Baryon acoustic oscillation (BAO) analyses usually report the anisotropic shift parameters $α_\perp(z)$ and $α_\parallel(z)$ relative to a fiducial cosmology, and these quantities are primarily used for cosmological parameter inference. Here we show that they can also be used to construct a direct internal consistency test of the background geometry. In particular, we derive a new null test of flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry written entirely in terms of the reported BAO shift parameters. The test is calibration free: the sound-horizon ratio $r_{\rm d}/r^{\rm fid}_{\rm d}$ cancels identically, so the relation is independent of the absolute BAO scale. We also derive a calibration-free reconstruction of the deceleration parameter $q(z)$ from the radial BAO sector. Applying these results to anisotropic DESI DR2 BAO measurements, we find no evidence for a breakdown of the flat-FLRW distance relation within current uncertainties. Our results show that anisotropic BAO measurements already provide a nontrivial internal geometric consistency test before performing any model fit.

We prove that if $Ω\subseteq\mathbb{R}^N$ is a set with finite perimeter with $\mathscr{H}^{N-1}(\partial Ω\setminus\partial^* Ω)=0$, then any set of finite perimeter $E\subseteq\mathbb{R}^N$ can be approximated by a polyhedral or smooth bounded set $F$ in such a way that both the total perimeter of $E$ and the perimeter of $E$ inside $Ω$ are approximated by those of $F$, and the boundary of $F$ has negligible intersection with the boundary of $Ω$. In addition, we address the approximation for perimeter and volume with densities, and we present counterexamples illustrating the sharpness of our assumptions. Our constructions rely on a technical result that replaces $E$ with a set $F$ which agrees with $E$ and has the same boundary inside $Ω$, while sharing no common boundary with $Ω$, and does so without substantially altering the perimeter or the volume of the original set.

Osteoporosis, a major global epidemic, often goes undetected until a fracture occurs, largely due to poor access to screening using gold standard methods, such as dual-energy X-ray absorptiometry (DXA). As a potential nonionizing radiation alternative, we present a transcutaneous spatially offset Raman spectroscopy (SORS) approach combined with machine learning (ML) to recover bone spectra through overlying soft tissue and extract diagnostic information. In a human cadaveric study spanning normal, osteopenic, and osteoporotic donors, we acquired paired Raman measurements from transcutaneous fingers at multiple spatial offsets (0, 3, and 6 mm) and from the corresponding exposed finger bones. Using this paired dataset, supervised machine-learning models were trained to reconstruct exposed-bone Raman spectra from transcutaneous measurements, enabling direct recovery of bone biochemical signatures from transcutaneous tissue. The ML predicted bone spectra preserved physiologically meaningful Raman features and demonstrated statistically significant differences between normal and osteoporotic groups across four key Raman-derived metrics (p < 0.05), representing, to our knowledge, the first demonstration of transcutaneous Raman discrimination between clinically established bone-health categories in a human cadaveric study. The ML-predicted spectra further correlated with distal-radius DXA T-scores (r = 0.73, RMSECV = 1.4), approaching the performance achieved using exposed-bone measurements (r = 0.9, RMSECV = 0.8). Finally, preliminary in vivo measurements from two volunteers revealed clear bone-related transcutaneous spectral features consistent with cadaveric data, supporting translational feasibility. Together, these results establish a foundation for nonionizing radiation, transcutaneous Raman assessment of bone health using supervised spectral extraction from accessible measurement sites

We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.

Linear inverse problems are highly common in practical real-world applications from industry to medical imaging. The forward operator is often built on some approximations of the studied system. Handling inaccuracies in the forward operator in the context of inverse problems is a relatively unstudied problem. In this work, we assume that we have a set of candidate forward operator matrices and suggest principal component analysis (PCA) for modeling their variation from the mean. We combine the original linear problem with the included forward operator inaccuracy into a bilinear tensor inverse problem and present two optimization algorithms and Gibbs sampling for approximately solving the problem. As a real-world test case, we apply the algorithms to account for the inaccuracy that is present in the sensitivity profiles or Jacobian matrices in diffuse optical tomography when an atlas-based model of the head anatomy is used instead of the subject's own anatomical model in neonates over a wide range of gestational ages (29--44 weeks). We report visual and numerical improvements in the spatial localization and contrast-to-noise-ratio in reconstructions of simulated hemodynamic activity.

Quantum computing experiments and testbeds with large qubit counts have until recently been a privilege afforded only to large companies or quantum technologies where scaling to hundreds or thousands of qubits does not require a substantial increase in quantum control hardware (neutral atoms, trapped ions, or spin defects). Superconducting and spin qubit testbeds critically depend on scaling their control systems beyond what a single electronics board can provide. Multi-board control systems combining RF, fast DC control, bias, and readout require precise synchronization and communication across many hardware and firmware components. To address this, we present XCOM, a network that synchronizes QICK boards and the absolute clocks governing quantum program execution to within 100 ps, free of drift and loss of lock. XCOM also provides deterministic, all-to-all simultaneous data communication with latency below 185 ns. Like QICK itself, XCOM is compatible with a broad range of qubit technologies and is designed to scale to large systems.

A classic result of Conway and Coxeter on frieze patterns has been generalized to a bijection between $p$-angulations of regular polygons and frieze patterns of type $Λ_p$. One of the features of Conway-Coxeter theory is a combinatorial procedure to obtain from the triangulation all entries of the corresponding frieze pattern. We first present a combinatorial algorithm, involving Chebyshev polynomials, for obtaining from a dissection all entries of the corresponding frieze pattern. As an application we obtain a characterisation of frieze patterns of types $Λ_4$ and $Λ_6$ in terms of all entries (not only the quiddity cycle). We then study infinite frieze patterns of type $Λ_p$, which appeared in a preprint by Banaian and Chen, generalizing the infinite frieze patterns of positive integers studied by Baur, Parsons and Tschabold. As our main result we obtain a combinatorial model for infinite frieze patterns of type $Λ_p$, these are in bijection with certain $p$-angulations of an infinite strip. This extends results by Baur, Parsons and Tschabold from $p=3$ to arbitrary $p\ge 3$, and also provides new insight in the classic case. Infinite frieze patterns of positive integers appear in the context of Weyl groupoids. In the final section we extend this to infinite frieze patterns of type $Λ_p$ for any $p\ge 3$ by introducing a generalization of Cartan graphs and Weyl groupoids. We show that, up to equivalence, there is a 1-1 correspondence between connected simply connected Cartan graphs of type $Λ_p$ of rank two with infinitely many vertices permitting a root system and infinite frieze patterns of type $Λ_p$.

Recent years have seen dramatic progress in the study of joint ergodicity, i.e. a scenario in which a multiple ergodic average converges in norm to the product of integrals of individual functions. This survey, accompanying the talk given by the author in the Perspectives on Ergodic Theory and its Interactions conference to celebrate Vitaly Bergelson's 75th birthday, aims to summarize these recent advances, outline crucial new tools, present various open problems, and highlight the main challenges currently faced in the study of multiple ergodic averages.

In this paper, the dynamical behavior of the accelerated expansion of the universe is studied within the framework of $f(T)$ gravity by considering a well-motivated functional form of $f(T)$. A specific form of the Hubble parameter is assumed, which under two different cases, leads to two distinct cosmological models expressed in terms of the redshift parameter $H(z)$, providing insights into cosmic dynamics. These models are employed to explore the expansion history of the universe and the evolution of several cosmological parameters. Using Bayesian statistical techniques based on the $χ^{2}$-minimization method, the median values of the model parameters are determined for both the cosmic chronometer (CC) and the joint (CC + Pantheon) datasets. The evolution of the deceleration parameter, energy density, pressure and the equation of state parameter for dark energy is analyzed. Additionally, the validity of the energy conditions and the nature of the statefinder diagnostic are examined. The present age of the universe is also estimated for the proposed models.

We present HECATEv2, the second release of the Heraklion Extragalactic Catalogue (HECATE), an all-sky, value-added galaxy catalogue comprising 204733 galaxies from the HyperLEDA database with recession velocity <14000 km/s (D~200 Mpc). This release focuses on qualitative upgrades of the provided information while maintaining the same parent galaxy sample as HECATEv1. Improvements include a new cosmology-based distance framework, expanded and homogenised optical and mid-infrared photometry from SDSS-DR17/NSA, PS1-DR2, and AllWISE, and new quality-control flags for stellar contamination, incorrect photometry, and coordinate inconsistencies. We also extend the galaxy-size coverage and derive stellar population parameters for a substantially larger fraction of the sample. Star-formation rates (SFR) and stellar masses (Mstar) are now available for >70% of galaxies using updated mid-IR/optical calibrations that account for stellar population age and dust attenuation, while gas-phase metallicities are derived for ~90%. Activity classifications are provided for >50% of galaxies based on spectroscopic and/or photometric diagnostics, and supermassive black hole masses for ~86%. In terms of L$_{B}$,L$_{Ks}$,SFR, and Mstar, HECATEv2 is among the most complete local-Universe catalogues with spectroscopic redshifts. We also provide spatial completeness maps as a function of distance and luminosity, highlighting variations across the sky. Compared to other catalogues (e.g. GLADE+, NED-LVS), HECATEv2 offers broader (optical, near- and far-IR photometry, metallicity, activity classifications) or comparable (mid-IR photometry, SFR, Mstar) coverage, making it a robust reference for studies of SMBH-host galaxy connections, gravitational-wave and high-energy transient hosts, population analyses, and rare galaxy subpopulations.

As insurers increasingly behave like financial intermediaries and actively participate in capital markets, understanding the dependence structure between insurance and financial risks becomes crucial for insurers' operations. This paper studies dynamic equilibrium insurance pricing when insurers face ambiguity about the correlation between insurance and financial risks and optimally choose underwriting and investment strategies under worst-case beliefs. Correlation ambiguity can generate multiple equilibrium regimes. Contrary to conventional intuition, we find ambiguity does not necessarily increase insurance prices nor reduce insurers' utility.

Multiple scattering of light by resonant vapor is characterized by Levy-type superdiffusion with a step size distribution $P(x) \propto 1/x^{1+α}$, with $0 < α < 2$. The Levy parameter $α$ was measured from $P(x)$, steady fluorescence, frequency-dependent fluorescence and time-resolved transmission, all of them in the forward direction. Here we report first measurements of this quantity from timeresolved backward fluorescence, i.e., photons that are backward diffused from light pulses exciting a hot rubidium vapor. We show experimentally that $α$ can be extracted from this diffuse reflection, and the results are consistent with time-resolved transmission (i.e., photons that are forward diffused) and steady frequency-dependent forward fluorescence. Theoretical simulations are consistent with these results. We also show that, although we measure $α = 1$ for both transmission and reflection, the backward photons have a non-negligible amount of single scattering events even for high density, contrary to the forward photons where multiple scattering dominates.

The ALICE collaboration reports the azimuthal-anisotropy coefficient $v_2$ of prompt D$^0$, D$^+$, D$^+_{\rm s}$ mesons and the first measurement of $v_2$ of prompt $Λ_{\rm c}$ baryons in semicentral Pb$-$Pb collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{\rm NN}} = 5.36$ TeV. The D mesons and $Λ_{\rm c}$ baryons are reconstructed in their hadronic decays at midrapidity ($ |y|<0.8$) in the transverse-momentum interval $0.5< p_{\rm T} < 24$ GeV/$c$. Similar $v_2$ values are measured for D$^0$ and D$^+$, while a hint of a difference ($2.6σ$) emerges between D$^0$ and D$^+_{\rm s}$ mesons in the $1 < p_{\rm T} < 5 $ GeV/$c$ interval. A larger $v_2$ for $Λ_{\rm c}$ baryons with respect to D$^0$ mesons is observed with $3.7σ$ significance for $4 < p_{\rm T} < 12$ GeV/$c$, providing evidence for the partonic origin of charm-hadron $v_2$ and hadron formation via quark coalescence. This interpretation is further supported by comparisons with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium.

This paper develops a dynamic equilibrium model of the insurance market that jointly characterizes insurers' underwriting, investment, recapitalization, and dividend policies under model uncertainty and financial frictions. Competitive insurers maximize shareholder value under a subjective worst-case probability measure, giving rise to liquidity-driven underwriting cycles and flight-to-quality behavior. While an equilibrium typically fails to exist in such dynamic liquidity management framework with external financial investment, we show that incorporating model uncertainty restores equilibrium existence under plausible parameter conditions. Moreover, the model uncovers a novel relationship between the correlation of insurance and financial market risks and the equilibrium insurance price: negative loadings may emerge when insurance gains and financial returns are positively correlated, contrary to conventional intuition.

Let $G$ be a reductive group quasi-split at $p$. Using arguments of Hansen--Thorne, we show that under the non-abelian Leopoldt conjecture (NALC), Hansen's $p$-adic overconvergent cohomology eigenvariety for $G$ is étale over its image in weight space at any non-critical classical tempered cuspidal point of `cohomological multiplicity one'. This applies to all non-critical classical cuspidal points if $G = \mathrm{Res}_{F/\mathbb{Q}}\mathrm{GL}_n$. We then let $π$ be a $p$-ordinary regular algebraic cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_{\mathbb{Q}})$ such that $π_p$ is Steinberg. Combining the above étaleness result for the classical point attached to $π$, and a local-global compatibility result from our earlier work, we deduce -- under a tangent vector hypothesis that is true for at least half the simple roots -- the equality of Fontaine--Mazur and automorphic $\mathcal{L}$-invariants for $π$. Where this assumption is satisfied, we deduce the NALC implies a conjecture of Gehrmann: that automorphic $\mathcal{L}$-invariants are independent of cohomological degree. Our approach is inspired by (and generalises) previous work of Gehrmann--Rosso. When $π= \operatorname{Sym}^{n-1} π_f$ is the symmetric power lift of a modular form, we verify all assumptions other than the NALC, and deduce a functoriality result for the automorphic $\mathcal{L}$-invariants.

Topology optimization (TO) is employed in engineering to optimize structural performance while maximizing material efficiency. However, traditional TO methods incur significant computational and time costs. Although research has leveraged generative AI to predict TO outcomes and validated feasibility and accuracy, existing approaches still suffer from limited customizability and impose a high cognitive load on users. Furthermore, balancing structural performance with aesthetic attributes remains a persistent challenge. We developed Sketch2Topo, which augments a diffusion-based TO model with image-to-image generation and image editing capabilities. With Sketch2Topo, users can use sketching to customize geometries and specify physical constraints. The tool also supports mask input, enabling users to perform TO on selected regions only, thereby supporting higher levels of customization. We summarize the workflow and details of the tool and conduct a brief quantitative evaluation. Finally, we explore application scenarios and discuss how hand-drawn input improves usability while balancing functionality and aesthetics.

Semiconductor heterostructures that combine components with different dimensionality provide an interesting way to manipulate the physical properties of the resulting material. Two-dimensional lead halide perovskites crystallize as flat microcrystals and have efficient in-plane exciton mobility, while perovskite nanocrystals are efficient emitters with a tunable bandgap that can self-assemble into microscopic superlattices. However, combining such intricate architectures into heterostructures has been challenging due to the mismatch in solubility properties and the challenging transfer procedures. Here we realize heterostructures where CsPbBr3 nanocrystal superlattices are deterministically grown along the faces of PEA2PbBr4 two-dimensional layered perovskite microcrystals. The growth can be limited to the lateral faces of the microcrystals and result in core-crown epitaxial heterostructures, or extended to the vertical direction leading to core-shell-like structures. The growth method is simple yet effective and versatile, and promises to be expanded to a large variety of other materials. We demonstrate that these heterostructures can be employed as efficient light-harvesting systems. In fact, energy can be transferred from the two-dimensional microcrystal domain to the superlattices, enabling switching between linear and non-linear carrier recombination regimes by tuning the excitation fluence. Moreover, by exploiting the lifetime shortening of CsPbBr3 nanocrystal emission upon sample cooling, we ensure that energy transfer occurs after the biexcitonic and single-excitonic decays of the nanocrystals, effectively extending the radiative recombination of superlattices.

Coordinating agents through hazardous environments, such as aid-delivering drones navigating conflict zones or field robots traversing deployment areas filled with obstacles, poses fundamental planning challenges. We introduce and analyze the computational complexity of a new multi-agent path planning problem that captures this setting. A group of identical agents begins at a common start location and must navigate a graph-based environment to reach a common target. The graph contains hazards that eliminate agents upon contact but then enter a known cooldown period before reactivating. In this discrete-time, fully-observable, deterministic setting, the planning task is to compute a movement schedule that maximizes the number of agents reaching the target. We first prove that, despite the exponentially large space of feasible plans, optimal plans require only polynomially-many steps, establishing membership in NP. We then show that the problem is NP-hard even when the environment graph is a tree. On the positive side, we present a polynomial-time algorithm for graphs consisting of vertex-disjoint paths from start to target. Our results establish a rich computational landscape for this problem, identifying both intractable and tractable fragments.

Gamma-Ray Burst GRB 241030A (z = 1.411) exhibited a bright afterglow (similar to GRB 221009A), detected across gamma-ray, X-ray, UV, and optical bands, providing a probe of GRB afterglow physics. We compiled multi-wavelength observations spanning from a minute to a week after the prompt emission, processing the data through a unified photometry pipeline. We analysed the observations both analytically and using Bayesian inference with two independent models. Our models assume that the afterglow emission arises from the strong forward shock of a laterally structured jet, with possible contributions from synchrotron self-Compton (SSC) scatterings. Our models reproduce X-ray to optical data, favouring a jet propagating into a constant-density interstellar medium, with a viewing angle within the jet core. However, both analyses require parameter values that are extreme compared to expectations from standard theory. In particular, our results imply extremely energetic jets despite regular prompt energy, leading to a very inefficient prompt emission. Furthermore, the jets are inefficient at accelerating particles, with low electron and magnetic energy fractions, leading to significant SSC emission. Our analyses indicate that the jets have large opening angles and propagate in high-density media. If the afterglow is indeed powered by radiation emitted behind a strong forward shock, our results place GRB 241030A within a sub-class of GRBs characterised by extreme kinetic energies, large jet opening angles, and very low prompt emission efficiencies, with strong SSC radiation. These predictions are difficult to reconcile with typical expectations from other GRBs. We therefore suggest that the afterglow of GRB 241030A is not solely powered by forward shock emission.

Given a graph $H$, the maximal anti-Ramsey function $f(n,e,H)$ denotes the minimum integer $f$ for which there exists an $n$-vertex graph $G$ with at least $e$ edges admitting an edge-coloring with $f$ colors in which each copy of $H$ in $G$ is rainbow. In the late 1980s, Burr, Erdős, Graham, and Sós conjectured that for every odd cycle $C_{2k+1}$ with $k \ge 3$, $f(n, \lfloor n^2/4 \rfloor + 1, C_{2k+1}) = n^2/8 + o(n^2)$. In this note, we confirm this conjecture for all $k \ge 4$. More generally, we establish the asymptotic formula $$f\left(n,e,C_{2k+1}\right)=\frac{e}{2}+\frac{n}{2}\sqrt{e-\frac{n^2}{4}}+o(n^2),$$ for the entire non-trivial range of $\left\lfloor n^2/4 \right\rfloor+1\le e\le \binom{n}{2}$.

In this talk, we present novel methods to investigate light-quark dipole interactions at colliders. Our approach includes: (1) measuring azimuthal asymmetries of a collinear dihadron in semi-inclusive deep inelastic lepton scattering off an unpolarized proton target at the Electron-Ion Collider, and (2) utilizing azimuthal asymmetries of dihadron $(h_1 h_2)$ produced in association with an additional hadron $h^\prime$ at lepton colliders. These asymmetries provide a unique means to observe transversely polarized quarks, which arise from quantum interference and are exclusively sensitive to dipole interactions at the leading power of the new physics scale. Consequently, they exhibit a linear dependence on the dipole couplings, free from contamination by other new physics effects. This approach has the potential to significantly strengthen current constraints by one to two orders of magnitude. By combining all possible channels of $h^\prime$, this novel approach enables the disentanglement of the up- and down-quark dipole moments. Additionally, by controlling the electron's longitudinal polarization and the center-of-mass energy, it separates the contributions mediated by photon and weak boson. Furthermore, it allows for a simultaneous determination of both real and imaginary parts of the dipole couplings, offering a new avenue for investigating potential $CP$-violating effects at high energies.

In HCI, frameworks function as a type of theoretical contribution, often supporting ideation, design, and evaluation. Yet, little is known about how they are actually used, what functions they serve, and which scholarly practices that shape them. To address this gap, we conducted a systematic review of 615 papers from a decade of CHI proceedings (2015-2024) that prominently featured the term framework. We classified these papers into six engagement types. We then examined the role, form, and essential components of newly proposed frameworks through a functional typology, analyzing how they are constructed, validated, and articulated for reuse. Our results show that enthusiasm for proposing new frameworks exceeds the willingness to iterate on existing ones. They also highlight the ambiguity in the function of frameworks and the scarcity of systematic validation. Based on these insights, we call for more rigorous, reflective, and cumulative practices in the development and use of frameworks in HCI.

In 1974, Erdős and Kleitman conjectured that if a family $\mathcal{F}\subseteq 2^{[n]}$ contains no matching of size \(s\) and is maximal with respect to this property, then $ |\mathcal{F}|\ge \left(1-2^{-(s-1)}\right)\cdot 2^{n}. $ For decades, the best general lower bound remained the trivial $2^{n-1}$. About a decade ago, Frankl and Tokushige emphasized that obtaining a bound of the form $\left(\frac{1}{2}+\varepsilon\right)\cdot 2^n$ for some $\varepsilon>0$ is a challenging problem. A breakthrough of Bucič, Letzter, Sudakov and Tran in 2018 showed that $ |\mathcal{F}|\ge \left(1-\frac{1}{s}\right)\cdot 2^n $ via two very elegant and quite different approaches. Our main result shows that $$ |\mathcal{F}|\ge \left( 1 - \frac{1}{s + (s-2)\frac{\log n}{2\sqrt{5}n}} \right)\cdot 2^n $$ by exploiting a connection to the cornerstone result of Kahn, Kalai and Linial on influences of Boolean functions. Independently, we can also obtain a weaker improvement combining the linear algebra method with a combinatorial twist.

This paper addresses the fundamental question of determining the minimum number of distinct control laws required for global controllability of nonlinear systems that exhibit singularities in their feedback linearising controllers. We introduce and rigorously prove the (k+1)-Controller Lemma, which establishes that for an nth order single-input single-output nonlinear system with a singularity manifold parameterised by k algebraically independent conditions, exactly k+1 distinct control laws are necessary and sufficient for complete state-space coverage. The sufficiency proof is constructive, employing the approximate linearisation methodology together with transversality arguments from differential topology. The necessity proof proceeds by contradiction, using the Implicit Function Theorem, a dimension-counting argument and structural constraints inherent to the approximate linearisation framework. The result is validated through exhaustive analysis of the ball-and-beam system, a fourth-order mechanical system that exhibits a two-parameter singularity at the third output derivative.

We study numerical schemes for Stochastic Partial Differential Equations (SPDEs). We introduce a general method of proof of non-asymptotic uniform in time error bounds on numerical integrators for SPDEs, ensuring the schemes capture both the transient and the long term dynamics faithfully. We then consider SPDEs with non-globally Lipshitz nonlinearities, which include for example the stochastic Allen-Cahn equation and some stochastic advection-diffusion equations. For the case of Allen-Cahn type SPDEs we show that the classic semi-implicit Euler time-discretization can exhibit finite time blow up. This motivates analysing other schemes which do not suffer from this blow-up problem. We consider three numerical schemes for SPDEs with non globally Lipshitz nonlinearity: a fully implicit scheme and two tamed schemes. For these schemes we prove non-asymptotic uniform in time error bounds by leveraging our general criterion, and provide numerical comparisons. While the main emphasis in this paper is on the properties of the time-discretization, the schemes we consider are full space-time discretization of the SPDE.

We present a synthetic notion of scalar curvature (and its integral) for Riemannian manifolds and metric measure spaces, defined in terms of the initial slope of a Gaussian (double) integral. We explicitly calculate the integral scalar curvature for Lipschitz gluings of smooth Riemannian manifolds and for cones. In dimension 2, the former coincides with the formula derived by Gauss-Bonnet, whereas the latter differs. The extension to the time-dependent case allows us to characterize Ricci flows as super Ricci flows with minimal integral curvature functional.

Masking is a countermeasure against Power Side Channel Attacks (PSCAs) in both software and hardware implementations of cryptographic algorithms. Compared to software masking, implementing masked hardware is time consuming and error prone. Recent approaches, therefore, rely on High Level Synthesis (HLS) tools to automatically generate masked Register Transfer Level (RTL) hardware from verified masked software, significantly reducing design effort. Since HLS was never developed for security, HLS optimizations may impact PSCA security of the generated RTL. As a result, verifying the PSCA security of HLS generated masked RTL is crucial. Existing hardware masking verification tools can verify masked hardware, but may produce false positives when applied to HLS generated designs with controller datapath architectures obtained due to resource-shared datapath obtained via HLS. This work proposes a hardware masking verification strategy for HLS generated masked hardware. Our toolflow MaskedHLSVerif, performs state-wise formal verification of controller datapath RTL obtained via HLS, thereby avoiding false positives caused by resource-shared datapaths. Our tool flow correctly verifies standard cryptographic benchmarks, consisting of cascaded masked gadgets and the PRESENT S-box masked with gadgets, where existing tools like REBECCA reports false positives. The proposed tool-flow is able to detect masking flaws induced by HLS-optimizations as well.

In classical information theory, both the form and performance of the optimal detector for additive noise channels can be precisely derived, based on the assumption that the channel noise follows a specific probability distribution or a mixture of known distributions, or that the exact distribution exists but is unknown. In this paper, we extend the analyses of detectors for additive noise channel to the situation where the probability model for analyzing channels is uncertain, utilizing nonlinear expectation theory. We consider two types of distribution uncertainties: one with no mean uncertainty but with variance uncertainty, and another with both mean and variance uncertainties. We derive the optimal detectors for binary input additive noise channel under the nonlinear expectation optimal criterion for both scenarios and provide their explicit forms. Our findings reveal that mean uncertainty significantly influences the form of the optimal detector, whereas variance uncertainty does not. Additionally, we propose an estimation method for the uncertain parameters of the channel noise. Finally, we present theoretical analyses and simulated performance results of the newly derived optimal detectors, and compare these results with the performance of optimal detector under classical information theory, which assumes a deterministic probability model. The results of experiments show that our new detection methods outperform conventional methods in most scenarios with uncertain probability models, showing the practical relevance of our theoretical contributions.

Diffusion in living tissues governs essential physiological processes and is well studied within cells. Yet how extracellular molecular motion emerges from the structural complexity of tissues remains unresolved. In the brain, molecules move extensively through the extracellular space (ECS) enabling key functions, with effective diffusivities reduced by factors of 2 to 5 relative to free solution. This slowing has traditionally been captured by the phenomenological concept of tortuosity, but tortuosity does not specify the microscopic mechanisms responsible for diffusion hindrance. Here we directly visualize three dimensional extracellular diffusion in brain tissue using ultrashort single walled carbon nanotubes as nearinfrared tracers, achieving nanometric spatial precision and video rate temporal resolution. We find that motion is locally Brownian and that transport does not require scale free stochastic dynamics. Instead, hindered diffusion emerges from a geometry controlled crossover: free diffusion at short length scales gives way to constrained transport beyond a characteristic structural scale of the ECS. Thus, tortuosity arises as an emergent, scale dependent property rather than an intrinsic material constant. Beyond its biological implications, this behavior places extracellular transport within the broader physics of diffusion in disordered media. Brain tissue acts as a natural realization of geometry constrained transport phenomena observed in porous materials and random obstacle systems, linking molecular motion in living matter to the general case of structurally heterogeneous environments.

In this paper, we study Monge's problem on Riemannian manifolds $(M, g)$ with positive sectional curvature. Assuming that the source and target measures are absolutely continuous with respect to the Riemannian volume measure, we generalize a variational method from the Euclidean setting to establish the existence of a transport density and an explicit disintegration of measures along optimal rays. These results extend the approach of Bianchini-Caravenna to the Riemannian context.