be two odd Artin representations. We use $p$-adic methods to investigate the part of the Mordell-Weil group $E(H) \otimes L$ on which the Galois group acts via $\varrho_1 \otimes \varrho_2$. When the rank of the group is two, Darmon-Lauder-Rotger used a dominant triple product $p$-adic $L$-function to study this group, and gave an Elliptic Stark Conjecture which relat…

This https://arxiv.org/abs/2307.12261 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On finite field analogues of determinants involving binomial coefficients
In this paper, we investigate certain cyclotomic matrices concerning the Jacobi sums over finite fields, which can be viewed as finite field analogues of certain matrices involving the Beta function. For example, let $q>1$ be a prime power and let $χ$ be a generator of the group of all multiplicative characters of $\mathbb{F}_q$. Then we prove that $$\det\left[J_q(χ^i,χ^j)\right]_{1\le i,j\le q-2}=(q-1)^{q-3},$$ where $J_q(χ^i,χ^j)$ is the Jacobi sum over $\mathbb{F}_q$. This can be view…

This https://arxiv.org/abs/2211.03987 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theta series of ternary quadratic lattice cosets
In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary theta functions correspond to the theta series for the genus, the deficiency of the theta series for the spinor genus from that of the genus, and the deficiency of the theta series for the class from that of the spinor genus, respectively. These three pieces …

This https://arxiv.org/abs/2205.00135 has been replaced.
link: https://scholar.google.com/scholar?q=a

Failing to hash into supersingular isogeny graphs
An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell$-isogeny graph which does not reveal the endomorphism ring, or a path to a curve of known endomo…

This https://arxiv.org/abs/2208.02242 has been replaced.
link: https://scholar.google.com/scholar?q=a

Increasing-decreasing patterns in the iteration of an arithmetic function
Let $Ω$ be a set of positive integers and let $f:Ω\rightarrow Ω$ be an arithmetic function. Let $V = (v_i)_{i=1}^n$ be a finite sequence of positive integers. An integer $m \in Ω$ has \textit{increasing-decreasing pattern} $V$ with respect to $f$ if, for all odd integers $i \in \{1,\ldots, n\}$, \[ f^{v_1+ \cdots + v_{i-1}}(m) < f^{v_1+ \cdots + v_{i-1}+1}(m) < \cdots < f^{v_1+ \cdots + v_{i-1}+v_{i}}(m) \] and, for all even integers $i \in \{2,\ldots, n\}$, \[ f^{v_1+ \cdots + v_{i-1}}(m) …

A Design Criterion for the Rayleigh Fading Wiretap Channel Based on $\ell^1$-norm Theta Functions
Niklas Miller
https://arxiv.org/abs/2405.04143 https://…

A Design Criterion for the Rayleigh Fading Wiretap Channel Based on $\ell^1$-norm Theta Functions
We show that the correct decoding probability of an eavesdropper and error probability of a legitimate receiver in a Rayleigh fading wiretap channel with lattice coset coding are both upper bounded by the theta function in the $\ell^1$-norm of the dual code lattices. Motivated by these findings, we derive a closed form expression for the $\ell^1$-norm theta function of any sublattice of $\mathbb{Q}^n$ and its dual, and prove that the lattice $\mathbb{Z}^n$ minimizes the theta function among all…