Tootfinder

OpenAI debuts ChatGPT Agent, which can control an entire computer and perform multi-step tasks, powered by a new dedicated model, rolling out to paid users (Hayden Field/The Verge)
https://www.theverge.com/ai-artificial-intel…

OpenAI’s new ChatGPT Agent can control an entire computer and do tasks for you
OpenAI debuted ChatGPT Agent, a tool that can complete work on your behalf using its own “virtual computer” and is a continuation of its Operator and Deep Research tools. 

Branches of localized patterned states
Bjorn Sandstede
https://arxiv.org/abs/2507.12277 https://arxiv.org/pdf/2507.12277

Branches of localized patterned states
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized patterned structures lie on a discrete stack of loops or on a single unbounded branch. The framework proposed here also connects closely with continuation algorithms that are often used to verify the hypotheses that guarantee the emergence of localized patterned st…

A Unifying Integral Representation of the Gamma Function and Its Reciprocal
Peter Reinhard Hansen, Chen Tong
https://arxiv.org/abs/2506.12112 https://

A Unifying Integral Representation of the Gamma Function and Its Reciprocal
We derive an integral expression $G(z)$ for the reciprocal gamma function, $1/Γ(z)=G(z)/π$, that is valid for all $z\in\mathbb{C}$, without the need for analytic continuation. The same integral avoids the singularities of the gamma function and satisfies $G(1-z)=Γ(z)\sin(πz)$ for all $z\in\mathbb{C}$.

Computational algorithm for downward continuation of gravity anomalies
D. K. Ivanov, L. N. Temirbekova, P. N. Vabishchevich
https://arxiv.org/abs/2507.08506

Computational algorithm for downward continuation of gravity anomalies
The downward continuation of potential fields from the Earth's surface into the subsurface is a critical task in gravity exploration, as it helps to identify the sources of gravity anomalies. This problem is often addressed by solving a first-kind integral equation using regularization techniques to stabilize an inherently unstable process. A similar approach is used in our work, where the continued field is represented as the potential of a simple layer or its vertical derivative. The constanc…

This must be what it was like with Japanese Internment in Canada
https://mas.to/@continuation/114808884448419943

Mode stability for self-similar blowup of slightly supercritical NLS: II. high-energy spectrum
Zexing Li
https://arxiv.org/abs/2507.11259 https://

Mode stability for self-similar blowup of slightly supercritical NLS: II. high-energy spectrum
In continuation of the study of the companion work, we prove the high-energy mode stability for linearized operator around self-similar profiles in [Bahri-Martel-Raphaël, 2021] for slightly mass-supercritical NLS in $1 \le d \le 10$. This concludes the asymptotic stability of such self-similar blowup, and answers the question from [Bahri-Martel-Raphaël, 2021] and [Merle-Raphaël-Szeftel, 2010]. As a byproduct, we characterize the spectrum for linearized operator around mass-critical ground st…

AC/DC: LLM-based Audio Comprehension via Dialogue Continuation
Yusuke Fujita, Tomoya Mizumoto, Atsushi Kojima, Lianbo Liu, Yui Sudo
https://arxiv.org/abs/2506.10312

AC/DC: LLM-based Audio Comprehension via Dialogue Continuation
We propose an instruction-following audio comprehension model that leverages the dialogue continuation ability of large language models (LLMs). Instead of directly generating target captions in training data, the proposed method trains a model to produce responses as if the input caption triggered a dialogue. This dialogue continuation training mitigates the caption variation problem. Learning to continue a dialogue effectively captures the caption's meaning beyond its surface-level words. As a…

Decay of Fourier transforms and analytic continuation of power-constructible functions
Georges Comte, Dan J. Miller, Tamara Servi
https://arxiv.org/abs/2507.06142

Decay of Fourier transforms and analytic continuation of power-constructible functions
For a subfield K of C, we denote by C^K the category of algebras of functions defined on the globally subanalytic sets that are generated by all K-powers and logarithms of positively-valued globally subanalytic functions. For any function f in C^\K(R), we study links between holomorphic extensions of f and the decay of its Fourier transform F[f] by using tameness properties of the globally subanalytic functions from which f is constructed. We first prove a number of theorems about analytic cont…

US confirms Trump ordered resumption of Ukraine military aid shipments: https://benborges.xyz/2025/07/09/us-confirms-trump-ordered-resumption.html

Discontinuity calculus and applications to two-body coupled-channel scattering
Hao-Jie Jing, Xiong-Hui Cao, Feng-Kun Guo
https://arxiv.org/abs/2507.06175 h…

Discontinuity calculus and applications to two-body coupled-channel scattering
We present a novel method, termed discontinuity calculus, for computing discontinuities of complex functions. This framework enables a systematic investigation of both analytic continuation and the topological structure of Riemann surfaces. We apply this calculus to analyze the analytic continuation of partial-wave amplitudes in two-body coupled-channel scattering problems and discuss their uniformization of the corresponding Riemann surfaces. This methodology offers new perspectives and tools …

Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2
Pavel Pokhilko, Dominika Zgid
https://arxiv.org/abs/2507.00290

Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2
Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the homotopy continuation approach to control the behavior of iterations. We used the homotopy continuation to locate multiple fully self-consistent GW solutions for NdNiO2 solid and to establish the corresponding Hartree-Fock limits. Some of the solutions found are…

Study of the uniform electron gas through parametrized partition functions
Tommaso Morresi, Giovanni Garberoglio, Hongwei Xiong, Yunuo Xiong
https://arxiv.org/abs/2506.10113

Study of the uniform electron gas through parametrized partition functions
We investigate the energy per particle, static structure factor, and momentum distribution of the uniform electron gas for different conditions defined by the dimensionless temperature $Θ= 0.25 - 1.0$ and average interparticle distance $r_s = 0.5 - 80.0$ using path-integral Monte Carlo (PIMC) simulations. For small $r_\text{s}$ ($r_\text{s}\leq10$) where the sign problem is particularly challenging, we employ a recent approach based on an analytic continuation of the partition function using a…

Soliton self-excitation under pulsed driving in a Kerr resonator
Matthew Macnaughtan, Zongda Li, Yiqing Xu, Xiaoming Wei, Zhongmin Yang, St\'ephane Coen, Miro Erkintalo, Stuart G. Murdoch
https://arxiv.org/abs/2506.10307

Soliton self-excitation under pulsed driving in a Kerr resonator
We present a novel regime of cavity soliton excitation in a Kerr resonator driven by a train of desynchronised pulses. In this regime, the soliton solution is shown to be the sole available state for the intracavity field, allowing for the automatic excitation of single solitons without the application of any external perturbations or parameter ramping. The self-excitation of cavity soliton frequency combs is validated through numerical continuation of the Lugiato-Lefever equation, direct numer…

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory
Harley Scammell, Oleg P. Sushkov
https://arxiv.org/abs/2505.24150

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory
Employing a semiclassical method based on analytic continuation, we compute the electron-hole pair production rate in biased bilayer graphene subject to an in-plane electric field. This approach, originally due to Zwaan, bypasses the need for exact solutions at turning points, which are generally unavailable beyond linear or quadratic band structures. Applying this technique to biased bilayer graphene reveals non-standard features of the asymptotic wavefunctions, in particular the necessity of …

Day 5
TL;DR: Continued work on backend security — role-based access is now fully wired up.
✅ Got fine-grained role-based access control fully working today.
• Roles loaded from PostgreSQL
• Injected into JWT during login
• Validated via custom `@Roles()` `RolesGuard`
• Authenticated via `@UseGuards(JwtAuthGuard)` globally
• Introduced `@Public()` decorator to bypass guards for public endpoints
• Swagger supports Bearer token for testing …

Continuation: Securing Routes with JWT and Role-Based Access Control
TL;DR: Continuing development on the backend platform — this time focusing on securing routes with JWT, implementing @Roles decorators, h...

As the Trump rollercoaster continues, Ukraine struggles to work out where it stands: https://benborges.xyz/2025/07/09/as-the-trump-rollercoaster-continues.html

This https://arxiv.org/abs/2401.13577 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Three-Torsion Subgroups and Wild Conductor Exponents of Plane Quartics
In this paper we give an algorithm to find the 3-torsion subgroup of the Jacobian of a smooth plane quartic curve with a marked rational point. We describe $3-$torsion points in terms of cubics which triply intersect the curve, and use this to define a system of equations whose solution set corresponds to the coefficients of these cubics. We compute the points of this zero-dimensional, degree $728$ scheme first by approximation, using homotopy continuation and Newton-Raphson, and then using con…

This https://arxiv.org/abs/2411.07103 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On a connection between total positivity and Bernoulli stopping problems
Consider the optimal stopping problem of maximising the expected payoff in a game where a nonnegative reward is granted upon stopping on a success in a sequence of independent Bernoulli trials. These Bernoulli stopping problems are characterised by a recurrence relation connecting the stopping and continuation payoffs. This recurrence is used to establish optimality of the myopic strategy under unimodal continuation payoffs. Further, by embedding the success epochs of the trials into a Markov c…

Combinatorial quantization of 4d 2-Chern-Simons theory II: Quantum invariants of higher ribbons in $D^4$
Hank Chen
https://arxiv.org/abs/2506.05785 https:/…

Combinatorial quantization of 4d 2-Chern-Simons theory II: Quantum invariants of higher ribbons in $D^4$
This is a continuation of the first paper (arXiv:2501.06486) of this series, where the framework for the combinatorial quantization of the 4d 2-Chern-Simons theory with an underlying compact structure Lie 2-group $\mathbb{G}$ was laid out. In this paper, we continue our quest and characterize additive module *-functors $ω:\mathfrak{C}_q(\mathbb{G}^{Γ^2})\rightarrow\mathsf{Hilb}$, which serve as a categorification of linear *-functionals (ie. a state) on a $C^*$-algebra. These allow us to cons…

Check Point acquires Israeli cyber startup firm Veriti for $100 million
https://www.ynetnews.com/business/article/byjdi4emee

Check Point acquires Israeli cyber startup firm Veriti for $100 million
The Israeli company, founded in 2021 by Check Point alumni, has developed a platform for identifying and fixing security gaps in real time 30 Veriti employees will join Check Point as part of the deal, which is a continuation of the company's Israeli acquisition strategy

Analytic Uniqueness of Ball Volume Interpolation: Categorical Invariance and Universal Characterization
Andreu Ballus Santacana
https://arxiv.org/abs/2506.06885

Analytic Uniqueness of Ball Volume Interpolation: Categorical Invariance and Universal Characterization
We show that the classical volume formula for the unit $x$-ball, \[ V_x = \frac{π^{x/2}}{Γ(x/2+1)}, \] can be characterized as the \emph{unique} analytic continuation of Haar measure normalization and unit ball volumes for $\mathrm{O}(n)$, under principles of categorical invariance and normalization at integer dimensions. We generalize this result to the unitary and symplectic cases, formalize invariance using categorical language, and construct explicit categorical examples with functorial d…

This https://arxiv.org/abs/2501.02367 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hegel and Modern Topology
In this paper we show how some fundamental concepts of modern topology can be understood philosophically in the light of Hegel's Logic as well how modern topological concepts can provide concrete illustrations of many of the concepts and deductions that Hegel used. This paper can be seen as a continuation of our paper \cite{pro} where we argued that the prototypes of many fundamental notions of modern topology were already found in Aristotle's Physics. This paper is divided into two parts. The …

A frequency function approach to quantitative unique continuation for elliptic equations
Blair Davey
https://arxiv.org/abs/2506.19130 https://

A frequency function approach to quantitative unique continuation for elliptic equations
We investigate the quantitative unique continuation properties of solutions to second order elliptic equations with bounded lower order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions to generalized Schrödinger equations of the form $- \nabla \cdot (A \nabla u) + W \cdot \nabla u + V u = 0$, where we assume that $A$ is bounded, elliptic, symmetric, and Lipschitz, while $W$ and $V$ belong to $L^\infty$. We also study the global uniq…

Some Historical Misconceptions and Inaccuracies Regarding The 1908 Tunguska Event
Andrei Ol'khovatov
https://arxiv.org/abs/2505.05484 https://

Some Historical Misconceptions and Inaccuracies Regarding The 1908 Tunguska Event
This paper is a continuation of a series of works, devoted to various aspects of the 1908 Tunguska event. A large number of hypotheses about its causes have been put forward already. However, so far none of them has received convincing evidence. This is probably why new hypotheses appear almost every year, not only in the mass-media, but also in scientific literature. At the same time, any hypothesis should not contradict the known facts about the event. Unfortunately, the authors of new hypoth…

This https://arxiv.org/abs/2502.06475 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics
Large numbers of relative periodic orbits (RPOs) have been found recently in doubly-periodic, two-dimensional Kolmogorov flow at moderate Reynolds numbers $Re \in \{40, 100\}$. While these solutions lead to robust statistical reconstructions at the $Re$-values where they were obtained, it is unclear how their dynamical importance evolves with increasing $Re$. We perform arclength continuation on this library of solutions to show that large numbers of RPOs quickly become dynamically irrelevant, …

This https://arxiv.org/abs/2207.12969 has been replaced.
link: https://scholar.google.com/scholar?q=a

Module Categories of the Generic Virasoro VOA and Quantum Groups
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group $\mathcal{U}_q (\mathfrak{sl}_{2})$ with $q$ determined by the central charge. This is a continuation of…

The SagbiHomotopy.jl package for solving polynomial systems
Barbara Betti, Viktoriia Borovik
https://arxiv.org/abs/2506.06264 https://

The SagbiHomotopy.jl package for solving polynomial systems
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start system based on SAGBI homotopies. For square horizontally parameterized systems, where each equation is a linear combination of a given set of polynomials, SAGBI homotopies significantly reduce the number of solution paths to track compared to polyhedral homotopies currently used by default in most software for numer…

Scaling Self-Supervised Representation Learning for Symbolic Piano Performance
Louis Bradshaw, Honglu Fan, Alexander Spangher, Stella Biderman, Simon Colton
https://arxiv.org/abs/2506.23869

Scaling Self-Supervised Representation Learning for Symbolic Piano Performance
We study the capabilities of generative autoregressive transformer models trained on large amounts of symbolic solo-piano transcriptions. After first pretraining on approximately 60,000 hours of music, we use a comparatively smaller, high-quality subset, to finetune models to produce musical continuations, perform symbolic classification tasks, and produce general-purpose contrastive MIDI embeddings by adapting the SimCLR framework to symbolic music. When evaluating piano continuation coherence…

This https://arxiv.org/abs/2504.14922 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nuc…

Emulating multi-channel scattering based on the eigenvector continuation in the discrete basis formalism
We construct an emulator for a multi-channel scattering problem based on the eigenvector continuation. To this end, we employ the Kohn variational principle formulated in the discrete basis formalism. We apply this to one-dimensional scattering problems with a Gaussian barrier. Both for a single-channel and two-channel problems, we demonstrate that the penetration probability as well as the wave functions are well reproduced by the emulator. In particular, the energy dependence of the penetrabi…

Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD
Miguel Salg, Fernando Romero-L\'opez, William I. Jay
https://arxiv.org/abs/2506.16161

Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD
We present a novel procedure for analyzing the lattice-QCD spectrum via the finite-volume formalism to obtain constraints on multi-hadron scattering amplitudes at both real and complex energies. This approach combines a Bayesian reconstruction of the scattering amplitude on the real axis with Nevanlinna interpolation for analytic continuation to complex-valued energies. The method is non-parametric, inherently accounting for parametrization dependence within the uncertainty. We demonstrate the …

An Application of Maximality to Nilpotent and Finitely Generated L-Subgroups of an L-Group
Iffat Jahan, Ananya Manas
https://arxiv.org/abs/2506.20192 https…

An Application of Maximality to Nilpotent and Finitely Generated L-Subgroups of an L-Group
This paper is a continuation of the study on maximal and Frattini L-subgroups of an L-group. The normality of the maximal L-subgroups of a nilpotent L-group is explored. Then, the concept of finitely generated L-subgroup is introduced and its relation with maximal condition on L-subgroups is established. Thereafter, several results pertaining to the notions of Frattini L-subgroup and finitely generated L-subgroups have been investigated.

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
Jungsoo Kang, Kevin Ruck
https://arxiv.org/abs/2506.01735

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy levels are of contact type. Then, using a version of Rabinowitz Floer homology and an analytic continuation argument, we establish the existence of a symmetric consecutive collision orbit and, furthermore, prove the existence of infinitely many such orbits f…

On the singular set of the free boundary for a Monge-Amp\`ere obstacle problem
Tianling Jin, Xushan Tu, Jingang Xiong
https://arxiv.org/abs/2506.08387 http…

On the singular set of the free boundary for a Monge-Ampère obstacle problem
This is a continuation of our earlier work [14] on the Monge-Ampère obstacle problem \[ \det D^2 v = v^q χ_{\{v>0\}}, \quad v \geq 0 \text{ convex} \] with $q \in [0,n)$, where we studied the regularity of the strictly convex part of the free boundary. In this work, we examine the non-strictly convex part of the free boundary and establish optimal dimension bounds for its flat portion. Additionally, we investigate the strong maximum principle and a stability property for this Monge-Ampère …

A three-dimensional, multi-wavelength view and time-dependent analysis of the Milky Way's local ionized gas
Lewis McCallum, Kenneth Wood, Robert Benjamin, Dhanesh Krishnarao, Anna F. McLeod
https://arxiv.org/abs/2506.17689

A three-dimensional, multi-wavelength view and time-dependent analysis of the Milky Way's local ionized gas
This work is the continuation of a series attempting to characterize the local warm ionized medium through both static and time dependent simulations. We build upon our three dimensional, observationally-derived simulation of the local photoionized interstellar medium - based on static photoionization simulations constrained by 3D dust maps - to include metals required to predict collisionally excited optical and infrared emission lines, providing the first all-sky prediction of a series of lin…

This https://arxiv.org/abs/2304.12647 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Learned Collusion
Q-learning can be described as an all-purpose automaton that provides estimates (Q-values) of the continuation values associated with each available action and follows the naive policy of almost always choosing the action with highest Q-value. We consider a family of automata based on Q-values, whose policy may systematically favor some actions over others, for example through a bias that favors cooperation. We look for stable equilibrium biases, easily learned under converging logit/best-respo…

Pentaquarks made of light quarks and their admixture to baryons
Nicholas Miesch, Edward Shuryak, Ismail Zahed
https://arxiv.org/abs/2507.01861 https://

Pentaquarks made of light quarks and their admixture to baryons
This paper is a continuation of our studies of multiquark hadrons. The anti-symmetrization of their wavefunctions required by Fermi statistics is nontivial, as it mixes orbital, color, spin and flavor structures. In our previous papers we developed a method to find them based on the representations of the permutation group, and derived the explicit wave functions for baryons excited to the first and second shells $(L=1,2)$, tetraquarks $qq\bar q\bar q$ and hexaquarks ($6q$). Now we apply it t…

General-domain FC-based shock-dynamics solver I: Basic elements
Oscar P. Bruno, Daniel V. Leibovici
https://arxiv.org/abs/2506.16076 https://

General-domain FC-based shock-dynamics solver I: Basic elements
This contribution, Part I in a two-part article series, presents a general-domain version of the FC-SDNN (Fourier Continuation Shock-detecting Neural Network) spectral scheme for the numerical solution of nonlinear conservation laws, which is applicable under arbitrary boundary conditions and in general domains. Like the previous simple-domain contribution (Journal of Computational Physics X 15, (2022)), the present approach relies on the use of the Fourier Continuation method for accurate spec…

Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$
Yubo Jin, Jian-Shu Li, Dongwen Liu, Binyong Sun
https://arxiv.org/abs/2506.20942

Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$
In this paper, we study the special values of Rankin-Selberg L-functions as a continuation of [LLS24]. Utilizing the modular symbol approach, we prove the rationality and period relations for critical values of Rankin-Selberg L-functions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$ over any number field that contains a CM field.

XPPLORE: Import, visualize, and analyze XPPAUT data in MATLAB
Matteo Martin, Anna Kishida Thomas, George Bard Ermentrout
https://arxiv.org/abs/2507.02709 h…

XPPLORE: Import, visualize, and analyze XPPAUT data in MATLAB
The analysis of ordinary differential equation (ODE) dynamical systems, particularly in applied disciplines such as mathematical biology and neuroscience, often requires flexible computational workflows tailored to model-specific questions. XPPAUT is a widely used tool combining numerical integration and continuation methods. Various XPPAUT toolboxes have emerged to customize analyses, however, they typically rely on summary '.dat' files and cannot parse the more informative '.auto' files, whic…

This https://arxiv.org/abs/2412.15168 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions
We study the dynamic structure factor $S(k,ω)$ of the spin-1/2 chain with long-range, power-law decaying unfrustrated (sign alternating) Heisenberg interactions $J_r \sim (-1)^{r-1} r^{-α}$ by means of stochastic analytic continuation (SAC) of imaginary-time correlations computed by quantum Monte Carlo calculations. We do so in both the long-range antiferromagnetic (AFM, for $α\lesssim 2.23$) and quasi-long-range-ordered (QLRO, for $α\gtrsim 2.23$) ground-state phases, employing diffe…

Parametric formal Gevrey asymptotic expansions in two complex time variable problems
Guoting Chen, Alberto Lastra, Stephane Malek
https://arxiv.org/abs/2506.00916

Parametric formal Gevrey asymptotic expansions in two complex time variable problems
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an auxiliary problem in the Borel plane overcomes the absence of adequate domains which would guarantee summability of the formal solution. Moreover, several exponential decay rates of the difference of analytic solutions with respect to the perturbation parameter …

An optimal fractional Hardy inequality on the discrete half-line
Ujjal Das, Rub\'en de la Fuente-Fern\'andez
https://arxiv.org/abs/2507.06716 https://arxiv.org/pdf/2507.06716 https://arxiv.org/html/2507.06716
arXiv:2507.06716v1 Announce Type: new
Abstract: In the context of Hardy inequalities for the fractional Laplacian $(-\Delta_{\mathbb{N}})^{\sigma}$ on the discrete half-line $\mathbb{N}$, we provide an optimal Hardy-weight $W^{\mathrm{op}}_{\sigma}$ for exponents $\sigma\in\left(0,1\right]$. As a consequence, we provide an estimate of the sharp constant in the fractional Hardy inequality with the classical Hardy-weight $n^{-2\sigma}$ on $\mathbb{N}$. It turns out that for $\sigma =1$ the Hardy-weight $W^{\mathrm{op}}_{1}$ is pointwise larger than the optimal Hardy-weight obtained by Keller--Pinchover--Pogorzelski near infinity. As an application of our main result, we obtain unique continuation results at infinity for the solutions of some fractional Schr\"odinger equation.
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This https://arxiv.org/abs/2505.19462 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

VoiceStar: Robust Zero-Shot Autoregressive TTS with Duration Control and Extrapolation
We present VoiceStar, the first zero-shot TTS model that achieves both output duration control and extrapolation. VoiceStar is an autoregressive encoder-decoder neural codec language model, that leverages a novel Progress-Monitoring Rotary Position Embedding (PM-RoPE) and is trained with Continuation-Prompt Mixed (CPM) training. PM-RoPE enables the model to better align text and speech tokens, indicates the target duration for the generated speech, and also allows the model to generate speech w…

Global weak solutions with higher regularity to the compressible isentropic Navier-Stokes equations in 2D bounded domains involving large initial data and vacuum
Shuai Wang, Guochun Wu, Xin Zhong
https://arxiv.org/abs/2507.05608

Global weak solutions with higher regularity to the compressible isentropic Navier-Stokes equations in 2D bounded domains involving large initial data and vacuum
This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence of weak solutions with higher regularity to the compressible isentropic Navier-Stokes equations in the half-plane involving large initial data and vacuum was established. We extend such a result to the case of two-dimensional bounded simply connected convex domains under a Navier-slip boundary condition. To overcome difficulties brought by boundary, some new estimates based on the effective viscous …

On the Minimality of the Conductor in Rank Bounds for Elliptic Curves
K. Lakshmanan
https://arxiv.org/abs/2506.20175 https://arxiv.or…

On the Minimality of the Conductor in Rank Bounds for Elliptic Curves
We show that no arithmetic invariant strictly smaller than the conductor of an elliptic curve over \( \mathbb{Q} \) can appear in a functional equation governing the analytic continuation of an associated \( L \)-function of degree two. In particular, any attempt to define a modified \( L \)-function for an elliptic curve with a smaller invariant in place of the conductor leads to a contradiction with the Modularity Theorem. As a consequence, the classical upper bound \( \operatorname{rank}(E) …

This https://arxiv.org/abs/2501.19118 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
Computing dynamical response functions in interacting lattice models is a long standing challenge in condensed matter physics. In view of recent results, the dc resistivity $ρ_\mathrm{dc}$ in the weak coupling regime of the Hubbard model is of great interest, yet it is not fully understood. The challenge lies in having to work with large lattices while avoiding analytical continuation. The weak-coupling $ρ_\mathrm{dc}$ results were so far computed at the level of the Boltzmann theory and at t…

This https://arxiv.org/abs/2501.08757 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the reactivity of the non-spatial and spatial dynamics, stability analyses, and numerical continuation to uncover detailed aspects of this system's pattern-forming potential. In addition to patterning in Turing unstable parameter regimes, reactivity of the spatial s…

Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
Kai Yu, Zhiyuan Li, Yikan Liu
https://arxiv.org/abs/2506.21070

Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we giv…

Periodic solutions for p(t)-Lienard equations with a singular nonlinearity of attractive type
Petru Jebelean, Jean Mawhin, Calin Serban
https://arxiv.org/abs/2506.04927

Periodic solutions for p(t)-Lienard equations with a singular nonlinearity of attractive type
We are concerned with the existence of $T$-periodic solutions to an equation of type $$\left (|u'(t))|^{p(t)-2} u'(t) \right )'+f(u(t))u'(t)+g(u(t))=h(t)\quad \mbox{ in }[0,T]$$ where $p:[0,T]\to(1,\infty)$ with $p(0)=p(T)$ and $h$ are continuous on $[0,T]$, $f,g$ are also continuous on $[0,\infty)$, respectively $(0,\infty)$. The mapping $g$ may have an attractive singularity (i.e. $g(x) \to +\infty$ as $x\to 0+$). Our approach relies on a continuation theorem obtained in the recent …

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
Daniel V. Leibovici, Oscar P. Bruno
https://arxiv.org/abs/2506.19370

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation of the scheme with high-quality weak and strong scalability properties, and it illustrates the overall methodology for a variety of tests for the 2D Euler equations--including supersonic and hypersonic flows and shocks past obstacles with corners. The result…

Constraint Maps: Insights and Related Themes
Alessio Figalli, Andr\'e Guerra, Sunghan Kim, Henrik Shahgholian
https://arxiv.org/abs/2506.23608 https://…

Constraint Maps: Insights and Related Themes
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along the way, we include several new results of independent value. In particular, we give optimal geometric conditions on the target manifold that guarantee a unique continuation result for the projected image map. We also prove that the gradient of a minimizing har…