Tootfinder

Sheffer Polynomials and the s-ordering of Exponential Boson Operators
Robert S. Maier
https://arxiv.org/abs/2508.13094 https://arxiv.org/pdf/2508.13094

Sheffer Polynomials and the s-ordering of Exponential Boson Operators
The s-ordered form of any product of single-mode boson creation and annihilation operators, containing only a single annihilator, is computed explicitly. The s-ordering concept originated in quantum optics, and subsumes normal, symmetric (Weyl), and anti-normal ordering for any two operators satisfying a canonical commutation relation. Because the s-ordering map can be viewed as producing a function of a complex variable, its inverse is a quantization map that takes such "classical" functions t…

Sectorial Green Functions in the Ternary Algebra C3 and Their Curved-Space Extension
Bora Akta\c{s}
https://arxiv.org/abs/2509.14244 https://arxiv.org/pdf/…

Sectorial Green Functions in the Ternary Algebra C3 and Their Curved-Space Extension
Green functions associated with higher-order differential operators typically lead to special-function expressions in curved or bounded geometries, obscuring analytic transparency. In this work we develop the sectorial Green function for the cubic operator $(D^3+1)$ within the ternary algebra $C_3$ (defined by $j^3=-1$). The algebra admits three exponential carriers and divides the complex plane into six Stokes sectors, in each of which the Green kernel assumes a closed exponential--trigonometr…

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping
Shihe Liu, Yunfeng Shi, Zhifei Zhang
https://arxiv.org/abs/2508.12714 https://

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping
In this paper, we prove the Anderson localization near the spectral edge for some alloy-type Anderson-Bernoulli model on $\mathbb{Z}^d$ with exponential long-range hopping. This extends the work of Bourgain [Geometric Aspects of Functional Analysis, LNM 1850: 77--99, 2004], in which he pioneered a novel multi-scale analysis to treat Bernoulli random variables. Our proof is mainly based on Bourgain's method. However, to establish the initial scales Green's function estimates, we adapt the approa…

Inversions in parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, Gabe Udell
https://arxiv.org/abs/2508.11587 https://…

Inversions in parking functions
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under r…

Quantum Resolution of Mass Inflation in Reissner-Nordstr\"{o}m Interiors via Wheeler-DeWitt Equation
Chen-Hsu Chien, Woosung Song, Gansukh Tumurtushaa, Dong-han Yeom
https://arxiv.org/abs/2509.13483

Quantum Resolution of Mass Inflation in Reissner-Nordström Interiors via Wheeler-DeWitt Equation
We construct a canonical quantization, the Wheeler-DeWitt equation, of the interior geometry of static and spherically symmetric black holes in Einstein-Maxwell-$Λ$ framework, focusing on Reissner-Nordström. The wave function of the Wheeler-DeWitt equation for the Reissner-Nordström black hole is set to be on-shell and exhibiting exponential damping away from the classical locus. Horizon boundary conditions for the wave function generate two regimes: a single inward mode from event horizon y…

Spectral Deformation Flow and Global Classification of Simply-Connected Closed Manifolds
Anton Alexa
https://arxiv.org/abs/2508.11652 https://arxiv.org/pdf…

Spectral Deformation Flow and Global Classification of Simply-Connected Closed Manifolds
We study the evolution of a spectral deformation flow for amplitudes $C_n(τ)$, governed by a second-order self-adjoint operator $\hat{C}$ on a compact domain. This flow leads to exponential stabilization $C_n(τ) \to π$, encoded in the spectral multi-function $C(v,τ,n)$, which describes the geometric deformation across scales. Building on prior results on spectral rigidity, completeness, and asymptotics of $\hat{C}$, we analyze conditions under which this convergence determines the full topo…

Analytic estimation of parameters of stochastic volatility diffusion models with exponential-affine characteristic function for currency option pricing
Miko{\l}aj {\L}ab\k{e}dzki
https://arxiv.org/abs/2507.11868

Analytic estimation of parameters of stochastic volatility diffusion models with exponential-affine characteristic function for currency option pricing
This dissertation develops and justifies a novel method for deriving approximate formulas to estimate two parameters in stochastic volatility diffusion models with exponentially-affine characteristic functions and single- or two-factor variance. These formulas aim to improve the accuracy of option pricing and enhance the calibration process by providing reliable initial values for local minimization algorithms. The parameters relate to the volatility of the stochastic factor in instantaneous va…

Rigidity for the heat equation with density on Riemannian manifolds through a conformal change
Alexander Grigor'yan, Giulia Meglioli, Alberto Roncoroni
https://arxiv.org/abs/2507.13230

Rigidity for the heat equation with density on Riemannian manifolds through a conformal change
We investigate uniqueness of solution to the heat equation with a density $ρ$ on complete, non-compact weighted Riemannian manifolds of infinite volume. Our main goal is to identify sufficient conditions under which the solution $u$ vanishes identically, assuming that $u$ belongs to a certain weighted Lebesgue space with exponential or polynomial weight, $L^p_ϕ$. We distinguish between the cases $p > 1$ and $p = 1$ which required stronger assumptions on the manifold and the density function $…

The End of Hyperbolic Growth in Human Population and CO$_2$ Emissions
Victor M. Yakovenko
https://arxiv.org/abs/2508.11038 https://arxiv.org/pdf/2508.11038…

The End of Hyperbolic Growth in Human Population and CO$_2$ Emissions
Using current empirical data from 10,000 BCE to 2023 CE, we re-examine a hyperbolic pattern of human population growth, which was identified by von Foerster et al. in 1960 with a predicted singularity in 2026. We find that human population initially grew exponentially in time as $N(t)\propto e^{t/T}$ with $T$=2080 years. This growth then gradually evolved to be super-exponential with a form similar to the Bose function in statistical physics. Around 1700, population growth further accelerated, …

Adaptive estimation in regression models for weakly dependent data and explanatory variable with known density
Karine Bertin, Lisandro Fermin, Miguel Padrino
https://arxiv.org/abs/2507.11725

Adaptive estimation in regression models for weakly dependent data and explanatory variable with known density
This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The accuracy of the estimation is measured using pointwise risk. A data-driven procedure is proposed using kernel estimation with bandwidth selected via the Goldenshluger-Lepski approach. We demonstrate that the resulting estimator satisfies an oracle-type inequality a…

Consensus-Based Optimization Beyond Finite-Time Analysis
Pascal Bianchi (IP Paris, S2A), Alexandru-Radu Dragomir (IP Paris, S2A), Victor Priser (IP Paris, S2A)
https://arxiv.org/abs/2509.12907

Consensus-Based Optimization Beyond Finite-Time Analysis
We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to finite horizons, we investigate its long-time behavior with fixed parameters. In the mean-field limit, a quantitative Laplace principle shows exponential convergence to a neighborhood of the minimizer x * . For finitely many particles, a block-wise analysis y…

Loglinear Hawkes processes
Tomasz R. Bielecki, Jacek Jakubowski, Matthias Kirchner, Mariusz Niew\k{e}g{\l}owski
https://arxiv.org/abs/2507.11265 https://…

Loglinear Hawkes processes
This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. In the main theorem, we give sufficient conditions for explosion and nonexplosion that cover a large class of practically relevant memory functions. We also investigate stability. In particular, we show that for nonpositive memory functions the loglinear Hawkes process is stable. The paper aims at providing a theoretical bas…

Mitigating Exponential Mixed Frequency Growth through Frequency Selection and Dimensional Separation in Quantum Machine Learning
Michael Poppel, David Bucher, Maximilian Zorn, Nico Kraus, Jonas Stein, Claudia Linnhoff-Popien
https://arxiv.org/abs/2508.10533

Mitigating Exponential Mixed Frequency Growth through Frequency Selection and Dimensional Separation in Quantum Machine Learning
To leverage the potential computational speedup of quantum computing (QC), research in quantum machine learning (QML) has gained increasing prominence. Angle encoding techniques in QML models have been shown to generate truncated Fourier series, offering asymptotically universal function approximation capabilities. By selecting efficient feature maps (FMs) within quantum circuits, one can leverage the exponential growth of Fourier frequencies for improved approximation. In multi-dimensional set…

Quantum-Corrected Thermodynamics and Plasma Lensing in Non-Minimally Coupled Symmetric Teleparallel Black Holes
Erdem Sucu, \.Izzet Sakall{\i}, \"Ozcan Sert, Yusuf Sucu
https://arxiv.org/abs/2508.11076

Quantum-Corrected Thermodynamics and Plasma Lensing in Non-Minimally Coupled Symmetric Teleparallel Black Holes
We investigate the thermodynamic and optical signatures of electrically charged black holes (BHs) in symmetric teleparallel gravity (STPG) with non-minimal electromagnetic coupling, incorporating quantum corrections and plasma dispersion effects. The BH solution, characterized by a coupling parameter $k$, generalizes the Reissner-Nordström spacetime through power-law modifications to electromagnetic terms in the metric function. We implement exponential corrections to the Bekenstein-Hawking en…

A conjecture related to the Newman phase
Shravan Mohan
https://arxiv.org/abs/2509.11278 https://arxiv.org/pdf/2509.11278

A conjecture related to the Newman phase
A conjecture is proposed concerning the recovery of a discrete magnitude spectrum through a nonlinear transformation involving the Newman's phase sequence. Given a discrete magnitude spectrum sampled from a continuous function, consider the process of applying a complex exponential with the Newman's phase sequence, computing the inverse discrete Fourier transform (IFFT), taking the absolute value of the result, and reversing the time-domain signal. The conjecture states that Newman's phase sequ…

Dynamical crossover between stretched- and compressed-exponential relaxation in a photoexcited crystal
Tyler Carbin, Joel Herman, Xinshu Zhang, Adrian B. Culver, Yu Zhang, Hengdi Zhao, Rahul Roy, Gang Cao, Anshul Kogar
https://arxiv.org/abs/2509.04814

Dynamical crossover between stretched- and compressed-exponential relaxation in a photoexcited crystal
Anomalous relaxation is one of the hallmarks of disordered systems. Following perturbation by an external source, many glassy, jammed and amorphous systems relax as a stretched or compressed exponential as a function of time. However, despite their ubiquity, the origins of and the connection between these phenomenological relaxation functions remains to be understood. Here, we observe a tunable crossover from stretched- to compressed-exponential relaxation by photoexciting single crystal Ca3Ru2…

Schanuel conjecture for 1-motives
Cristiana Bertolin
https://arxiv.org/abs/2509.08700 https://arxiv.org/pdf/2509.08700

Schanuel conjecture for 1-motives
Schanuel Conjecture contains all ``reasonable" statements that can be made on the values of the exponential function. In particular it implies the Lindemann-Weierstrass Theorem. In my Ph.D. I showed that Schanuel Conjecture has a geometrical origin: it is equivalent to the Grothendieck-André periods Conjecture applied to a 1-motive without abelian part. In this paper, we state a conjecture in Schanuel style, which will imply conjectures in Lindemann-Weierstrass style, for the semi-elliptic e…

Taylor expansions over generalised power series
Vincent Bagayoko, Vincenzo Mantova
https://arxiv.org/abs/2509.08473 https://arxiv.org/pdf/2509.08473…

Taylor expansions over generalised power series
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an exponential function, and apply this to the case of standard fields of transseries, such as $\log$-$\exp$ transseries and $ω$-series.

A fourth-order exponential time differencing scheme with real and distinct poles rational approximation for solving non-linear reaction-diffusion systems
Wisdom Kwame Attipoe, Andreas Kleefeld, Emmanuel Asante-Asamani
https://arxiv.org/abs/2507.01245

A fourth-order exponential time differencing scheme with real and distinct poles rational approximation for solving non-linear reaction-diffusion systems
A fourth-order, L-stable, exponential time differencing Runge-Kutta type scheme is developed to solve nonlinear systems of reaction diffusion equations with nonsmooth data. The new scheme, ETDRK4RDP, is constructed by approximating the matrix exponentials in the ETDRK4 scheme with a fourth order, L-acceptable, non-Padé rational function having real and distinct poles (RDP). Using RDP rational functions to construct the scheme ensures efficient damping of spurious oscillations arising from non-…

Turnpike properties in linear quadratic Gaussian N-player differential games
Asaf Cohen, Jiamin Jian
https://arxiv.org/abs/2507.11632 https://

Turnpike properties in linear quadratic Gaussian N-player differential games
We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By analyzing convergence toward the corresponding ergodic game, we establish exponential convergence estimates between the solutions of the finite-horizon Riccati system and the associated algebraic Riccati system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a tu…

Shear Particle Acceleration in Structured Gamma-Ray Burst Jets: III. The Radiation Physics of Bright Prompt Optical Flash
Zi-Qi Wang, Xiao-Li Huang, En-Wei Liang
https://arxiv.org/abs/2508.06798

Shear Particle Acceleration in Structured Gamma-Ray Burst Jets: III. The Radiation Physics of Bright Prompt Optical Flash
The radiation physics of bright prompt optical emission of gamma-ray bursts (GRBs) remains a puzzle. Assuming that the GRB ejecta is structured, we investigated this issue by characterizing the ejecta as an ultra-relativistic uniform jet core surrounded by a mild-relativistic cocoon. The mixed jet-cocoon (MJC) region can accelerate particles through the shear acceleration mechanism. Parameterizing the radial velocity profile of the MJC region with an exponential function and assuming a uniform …

A scalable quantum-neural hybrid variational algorithm for ground state estimation
Minwoo Kim, Kyoung Keun Park, Uihwan Jeong, Sanghyeon Lee, Taehyun Kim
https://arxiv.org/abs/2507.11002

A scalable quantum-neural hybrid variational algorithm for ground state estimation
We propose the unitary variational quantum-neural hybrid eigensolver (U-VQNHE), which improves upon the original VQNHE by enforcing unitary neural transformations. The non-unitary nature of VQNHE causes normalization issues and divergence of the loss function during training, leading to exponential scaling of measurement overhead with qubit number. U-VQNHE resolves these issues, significantly reduces required measurements, and retains improved accuracy and stability over standard variational qu…

Yet another exponential Hopfield model
Linda Albanese, Andrea Alessandrelli, Adriano Barra, Peter Sollich
https://arxiv.org/abs/2509.06905 https://arxiv.or…

Yet another exponential Hopfield model
We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined through exponentials of standard quadratic loss functions, which naturally favors configurations corresponding to perfect recall. Despite not being a mean-field system, the model admits a tractable mathematical analysis of its dynamics and retrieval propertie…

Exponential Discounting under Partial Efficiency
Charles Gauthier
https://arxiv.org/abs/2508.20249 https://arxiv.org/pdf/2508.20249

Exponential Discounting under Partial Efficiency
This paper derives a novel representation of the exponential discounting model that allows one to assess departures from the model via a measure of efficiency. The approach uses a revealed preference methodology that does not make any parametric assumption on the utility function and allows for unrestricted heterogeneity. The method is illustrated using longitudinal data from checkout scanners and gives insights into sources of departure from exponential discounting.

A unifying perspective on measuring transient planar extensional viscosity from exponential shear
L. A. Kroo, R. A. Nicholson, M. W Boehm, S. K. Baier, G. H. McKinley
https://arxiv.org/abs/2506.16667

A unifying perspective on measuring transient planar extensional viscosity from exponential shear
Here we present an experimentally practical and robust method to compute the transient extensional viscosity from exponential shear on a wide variety of viscoelastic complex fluids. To achieve this, we derive an analytical, frame-invariant continuum solution for the exponential shear material function, valid over all Weissenberg numbers. Specifically, we amend the original framework of Doshi and Dealy proposed in 1987 to explicitly address the effect of rotation of material elements, due to the…

Hausdorff dimension of self-similar measures and sets with common fixed point structure
Bal\'azs B\'ar\'any, Manuj Verma
https://arxiv.org/abs/2507.05835

Hausdorff dimension of self-similar measures and sets with common fixed point structure
In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of a Hausdorff co-dimension one exceptional set of natural parameters, such systems satisfy a weak exponential separation. This significantly strengthens the previous result of the first author and Szvák. As an application, we give the Hausdorff dimension of s…

There and Back Again: Revisiting the Failure of Concatenation in Mittag-Leffler Functions
Paulo M. Carvalho-Neto, Cesar E. T. Ledesma
https://arxiv.org/abs/2508.05788 https://…

There and Back Again: Revisiting the Failure of Concatenation in Mittag-Leffler Functions
The function $t \mapsto E_α(λt^α)$ is widely regarded as the fractional analogue of the exponential function, yet its algebraic properties remain poorly understood. In particular, standard references lack a rigorous proof of the failure of the semigroup property. In this work, we fill this gap by providing an analytical proof that the semigroup property holds if and only if either $α= 1$ or $λ= 0$. Our result establishes a precise criterion for when Mittag-Leffler dynamics are compatible w…

Completely Integrable Gradient System on the bivariate beta statistical manifold
Prosper Rosaire Mama Assandje, Joseph Dongho, Thomas Bouetou Bouetou
https://arxiv.org/abs/2508.04523

Completely Integrable Gradient System on the bivariate beta statistical manifold
This paper investigates the geometry of a completely integrable gradient system defined on the three parameter bivariate beta statistical manifold of the first kind. We prove that the associated vector field is Hamiltonian and admits a Lax pair representation implying complete integrability. We show that the potential function derived from exponential family structure defines a Riemannian metric equivalent to the Fisher information metric. By applying Stirling's approximation to the gamma funct…

Standard Model Mass Spectrum and Interactions In The Holomorphic Unified Field Theory
J. W. Moffat, E. J. Thompson
https://arxiv.org/abs/2508.02747 https://

Standard Model Mass Spectrum and Interactions In The Holomorphic Unified Field Theory
We present a unified, ultraviolet-finite framework for the full Standard Model particle mass spectrum based on the Holomorphic Unified Field Theory augmented by nonlocal entire-function regulators. Starting from a single holomorphic action on the complexified spacetime manifold $M^4_{\mathbb{C}}$, with a Hermitian metric unifying gravity, gauge and matter sectors, we embed exponential regulator insertions to render all loop integrals finite without breaking gauge or diffeomorphism invariance. A…

Computational Methods and Verification Theorem for Portfolio-Consumption Optimization under Exponential O-U Dynamics
Zhaoxiang Zhong, Haiming Song
https://arxiv.org/abs/2508.06491

Computational Methods and Verification Theorem for Portfolio-Consumption Optimization under Exponential O-U Dynamics
In this paper, we focus on the problem of optimal portfolio-consumption policies in a multi-asset financial market, where the n risky assets follow Exponential Ornstein-Uhlenbeck processes, along with one risk-free bond. The investor's preferences are modeled using Constant Relative Risk Aversion utility with state-dependent stochastic discounting. The problem can be formulated as a high-dimensional stochastic optimal control problem, wherein the associated value function satisfies a Hamilton-J…

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes
Ziling Heng, Peng Wang, Chengju Li
https://arxiv.org/abs/2506.23198

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes
Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let $V_n^{(p)}$ be an $n$-dimensional vector space over $\gf_p$ for a prime $p$. In this paper, we study the hybrid character sums of the form \begin{eqnarray*} \sum_{x \in V_n^{(p)}}ψ\left(F(x)\right)χ_1\left(a x\right), \end{eqnarray*} where $F$ is a function fro…

An Efficient Exponential Sum Approximation of Power-Law Kernels for Solving Fractional Differential Equation
Renu Chaudhary, Kai Diethelm, Afshin Farhadi, Fred A. Fuchs
https://arxiv.org/abs/2508.20311

An Efficient Exponential Sum Approximation of Power-Law Kernels for Solving Fractional Differential Equation
In this work, we present a comprehensive framework for approximating the weakly singular power-law kernel $t^{α-1}$ of fractional integral and differential operators, where $α\in (0,1)$ and $t \in [δ,T]$ with $0<δ

Witnessing and guiding sets of tangles
Annegret Seibt
https://arxiv.org/abs/2507.04394 https://arxiv.org/pdf/2507.04394

Witnessing and guiding sets of tangles
Tangles o er a way to indirectly but precisely capture cluster-like though possibly fuzzy substructures in discrete data. In this paper, we analyze witnessing and guiding sets of tangles that can help to find proper cluster candidates for given tangles. We show that every k-tangle has a witnessing set whose size is bounded in an exponential function in k which improves a result of Grohe and Schweizer. Further, we generalize a result of Diestel, Elbracht and Jacobs by providing a characterizatio…

On the Moments of Exponential Sums over r-Free Polynomials
Ben Doyle
https://arxiv.org/abs/2506.20581 https://arxiv.org/pdf/2506.2058…

On the Moments of Exponential Sums over r-Free Polynomials
Let $\mathbb{F}_q[t]$ denote the ring of polynomials over the finite field $\mathbb{F}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of $k$th moments of exponential sums over $r$-free polynomials in $\mathbb{F}_q[t]$ for all $k>0$. In the supercritical case $k>1+1/r$, we acquire an asymptotic formula using a function field analogue of the Hardy-Littlewood circle method.

Stochastic-tail of the curvature perturbation in hybrid inflation
Tomoaki Murata, Yuichiro Tada
https://arxiv.org/abs/2507.22439 https://arxiv.org/pdf/2507…

Stochastic-tail of the curvature perturbation in hybrid inflation
The exponential-tail behaviours of the probability density function (PDF) of the primordial curvature perturbation are confirmed in the mild-waterfall variants of hybrid inflation with the use of the stochastic formalism of inflation. On top of these tails, effective upper bounds on the curvature perturbation are also observed, corresponding to the exact hilltop trajectory during the waterfall phase. We find that in the model where the leading and higher-order terms in the expansion of the infl…

On unbiased estimators for functions of the rate parameter of the exponential distribution
Roberto Vila, Eduardo Yoshio Nakano
https://arxiv.org/abs/2506.20005

On unbiased estimators for functions of the rate parameter of the exponential distribution
In this paper, we explicitly derive unbiased estimators for various functions of the rate parameter of the exponential distribution, including powers of the rate parameter, the $q$th quantile, the $p$th moment, the survival function, the maximum, minimum, probability density function, mean past lifetime, moment generating function, and others. It is also noteworthy that this work corrects a general formula originally proposed by Tate, R. F. (Ann. Math. Statist., 30(2): 341-366, 1959) for constr…

A normalizing flow approach for the inference of star cluster properties from unresolved broadband photometry I: Comparison to spectral energy distribution fitting
Daniel Walter, Victor F. Ksoll, Ralf S. Klessen, Mederic Boquien, Aida Wofford, Francesco Belfiore, Daniel A. Dale, Kathryn Grasha, David A. Thilker, Leonardo Ubeda, Thomas G. Williams
https://

A normalizing flow approach for the inference of star cluster properties from unresolved broadband photometry I: Comparison to spectral energy distribution fitting
Estimating properties of star clusters from unresolved broadband photometry is a challenging problem that is classically tackled by spectral energy distribution (SED) fitting methods that are based on simple stellar population (SSP) models. However, because of their exponential scaling, grid-based methods suffer from computational limitations. In addition, stochastic latent variables in the model can make the computation of the likelihood function intractable. These limitations can be overcome …

On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights
Patricia Szokol
https://arxiv.org/abs/2508.18029 https://

On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights
The famous Bernstein conjecture about optimal node systems of classical polynomial Lagrange interpolation, standing unresolved for over half a century, was solved by T. Kilgore in 1978. Immediately following him, also the additional conjecture of Erdős was solved by deBoor and Pinkus. These breakthrough achievements were built on a fundamental auxiliary result on nonsingularity of derivative (Jacobian) matrices of certain interval maxima in function of the nodes. After the above breakthrough, …

Solution of Stochastic Facility Location Problems with Combinatorially many Decision-Dependent Distributions
Giovanni Pantuso
https://arxiv.org/abs/2509.09816 https://

Solution of Stochastic Facility Location Problems with Combinatorially many Decision-Dependent Distributions
This article describes a model and an exact solution method for facility location problems with decision-dependent uncertainties. The model allows characterizing the probability distribution of the random elements as a function of the choice of open facilities. This, in turn, generates a combinatorial number of potential distributions of the random elements. Though general in the relationship between location decisions and distributions, the proposed model is, however, exponential in size. We s…

An unconditional lower bound for the active-set method in convex quadratic maximization
Eleon Bach, Yann Disser, Sophie Huiberts, Nils Mosis
https://arxiv.org/abs/2507.16648

An unconditional lower bound for the active-set method in convex quadratic maximization
We prove that the active-set method needs an exponential number of iterations in the worst-case to maximize a convex quadratic function subject to linear constraints, regardless of the pivot rule used. This substantially improves over the best previously known lower bound [IPCO 2025], which needs objective functions of polynomial degrees $ω(\log d)$ in dimension $d$, to a bound using a convex polynomial of degree 2. In particular, our result firmly resolves the open question [IPCO 2025] of whe…

Soliton Synchronization with Randomness: Rogue Waves and Universality
Manuela Girotti, Tamara Grava, Robert Jenkins, Guido Mazzuca, Ken McLaughlin, Maxim Yattselev
https://arxiv.org/abs/2507.01253

Soliton Synchronization with Randomness: Rogue Waves and Universality
We consider an $N$-soliton solution of the focusing nonlinear Schrödinger equations. We give conditions for the synchronous collision of these $N$ solitons. When the solitons velocities are well separated and the solitons have equal amplitude, we show that the local wave profile at the collision point scales as the $\operatorname{sinc}(x)$ function. We show that this behaviour persists when the amplitudes of the solitons are i.i.d. sub-exponential random variables. Namely the central collision…

Approximating functions on ${\mathbb R}^ $ by exponential sums
Alexey Kuznetsov, Armin Mohammadioroojeh
https://arxiv.org/abs/2508.19095 https://arxiv.org/…

Approximating functions on ${\mathbb R}^+$ by exponential sums
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Padé approximation of the Laplace transform and employs a highly efficient continued fraction technique to construct the corresponding rational approximant. We demonstrate the accuracy of this method through a variety of examples, including the Gaussian function, probability density functions of the …

On a dense set of functions determined by sampled Gabor magnitude
Matthias Wellershoff
https://arxiv.org/abs/2507.14556 https://arxiv…

On a dense set of functions determined by sampled Gabor magnitude
We study the problem of recovering a function from the magnitude of its Gabor transform sampled on a discrete set. While it is known that uniqueness fails for general square integrable functions, we show that phase retrieval is possible for a dense class of signals: specifically, those whose Bargmann transforms are entire functions of exponential type. Our main result characterises when such functions can be uniquely recovered (up to a global phase) from magnitude only data sampled on uniformly…

Artificial intelligence for representing and characterizing quantum systems
Yuxuan Du, Yan Zhu, Yuan-Hang Zhang, Min-Hsiu Hsieh, Patrick Rebentrost, Weibo Gao, Ya-Dong Wu, Jens Eisert, Giulio Chiribella, Dacheng Tao, Barry C. Sanders
https://arxiv.org/abs/2509.04923

Artificial intelligence for representing and characterizing quantum systems
Efficient characterization of large-scale quantum systems, especially those produced by quantum analog simulators and megaquop quantum computers, poses a central challenge in quantum science due to the exponential scaling of the Hilbert space with respect to system size. Recent advances in artificial intelligence (AI), with its aptitude for high-dimensional pattern recognition and function approximation, have emerged as a powerful tool to address this challenge. A growing body of research has l…

Optimal Dividend Control with Transaction Costs under Exponential Parisian Ruin for a Refracted Levy Risk Model
Zhongqin Gao, Yan Lv, Jingmin He
https://arxiv.org/abs/2509.03068

Optimal Dividend Control with Transaction Costs under Exponential Parisian Ruin for a Refracted Levy Risk Model
This paper concerns an optimal impulse control problem associated with a refracted Lévy process, involving the reduction of reserves to a predetermined level whenever they exceed a specified threshold. The ruin time is determined by Parisian exponential delays and limited by a lower ultimate bankrupt barrier. We initially obtained the necessary and sufficient conditions for the value function and the optimal impulse control policy. Given a candidate for the optimal strategy, the corresponding …

Fourier decay of equilibrium states and the Fibonacci Hamiltonian
Ga\'etan Leclerc
https://arxiv.org/abs/2507.23731 https://arxiv.org/pdf/2507.23731

Fourier decay of equilibrium states and the Fibonacci Hamiltonian
We show positivity of the lower Fourier dimension for equilibrium states of nonlinear, area preserving, Axiom A diffeomorphisms on surfaces. To do so, we use the sum-product phenomenon to reduce Fourier decay to the study of some temporal distance function for a well chosen suspension flow, whose mixing properties reflects the nonlinearity of our base dynamics. We then generalize in an Axiom A setting the methods of Tsujii-Zhang, dealing with exponential mixing of three-dimensional Anosov flows…

Forrelation is Extremally Hard
Uma Girish, Rocco Servedio
https://arxiv.org/abs/2508.02514 https://arxiv.org/pdf/2508.02514

Forrelation is Extremally Hard
The Forrelation problem is a central problem that demonstrates an exponential separation between quantum and classical capabilities. In this problem, given query access to $n$-bit Boolean functions $f$ and $g$, the goal is to estimate the Forrelation function $\mathrm{forr}(f,g)$, which measures the correlation between $g$ and the Fourier transform of $f$. In this work we provide a new linear algebraic perspective on the Forrelation problem, as opposed to prior analytic approaches. We establi…

A standard CLT for triangles in a class of ERGs
Elena Magnanini, Giacomo Passuello
https://arxiv.org/abs/2507.17484 https://arxiv.org/pdf/2507.17484…

A standard CLT for triangles in a class of ERGs
We prove a standard Central Limit Theorem for the (normalized) number of triangles in a class of Exponential Random Graphs derived from a slight modification of the edge-triangle model. Our main theorem covers the whole analyticity region of the free energy, and is based on a polynomial representation of the partition function.

Time-inconsistent singular control problems: Reflection and Absolutely continuous controls with exploding rates
Andi Bodnariu, Kristoffer Lindensj\"o, Neofytos Rodosthenous
https://arxiv.org/abs/2507.04836

Time-inconsistent singular control problems: Reflection and Absolutely continuous controls with exploding rates
We study a time-inconsistent singular stochastic control problem for a general one-dimensional diffusion, where time-inconsistency arises from a non-exponential discount function. To address this, we adopt a game-theoretic framework and study the optimality of a novel class of controls that encompasses both traditional singular controls -- responsible for generating multiple jumps and reflective boundaries (strong thresholds) -- and new mild threshold control strategies, which allow for the exp…