Tootfinder

In a short blog post for the MacArthur Foundation, my colleague Veronica Thamaini and I discuss the Abstract Wikipedia proposal, one of five finalists for the ongoing 100&Change program.
A Path to a World Where Everyone Can Share in the Sum of All Knowledge
https://www.

A Path to a World Where Everyone Can Share in the Sum of All Knowledge

$b \to c$ semileptonic sum rule: Current status and prospects
Motoi Endo, Syuhei Iguro, Satoshi Mishima, Ryoutaro Watanabe
https://arxiv.org/abs/2508.06322 https://

$b \to c$ semileptonic sum rule: Current status and prospects
The $b \to c$ semileptonic sum rules provide relations between the decay rates of $B \to D^{(*)} τ\barν$ and $Λ_b \to Λ_c τ\barν$. Starting from the heavy quark and zero-recoil limits, we revisit the derivation of the sum rule for total decay rates. We then examine deviations from the limits and investigate corrections arising from realistic hadron masses and higher-order contributions to form factors, taking account of uncertainties. We show that these corrections are negligible compared…

Enhancing Sum Capacity via Quantum and No-Signaling Cooperation Between Transmitters
Seung-Hyun Nam, Hyun-Young Park, Jiyoung Yun, Ashutosh Rai, Si-Hyeon Lee, Joonwoo Bae
https://arxiv.org/abs/2509.08219

Enhancing Sum Capacity via Quantum and No-Signaling Cooperation Between Transmitters
We consider a communication scenario over a discrete memoryless interference channel or multiple access channel without feedback, where transmitters exploit classical, quantum, or no-signaling cooperation. In this scenario, several previous works have shown that the sum capacities of channels involving pseudo-telepathy games can be enhanced by quantum or no-signaling cooperation. However, a full characterization of which channels admit such an improvement remains open. By focusing on the common…

Exact Sum Rules and Zeta Generating Formulas from the ODE/IM correspondence
Syo Kamata
https://arxiv.org/abs/2508.06366 https://arxiv.org/pdf/2508.06366

Exact Sum Rules and Zeta Generating Formulas from the ODE/IM correspondence
We formulate exact sum rules (ESRs) and zeta generating formulas (ZGFs) for quantum mechanics defined by the ${\cal PT}$-symmetric potential $V_{\cal PT}(x) = x^{2K} (ix)^\varepsilon$ with $K,\varepsilon \in \mathbb{N}$, as well as the Hermitian potential $V_{\cal H}(x) = x^{2 K}$ with $K \in {\mathbb N} + 1$, based on the fusion relations of the $A_{2M-1}$ T-system in the framework of the ODE/IM correspondence. In this setup, the fusion relations on the integrable model (IM) side correspond to…

Regular sets in Cayley sum graphs on generalized dicyclic groups
Meiqi Peng, Yuefeng Yang, Wenying Zhu
https://arxiv.org/abs/2507.07736 https://

Regular sets in Cayley sum graphs on generalized dicyclic groups
For a graph $Γ=(V(Γ),E(Γ))$, a subset $C$ of $V(Γ)$ is called an $(α,β)$-regular set in $Γ$, if every vertex of $C$ is adjacent to exactly $α$ vertices of $C$ and every vertex of $V(Γ)\setminus C$ is adjacent to exactly $β$ vertices of $C$. In particular, if $C$ is an $(α,β)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(α,β)$-regular set of $G$. In this paper, we consider a generalized dicyclic group $G$ and for each s…

A New Framework for the Sum of Squared $\kappa$-$\mu$ RVs with Application to Sub-THz Systems
Gustavo Rodrigues de Lima Tejerina, Italo Atzeni
https://arxiv.org/abs/2508.06242 h…

A New Framework for the Sum of Squared $κ$-$μ$ RVs with Application to Sub-THz Systems
In this paper, we adopt the $κ$-$μ$ model to characterize the propagation in the sub-THz band. We develop a new exact representation of the sum of squared independent and identically distributed $κ$-$μ$ random variables, which can be used to express the power of the received signal in multi-antenna systems. Unlike existing ones, the proposed analytical framework is remarkably tractable and computationally efficient, and thus can be conveniently employed to analyze systems with massive anten…

Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures
James P. Crutchfield
https://arxiv.org/abs/2507.07343 https://

Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures
We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures, demonstrating how statistical mixtures miss key aspects of emergent hierarchical organization. This leads us to identify a new kind of structural complexity inherent in multicomponent systems and to draw out broad consequences for system ergodicity.

Samsung agrees to acquire Seattle-based Xealth, which helps healthcare providers manage digital health tools and has raised over $50M, for an undisclosed sum (Taylor Soper/GeekWire)
https://www.geekwire.com/2025/samsung-acquiring…

Sparsifying Sums of Positive Semidefinite Matrices
Arpon Basu, Pravesh K. Kothari, Yang P. Liu, Raghu Meka
https://arxiv.org/abs/2508.08169 https://arxiv.o…

Sparsifying Sums of Positive Semidefinite Matrices
In this paper, we revisit spectral sparsification for sums of arbitrary positive semidefinite (PSD) matrices. Concretely, for any collection of PSD matrices $\mathcal{A} = \{A_1, A_2, \ldots, A_r\} \subset \mathbb{R}^{n \times n}$, given any subset $T \subseteq [r]$, our goal is to find sparse weights $μ\in \mathbb{R}_{\geq 0}^r$ such that $(1 - ε) \sum_{i \in T} A_i \preceq \sum_{i \in T} μ_i A_i \preceq (1 + ε) \sum_{i \in T} A_i.$ This generalizes spectral sparsification of graphs which …

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Shota Takahashi, Koichi Kumagai, Atsunori Sakurai, Tatsuto Mochizuki, Tomonori Hirano, Akihiro Morita, Toshiki Sugimoto
https://arxiv.org/abs/2509.09179

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Sum-frequency generation (SFG) is a powerful second-order nonlinear spectroscopic technique that provides detailed insights into molecular structures and absolute orientations at surfaces and interfaces. However, conventional SFG based on far-field schemes suffers from the diffraction limit of light, which inherently averages spectroscopic information over micrometer-scale regions and obscures nanoscale structural inhomogeneity. Here, we overcome this fundamental limitation by leveraging a high…

The differences between Severance and The Pitt in terms of budget, star power, time between seasons, and genre attest to changes in priorities for streamers (John Koblin/New York Times)
https://www.nytimes.com/2025/09/11/business/media/severance-the-pitt-emmys…

How ‘Severance’ and ‘The Pitt’ Sum Up the TV Business
The industry is in a state of transition. The front-runners for best drama at the Emmys this Sunday explain the competing tensions.

Descent problem for certificate of non-negativity on semi-algebraic sets
Manoj K. Keshari, Debapriya Ojha, Niladri Sekhar Patra
https://arxiv.org/abs/2508.07060 https://

Descent problem for certificate of non-negativity on semi-algebraic sets
Let $F$ be a subfield of $\mathbb R$ and let $K$ be a basic closed semi-algebraic set in $\mathbb R$ with $\partial K\subset F$. Let $\mathcal N$ be the natural choice of generators of $K$. We show that if $f\in F[x]$ is $\geq 0$ on $K$, then $f$ can be written as $$f=\sum_{e\in\{0,1\}^s } a_eσ_e g^e $$ where $a_e\in F_{\geq 0}$, $σ_e\in \sum F[x]^2$ and $g^{e}=g_1^{e_1} \cdots g_s^{e_s}$. In other words, the preordering $T_{\mathcal N}$ of $F[x]$ is saturated. In case $F=\mathbb R$, this res…

Asymptotic properties of zeros of Riemann zeta function
Juan Arias de Reyna, Yves Meyer
https://arxiv.org/abs/2507.07253 https://arxi…

Asymptotic properties of zeros of Riemann zeta function
We try to define the sequence of zeros of the Riemann zeta function by an intrinsic property. Let $(z_k)_{k\in \mathbb{N}}$ be the sequence of nontrivial zeros of $ζ(s)$ with positive imaginary part. We write $z_k= 1/2+iτ_k$ (RH says that these $τ_k$ are all real). Then the sequence $(τ_k)_{k\in \mathbb{N}},$ satisfies the following asymptotic relation \[\sum_{k\in\mathbb{N}}\frac{2x}{x^2+τ_k^2}\simeq \frac12\log\frac{x}{2π}+\sum_{n=1}^\infty \frac{a_n}{x^n},\,\,x\to +\infty\] where $a_{2…

Stochastic Bandits for Crowdsourcing and Multi-Platform Autobidding
Fran\c{c}ois Bachoc, Nicol\`o Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni
https://arxiv.org/abs/2508.05844

Stochastic Bandits for Crowdsourcing and Multi-Platform Autobidding
Motivated by applications in crowdsourcing, where a fixed sum of money is split among $K$ workers, and autobidding, where a fixed budget is used to bid in $K$ simultaneous auctions, we define a stochastic bandit model where arms belong to the $K$-dimensional probability simplex and represent the fraction of budget allocated to each task/auction. The reward in each round is the sum of $K$ stochastic rewards, where each of these rewards is unlocked with a probability that varies with the fraction…

A New Classification of Positive Integers Via New Divisor Functions
Brahim Mittou
https://arxiv.org/abs/2509.08844 https://arxiv.org/pdf/2509.08844

A New Classification of Positive Integers Via New Divisor Functions
Let $d_1 = 1 < d_2 < d_3 < \cdots < d_{τ(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $α$, we define and study some properties of two new divisor functions $σ_{e,α}$ and $σ_{o,α}$. The first computes the sum of the $α$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $α$-th powers of the divisors of $n$ with odd indices. We also introduce a new type of positive in…

On the Bit Size of Sum-of-Squares Proofs for Symmetric Formulations
Alex Bortolotti, Monaldo Mastrolilli, Marilena Palomba, Luis Felipe Vargas
https://arxiv.org/abs/2509.06928 h…

On the Bit Size of Sum-of-Squares Proofs for Symmetric Formulations
The Sum-of-Squares (SoS) hierarchy is a powerful framework for polynomial optimization and proof complexity, offering tight semidefinite relaxations that capture many classical algorithms. Despite its broad applicability, several works have revealed fundamental limitations to SoS automatability. (i) While low-degree SoS proofs are often desirable for tractability, recent works have revealed they may require coefficients of prohibitively large bit size, rendering them computationally infeasible.…

Decentralized Stochastic Nonconvex Optimization under the Relaxed Smoothness
Luo Luo, Xue Cui, Tingkai Jia, Cheng Chen
https://arxiv.org/abs/2509.08726 https://

Decentralized Stochastic Nonconvex Optimization under the Relaxed Smoothness
This paper studies decentralized optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};ξ_i)\right]$ which is $(L_0,L_1)$-smooth but possibly nonconvex and the random variable $ξ_i$ follows distribution ${\mathcal D}_i$. We propose a novel algorithm called decentralized normalized stochastic gradient descent (DNSGD), which can achieve the $ε$-stationary point on each local agent.…

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Mircea Cimpoeas
https://arxiv.org/abs/2509.09418 https://arxiv.org…

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Let $\mathbf a:=(a_1,\ldots,a_r)$ be a sequence of positive integers, $d\geq 2$ and $j\geq 1$, some integers. We study the functions $p_{\mathbf a,d}(n):=$ the number of integer solutions $(x_1,\dots,x_r)$ of $\sum_{i=1}^r a_ix_i=n$, with $x_i\geq 0$ and $x_i \equiv 0,1(\bmod\;d)$, for all $1\leq i\leq r$, and $p_{\mathbf a,d}(n;j):=$ the number of $(x_1,\ldots,x_r)$ as above which satisfy also the condition $\sum_{i=1}^r \left(x_i-(d-2)\left\lfloor \frac{x_i}{d} \right\rfloor\right) =j$. We …

The open XXZ chain at $\Delta=-1/2$ and totally-symmetric alternating sign matrices
Jean Li\'enardy, Christian Walmsley Hagendorf
https://arxiv.org/abs/2509.09209 https://…

The open XXZ chain at $Δ=-1/2$ and totally-symmetric alternating sign matrices
The open XXZ spin chain with the anisotropy parameter $Δ=-\frac12$, diagonal boundary fields that depend on a parameter $x$, and finite length $N$ is studied. In a natural normalisation, the components of its ground-state vector are polynomials in $x$ with integer coefficients. It is shown that their sum is given by a generating function for the weighted enumeration of totally-symmetric alternating sign matrices with weights depending on $x$.

Moduli spaces of open strings have polylogarithmic Mirzakhani volumes
Yi Huang, Ivan Telpukhovskiy
https://arxiv.org/abs/2509.09401 https://arxiv.org/pdf/2…

Moduli spaces of open strings have polylogarithmic Mirzakhani volumes
We show that the Mirzakhani volume, as introduced by Chekhov, of the moduli space of every non-contractible crowned hyperbolic surface is naturally expressible as a sum of Gaussian rational multiples of polylogarithms evaluated at $\pm1$ and $\pm\sqrt{-1}$.

On the sum of the angles between three vectors
Iosif Pinelis
https://arxiv.org/abs/2508.04759 https://arxiv.org/pdf/2508.04759

On the sum of the angles between three vectors
For any three nonzero vectors $a,b,c$ in $\mathbb R^2$, we obtain a necessary and sufficient condition for the sum of the three pairwise angles between these vectors to equal $2π$. As an easy consequence of this, a proof of Euclid's theorem that the sum of the interior angles of any triangle is $π$ is provided. So, the main result of this note can be considered a generalization of Euclid's theorem. To a large extent, the consideration is reduced almost immediately to a choice for the sum of t…

Numerical Considerations in Weighted Model Counting
Randal E. Bryant
https://arxiv.org/abs/2508.06264 https://arxiv.org/pdf/2508.06264

Numerical Considerations in Weighted Model Counting
Weighted model counting computes the sum of the rational-valued weights associated with the satisfying assignments for a Boolean formula, where the weight of an assignment is given by the product of the weights assigned to the positive and negated variables comprising the assignment. Weighted model counting finds applications across a variety of domains including probabilistic reasoning and quantitative risk assessment. Most weighted model counting programs operate by (explicitly or implicitl…

Syzygies of some invariant rings with cyclic group actions
Christin Sum
https://arxiv.org/abs/2508.05879 https://arxiv.org/pdf/2508.05879

Syzygies of some invariant rings with cyclic group actions
We investigate actions of cyclic groups on polynomial rings with two variables, and the minimal free resolution of the corresponding invariant ring. In particular, we fully classify several cases, including the case the defining ideal has codimension two, and when the multidegrees of generating invariants lie on the union of two lines.

Exploring Efficient Directional and Distance Cues for Regional Speech Separation
Yiheng Jiang, Haoxu Wang, Yafeng Chen, Gang Qiao, Biao Tian
https://arxiv.org/abs/2508.07563 htt…

Exploring Efficient Directional and Distance Cues for Regional Speech Separation
In this paper, we introduce a neural network-based method for regional speech separation using a microphone array. This approach leverages novel spatial cues to extract the sound source not only from specified direction but also within defined distance. Specifically, our method employs an improved delay-and-sum technique to obtain directional cues, substantially enhancing the signal from the target direction. We further enhance separation by incorporating the direct-to-reverberant ratio into th…

Reionization optical depth and CMB-BAO tension in punctuated inflation
Zhiqi Huang
https://arxiv.org/abs/2509.09086 https://arxiv.org/pdf/2509.09086…

Reionization optical depth and CMB-BAO tension in punctuated inflation
Within the standard six-parameter Lambda cold dark matter ($Λ$CDM) model, a $2$-$3σ$ tension persists between baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) and observations of the cosmic microwave background (CMB). Although this tension has often been interpreted as evidence for dynamical dark energy or a sum of neutrino masses below the established minimum, recent studies suggest it may instead originate from an underestimation of the rei…

A c-theorem for the effective central charge in the R=1 replica limit, and applications to systems with measurement-induced randomness
Rushikesh A. Patil, Andreas W. W. Ludwig
https://arxiv.org/abs/2507.07959

A c-theorem for the effective central charge in the R=1 replica limit, and applications to systems with measurement-induced randomness
We present a general theorem demonstrating non-perturbatively the decrease of the "effective central charge" $c_{\text{eff}}=(d c/dR)|_{R=1}$ under renormalization group (RG) flow in the $R\rightarrow1$ replica limit of a $R$-copy $2D$ conformal field theory (CFT) action $S_{*}$ perturbed by a replica interaction of the form $$-\mathbb{S}=-\sum_{a=1}^{R}S_{*}^{(a)}+Δ\int d^2 x \sum_{\substack{a,b=1\\ a\neq b}}^{R}φ^{(a)}(x)φ^{(b)}(x).$$ Here $φ$ is a scaling field belonging to the CFT …

Nadirashvili' Conjecture for Elliptic PDEs and its Applications
Jiahuan Li, Junyuan Wang, Zhichen Ying
https://arxiv.org/abs/2508.07861 https://arxiv.o…

Nadirashvili' Conjecture for Elliptic PDEs and its Applications
In this article, we investigate the conjecture posed by Nadirashvili in \cite{nadirashvilli1997geometry}. It states that if a harmonic function has bounded nodal volume in the unit ball, then the supermum over the half-ball can be bounded by a finite sum of derivatives at the center. The main tool in this paper is the lower bound of nodal sets, which is first proved in \cite{MR3739232}. Also we combine the propagation of smallness property and elliptic estimates to give a positive answer to thi…

Integrality and Specialized Symmetric Functions
Allan Berele
https://arxiv.org/abs/2508.08018 https://arxiv.org/pdf/2508.08018

Integrality and Specialized Symmetric Functions
Given $d_1,\ldots,d_k$ in the field $F$, there is a weighted trace function $F^k\rightarrow F$ given by $tr(x_1,\ldots,x_k)=\sum d_ix_i$. We prove that $F^k$ satisfies trace identities of the forms $α(d_1,\ldots,d_k) x^N=$ a linear combination of terms with lower powers of $x$; and $tr(y_1)\cdots tr(y_n)=$ a linear combination of terms with fewer traces. The approach uses specialized symmetric functions.

Quantum Radar for ISAC: Sum-Rate Optimization
Abdulmohsen Alsaui, Neel Kanth Kundu, Hyundong Shin, Octavia A. Dobre
https://arxiv.org/abs/2509.06070 https://

Quantum Radar for ISAC: Sum-Rate Optimization
Integrated sensing and communication (ISAC) is emerging as a key enabler for spectrum-efficient and hardware-converged wireless networks. However, classical radar systems within ISAC architectures face fundamental limitations under low signal power and high-noise conditions. This paper proposes a novel framework that embeds quantum illumination radar into a base station to simultaneously support full-duplex classical communication and quantum-enhanced target detection. The resulting integrated …

Chromatic Calorimetry -- A Novel Approach to Validate Energy Resolution and Particle Discrimination
Devanshi Arora
https://arxiv.org/abs/2509.09511 https://

Chromatic Calorimetry -- A Novel Approach to Validate Energy Resolution and Particle Discrimination
Chromatic calorimetry (CCAL) analyses particle detection by utilizing scintillators with distinct emission wavelengths to measure the longitudinal energy deposition of particle showers in high-energy physics, improving particle identification (PID) and energy resolution. By stacking scintillators in order of decreasing emission wavelength, CCAL enables layer-specific energy measurements, analyzed via amplitude fractions ($f_i = A_i / \sum_j A_j$) and center of gravity ($\langle z_{\text{cog}} \…

@… Hi Sean. I’ve been doing science all night, and I think I’ve uncovered a new layer to Autechre (the “tapestry behind the cotton wool”, as Virgina Woolf might put it.) Please bear with me as I explain:
A = 1
U = 21
T = 20
E = 5
C = 3
H = 8
R = 18
E = 5
− [1, 21, 20, 5, 3, 8, 18, 5]
Sum = 81
Your name, Se…

Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum
Ivan Hadinata
https://arxiv.org/abs/2507.03813 https://arxiv.o…

Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum
In this paper, we present the existence and uniqueness property on a finite sum involving a polynomial and a homogeneous linear recurrence sequence. This finite sum is of the form $\sum_{k=1}^n P(k)s_{hk+r}$ where $n$ is a positive integer, $P(x)$ is a polynomial in $\mathbb C[x]$, $h$ and $r$ are some integers, and $(s_k)_{k\in\mathbb Z}$ is a homogeneous linear recurrence sequence of degree $m\geq 2$ with some constraints.

Sum Rules in Quantum Liquids
Riccardo Fantoni
https://arxiv.org/abs/2507.07950 https://arxiv.org/pdf/2507.07950

Sum Rules in Quantum Liquids
We review the linear response theory in the horizontal quantum liquids framework spanning from Coulomb liquids to Atomic gases. There are several well known references about this subject, like the onset of the Kramers-Kronig relations and the fluctuation-dissipation theorem. For the Coulomb systems we show the connection between the linear response function and the dielectric function which settles a parallelism between statistical mechanics and electrostatic properties. For (very degenerate, d…

Crosslisted article(s) found for physics.chem-ph. https://arxiv.org/list/physics.chem-ph/new
[1/1]:
- Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Takahashi, Kumagai, Sakurai, Mochizuki, Hirano, Morita, Sugimoto

On the CQC Conjecture
Hasan Iqbal
https://arxiv.org/abs/2509.08286 https://arxiv.org/pdf/2509.08286

On the CQC Conjecture
The CQC conjecture by Schneeloch et al. (Physical Review A 90.6, 2014) asserts that the sum of classical mutual information between two parties obtained by measuring individual systems in two mutually unbiased bases can not exceed their shared quantum mutual information. This remarkable conjecture, which deserves more work, still remains open. In this article, using a result by Coles and Piani (Physical Review A 89.2, 2014), we derive a sufficient condition for which the CQC conjecture holds. W…

NFL summer trade proposals: Alvin Kamara to the Broncos and other big-name deals for 2025

https://www.cbssports.com/nfl/news/nfl-summer-trade…

Efficient Defection: Overage-Proportional Rationing Attains the Cooperative Frontier
Florian Lengyel
https://arxiv.org/abs/2509.07145 https://arxiv.org/pdf…

Efficient Defection: Overage-Proportional Rationing Attains the Cooperative Frontier
We study a noncooperative $n$-player game of slack allocation in which each player $j$ has entitlement $L_j>0$ and chooses a claim $C_j\ge0$. Let $v_j=(C_j-L_j)_+$ (overage) and $s_j=(L_j-C_j)_+$ (slack); set $X=\sum_j v_j$ and $I=\sum_j s_j$. At the end of the period an overage-proportional clearing rule allocates cooperative surplus $I$ to defectors in proportion to $v_j$; cooperators receive $C_j$. We show: (i) the selfish outcome reproduces the cooperative payoff vector $(L_1,\dots,L_n)$; (…

Integral representation for a product of two Jacobi functions of the second kind
Howard S. Cohl, Loyal Durand
https://arxiv.org/abs/2508.08085 https://arxi…

Integral representation for a product of two Jacobi functions of the second kind
By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive a Bateman-type sum for a product of two Jacobi functions of the second kind. From this integral representation we derive integral representations for the Jacobi function of the first kind in both the hyperbolic and trigonometric contexts. From the integral re…

Randomly twisted bilayer graphene -- the cascade transitions
Baruch Horovitz, Pierre Le Doussal
https://arxiv.org/abs/2508.07024 https://arxiv.org/pdf/2508…

Randomly twisted bilayer graphene -- the cascade transitions
Twisted bilayer graphene (TBG) is known to have disorder in its twist angle. We show that in terms of a Dirac equation with a random gauge potential ${\bf A}({\bf r})$ this disorder becomes huge when the average twist angle is near the magic angle where the Dirac velocity vanishes. The density of states (DOS) then diverges at the Dirac point as $ρ(E)\sim E^{(2/z)-1}$ with $z\gg 1$ and we deduce that all electrons occupy energies very near $E=0$. We prove a sum rule on the disorder averaged eig…

Square Functions and Variational Estimates for Ritt Operators on $L^1$
Jennifer Hults, Karin Reinhold-Larsson
https://arxiv.org/abs/2507.07256 https://

Square Functions and Variational Estimates for Ritt Operators on $L^1$
Let $T$ be a bounded operator. We say $T$ is a Ritt operator if $\sup_n n\lVert T^n-T^{n+1}\rVert<\infty$. It is know that when $T$ is a positive contraction and a Ritt operator in $L^p$, $1

Joint calibration of the volatility surface and variance term structure
Jiwook Yoo
https://arxiv.org/abs/2509.08096 https://arxiv.org/pdf/2509.08096…

Joint calibration of the volatility surface and variance term structure
This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared errors in Black-Scholes implied volatilities, can produce model-implied variance term structures with large errors relative to those observed in the market and implied by option prices. I show that this can occur even when the model-implied volatility surface clos…

Correlators from Amplitubes
Ross Glew
https://arxiv.org/abs/2507.07199 https://arxiv.org/pdf/2507.07199

Correlators from Amplitubes
Recently, the wavefunction coefficients for conformally coupled scalars in an FRW cosmology have been presented as a sum over amplitude-like functions known as {\it amplitubes}. In this work we extend this analysis to full {\it correlation functions}. Remarkably, the amplitube expansion of the correlator exhibits many vanishing contributions that are otherwise present in the expansion of the wavefunction. Moreover, while the wavefunction coefficients suffer from relative minus signs between ter…

Invariants for sum-rank metric codes
Paolo Santonastaso, Ferdinando Zullo
https://arxiv.org/abs/2507.04158 https://arxiv.org/pdf/2507…

Invariants for sum-rank metric codes
The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new invariants for sum-rank metric codes: generalised idealisers, the centraliser, the center, and a refined notion of linearity. These lead to the definition of nuclear parameters, inspired by those used in division algebra theory, where they are crucial for pro…

Unidimensional semi-discrete partial optimal transport
Adrien Cances, Hugo Leclerc
https://arxiv.org/abs/2509.08799 https://arxiv.org/pdf/2509.08799…

Unidimensional semi-discrete partial optimal transport
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises naturally in applications such as risk management, the modeling of crowd motion, and sliced partial transport algorithms for point cloud registration. Unlike higher-dimensional settings, the dual functional in the unidimensional case exhibits reduced regularity. To …

Simple complexes on a flopped curve
Parth Shimpi
https://arxiv.org/abs/2508.06437 https://arxiv.org/pdf/2508.06437

Simple complexes on a flopped curve
Studying crepant blow-ups of (compound) du Val singularities, we classify complexes of coherent sheaves which admit no negative self-extensions -- such a complex, up to flops and mutation equivalences, must either be (1) a module over a derived-equivalent algebra, or (2) a two-term extension of a coherent sheaf by skyscraper sheaves, or (3) a direct sum of shifts of skyscrapers. This translates into classifications of bricks, spherical objects, stability conditions, and algebraic t-structures i…

Analysis of the hidden-charm pentaquark candidates in the $J/\psi p$ mass spectrum with QCD sum rules
Zhi-Gang Wang
https://arxiv.org/abs/2509.05648 https://

Analysis of the hidden-charm pentaquark candidates in the $J/ψp$ mass spectrum with QCD sum rules
In this work, we distinguish the isospin unambiguously to construct the diquark-diquark-antiquark type five-quark currents with the isospin $I=\frac{1}{2}$, and study the $uudc\bar{c}$ pentaquark states with the QCD sum rules systematically for the first time. Then we obtain the mass spectrum of the diquark-diquark-antiquark type $uudc\bar{c}$ pentaquark states with the isospin-spin-parity $IJ^P=\frac{1}{2}{\frac{1}{2}}^-$, $\frac{1}{2}{\frac{3}{2}}^-$ and $\frac{1}{2}{\frac{5}{2}}^-$, and make…

Nearly Optimal Bounds for Stochastic Online Sorting
Yang Hu
https://arxiv.org/abs/2508.07823 https://arxiv.org/pdf/2508.07823

Nearly Optimal Bounds for Stochastic Online Sorting
In the online sorting problem, we have an array $A$ of $n$ cells, and receive a stream of $n$ items $x_1,\dots,x_n\in [0,1]$. When an item arrives, we need to immediately and irrevocably place it into an empty cell. The goal is to minimize the sum of absolute differences between adjacent items, which is called the \emph{cost} of the algorithm. It has been shown by Aamand, Abrahamsen, Beretta, and Kleist (SODA 2023) that when the stream $x_1,\dots,x_n$ is generated adversarially, the optimal cos…

Entire solutions of a certain type differential-difference equation and differential-difference analogue of Bruck conjecture
Junfeng Xu, Sujoy Majumder, Debabrata Pramanik
https://arxiv.org/abs/2509.06783

Entire solutions of a certain type differential-difference equation and differential-difference analogue of Bruck conjecture
In the paper, we find out the precise form of the finite order entire solutions of the following differential-difference equation \[f^{(k)}(z)=\sideset{}{^n_{j=0}}{\sum} a_j f(z+jc),\] where $a_0, a_1,\ldots,a_n(\neq 0)\in\mathbb{C}$. Also in the paper we study the differential-difference analogue of Brück conjecture and derive a uniqueness result of finite order entire function $f(z)$ having a Borel exceptional small function of $f(z)$, when $f^{(k)}(z)$ and $\sideset{}{^n_{j=0}}{\sum} a_j f(…

Arithmetic and Asymptotic Properties of Restricted Totient Sums
Es-said En-naoui
https://arxiv.org/abs/2509.07004 https://arxiv.org/pdf/2509.07004

Arithmetic and Asymptotic Properties of Restricted Totient Sums
This article extends our previous study on the summatory behavior of Euler's totient function $φ(n)$. We investigate two complementary restricted sums, $Υ(x,p)=\sum_{\substack{k\le x\\\gcd(k,p)=1}}φ(k)$ and $Δ(x,p)=\sum_{\substack{k\le x\\p\mid k}}φ(k)$, which satisfy the decomposition $Ψ(x)=\sum_{k\le x}φ(k)=Υ(x,p)+Δ(x,p)$. We establish recurrence formulas, congruence relations, and generating function identities for $Δ(x,p)$. In particular, we prove that $Δ(x,p)\equiv 0\pmod{p-1}$ …

Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$
Ali Alsetri, Xuancheng Shao
https://arxiv.org/abs/2509.07765 https://

Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$
We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank $2$ in prime fields $\mathbb{F}_p$. The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of numbers. A key step in our argument involves establishing new upper bounds for the sizes of Bohr sets, which may be of independent interest.

How to simulate magic state cultivation with around $8$ Clifford terms on average
Kwok Ho Wan, Zhenghao Zhong
https://arxiv.org/abs/2509.08658 https://arxi…

How to simulate magic state cultivation with around $8$ Clifford terms on average
Building upon [arXiv:2509.01224], we present a sketch on how to simulate the non-Clifford $d=5$ magic state cultivation circuits [arXiv:2409.17595] with a sum of $\approx 8$ Clifford ZX-diagrams on average, at $0.1\%$ noise. Compared to a magic cat state stabiliser decomposition of all $53$ non-Clifford spiders ($6{,}377{,}292$ terms required), this is more than $7 \times 10^{5}$ times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non…

Remarks on the Brouwer Conjecture
Oliver Knill
https://arxiv.org/abs/2508.07550 https://arxiv.org/pdf/2508.07550 …

Remarks on the Brouwer Conjecture
The Brouwer conjecture (BC) in spectral graph theory claims that the sum of the largest k Kirchhoff eigenvalues of a graph are bounded above by the number m of edges plus k(k+1)/2. We show that (BC) holds for all graphs with n vertices if n is larger or equal than 4 times the square of the maximal vertex degree. We also note that the weaker upper bound m+k(k+1) holds unconditionally. We also note that (BC) for graphs implies (BC) for quivers.

Sharp multiscale control for high order nonlinear equations
Fr\'ed\'eric Robert
https://arxiv.org/abs/2509.07517 https://arxiv.org/pdf/2509.07517…

Sharp multiscale control for high order nonlinear equations
We analyze the behavior of families $(u_α)_{α>0}$ of solutions to the high-order critical equation $P_αu_α=Δ_g^k u_α+\hbox{lot}=|u_α|^{2^\star-2}u_α$ on a Riemannian manifold $M$, with a uniform bound on the Dirichlet energy. We prove a sharp pointwise control of the $u_α$'s by a sum of bubbles uniformly with respect to $α\to +\infty$, that is $|u_α|\leq C\Vert u_\infty \Vert_\infty +C\sum_{i=1}^NB_{i,α}$ where $u_\infty \in C^{2k}(M)$ and the $(B_{i,α})_α$, $i…

Jordan homomorphisms and T-ideals
Matej Bre\v{s}ar, Efim Zelmanov
https://arxiv.org/abs/2508.07191 https://arxiv.org/pdf/2508.07191

Jordan homomorphisms and T-ideals
Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $φ:A\to B$ is the sum of a homomorphism and an antihomomorphism. Our second main result concerns (not necessarily surjective) Jordan homomorphisms from $H(A,*)$ to $B$, where $*$ is an involution on $A$ and $H(A,*)=\{a\in A\,|\, a^*=a\}$. We show that there exists a ${\rm T}$-ideal $G$ having…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- On the sum of the angles between three vectors
Iosif Pinelis
https://

Hermitian K-theory of Lagrangian Grassmannians via reducible Gorenstein models
Tao Huang, Heng Xie
https://arxiv.org/abs/2508.07166 https://arxiv.org/pdf/2…

Hermitian K-theory of Lagrangian Grassmannians via reducible Gorenstein models
We construct a family of moduli spaces, called generalized Lagrangian flag schemes, that are reducible Gorenstein (hence singular), and that admit well-behaved pushforward and pullback operations in Hermitian $K$-theory. These schemes arise naturally in our computations. Using them, we prove that the Hermitian $K$-theory of a Lagrangian Grassmannian over a regular base splits as a direct sum of copies of the base's (Hermitian) $K$-theory, indexed by certain shifted Young diagrams. The isomorphi…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- An Accelerated Variance Reduced Extra-Point Approach to Finite-Sum VI and Optimization
Kevin Huang, Nuozhou Wang, Shuzhong Zhang

GlobalFoundries agrees to acquire MIPS, a developer of RISC-V-based solutions and IP, with the deal expected to close in H2 2025 (Anton Shilov/Tom's Hardware)
https://www.tomshardware.com/pc-components…

GlobalFoundries to make RISC-V CPUs — fab acquires MIPS, will integrate RISC-V and AI IP into its portfolio
For an unknown sum.

Existence of Anisotropic Minkowski Content
Filip Fry\v{s}
https://arxiv.org/abs/2508.08156 https://arxiv.org/pdf/2508.08156

Existence of Anisotropic Minkowski Content
This paper is devoted to the existence of anisotropic Minkowski content and anisotropic outer Minkowski content. Our result is that the Minkowski content of the topological boundary of a given set of finite perimeter $E$ coincides with the perimeter of $E$ if and only if the anisotropic Minkowski content of the topological boundary of $E$ coincides with half of the sum of the anisotropic perimeter of $E$ and the anisotropic perimeter of the complement of $E$. As a consequence, we find that the …

Polarized Deep Inelastic Scattering as $x \to 1$ using Soft Collinear Effective Theory
Jaipratap Singh Grewal, Aneesh V. Manohar, Jyotirmoy Roy
https://arxiv.org/abs/2507.07175

Polarized Deep Inelastic Scattering as $x \to 1$ using Soft Collinear Effective Theory
We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions $g_1(x)$ and $g_2(x)$, and to sum Sudakov double logarithms of $1-x$. The analysis is done both in terms of lightcone parton distributions and their moments. Computing $g_2$ requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the par…

The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces
S. V. Dzhenzher, V. Zh. Sakbaev
https://arxiv.org/abs/2507.07658 ht…

The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces
We consider random linear continuous operators $Ω\to \mathcal{L}(X, X)$ on a Banach space $X$. For example, such random operators may be random quantum channels. The Law of Large Numbers is known when $X$ is a Hilbert space, in the form of the usual Law of Large Numbers for random operators, and in some other particular cases. Instead of the sum of i.i.d. variables, there may be considered the composition of random semigroups $e^{A_it/n}$. We obtain the Strong Law of Large Numbers in Strong Op…

Complete characterization of $2$-near perfect numbers with exactly 2 prime factors
Richard Fearon, Henry Foushee, Benjamin Porosoff, Alexander Skula, Joshua Zelinsky, Kyle Zhang
https://arxiv.org/abs/2508.06651

Complete characterization of $2$-near perfect numbers with exactly 2 prime factors
Let $σ(n)$ be the sum of the positive divisors of $n$. A positive integer $n$ is said to be $2$-near perfect when $σ(n)=2n+d_1+d_2$, where $d_1$ and $d_2$ are distinct positive divisors of $n$. We show that there are no odd $2$-near perfect numbers with exactly two prime factors, and that all even $2$-near perfect numbers (i.e. those of the form $2^kp^m$, where $p$ is an odd prime) belong to a specific family, provided that $m$ is at least 3. In combination with prior work, these results prod…

A near-linear time approximation scheme for $(k,\ell)$-median clustering under discrete Fr\'echet distance
Anne Driemel, Jan H\"ockendorff, Ioannis Psarros, Christian Sohler
https://arxiv.org/abs/2508.07008

A near-linear time approximation scheme for $(k,\ell)$-median clustering under discrete Fréchet distance
A time series of complexity $m$ is a sequence of $m$ real valued measurements. The discrete Fréchet distance $d_{dF}(x,y)$ is a distance measure between two time series $x$ and $y$ of possibly different complexity. Given a set of $n$ time series represented as $m$-dimensional vectors over the reals, the $(k,\ell)$-median problem under discrete Fréchet distance aims to find a set $C$ of $k$ time series of complexity $\ell$ such that $$\sum_{x\in P} \min_{c\in C} d_{dF}(x,c)$$ is minimized. In …

Retrocausal capacity of a quantum channel
Kaiyuan Ji, Seth Lloyd, Mark M. Wilde
https://arxiv.org/abs/2509.08965 https://arxiv.org/pdf/2509.08965

Retrocausal capacity of a quantum channel
We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve (P-CTC) represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities of a quantum channel, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-i…

One-weight codes in the sum-rank metric
Usman Mushrraf, Ferdinando Zullo
https://arxiv.org/abs/2508.04262 https://arxiv.org/pdf/2508.04262

One-weight codes in the sum-rank metric
One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics - being equivalent to (direct sums of) simplex codes - the sum-rank metric presents a far more intricate landscape. In this work, we explore the geometry of one-weight sum-rank metric codes, focusing on three distinct classes. First, we introduce and classify …

Diminished Sombor index and its relationship with topological indices
F. Movahedi
https://arxiv.org/abs/2508.06532 https://arxiv.org/pdf/2508.06532

Diminished Sombor index and its relationship with topological indices
In this paper, we investigate the Diminished Sombor index (DSO), a recently introduced degree-based topological index for a simple graph $G$, defined as \[ DSO(G) = \sum_{uv \in E} \frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v}, \] where $d_u$ denotes the degree of a vertex $u \in V$. We establish several sharp bounds for this index in terms of classical topological indices such as the Zagreb, Albertson, Harmonic, Randić, and geometric-arithmetic indices. The relationships and inequalities between DSO and…

Dissipativity-based time domain decomposition for optimal control of hyperbolic PDEs
B\'alint Farkas, Birgit Jacob, Manuel Schaller, Merlin Schmitz
https://arxiv.org/abs/2507.07812

Dissipativity-based time domain decomposition for optimal control of hyperbolic PDEs
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state and adjoint equation, as a sum of dissipative operators, which enables a Peaceman-Rachford-type fixed-point iteration. The iteration steps may be understood and implemented as solutions of many decoupled, and therefore highly parallelizable, time-distributed …

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
Miguel Tierz
https://arxiv.org/abs/2509.09640 https://

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
We show that, for sudden quenches, the work distribution reduces to the statistics of traces of powers of Haar unitaries, which are random unitary matrices drawn uniformly from the unitary group. For translation-invariant quadratic fermionic chains with interactions extending to $m$ neighbors and periodic boundary conditions, the Loschmidt amplitude admits a unitary matrix-model / Toeplitz representation, which yields a work variable of the form $W=\sum_{r\le m} a_r\,\mathrm{Re}\,\mathrm{Tr}\,U…

On certain root number $1$ cases of the cube sum problem
Shamik Das, Somnath Jha
https://arxiv.org/abs/2508.05361 https://arxiv.org/pdf/2508.05361

On certain root number $1$ cases of the cube sum problem
We consider certain families of integers $n$ determined by some congruence condition, such that the global root number of the elliptic curve $E_{-432n^2}: Y^2=X^3-432n^2$ is $1$ for every $n$, however a given $n$ may or may not be a sum of two rational cubes. We give explicit criteria in terms of the $2$-parts and $3$-parts of the ideal class groups of certain cubic number fields to determine whether such an $n$ is a cube sum. In particular, we study integers $n$ divisible by $3$ such that the …

Light baryonium states with exotic quantum numbers
Bing-Dong Wan
https://arxiv.org/abs/2508.07822 https://arxiv.org/pdf/2508.07822

Light baryonium states with exotic quantum numbers
The existence of baryonium-bound or resonant states composed of a baryon and an antibaryon-has long been postulated as a natural extension of conventional hadron spectroscopy. In the present work, we conduct a systematic investigation of the mass spectrum and internal configurations of light baryonium candidates exhibiting exotic quantum numbers that are inaccessible within the framework of the traditional quark model. Employing the method of QCD sum rules, we analyze nucleon-antinucleon and li…

On the spectrum and energy of graphs with self-loops
Kevin Fung, Johnny Lim
https://arxiv.org/abs/2508.07004 https://arxiv.org/pdf/2508.07004

On the spectrum and energy of graphs with self-loops
A digraph with self-loops $D_S$ with vertex set $\mathcal{V}$ is a simple digraph with a self-loop attached at every vertex in $S \subset \mathcal{V}.$ In this paper, we study the energy $E(D_S)$ of $D_S$ and its properties, which extend several classical results on simple directed graphs. If $D_1,...,D_k$ are the strong components of $D_S,$ we establish a necessary and sufficient condition for $E(D_S) \leq \sum^k_{i=1} E(D_i),$ for which the strict inequality exists for $S\neq \emptyset.$ We a…

Fundamental limit of Sum Capacity in Pinching Antenna Assisted Multiple Access Channel
Guangji Chen, Qingqing Wu, Kangda Zhi
https://arxiv.org/abs/2508.05309 https://

Fundamental limit of Sum Capacity in Pinching Antenna Assisted Multiple Access Channel
Pinching antenna systems (PASSs) have recently shown their promising ability to flexibly reconfigure wireless channels via dynamically adjusting the positions of pinching antennas over a dielectric waveguide, termed as pinching beamforming. This paper studies the fundamental limit of the sum capacity for a PASSassisted multiple access channel, in which multiple users transmit individual messages to a BS under the average power constraint. To this end, we consider a dynamic pinching beamforming …

Subset Sum in Near-Linear Pseudopolynomial Time and Polynomial Space
Thejas Radhika Sajith
https://arxiv.org/abs/2508.04726 https://arxiv.org/pdf/2508.0472…

Subset Sum in Near-Linear Pseudopolynomial Time and Polynomial Space
Given a multiset $A = \{a_1, \dots, a_n\}$ of positive integers and a target integer $t$, the Subset Sum problem asks if there is a subset of $A$ that sums to $t$. Bellman's [1957] classical dynamic programming algorithm runs in $O(nt)$ time and $O(t)$ space. Since then, there have been multiple improvements in both time and space complexity. Notably, Bringmann [SODA 2017] uses a two-step color-coding technique to obtain a randomized algorithm that runs in $\tilde{O}(n+t)$ time and $\tilde{O}…

A study on preservation of parallel pairs and triangle equality attainment pairs
Jayanta Manna, Kalidas Mandal, Kallol Paul, Debmalya Sain
https://arxiv.org/abs/2507.07774

A study on preservation of parallel pairs and triangle equality attainment pairs
This paper investigates the structure and preservation of parallel pairs and triangle equality attainment (TEA) pairs in normed linear spaces. We begin by providing functional characterizations of these pairs in normed linear spaces and provide a characterization of finite-dimensional Banach spaces with numerical index one. We then study parallel pairs and TEA pairs in the $p$-direct sum of normed linear spaces. Next, we show that in finite-dimensional Banach spaces, a bijective bounded linear …

Optimal Dividend, Reinsurance, and Capital Injection Strategies for an Insurer with Two Collaborating Business Lines
Tim J. Boonen, Engel John C. Dela Vega, Bin Zou
https://arxiv.org/abs/2508.08130

Optimal Dividend, Reinsurance, and Capital Injection Strategies for an Insurer with Two Collaborating Business Lines
This paper considers an insurer with two collaborating business lines, and the risk exposure of each line follows a diffusion risk model. The manager of the insurer makes three decisions for each line: (i) dividend payout, (ii) (proportional) reinsurance coverage, and (iii) capital injection (from one line into the other). The manager seeks an optimal dividend, reinsurance, and capital injection strategy to maximize the expected weighted sum of the total dividend payments until the first ruin. …

Large character sums with multiplicative coefficients
Zikang Dong, Yutong Song, Weijia Wang, Hao Zhang, Shengbo Zhao
https://arxiv.org/abs/2509.09649 https://

Large character sums with multiplicative coefficients
In this paper, we investigate large values of Dirichlet character sums with multiplicative coefficients $\sum_{n\le N}f(n)χ(n)$. We prove a new Omega result in the region $\exp((\log q)^{\frac12+δ})\le N\le\sqrt q$, where $q$ is the prime modulus.

Sums of squares of integers from residue classes
Daejun Kim
https://arxiv.org/abs/2508.08106 https://arxiv.org/pdf/2508.08106

Sums of squares of integers from residue classes
A subset $\mathcal{A}\subseteq\mathbb{Z}$ is called $s$-almost square universal if every sufficiently large positive integer can be written as a sum of at most $s$ squares of integers from $\mathcal{A}$. In this article, we study the minimal number $\mathrm{ASU}(\mathcal{A}_{d,m})$ with this property, where $\mathcal{A}_{d,m}$ denotes the residue class of $d$ modulo $m$, with $m\in\mathbb{N}$ and $d\in\mathbb{Z}$. We further prove that $\mathcal{A}_{d,m}$ is $s$-square universal for some $s\in\…

Subgroup perfect codes of $S_n$ in Cayley sum graphs
Ankan Shaw, Biswajit Mondal, Satya Bagchi
https://arxiv.org/abs/2509.05069 https://arxiv.org/pdf/2509.…

Subgroup perfect codes of $S_n$ in Cayley sum graphs
A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent, and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. Let $ G $ be a finite group, and let $ S $ be a square-free normal subset of $ G $. The Cayley sum graph of $ G $ with respect to $ S $ is a simple graph with vertex set $ G $ and two vertices $ x $ and $ y $ are adjacent if $ xy\in S .$ A subset $ C $ of $ G $ is called perfect code of $ G $ if there exists a …

Topped baryons from QCD sum rules
Shu-Wei Zhang, Wei-Han Tan, Xuan Luo, Hua-Xing Chen
https://arxiv.org/abs/2507.05895 https://arxiv.…

Topped baryons from QCD sum rules
The recent CMS observation of a near-threshold enhancement in top quark pair production provides the first experimental indication of a short-lived pseudoscalar $t\bar{t}$ bound state, commonly referred to as toponium. While most existing studies focus on toponium using perturbative QCD near threshold, baryonic configurations containing a single top quark -- singly topped baryons -- offer a complementary nonperturbative perspective. Notably, singly topped baryons are expected to exhibit a longe…

A Novel Summation Formula for the Hurwitz-Kronecker Class Number
Yi-Ju Tsai (Shanghai Jiao Tong University)
https://arxiv.org/abs/2509.08281 https://arxiv.…

A Novel Summation Formula for the Hurwitz-Kronecker Class Number
The purpose of this paper is to present a novel and elegant summation formula for $H_w$, the Kronecker-Hurwitz class number. Specifically, for any prime $p$, we have the formula: $$ \sum_{t^2

Best approximation of a three-variable function by sum of one-variable coordinate functions
Rashid A. Aliev, Vugar A. Guliyev, Amil F. Jabiyev
https://arxiv.org/abs/2507.04747

Best approximation of a three-variable function by sum of one-variable coordinate functions
Consider the following approximation problem of a continuous function of three variables by the sum of three continuous functions of one variable: \[ E(f,Ω)=\inf||f(x,y,z)-ϕ(x)-ψ(y)-ω(z)||_{\infty}=? \] where $f(x,y,z)$ is a given continuous function defined on $Ω=[0,1]^3$ and the infimum runs over all triplets of continuous functions $ϕ(x),ψ(y),ω(z)$ defined on the unit interval $[0,1]$. In this paper, we will prove a formula to calculate the error $E(f,Ω)$ und…

An Equivalent Representation of Generalized Differentials
Valentin Suder
https://arxiv.org/abs/2507.07337 https://arxiv.org/pdf/2507.…

An Equivalent Representation of Generalized Differentials
We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic $p$. The result is obtained by counting the number of subsets of the prime field with a fixed cardinality for which the sum of their elements is constant. We then ask related questions regarding the diversity of higher-order derivatives.

Fractional Programming for Stochastic Precoding over Generalized Fading Channels
Wenyu Wang, Kaiming Shen
https://arxiv.org/abs/2507.06944 https://

Fractional Programming for Stochastic Precoding over Generalized Fading Channels
This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular probability distribution model for fading channels (which is typically Gaussian), our approach merely relies on the first and second moments of fading channels. For the stochastic precoding problem, a naive idea is to directly apply the fractional programming (FP) meth…

Low degree sum-of-squares bounds for the stability number: a copositive approach
Luis Felipe Vargas, Juan C. Vera, Peter J. C. Dickinson
https://arxiv.org/abs/2509.04949 https:/…

Low degree sum-of-squares bounds for the stability number: a copositive approach
The stability number of a graph $G$, denoted as $α(G)$, is the maximum size of an independent (stable) set in $G$. Semidefinite programming (SDP) methods, which originated from Lovász's theta number and expanded through lift-and-project hierarchies as well as sums of squares (SOS) relaxations, provide powerful tools for approximating $α(G)$. We build upon the copositive formulation of $α(G)$ and introduce a novel SDP-based hierarchy of inner approximations to the copositive cone COP$_n$, …

Bounds of Trees with Degree Sequence-Based Topological Indices on Specialized Graph Classes
Jasem Hamoud, Duaa Abdullah
https://arxiv.org/abs/2508.04518 https://

Bounds of Trees with Degree Sequence-Based Topological Indices on Specialized Graph Classes
In this paper, the investigates Adriatic indices, specifically the sum lordeg index where it defined as $SL(G) = \sum_{u \in V(G)} °_G(u) \sqrt{\ln °_G(u)}$ and the variable sum exdeg index $SEI_a(G)$ for $a>0$, $a\neq 1$. We present several sharp bounds and characterizations of these and related topological indices on specialized graph classes, including regular graphs, thorny graphs, and chemical trees. Using the strict convexity of function $f$, inequalities for degree-based graph invarian…

Every real number is a sum of two real numbers with diverging partial quotients
Dmitry Gayfulin, Erez Nesharim
https://arxiv.org/abs/2507.04521 https://

Every real number is a sum of two real numbers with diverging partial quotients
We show that every irrational number is a sum of two real numbers with diverging partial quotients. The proof is constructive. The key towards these results is an algorithm which was recently developed by Nikita Shulga, and our study of this algorithm is of independent interest.

Hybrid Quantum Convolutional Neural Network-Aided Pilot Assignment in Cell-Free Massive MIMO Systems
Doan Hieu Nguyen, Xuan Tung Nguyen, Seon-Geun Jeong, Trinh Van Chien, Lajos Hanzo, Won Joo Hwang
https://arxiv.org/abs/2507.06585

Hybrid Quantum Convolutional Neural Network-Aided Pilot Assignment in Cell-Free Massive MIMO Systems
A sophisticated hybrid quantum convolutional neural network (HQCNN) is conceived for handling the pilot assignment task in cell-free massive MIMO systems, while maximizing the total ergodic sum throughput. The existing model-based solutions found in the literature are inefficient and/or computationally demanding. Similarly, conventional deep neural networks may struggle in the face of high-dimensional inputs, require complex architectures, and their convergence is slow due to training numerous …

Robust signal decompositions on the circle
Aral Kose, Daniel Liberzon
https://arxiv.org/abs/2507.07007 https://arxiv.org/pdf/2507.070…

Robust signal decompositions on the circle
We consider the problem of decomposing a piecewise constant function on the circle into a sum of indicator functions of closed circular disks in the plane, whose number and location are not a priori known. This represents a situation where an agent moving on the circle is able to sense its proximity to some landmarks, and the goal is to estimate the number of these landmarks and their possible locations -- which can in turn enable control tasks such as motion planning and obstacle avoidance. Mo…

Triple convolution sums of the generalised divisor functions
Bikram Misra, Biswajyoti Saha
https://arxiv.org/abs/2509.04610 https://arxiv.org/pdf/2509.0461…

Triple convolution sums of the generalised divisor functions
We study the triple convolution sum of the generalised divisor functions given by $$\sum_{n\leq x} d_k(n+h)d_l(n)d_m(n-h),$$ where $h \le x^{1-ε}$ for any $ε>0$ and $d_k(n)$ denotes the generalised divisor function which counts the number of ways $n$ can be written as product of $k$ many positive integers. The purpose of this paper is two-fold. Firstly, we note a predicted asymptotic estimate for the above sum, where the constant appearing in the estimate can be obtained from the theory of Di…

QCD condensates and $\alpha_s$ from $e^ e^-$ and $\tau$-decays
Stephan Narison (LUPM-CNRS Montpellier-FR,iHEPMAD-Univ. Antananarivo-MG)
https://arxiv.org/abs/2508.05434 https://…

QCD condensates and $α_s$ from $e^+e^-$ and $τ$-decays
In this talk, I review the determinations of the QCD condensates and $α_s$ within the SVZ expansion using the ratio of Laplace sum rule (LSR) and $τ$-like moments in $e^+e^-\to I=1$ Hadrons and in $τ\to ν_τ+$Hadrons Axial-vector (A) and V-A channels. Some misprints in the original papers [1-3] have been corrected. We found that the value of the gluon condensate agrees with the one $\langle α_s G^2\rangle=(6.35\pm 0.35)\times 10^{-2}$ GeV$^4$ from quarkonia and some other sum rules but les…

On the Estrada Index and Spectral Properties of $k$-Uniform Hypergraphs
Liya Jess Kurian, Chithra A. V
https://arxiv.org/abs/2507.06322 https://

On the Estrada Index and Spectral Properties of $k$-Uniform Hypergraphs
Various properties of a hypergraph can be explored through its spectrum. In this paper,we estimate the bound for the sum of $t,\,t\in[1,n]$, largest eigenvalues of a $k$-uniform hypergraph of order $n$. Also, we characterize the $k$-uniform hypergraph with two distinct eigenvalues. We establish bounds for the Estrada index of $k$-uniform hypergraphs based on their number of edges, order and energy. In addition, we obtain the second largest Estrada index among the unicyclic hypergraphs.

Two-Timescale Sum-Rate Maximization for Movable Antenna Enhanced Systems
Xintai Chen, Biqian Feng, Yongpeng Wu, Derrick Wing Kwan Ng, Robert Schober
https://arxiv.org/abs/2509.04062

Two-Timescale Sum-Rate Maximization for Movable Antenna Enhanced Systems
This paper studies a novel movable antenna (MA)-enhanced multiuser multiple-input multiple-output downlink system designed to improve wireless communication performance. We aim to maximize the average achievable sum rate through two-timescale optimization exploiting instantaneous channel state information at the receiver (I-CSIR) for receive antenna position vector (APV) design and statistical channel state information at the transmitter (S-CSIT) for transmit APV and covariance matrix design. W…

On the sum-of-squares function
Vitalii V. Iudelevich
https://arxiv.org/abs/2508.02701 https://arxiv.org/pdf/2508.02701

On the sum-of-squares function
In this paper, we derive the following asymptotic formula $$ \mathop{{\sum}'}_{n\leqslant x}\dfrac{r(n)}{r(n+1)} = {x}{(\ln x)^{-3/4}}(c+o(1)),\ \ x \to +\infty,$$ where $r(n)$ is the number of representations of $n$ as a sum of two squares, $c$ is a positive constant, and the prime indicates summation over those $n$ for which $r(n+1)\neq 0$.

Solving Zero-Sum Games with Fewer Matrix-Vector Products
Ishani Karmarkar, Liam O'Carroll, Aaron Sidford
https://arxiv.org/abs/2509.04426 https://arxiv…

Solving Zero-Sum Games with Fewer Matrix-Vector Products
In this paper we consider the problem of computing an $ε$-approximate Nash Equilibrium of a zero-sum game in a payoff matrix $A \in \mathbb{R}^{m \times n}$ with $O(1)$-bounded entries given access to a matrix-vector product oracle for $A$ and its transpose $A^\top$. We provide a deterministic algorithm that solves the problem using $\tilde{O}(ε^{-8/9})$-oracle queries, where $\tilde{O}(\cdot)$ hides factors polylogarithmic in $m$, $n$, and $ε^{-1}$. Our result improves upon the state-of-the…

The Neighbour Sum Problem on Trees
Sayan Dutta, Sohom Gupta
https://arxiv.org/abs/2506.23965 https://arxiv.org/pdf/2506.23965

The Neighbour Sum Problem on Trees
A graph $\mathcal G = (\mathcal V, \mathcal E)$ is said to satisfy the Neighbour Sum Property if there exists some $f:\mathcal V\to\mathbb R$ such that $f\not\equiv 0$ and it maps every vertex to the sum of the values taken by its neighbours. In this article, we provide an algorithm to check whether a given finite tree satisfies the neighbour sum property. We also find a large class of trees on $n$ vertices that satisfy the property.

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints
Nata\v{s}a Kreji\'c, Nata\v{s}a Krklec Jerinki\'c, Tijana Ostoji\'c, Nemanja Vu\v{c}i\'cevi\'c
https://arxiv.org/abs/2508.02299

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one end, to increasing sample size that achieves the full sample eventually, on the other end of the spec…

A weighted divisor problem and exponential sum
Kritika Aggarwal, Debika Banerjee
https://arxiv.org/abs/2507.01891 https://arxiv.org/p…

A weighted divisor problem and exponential sum
In this paper, we investigate a weighted divisor problem involving the exponential sum of $D_{(1)}(n)$, the $n$th coefficient in the Dirichlet series expansion of $ζ'(s)^2$. We establish a truncated Voronoï type formula for the error term of $\sum_{n\leq x}D_{(1)}(n)e(nh/k)$, analogous to the results obtained by Jutila. Utilizing this truncated formula, we derive a mean square estimate of the error term. In addition, we study the associated Riesz sum and the corresponding error term, along wi…

$q$-Congruences for Z.-W. Sun's generalized polynomials $w^{(\alpha)}_k(x)$
Lin-Yue Li, Rong-Hua Wang
https://arxiv.org/abs/2507.04653 https://

$q$-Congruences for Z.-W. Sun's generalized polynomials $w^{(α)}_k(x)$
In 2022, Z.-W. Sun defined \begin{equation*} w_k^{(α)}{(x)}=\sum_{j=1}^{k}w(k,j)^αx^{j-1}, \end{equation*} where $k,α$ are positive integers and $w(k,j)=\frac{1}{j}\binom{k-1}{j-1}\binom{k+j}{j-1}$. Let $(x)_{0}=1$ and $(x)_{n}=x(x+1)\cdots(x+n-1)$ for all $n\geq 1$. In this paper, it is proved by $q$-congruences that for any positive integers ${α,β, m,n,r}$, we have \begin{equation*} \frac{(2,n)}{n(n+1)(n+2)}\sum_{k=1}^{n}k^r(k+1)^r(2k+1)w_{k}^{(α)}(x)^{m}\in\mathbb{Z}[x], \end{equation*…

On exotic matrix exponential sums and Bessel-Speh functions
Elad Zelingher
https://arxiv.org/abs/2507.06394 https://arxiv.org/pdf/250…

On exotic matrix exponential sums and Bessel-Speh functions
We define the notions of non-abelian exotic Gauss sums and of exotic matrix Kloosterman sums, the latter one generalizing the notions of Katz's exotic Kloosterman sums and of twisted matrix Kloosterman sums. Using Kondo's Gauss sum and results about Shintani lifts, we reduce non-abelian exotic Gauss sums to products of classical (exotic) Gauss sums. Using Macdonald's characteristic maps, we generalize our previous result and show that exotic matrix Kloosterman sums can be expressed as products …

On the distribution of the Fourier coefficients over two sparse sequences
Venkatasubbareddy Kampamolla
https://arxiv.org/abs/2509.07037 https://arxiv.org/p…

On the distribution of the Fourier coefficients over two sparse sequences
Let $j\geq 3$ be any fixed integer and $f$ be a primitive holomorphic cusp form of even integral weight $κ\geq 2$ for the full modular group $SL(2,\mathbb{Z})$. We write $λ_{{\rm{sym}^j }f}(n)$ for the $n^\text{th}$ normalized Fourier coefficient of $L(s,{\rm{sym}}^j f)$. In this article, we establish asymptotic formulae for the discrete sums of the Fourier coefficients $λ_{\rm{sym}^j f}^2(n)$ over two sparse sequence of integers, which can be written as the sum of four integral squares and …