Tootfinder

The surprising strength of weak classifiers for validating neural posterior estimates
Vansh Bansal, Tianyu Chen, James G. Scott
https://arxiv.org/abs/2507.17026

The surprising strength of weak classifiers for validating neural posterior estimates
Neural Posterior Estimation (NPE) has emerged as a powerful approach for amortized Bayesian inference when the true posterior $p(θ\mid y)$ is intractable or difficult to sample. But evaluating the accuracy of neural posterior estimates remains challenging, with existing methods suffering from major limitations. One appealing and widely used method is the classifier two-sample test (C2ST), where a classifier is trained to distinguish samples from the true posterior $p(θ\mid y)$ versus the lear…

Semi-discrete heat equations with variable coefficients and the parametrix method
Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H. C. Pang
https://arxiv.org/abs/2506.18649

Semi-discrete heat equations with variable coefficients and the parametrix method
We develop a parametrix approach for constructing solutions and establishing grid-size independent estimates for semi-discrete heat equations with variable coefficients. While the classical continuous setting benefits from Gaussian estimates of the constant coefficient heat kernel, such estimates are not available in the semi-discrete context. To address this complication, we derive estimates involving products of heavy-tailed Lorentz (also known as Cauchy) probability densities. These Lorentzi…

Improved geometric and recollision estimates for the invariance principle of the random Lorentz gas
Raphael Winter, Karsten Matthies
https://arxiv.org/abs/2506.18539

Improved geometric and recollision estimates for the invariance principle of the random Lorentz gas
By improving geometric recollision estimates for a random Lorentz gas, we extend the timescale $T(r)$ of the invariance principle for a Lorentz gas with particle size $r$ obtained by Lutsko and Toth (2020) from $\lim_{r \rightarrow 0} T(r) r^{2} |\log(r)|^2 =0$ to $\lim_{r \rightarrow 0} T(r) r^{2} |\log(r)| =0$. We show that this is the maximal reachable timescale with the coupling of stochastic processes introduced in the original result. In our improved geometric estimate…

Intel reports Q2 revenue flat YoY at $12.9B, vs. $11.9B est., a $2.9B loss due to restructuring and impairment charges, and forecasts Q3 revenue above estimates (Michael Acton/Financial Times)
https://www.ft.com/content/1d4eeada-8d49-4827-bdfa-d93d3dd0dd95

Asymptotic estimates for solutions of inhomogeneous non-divergence diffusion equations with drifts
Luan Hoang, Akif Ibragimov
https://arxiv.org/abs/2506.19059

Asymptotic estimates for solutions of inhomogeneous non-divergence diffusion equations with drifts
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition. Starting with the reduced linear problem, we obtain the asymptotic estimates for the solutions, as time $t\to\infty$, depending on the asymptotic behavior of the forcing term and boundary data. These are established in both cases when the drifts are uniformly boun…

Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs
Feng-Yu Wang, Xiao-Yu Zhao
https://arxiv.org/abs/2506.19429

Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs
By establishing a local version of Bismut formula for Dirichlet semigroups on a regular domain, gradient estimates are derived for killed SDEs with singular drifts. As an application, the total variation distance between two solutions of killed DDSDEs is bounded above by the truncated $1$-Wasserstein distance of initial distributions, in the regular and singular cases respectively.

un_migrations: UN migration stock (2015)
A network of migration between countries, collected by the United Nations. A directed edge gives the flow of migration, and an edge property gives the number of migrants, for each given year and sex. Estimates are presented for 1990, 1995, 2000, 2005, 2010 and 2015 and are available for all countries and areas of the world. The estimates are based on official statistics on the foreign-born or the foreign population.
This network has 232 no…

Conservative fusion of unbiased partial state estimates: CI is optimal
Jochen Trumpf, Behzad Zamani, Chris Manzie
https://arxiv.org/abs/2507.16216 https://…

Conservative fusion of unbiased partial state estimates: CI is optimal
We show that Covariance Intersection (CI) is optimal amongst all conservative unbiased linear fusion rules also in the general case of information fusion of two unbiased partial state estimates, significantly generalizing the known optimality result for fusion of full state estimates. In fact, we prove the much stronger result that three different optimization problems are equivalent, namely the abstract optimal conservative unbiased linear information fusion problem with respect to a strictly …

Improving precision of cumulative incidence estimates in randomized controlled trials with external controls
Zehao Su, Helene C. W. Rytgaard, Henrik Ravn, Frank Eriksson
https://arxiv.org/abs/2506.18415

Improving precision of cumulative incidence estimates in randomized controlled trials with external controls
Augmenting the control arm in clinical trials with external data can improve statistical power for demonstrating treatment effects. In many time-to-event outcome trials, participants are subject to truncation by death. Direct application of methods for competing risks analysis on the joint data may introduce bias, for example, due to covariate shifts between the populations. In this work, we consider transportability of the conditional cause-specific hazard of the event of interest under the co…

Off-diagonal estimates of the Bergman kernel associated to Siegel varieties
Anilatmaja Aryasomayajula, Harinarayanan G
https://arxiv.org/abs/2506.17583 htt…

Off-diagonal estimates of the Bergman kernel associated to Siegel varieties
For $g\geq 2$, let $Γ\subset\mathrm{Sp}(2g,\mathbb{R})$ be a discrete subgroup, which is either a cocompact subgroup or an arithmetic subgroup without torsion elements, and let $\mathbb{H}_{g}$ denote the Siegel upper half space of genus $g$. Let $X_Γ:=Γ\backslash\mathbb{H}_{g}$ denote the quotient space, which is a complex manifold of dimension $g(g+1)/2$. Let $Ω_{X_Γ}$ denote the cotangent bundle, and let $\ell:=\mathrm{det}(Ω_{X_Γ})$ denote the determinant line bundle of $Ω_{X_Γ}$. …

Poverty Targeting with Imperfect Information
Juan C. Yamin
https://arxiv.org/abs/2506.18188 https://arxiv.org/pdf/2506.18188

Poverty Targeting with Imperfect Information
A key challenge for targeted antipoverty programs in developing countries is that policymakers must rely on estimated rather than observed income, which leads to substantial targeting errors. I propose a statistical decision framework in which a benevolent planner, subject to a budget constraint and equipped only with noisy income estimates, allocates cash transfers to the poorest individuals. In this setting, the commonly used plug-in rule, which allocates transfers based on point estimates, i…

Sharp $L^p$-estimates for wave equation on $ax b$ groups
Yunxiang Wang, Lixin Yan
https://arxiv.org/abs/2506.17531 https://arxiv.org/…

Sharp $L^p$-estimates for wave equation on $ax+b$ groups
Let $G$ be the group $\mathbb{R}_+\ltimes \mathbb{R}^n$ endowed with Riemannian symmetric space metric $d$ and the right Haar measure $\mathrm{d} ρ$ which is of $ax+b$ type, and $L$ be the positive definite distinguished left invariant Laplacian on $G$. Let $u=u(t,\cdot)$ be the solution of $u_{tt}+Lu=0$ with initial conditions $u|_{t=0}=f$ and $u_t|_{t=0}=g$. In this article we show that for a fixed $t \in{\mathbb R}$ and every $1

Near-optimal estimates for the $\ell^p$-Lipschitz constants of deep random ReLU neural networks
Sjoerd Dirksen, Patrick Finke, Paul Geuchen, Dominik St\"oger, Felix Voigtlaender
https://arxiv.org/abs/2506.19695

Near-optimal estimates for the $\ell^p$-Lipschitz constants of deep random ReLU neural networks
This paper studies the $\ell^p$-Lipschitz constants of ReLU neural networks $Φ: \mathbb{R}^d \to \mathbb{R}$ with random parameters for $p \in [1,\infty]$. The distribution of the weights follows a variant of the He initialization and the biases are drawn from symmetric distributions. We derive high probability upper and lower bounds for wide networks that differ at most by a factor that is logarithmic in the network's width and linear in its depth. In the special case of shallow networks, we …

PDD Holdings, which owns Pinduoduo and Temu, reports Q2 revenue up 7% YoY to ~$14.53B, above est., and net income down 5% YoY to ~$4.5B, driven by discounts (Reuters)
https://www.reuters.com/world/china/temu-owner-pdd-tops-quarterly-revenue-est…

Metric Poissonian pair correlation for real sequences and energy estimates
Bryce Kerr, Hongliang Wang
https://arxiv.org/abs/2506.17031 https://

Metric Poissonian pair correlation for real sequences and energy estimates
In this paper, we establish new conditions under which a sequence of real numbers has metric Poissonian pair correlation. Our conditions improve upon results of Aistleitner, El-Baz and Munsch, and resolve one of their open problems for sequences that grow faster than a quadratic polynomial. As applications, we show that quantitatively convex and polynomial sequences are metric Poissonian.

It’s official. Spain will not be part of the 5% NATO club anytime soon. #nato
“Last year, Spain spent 1.28% per NATO estimates on military expenditure, making it the alliance’s lowest spender. In April, Sšnchez announced that the government would raise defense spending to 2% this year, a move that he received pushback for at home including from some allies.”
https://flipboard.com/@associatedpress/international-news-miluvhmaz/-/a-5474v_JLSsmGm00Dw93SHg:a:3199720-/0

Modular Robot and Landmark Localisation Using Relative Bearing Measurements
Behzad Zamani, Jochen Trumpf, Chris Manzie
https://arxiv.org/abs/2507.18070 https://

Modular Robot and Landmark Localisation Using Relative Bearing Measurements
In this paper we propose a modular nonlinear least squares filtering approach for systems composed of independent subsystems. The state and error covariance estimate of each subsystem is updated independently, even when a relative measurement simultaneously depends on the states of multiple subsystems. We integrate the Covariance Intersection (CI) algorithm as part of our solution in order to prevent double counting of information when subsystems share estimates with each other. An alternative …

Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets
Noga Alon, Shakhar Smorodinsky
https://arxiv.org/abs/2506.17777 https…

Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets
We define and study an extension of the notion of the VC-dimension of a hypergraph and apply it to establish a Tverberg type theorem for unions of convex sets. We also prove a new Radon type theorem for unions of convex sets, vastly improving the estimates in an earlier result of Bárány and Kalai.

Effective bounds for polynomial systems defined over the rationals
Teresa Krick
https://arxiv.org/abs/2506.18144 https://arxiv.org/pd…

Effective bounds for polynomial systems defined over the rationals
This survey paper was primarily written as as the support for a course pesented at the JNCF2025: it aims to present some material that illustrates the kind of estimates one can obtain in effective algebraic geometry, for affine polynomial equation systems defined over the rational numbers Q, and focuses on the case of finite varieties.

The solution (or at least a step towards one) would have been the treaty Iran and USA signed, but which Trump withdrew from. https://mastodon.social/@jmcrookston/114727962307106386

ChatGPT 5 power consumption could be as much as eight times higher than GPT 4
— Research institute estimates medium-sized GPT-5 response can consume up to 40 watt-hours of electricity

ChatGPT 5 power consumption could be as much as eight times higher than GPT 4 — research institute estimates medium-sized GPT-5 response can consume up to 40 watt-hours of electricity
But the figures rely on hardware and usage assumptions that may be inaccurate.

Error estimates and adaptivity for a least-squares method applied to the Monge-Amp\`ere equation
Alexandre Caboussat, Anna Peruso, Marco Picasso
https://arxiv.org/abs/2507.17569

Error estimates and adaptivity for a least-squares method applied to the Monge-Ampère equation
We introduce novel a posteriori error indicators for a nonlinear least-squares solver for smooth solutions of the Monge--Ampère equation on convex polygonal domains in $\mathbb{R}^2$. At each iteration, our iterative scheme decouples the problem into (i) a pointwise nonlinear minimization problem and (ii) a linear biharmonic variational problem. For the latter, we derive an equivalence to a biharmonic problem with Navier boundary conditions and solve it via mixed piecewise-linear finite elemen…

Estimating the variance-covariance matrix of two-step estimates of latent variable models: A general simulation-based approach
Roberto Di Mari, Jouni Kuha
https://arxiv.org/abs/2507.16324

Estimating the variance-covariance matrix of two-step estimates of latent variable models: A general simulation-based approach
We propose a general procedure for estimating the variance-covariance matrix of two-step estimates of structural parameters in latent variable models. The method is partially simulation-based, in that it includes drawing simulated values of the measurement parameters of the model from their sampling distribution obtained from the first step of two-step estimation, and using them to quantify part of the variability in the parameter estimates from the second step. This is asymptotically equal wit…

On the Penumbra-to-Umbra Ratio from 1660 to 1676
Nadezhda Zolotova, Mikhail Vokhmyanin
https://arxiv.org/abs/2506.18361 https://arxiv…

On the Penumbra-to-Umbra Ratio from 1660 to 1676
Sunspot engravings made in the Maunder minimum are used to evaluate the fine structure of sunspots. Based on 78 images of the full solar disk and 77 images of individual sunspots, we have evaluated the ratio of penumbral-to-umbral area (P/U) to be 4.2 $\pm$ 2.5 and 3.8 $\pm$ 2.3, respectively. These results are consistent with previous estimates before, during, and after the Maunder minimum, as well as with the P/U ratio observed in the largest sunspot groups in solar cycle 24. This suggests th…

Negatively curved K\"ahler metrics on total spaces of a class of vector bundles
Hanyu Wu, Bo Yang
https://arxiv.org/abs/2508.16354 https://arxiv.org/p…

Negatively curved Kähler metrics on total spaces of a class of vector bundles
In this paper we show an abundance of complete Kähler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved Kähler metrics. We prove dimension estimates on holomorphic functions on these manifolds, as well as Liouville theorems for holomorphic mappings between them.

"Researchers develop satellite-based method to boost accuracy of coal plant CO₂ emission estimates"
#FossilFuels #Emissions #Climate

Researchers develop satellite-based method to boost accuracy of coal plant CO₂ emission estimates
A new satellite-based method developed by Chinese researchers improves the accuracy of carbon dioxide (CO2) emission estimates from coal-fired power plants, according to a study published in Environmental Science & Technology.

Electron-muon conversion in nuclei and rare decays induced by LFV dark photon
Alexey S. Zhevlakov, Sergey Kuleshov, Valery E. Lyubovitskij, Evgenie O. Oleynik
https://arxiv.org/abs/2507.17733

Electron-muon conversion in nuclei and rare decays induced by LFV dark photon
We study lepton flavor violation (LFV) effects occurring in the $e-μ$ conversion in nuclei and in the rare radiative decays $η(η') \to γμe$ of the $η$ and $η'$ mesons with a special impact of the sub-GeV mass vector mediator (dark photon). In the case of the lepton conversion we make estimates for running and future experiments operating with electron beams at fixed target. Obtained results are implemented in analysis of the LFV decays $η(η') \to γμe$. In particular, we derive the fo…

Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups
Martin R Bridson
https://arxiv.org/abs/2507.17598 https://arxiv.org/pdf/2507.…

Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups
We investigate the complexity of the conjugacy problem for fibre products in torsion-free hyperbolic groups. Let $G$ be a torsion-free hyperbolic group and let $P

CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates
Tianyu Chen, Vansh Bansal, James G. Scott
https://arxiv.org/abs/2507.17030

CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates
We consider the problem of validating whether a neural posterior estimate \( q(θ\mid x) \) is an accurate approximation to the true, unknown true posterior \( p(θ\mid x) \). Existing methods for evaluating the quality of an NPE estimate are largely derived from classifier-based tests or divergence measures, but these suffer from several practical drawbacks. As an alternative, we introduce the \emph{Conditional Localization Test} (CoLT), a principled method designed to detect discrepancies bet…

Orthonormal Strichartz estimates on torus and waveguide manifold and applications
Divyang G. Bhimani, Subhash. R. Choudhary
https://arxiv.org/abs/2507.16712

Orthonormal Strichartz estimates on torus and waveguide manifold and applications
We establish orthonormal Strichartz estimates for the fractional Schrödinger equations on torus and waveguide manifold. In the process, we also improve $\ell^2$ decoupling inequality and establish classical fractional Strichartz estimates on waveguide manifold. This maybe of independent interest. As an application, we establish local well-posednes for the Hartree equations with infinitely many particles with non-trace class initial data.

Conformal Safety Shielding for Imperfect-Perception Agents
William Scarbro, Calum Imrie, Sinem Getir Yaman, Kavan Fatehi, Corina S. Pasareanu, Radu Calinescu, Ravi Mangal
https://arxiv.org/abs/2506.17275

Conformal Safety Shielding for Imperfect-Perception Agents
We consider the problem of safe control in discrete autonomous agents that use learned components for imperfect perception (or more generally, state estimation) from high-dimensional observations. We propose a shield construction that provides run-time safety guarantees under perception errors by restricting the actions available to an agent, modeled as a Markov decision process, as a function of the state estimates. Our construction uses conformal prediction for the perception component, which…

The Renormalized Yukawa Hamiltonian: Spectrum, Parton Distribution Functons, and Resource Estimates for Quantum Simulation
Carter M. Gustin, Kamil Serafin, William A. Simon, Alexis Ralli, Gary R. Goldstein, Peter J. Love
https://arxiv.org/abs/2508.14837

The Renormalized Yukawa Hamiltonian: Spectrum, Parton Distribution Functons, and Resource Estimates for Quantum Simulation
We apply the Renormalization Group Procedure for Effective Particles (RGPEP) to the front form Yukawa Hamiltonian, yielding a renormalized (effective) Hamiltonian, accurate up to second order in the coupling strength. Subsequently, we examine the spectrum and parton distribution functions produced by the renormalized Hamiltonian, and show that the addition of counterterms leads to finite results. Resource estimates for quantum simulation are calculated for a single `Ladder Operator Block Encodi…

Ejecta Mass Estimates from the DART Impact Plume Inferred from LICIACube Images: #DART Impact to Inform Planetary Defense: https://science.nasa.gov/missions/dart/close-up-views-of-nasas-dart-impact-to-inform-planetary-defense/

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
Adrian Padilla-Segarra, Pascal Noble, Olivier Roustant, \'Eric Savin
https://arxiv.org/abs/2507.17582

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions, or kernels, to obtain such estimates. In this paper, we derive physics-informed kernels for simulating two-dimensional velocity fields of an incompressible (divergence-free) flow around aerodynamic profiles. These kernels allow to define Gaussian process pri…

Crypto folks (maybe @… ): what's the latest estimates on difficulty of real world factorization attacks on a single 1024 bit RSA modulus?
Like, i know it's "plausible enough for a state level attacker to break that you shouldn't be using 1024 bit keys" but nobody's ever demonstrated an actual factorization yet.
So in terms of co…

And yes, the US Congress, with many #Democrats voting in favor, continues to send weapons to Israel. Why?
“If they recycle the Israeli bombs that didn’t explode there is an endless supply of explosives, and the genocide provides an infinite recruiting pool for new members.”
"American intelligence estimates suggest Hamas has recruited 15,000 operatives during the war, about twice a…

And yes, the US Congress, with many #Democrats voting in favor, continues to send weapons to Israel. Why?
“If they recycle the Israeli bombs that didn’t explode there is an endless supply of explosives, and the genocide provides an infinite recruiting pool for new members.”
"American intelligence estimates suggest Hamas has recruited 15,000 operatives during the war, about twice a…

A Weighted Likelihood Approach Based on Statistical Data Depths
Claudio Agostinelli, Ayanendranath Basu, Giulia Bertagnolli, Arun Kumar Kuchibhotla
https://arxiv.org/abs/2507.16998

A Weighted Likelihood Approach Based on Statistical Data Depths
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical depth of each data point relative to the model, as opposed to the sample. An observation is considered regular when the corresponding difference of these two depths is close to zero. When this difference is large the observation score contribution is downweight…

Quadratic estimates for the $H^\infty$-functional calculus of bisectorial Clifford operators
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
https://arxiv.org/abs/2506.16783

Quadratic estimates for the $H^\infty$-functional calculus of bisectorial Clifford operators
The $H^\infty$-functional calculus is a two-step procedure, introduced by A. McIntosh, that allows the definition of functions of sectorial operators in Banach spaces. It plays a crucial role in the spectral theory of differential operators, as well as in their applications to evolution equations and various other fields of science. An extension of the $H^\infty$-functional calculus also exists in the hypercomplex setting, where it is based on the notion of $S$-spectrum. Originally this was don…

SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction
Lukas Radl, Felix Windisch, Thomas Deixelberger, Jozef Hladky, Michael Steiner, Dieter Schmalstieg, Markus Steinberger
https://arxiv.org/abs/2506.19139

SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction
Recent advances in 3D Gaussian representations have significantly improved the quality and efficiency of image-based scene reconstruction. Their explicit nature facilitates real-time rendering and fast optimization, yet extracting accurate surfaces - particularly in large-scale, unbounded environments - remains a difficult task. Many existing methods rely on approximate depth estimates and global sorting heuristics, which can introduce artifacts and limit the fidelity of the reconstructed mesh.…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[2/8]:
- How to Leverage Predictive Uncertainty Estimates for Reducing Catastrophic Forgetting in Online C...
Giuseppe Serra, Ben Werner, Florian Buettner

Relativistic Calculations of Energy Levels, Field Shift Factors, and Polarizabilities of Mercury and Copernicium
Hongxu Liu, Jize Han, Yanmei Yu, Yanfeng Ge, Yong Liu, Zhiguo Huang
https://arxiv.org/abs/2507.18490 https://arxiv.org/pdf/2507.18490 https://arxiv.org/html/2507.18490
arXiv:2507.18490v1 Announce Type: new
Abstract: Mercury (Hg) and superheavy element copernicium (Cn) are investigated using equation-of-motion relativistic coupled-cluster (EOM-RCC) and configuration interaction plus many-body perturbation theory (CI MBPT) methods. Key atomic properties including ionization potentials (IP), excitation energies (EEs), isotope field shift factors (F), and static electric dipole polarizabilities ({\alpha}) are calculated for ground and low-lying excited states. To evaluate the theoretical accuracy, calculations for both Hg and Cn are performed, with experimental data of Hg serving as benchmarks. Furthermore, basis set dependence has been systematically evaluated in the EOM-RCC calculations, with corresponding uncertainty estimates having been provided. The calculated atomic properties could provide valuable insights into the electronic structure and chemical behavior of superheavy elements.
toXiv_bot_toot

The Theory of Economic Complexity
C\'esar A. Hidalgo, Viktor Stojkoski
https://arxiv.org/abs/2506.18829 https://arxiv.org/pdf/250…

The Theory of Economic Complexity
Economic complexity estimates rely on eigenvectors derived from matrices of specialization to explain differences in economic growth, inequality, and sustainability. Yet, despite their widespread use, we still lack a principled theory that can deduce these eigenvectors from first principles and place them in the context of a mechanistic model. Here, we calculate these eigenvectors analytically for a model where the output of an economy in an activity increases with the probability the economy i…

On MAP estimates and source conditions for drift identification in SDEs
Daniel Tenbrinck, Nikolas Uesseler, Philipp Wacker, Benedikt Wirth
https://arxiv.org/abs/2507.18443 https…

On MAP estimates and source conditions for drift identification in SDEs
We consider the inverse problem of identifying the drift in an SDE from $n$ observations of its solution at $M+1$ distinct time points. We derive a corresponding MAP estimate, we prove differentiability properties as well as a so-called tangential cone condition for the forward operator, and we review the existing theory for related problems, which under a slightly stronger tangential cone condition would additionally yield convergence rates for the MAP estimate as $n\to\infty$. Numerical simul…

Rate estimates for weighted total variation norm in terms of Wasserstein distances
Iv\'an Ivkovic, Mikl\'os R\'asonyi
https://arxiv.org/abs/2506.16088

Rate estimates for weighted total variation norm in terms of Wasserstein distances
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment conditions. We apply our results to convergence of functionals in Malliavin calculus.

Optimal Calibrated Signaling in Digital Auctions
Zhicheng Du, Wei Tang, Zihe Wang, Shuo Zhang
https://arxiv.org/abs/2507.17187 https://arxiv.org/pdf/2507.1…

Optimal Calibrated Signaling in Digital Auctions
In digital advertising, online platforms allocate ad impressions through real-time auctions, where advertisers typically rely on autobidding agents to optimize bids on their behalf. Unlike traditional auctions for physical goods, the value of an ad impression is uncertain and depends on the unknown click-through rate (CTR). While platforms can estimate CTRs more accurately using proprietary machine learning algorithms, these estimates/algorithms remain opaque to advertisers. This information as…

Assessment of the Earth orientation parameter accuracy from concurrent VLBI observations
Leonid Petrov, Christian Ploetz, Matthias Schartner
https://arxiv.org/abs/2506.15859

Assessment of the Earth orientation parameter accuracy from concurrent VLBI observations
We have assessed accuracy of estimates of Earth orientation parameters (EOP) determined from several very long baseline interferometry (VLBI) observing programs that ran concurrently at different networks. We consider that the root mean square of differences in EOP estimates derived from concurrent observations is a reliable measure of accuracy. We confirmed that formal errors based on the assumption that the noise in observables is uncorrelated are close to useless. We found no evidence that a…

Index insurance under demand and solvency constraints
Olivier Lopez (CREST), Daniel Nkameni (CREST)
https://arxiv.org/abs/2507.18240 https://arxiv.org/pdf/…

Index insurance under demand and solvency constraints
Index insurance is often proposed to reduce protection gaps, especially for emerging risks. Unlike traditional insurance, it bases compensation on a measurable index, enabling faster payouts and lower claim management costs. This approach benefits both policyholders, through quick payments, and insurers, through reduced costs and better risk control due to reliable data and robust statistical estimates. An important difference with the concept of Cat Bonds is that the feasibility of such covera…

Bangladesh turns to nature for biodegradable plates to replace plastic ones https://news.mongabay.com/short-article/2025/07/bangladesh-turns-to-nature-for-biodegradable-plants-to-replace-plastic-ones/

Bangladesh turns to nature for biodegradable plates to replace plastic ones
In Bangladesh, disposable tableware, including plates made of areca palm leaves, is gaining popularity as a good alternative to single-use plastic during social gatherings and festival celebrations, Mongabay’s Abu Siddique reported in May. A survey from 2018 estimates that Bangladesh used around 250 metric tons of single-use plastic tableware and straws every month. However, since […]

Density estimates for Ginzburg-Landau energies with degenerate double-well potentials
Ovidiu Savin, Chilin Zhang
https://arxiv.org/abs/2506.17000 https://

Density estimates for Ginzburg-Landau energies with degenerate double-well potentials
We consider a class of Allen-Cahn equations associated with Ginzburg-Landau energies involving degenerate double-well potentials that vanish of order $m$ at the minima \begin{equation} J(v,Ω)=\int_Ω\Big\{|\nabla v|^{p}+(1-v^{2})^{m}\Big\}dx,\quad 1

Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces
Ronno Das, Brian Lehmann, Sho Tanimoto, Philip Tosteson
https://arxiv.org/abs/2506.17071

Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces
We prove a version of Manin's conjecture (over $\mathbb{F}_{q}$ for $q$ large) and the Cohen--Jones--Segal conjecture (over $\mathbb{C}$) for maps from rational curves to split quartic del Pezzo surfaces. The proofs share a common method which builds upon prior work of the first and fourth authors. The main ingredients of this method are (i) the construction of bar complexes formalizing the inclusion-exclusion principle and its point counting estimates, (ii) dimension estimates for spaces of ra…

The unreasonable likelihood of being: origin of life, terraforming, and AI
Robert G. Endres
https://arxiv.org/abs/2507.18545 https://arxiv.org/pdf/2507.185…

The unreasonable likelihood of being: origin of life, terraforming, and AI
The origin of life on Earth via the spontaneous emergence of a protocell prior to Darwinian evolution remains a fundamental open question in physics and chemistry. Here, we develop a conceptual framework based on information theory and algorithmic complexity. Using estimates grounded in modern computational models, we evaluate the difficulty of assembling structured biological information under plausible prebiotic conditions. Our results highlight the formidable entropic and informational barri…

🌍 Satellite data reveal African grasslands' carbon uptake rises with rainfall, unlike forests and savannas
https://phys.org/news/2025-07-satellite-reveal-african-grasslands-carbon.html

Satellite data reveal African grasslands' carbon uptake rises with rainfall, unlike forests and savannas
Africa is a source of uncertainty in carbon cycle calculations. By some estimates, the continent's landscapes emit 2.1 billion tons more carbon dioxide than they take up each year—about equal to 1.5 times the annual emissions from coal-fired power plants. But other estimates are almost the complete opposite, suggesting that the continent's copious plant matter takes up 2.0 billion more tons of carbon dioxide per year than it releases.

Transport Properties of QGP within a Bayesian Holographic QCD Model
Bing Chen, Liqiang Zhu, Xun Chen, Defu Hou, Xurong Chen
https://arxiv.org/abs/2508.16167 https://

Transport Properties of QGP within a Bayesian Holographic QCD Model
Using a holographic QCD model augmented by Bayesian inference, we calculate key transport coefficients of the quark-gluon plasma (QGP)$\text{-}$including the drag force, jet quenching parameter, heavy quark diffusion coefficient, and shear and bulk viscosities$\text{-}$at finite temperature and chemical potential. Posterior parameter distributions at the 68\% and 95\% confidence levels (CL), as well as the maximum a posteriori (MAP) estimates, are employed to quantify uncertainties. Our finding…

un_migrations: UN migration stock (2015)
A network of migration between countries, collected by the United Nations. A directed edge gives the flow of migration, and an edge property gives the number of migrants, for each given year and sex. Estimates are presented for 1990, 1995, 2000, 2005, 2010 and 2015 and are available for all countries and areas of the world. The estimates are based on official statistics on the foreign-born or the foreign population.
This network has 232 no…

Regularity of the score function in generative models
Arthur St\'ephanovitch
https://arxiv.org/abs/2506.19559 https://arxiv.org/p…

Regularity of the score function in generative models
We study the regularity of the score function in score-based generative models and show that it naturally adapts to the smoothness of the data distribution. Under minimal assumptions, we establish Lipschitz estimates that directly support convergence and stability analyses in both diffusion and ODE-based generative models. In addition, we derive higher-order regularity bounds, which simplify existing arguments for optimally approximating the score function using neural networks.

A remark on the majorant property for random sets
Hongki Jung
https://arxiv.org/abs/2507.16935 https://arxiv.org/pdf/2507.16935

A remark on the majorant property for random sets
We improve upon the majorant estimates introduced by Mockenhaupt and Schlag by applying Bourgain's $Λ(p)$ property to random sets.

Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix
Alexander V. Sobolev
https://arxiv.org/abs/2506.16178

Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix
Consider a bound state (an eigenfunction) $ψ$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $γ$ and of the one-particle kinetic energy density matrix $τ$ associated with $ψ$. The paper contains two results. First, we obtain the bounds $λ_k(γ)\le C_1 k^{-8/3}$ and $λ_k(τ)\le C_2 k^{-2}$ with some positive constants $C_1, C_2$ that depend explicitly on the eigenfunction $ψ$. The sharpness of these bounds is confirmed by the asymptotic results obta…

PS-GS: Gaussian Splatting for Multi-View Photometric Stereo
Yixiao Chen, Bin Liang, Hanzhi Guo, Yongqing Cheng, Jiayi Zhao, Dongdong Weng
https://arxiv.org/abs/2507.18231 https:…

PS-GS: Gaussian Splatting for Multi-View Photometric Stereo
Integrating inverse rendering with multi-view photometric stereo (MVPS) yields more accurate 3D reconstructions than the inverse rendering approaches that rely on fixed environment illumination. However, efficient inverse rendering with MVPS remains challenging. To fill this gap, we introduce the Gaussian Splatting for Multi-view Photometric Stereo (PS-GS), which efficiently and jointly estimates the geometry, materials, and lighting of the object that is illuminated by diverse directional ligh…

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
Davide Addona, Vincenzo Leone, Luca Lorenzi, Abdelaziz Rhandi
https://arxiv.org/abs/2507.16368

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for every $p\in (1,\infty)$. We apply this result to the elliptic operator $-{\rm div}(Q\nabla)+V$, where the potential term V is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb R^d)$ and, for almost every $x\in \mathbb R^d$, $V(x)$ is a symm…

$\mathrm{GL}_n$ large sieves and density estimates via positive semi-definiteness
Alexandru Pascadi, Jesse Thorner
https://arxiv.org/abs/2508.14888 https://

$\mathrm{GL}_n$ large sieves and density estimates via positive semi-definiteness
Let $\mathfrak{F}_n$ be the set of unitary cuspidal automorphic representations of $\mathrm{GL}_n$ over a number field $F$, and let $\mathcal{S}\subseteq\mathfrak{F}_n$ be a finite subset. Given $π_0\in\mathfrak{F}_{n_0}$, we establish large sieve inequalities for the families $\{L(s,π)\colon π\in\mathcal{S}\}$ and $\{L(s,π\timesπ_0)\colon π\in\mathcal{S}\}$ that, unlike previous results, are independent of progress towards the generalized Ramanujan conjecture and simultaneously handle th…

Palo Alto Networks reports Q4 revenue up 16% YoY to $2.54B, vs. $2.5B est., and Q1 and FY 2026 guidance above estimates; PANW jumps 4% after hours (Samantha Subin/CNBC)
https://www.cnbc.com/2025/08/18/palo-alto-panw-earnings-q4-2025.html

Palo Alto Networks reports earnings beat, says founder Nir Zuk retiring from company
Palo Alto Networks surpassed Wall Street's fiscal fourth-quarter estimates and issued upbeat guidance.

Green's function and volume noncollapsing estimates for the K\"ahler-Ricci flow
Weiqi Zhang, Yashan Zhang
https://arxiv.org/abs/2508.13646 https://

Green's function and volume noncollapsing estimates for the Kähler-Ricci flow
We prove a local volume noncollapsing property for the long-time Kähler-Ricci flow on a minimal Kähler manifold, improving previous results of Guo-Phong-Song-Sturm, Guedj-Tô and Vu. Similar result is also proved for a twisted Kähler-Ricci flow on non-minimal Kähler manifolds. In the course of proof, we develop new Green's function estimates for a general Kähler family under the $L^{p>1}$ and $L^1(\log L)^{q>n}$ volume density conditions.

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
Hedayat Fathi, Marzia A. Cremona, Federico Severino
https://arxiv.org/abs/2506.17773

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. …

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and {\it Gaia} DR3 parallaxes. III. Main-sequence stars
G. Valle, M. Dell'Omodarme, P. G. Prada Moroni, S. Degl'Innocenti
https://arxiv.org/abs/2506.15462

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and {\it Gaia} DR3 parallaxes. III. Main-sequence stars
We compare the radii derived from the asteroseismic scaling relations with those from surface brightness-colour relations (SBCRs) combined with the Gaia DR3 parallaxes for main-sequence (MS) stars. The atmospheric and asteroseismic parameters were sourced from the recently released KEYSTONE catalogue and matched to Gaia DR3 and TESS Input Catalog v8.2. We computed SBCR-based radii using two different SBCRs, and estimated their relative differences with respect to radius estimates from asterosei…

Normal and Dynamical Typicality in a Random Matrix Model
L\'aszl\'o Erd\H{o}s, Joscha Henheik, Cornelia Vogel
https://arxiv.org/abs/2506.17177 http…

Normal and Dynamical Typicality in a Random Matrix Model
We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices [arXiv:2403.10359] and an intricate analysis of the deterministic approximation.

On the minimal integral energy of majorants of the Wiener process
Sergey Nikitin
https://arxiv.org/abs/2507.17468 https://arxiv.org/pdf/2507.17468

On the minimal integral energy of majorants of the Wiener process
We consider the asymptotic behavior (over long time intervals) of the minimal integral energy \[ |h|_T^ψ= \int_0^T ψ(h^\prime(t)) \, \mathrm{d}t \] of majorants of the Wiener process $ W(\cdot) $ satisfying the constraints $ h(0) = r $, $ h(t) \geq W(t) $ for $ 0 \leq t \leq T $. The results significantly generalize previous asymptotic estimates obtained for the case of kinetic energy $ ψ(u) = u^2 $, revealing that this case, where the minimal energy grows logarithmically, is a cri…

Strichartz estimates for higher order Schr\"odinger equations with Partial regular initial data
Vishvesh Kumar, Shyam Swarup Mondal, Iswarya Sitiraju, Manli Song
https://arxiv.org/abs/2508.15670

Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
In this paper, we establish refined Strichartz estimates for higher-order Schrödinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev regularity but only regularity with respect to a subset of the spatial variables. As an application of these estimates, we investigate the well-posedness of nonlinear Schrödinger equations with power-type nonlinearities. In addition, we extend our analysis to t…

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs
Thomas Hangelbroek, Francis J. Narcowich, Joseph D. Ward
https://arxiv.org/abs/2507.15137

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs
In this paper, a theoretical framework is presented for the use of a Kansa-like method to numerically solve elliptic partial differential equations on spheres and other manifolds. The theory addresses both the stability of the method and provides error estimates for two different approximation methods. A Kansa-like matrix is obtained by replacing the test point set $X$, used in the traditional Kansa method, by a larger set $Y$, which is a norming set for the underlying trial space…

Calibrated and uncertain? Evaluating uncertainty estimates in binary classification models
Aurora Grefsrud, Nello Blaser, Trygve Buanes
https://arxiv.org/abs/2508.11460 https://…

Calibrated and uncertain? Evaluating uncertainty estimates in binary classification models
Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning techniques, uncertainty quantification has become exceedingly difficult and a plethora of techniques have been proposed. In this case study, we use the unifying framework of approximate Bayesian inference combined with empirical tests on carefully created synthe…

Model-robust standardization in stepped wedge designs
Xi Fang, Xueqi Wang, Patrick J. Heagerty, Bingkai Wang, Fan Li
https://arxiv.org/abs/2507.17190 https://

Model-robust standardization in stepped wedge designs
Stepped-wedge cluster-randomized trials (SW-CRTs) are widely used in healthcare and implementation science, providing an ethical advantage by ensuring all clusters eventually receive the intervention. The staggered rollout of treatment introduces complexities in defining and estimating treatment effect estimands, particularly under informative sizes. Traditional model-based methods, including generalized estimating equations (GEE) and linear mixed models (LMM), produce estimates that depend on …

Weighted $L^2$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions
Zhenbin Cao, Jingyue Li, Changxing Miao, Yixuan Pang
https://arxiv.org/abs/2506.18657

Weighted $L^2$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions
We systematically study weighted $L^2$ restriction for quadratic manifolds of arbitrary codimensions by sharp uniform Fourier decay estimates and a refinement of the Du-Zhang method. Comparison with prior results is also discussed. In addition,we obtain an almost complete relation diagram for all existing nondegeneracy conditions for quadratic manifolds of arbitrary codimensions. These conditions come from various topics in harmonic analysis related to "curvature": Fourier restriction, decoupli…

Strichartz estimates involving orthonormal systems at the critical summability exponent
Guoxia Feng, Manli Song, Huoxiong Wu
https://arxiv.org/abs/2507.14974

Strichartz estimates involving orthonormal systems at the critical summability exponent
The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schrödinger operator $e^{itΔ}$ with initial data from the homogeneous Sobolev space $\dot{H}^s (\mathbb{R}^n)$. We prove new global strong-type orthonormal Strichartz estimates in the interior of $ODCA$ at the optimal summability exponent $α=q$, thereby substantially supplymenting the work of Bez-Hong-Lee-Nakamura-Sawano \cite{Bez-Hong-Lee-Nakamura-Sawano}. …

Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates
Tianhao Hu, Xinchi Huang, Bangti Jin, Qimeng Quan, Zhi Zhou
https://arxiv.org/abs/2508.15406

Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and Hölder stability for the inverse problem with and without boundary conditions, respectively, using suitable Carleman estimates. Then we propose a numerical approach for solving the inverse problem using conforming finite element approximations in both time and space. Mor…

The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,\sigma}$ open sets
Kyeong-Hun Kim, Junhee Ryu
https://arxiv.org/abs/2507.17166

The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,σ}$ open sets
This paper provides a comprehensive Sobolev regularity theory for the Dirichlet problem of stochastic partial differential equations in $C^{1,σ}$ open sets. We consider substantially large classes of nonlocal operators and generalized Gaussian noise. Our main results include the existence and uniqueness of strong solutions in weighted Sobolev spaces, along with maximal $L_p$-regularity estimates for the solutions.

Spatialize v1.0: A Python/C Library for Ensemble Spatial Interpolation
Alvaro F. Ega\~na, Alejandro Ehrenfeld, Felipe Garrido, Mar\'ia Jes\'us Valenzuela, Juan F. S\'anchez-P\'erez
https://arxiv.org/abs/2507.17867

Spatialize v1.0: A Python/C++ Library for Ensemble Spatial Interpolation
In this paper, we present Spatialize, an open-source library that implements ensemble spatial interpolation, a novel method that combines the simplicity of basic interpolation methods with the power of classical geostatistical tools, like Kriging. It leverages the richness of stochastic modelling and ensemble learning, making it robust, scalable and suitable for large datasets. In addition, Spatialize provides a powerful framework for uncertainty quantification, offering both point estimates an…

Shi-type and Hamilton-type gradient estimates for a general parabolic equation under compact Finsler $CD(-K,N)$ geometric flows
Yijie Miao, Bin Shen
https://arxiv.org/abs/2506.14776

Shi-type and Hamilton-type gradient estimates for a general parabolic equation under compact Finsler $CD(-K,N)$ geometric flows
Recently, the Li-Yau-type gradient estimates for positive solutions to parabolic equations \begin{equation} \partial_t u=Δu+\mathcal{R}_1u+\mathcal{R}_2u^α+\mathcal{R}_3u(\log u)^β,\notag \end{equation} under the general compact Finsler $CD(-K,N)$ geometric flow are studied. Here $\mathcal{R}_1$,$\mathcal{R}_2$,$\mathcal{R}_3$ $\in$ $ C^{1}(M,[0,T])$, $α$ and $β$ are both positive constants, $T$ is the maximal existence time for the flow. However, compared with the Riemannian ca…

Conditional estimates on the argument of Dirichlet $L$-functions with applications to low-lying zeros
Tianyu Zhao
https://arxiv.org/abs/2508.13301 https://…

Conditional estimates on the argument of Dirichlet $L$-functions with applications to low-lying zeros
Under the generalized Riemann hypothesis, we use Beurling-Selberg extremal functions to bound the mean and mean square of the argument of Dirichlet $L$-functions to a large prime modulus $q$. As applications, we give alternative proofs of several results on low-lying zeros of $L(s,χ)$ and obtain a new lower bound on the proportion of $L(s,χ)$ modulo $q$ with zeros close to the central point. In particular, we show conditionally that for any $β>1/4$, there exist a positive proportion of Diric…

Google releases a study saying a median Gemini text prompt uses 0.26mm of water and makes ~0.03g CO2; critics call it misleading for omitting indirect water use (Justine Calma/The Verge)
https://www.theverge.com/report/763080/google-ai-gemini-water-energy…

Google says a typical AI text prompt only uses 5 drops of water — experts say that’s misleading
Google estimates that a Gemini text prompt uses a minimal amount of water and energy, but experts say the study paints an incomplete picture of AI’s environmental toll.

un_migrations: UN migration stock (2015)
A network of migration between countries, collected by the United Nations. A directed edge gives the flow of migration, and an edge property gives the number of migrants, for each given year and sex. Estimates are presented for 1990, 1995, 2000, 2005, 2010 and 2015 and are available for all countries and areas of the world. The estimates are based on official statistics on the foreign-born or the foreign population.
This network has 232 no…

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
Dakang Cen, Zhiyuan Li, Wenlong Zhang
https://arxiv.org/abs/2506.18948

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. The optimal error estimates of stochastic convergence not only balance discretization errors, the noise, and the number of observation points, but also …

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
Giuseppe Spadaro, Domenico Vuono
https://arxiv.org/abs/2507.16402

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required.

Design and analysis of twisted and BGG Stokes-de Rham polytopal complexes
Daniele A. Di Pietro, J\'er\^ome Droniou, Kaibo Hu, Arax Leroy
https://arxiv.org/abs/2507.17333 htt…

Design and analysis of twisted and BGG Stokes-de Rham polytopal complexes
We design a discrete Bernstein--Gelfand--Gelfand (BGG) diagram on polygonal meshes based on the DDR framework; the diagram is made of a discrete Stokes polygonal complex and a tensorised Discrete De Rham complex, and the BGG construction leads to a novel elasticity complex applicable on generic polygonal meshes. Complete homological and analytical properties of the discrete Stokes complex are established, including primal and adjoint consistency estimates as well as Poincaré inequalities. Homo…

Gradient continuity estimates for elliptic equations of singular $p$-Laplace type with measure data
Longjuan Xu, Yirui Zhao
https://arxiv.org/abs/2507.15029

Gradient continuity estimates for elliptic equations of singular $p$-Laplace type with measure data
In this paper, we are concerned with elliptic equations of $p$-Laplace type with measure data, which is given by $-div\big(a(x)(|\nabla u|^2+s^2)^{\frac{p-2}{2}}\nabla u\big)=μ$ with $p>1$ and $s\geq0$. Under the assumption that the modulus of continuity of the coefficient $a(x)$ in the $L^2$-mean sense satisfies the Dini condition, we prove a new comparison estimate and use it to derive interior and global gradient pointwise estimates by Wolff potential for $p\geq 2$ and Riesz poten…

Asana reports Q1 revenue of $187.3M, vs. $185.5M est., up 9% YoY vs. 26% last year, and adjusted EPS of $0.05, vs. $0.02 est.; ASAN falls 8% after hours (Duncan Riley/SiliconANGLE)
https://siliconangle.com/2025/06/03/asan…

Asana shares drop as earnings results top estimates but revenue growth slows - SiliconANGLE
Asana shares drop as earnings results top estimates but revenue growth slows - SiliconANGLE

The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates
Jonah A. J. Duncan, Luc Nguyen
https://arxiv.org/abs/2507.16383

The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates
In this paper we give a complete classification of positive viscosity solutions $w$ to conformally invariant equations of the form \begin{align}\label{ab}\tag{$*$} \begin{cases} f(λ(-A_w)) = \frac{1}{2}, \quad λ(-A_w)\inΓ& \text{in }\mathbb{R}_+^n \newline w = 0 & \text{on }\partial\mathbb{R}_+^n, \end{cases} \end{align} where $A_w$ is the Schouten tensor of the metric $g_w = w^{-2}|dx|^2$, $Γ\subset\mathbb{R}^n$ is a symmetric convex cone and $f$ is an associated de…

Baidu reports Q2 revenue down 4% YoY to ~$4.6B, slightly below est., and online ad revenue down 15% YoY to ~$2.3B, as China's ad market remains weak (Deborah Sophia/Reuters)
https://www.reuters.com/business/media-telecom/chinas-b…

Bridge Sampling Diagnostics
Giorgio Micaletto, Aki Vehtari
https://arxiv.org/abs/2508.14487 https://arxiv.org/pdf/2508.14487…

Bridge Sampling Diagnostics
In Bayesian statistics, the marginal likelihood is used for model selection and averaging, yet it is often challenging to compute accurately for complex models. Approaches such as bridge sampling, while effective, may suffer from issues of high variability of the estimates. We present how to estimate Monte Carlo standard error (MCSE) for bridge sampling, and how to diagnose the reliability of MCSE estimates using Pareto-$\hat{k}$ and block reshuffling diagnostics without the need to repeatedly …

Gradient regularity for double-phase orthotropic functionals
Stefano Almi, Chiara Leone, Gianluigi Manzo
https://arxiv.org/abs/2507.18474 https://arxiv.org…

Gradient regularity for double-phase orthotropic functionals
We prove higher integrability for local minimizers of the double-phase orthotropic functional \[ \sum_{i=1}^{n}\int_Ω\left(\left|u_{x_i}\right|^p+a(x)\left| u_{x_i}\right|^q\right)dx \] when the weight function $a \geq0$ is assumed to be $α$-Hölder continuous, while the exponents $p, q$ are such that $2 \leq p \leq q$ and $\frac{q}{p} < 1 + \fracα{n}$. Under natural Sobolev regularity of~$a$, we further obtain explicit Lipschitz regularity estimates for local minimizer…

Asymptotic stability of the $2D$ temperature-dependent tropical climate model with the sharp decay rates
Hyunjin In, Dong-ha Kim, Junha Kim
https://arxiv.org/abs/2507.17197 http…

Asymptotic stability of the $2D$ temperature-dependent tropical climate model with the sharp decay rates
We investigate the asymptotic stability of a tropical climate model posed on $\bR^2$, with temperature-dependent diffusion in the barotropic mode $u$ and linear damping in the first baroclinic mode $v$. We consider two distinct cases for the barotropic component: one with linear damping and one without. For both cases, we prove the small data global existence of smooth solutions. Furthermore, we establish sharp temporal decay estimates for solutions in arbitrary Sobolev norms $H^m (\bR^2)$, $m …

A Bayesian block maxima over threshold approach applied to corrosion assessment in heat exchanger tubes
Jess Spearing, Jarno Hartog
https://arxiv.org/abs/2507.16416

A Bayesian block maxima over threshold approach applied to corrosion assessment in heat exchanger tubes
Corrosion poses a hurdle for numerous industrial processes, and though corrosion can be measured directly, statistical approaches are often required to either correct for measurement error or extrapolate estimates of corrosion severity where measurements are unavailable. This article considers corrosion in heat exchangers tubes, where corrosion is typically reported in terms of maximum pit depth per inspected tube, and only a small proportion of tubes are inspected, suggesting extreme value the…

Cloudflare reports Q2 revenue up 28% YoY to $512.3M, vs. $501.21M est., and forecasts Q3 revenue of $543.5M to $544.5M, vs. $538.6M est. (Duncan Riley/SiliconANGLE)
https://siliconangle.com/2025/07/31/cloudflare-beats-second-quart…

Cloudflare beats earnings estimates with strong revenue and customer growth - SiliconANGLE
Cloudflare beats earnings estimates with strong revenue and customer growth - SiliconANGLE

Estimates for pseudo-differential operators on the torus revisited. III
Duv\'an Cardona, Manuel Mart\'inez
https://arxiv.org/abs/2508.13338 https://

Estimates for pseudo-differential operators on the torus revisited. III
This paper finishes the goal of the authors started in two previous manuscripts dedicated to revisiting the continuity properties of toroidal pseudo-differential operators with symbols in the Hörmander classes. Here we prove pointwise estimates in terms of the Fefferman-Stein sharp maximal function and of the Hardy-Littlewood maximal function. Combining these estimates with the properties of Muckenhoupt's weight class $A_p$ we obtain boundedness theorems for pseudo-differential operators betwe…

The fundamental problem of risk prediction for individuals: health AI, uncertainty, and personalized medicine
Lasai Barre\~nada, Ewout W Steyerberg, Dirk Timmerman, Doranne Thomassen, Laure Wynants, Ben Van Calster
https://arxiv.org/abs/2506.17141

The fundamental problem of risk prediction for individuals: health AI, uncertainty, and personalized medicine
Background: Clinical prediction models for a health condition are commonly evaluated regarding performance for a population, although decisions are made for individuals. The classic view relates uncertainty in risk estimates for individuals to sample size (estimation uncertainty) but uncertainty can also be caused by model uncertainty (variability in modeling choices) and applicability uncertainty (variability in measurement procedures and between populations). Methods: We used real and synthet…

Schauder estimates for parabolic $p$-Laplace systems
Verena B\"ogelein, Frank Duzaar, Ugo Gianazza, Naian Liao, Christoph Scheven
https://arxiv.org/abs/2507.15722

Schauder estimates for parabolic $p$-Laplace systems
We establish the local Hölder regularity of the spatial gradient of bounded weak solutions $u\colon E_T\to\R^k$ to the non-linear system of parabolic type \begin{equation*} \partial_tu-\Div\Big( a(x,t)\big(μ^2+|Du|^2\big)^\frac{p-2}2Du\Big)=0 \qquad\mbox{in $E_T$}, \end{equation*} where $p>1$, $μ\in[0,1]$, and the coefficient $a\in L^\infty(E_T)$ is bounded below by a positive constant and is Hölder continuous in the space variable $x$. As an application, we prove Hölder esti…

Decay estimates of wave equations in un-isotropic media
Sergiu Klainerman, Xuecheng Wang
https://arxiv.org/abs/2508.12049 https://arxiv.org/pdf/2508.12049

Decay estimates of wave equations in un-isotropic media
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As application we give two surprisingly simple proofs for small data global regularity results non-isotropic systems of wave equations in $\mathbb{R}^{1+3}$ with cubic semilinear nonlinearities. We hope that the techniques presented here are relevant for the more diffi…

Optimal boundary regularity for mixed local and nonlocal equations
Nicola Abatangelo, Elisa Affili, Matteo Cozzi
https://arxiv.org/abs/2507.13711 https://

Optimal boundary regularity for mixed local and nonlocal equations
We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach makes use of weighted Hölder spaces as well as regularity estimates for the Laplacian in this context and a fixed-point argument. We show the optimality of the obtained estimates by means of a counterexample that we have striven to keep as explicit as possib…

Maz'ya-type bounds for sharp constants in fractional Poincar\'e-Sobolev inequalities
Francesco Bozzola, Matteo Talluri
https://arxiv.org/abs/2508.15564 https://

Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities
We prove estimates for the sharp constants in fractional Poincaré-Sobolev inequalities associated to an open set, in terms of a nonlocal capacitary extension of its inradius. This work builds upon previous results obtained in the local case by Maz'ya and Shubin and by the first author and Brasco. We rely on a new Maz'ya-Poincaré inequality and, incidentally, we also prove new fractional Poincaré-Wirtinger-type estimates. These inequalities display sharp limiting behaviours with respect to th…

Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds
Loth Damagui Chabi, Philippe Souplet
https://arxiv.org/abs/2507.12190

Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds
We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and significantly improve on all previous estimates of this type. As applications, we derive a new and sharp, space only, local pseudo-Harnack inequality, as well as estimates of the spatial modulus of continuity of solutions.

Carleman estimates for stationary $Q$-valued maps: a variational approach
Aria Halavati, Luca Spolaor
https://arxiv.org/abs/2508.14388 https://arxiv.org/pd…

Carleman estimates for stationary $Q$-valued maps: a variational approach
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to De Lellis-Spadaro.