Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical systems on Hilbert spaces including the two-dimensional Navier-Stokes equations and the Lorenz '63 and '96 equations. For nonlinear model dynamics, the ensemble Kalman filter (EnKF) is often used to approximate the mean and covariance of the probability distribution with a set of particles called an ensemble. In this paper, we consider a deterministic version of the EnKF known as the ensemble transform Kalman filter (ETKF), performing well even with limited ensemble sizes in comparison to other stochastic implementations of the EnKF. When the ETKF is applied to large-scale systems, an ad-hoc numerical technique called a covariance inflation is often employed to reduce approximation errors. Despite the practical effectiveness of the ETKF, little is theoretically known. The present study aims to establish the theoretical analysis of the ETKF. We obtain that the estimation error of the ETKF with and without the covariance inflation is bounded for any finite time. In particular, the uniform-in-time error bound is obtained when an inflation parameter is chosen appropriately, justifying the effectiveness of the covariance inflation in the ETKF.

Computational modeling of the melt pool dynamics in laser-based powder bed fusion metal additive manufacturing (PBF-LB/M) promises to shed light on fundamental mechanisms of defect generation. These processes are accompanied by rapid evaporation so that the evaporation-induced recoil pressure and cooling arise as major driving forces for fluid dynamics and temperature evolution. The magnitude of these interface fluxes depends exponentially on the melt pool surface temperature, which, therefore, has to be predicted with high accuracy. The present work utilizes a diffuse interface finite element model based on a continuum surface flux (CSF) description of interface fluxes to study dimensionally reduced thermal two-phase problems representative for PBF-LB/M in a finite element framework. It is demonstrated that the extreme temperature gradients combined with the high ratios of material properties between metal and ambient gas lead to significant errors in the interface temperatures and fluxes when classical CSF approaches, along with typical interface thicknesses and discretizations, are applied. It is expected that this finding is also relevant for other types of diffuse interface PBF-LB/M melt pool models. A novel parameter-scaled CSF approach is proposed, which is constructed to yield a smoother temperature field in the diffuse interface region, significantly increasing the solution accuracy. The interface thickness required to predict the temperature field with a given level of accuracy is less restrictive by at least one order of magnitude for the proposed parameter-scaled approach compared to classical CSF, drastically reducing computational costs. Finally, we showcase the general applicability of the parameter-scaled CSF to a 3D simulation of stationary laser melting of PBF-LB/M considering the fully coupled thermo-hydrodynamic multi-phase problem, including phase change.

In this paper we construct $n$-valued maps on $k$-dimensional tori, where $n,k\geq 2$, that are not homotopic to affine $n$-valued maps. This is in high contrast with the single valued case, where any such map is homotopic to an affine (even linear) map. We do this by investigating necessary and sufficient algebraic conditions on certain induced morphisms.

We establish a monotonicity-type property of volume of central hyperplane sections of the 1-symmetric convex bodies, with applications to chessboard cutting. We parallel this for projections with a new convexity-type property for Rademacher sums.

We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn from $p(k)\sim k^{μ-1}$ for $k\to0$. When $μ>1$, the scaling of the standard Edwards-Wilkinson model is recovered. When $μ<1$, the elastic line exhibits an anomalous scaling of the type observed in many growth models and experiments. Here we derive and use the exact expression for the exact probability distribution of the line shape at equilibrium, as well as the spectral properties of the matrix containing the random couplings, to fully characterize the sample to sample fluctuations. Our results lead to novel scaling predictions that partially disagree with previous works, but which are corroborated by numerical simulations. We also provide a novel interpretation of the anomalous scaling in terms of the abrupt jumps in the line's shape that dominate the average value of the observable.

We study relative differential and integral forms on families of supermanifolds and their cohomology. We prove a relative Poincaré--Verdier duality and show that it relates the cohomology of differential and integral forms, admitting a concrete geometric realization via Berezin fiber integration. We further introduce the Poincaré--dual integral form associated to an embedded even family and prove that it satisfies the correct localization property. We then apply these results to supergravity, focusing on the $3d$ case. In this setting, we show that relative Poincaré duality provides the natural framework for encoding the data needed to relate a superspace formulation to the physical spacetime, thereby yielding a rigorous definition of picture changing operators used in the physics literature. Building on this, after a careful analysis of the space of fields and the relevant constraints, we prove that the component, superspace, and geometric formulation of the theory are all equivalent. Finally, under suitable hypotheses, we argue that our construction illustrates a general principle governing the mathematical formulation of classical field theories on supermanifolds.

Counterfactuals in quantitative trade and spatial models are functions of the current state of the world and the model parameters. Common practice treats the current state of the world as perfectly observed, but there is good reason to believe that it is measured with error. This paper provides tools for quantifying uncertainty about counterfactuals when the current state of the world is measured with error. I recommend an empirical Bayes approach to uncertainty quantification, and show that it is both practical and theoretically justified. I apply the proposed method to the settings in Adao, Costinot, and Donaldson (2017) and Allen and Arkolakis (2022) and find non-trivial uncertainty about counterfactuals.

In recent years, the proliferation of disinformation has become an issue against the backdrop of the spread of social media. In this study, we focus on socialbots, one of the causes of this problem, and analyze several domestic cases to clarify the actual activities and influence of socialbots. As a result of this analysis, we found that the influence of socialbots is greater in Japan than in the U.S. presidential election of 2016, which is a representative case of socialbot influence, and that socialbots retweeted by humans are not significantly different from human accounts. In addition, socialbot accounts retweeted by humans are not significantly different from human accounts. This paper also discusses specific methods and perspectives for further analysis and research on the influence of socialbots.

We prove well-posedness in weighted tent spaces of weak solutions to the Cauchy problem $\partial_t u - \mathrm{div} A \nabla u = f, u(0)=0$, where the source $f$ also lies in (different) weighted tent spaces, provided the complex coefficient matrix $A$ is bounded, measurable, time-independent, and uniformly elliptic. To achieve this, we extend the theory of singular integral operators on tent spaces via off-diagonal estimates introduced by [arXiv:1112.4292] to obtain estimates on solutions $u$, and also $\nabla u$, $\partial_t u$, and $\mathrm{div} A \nabla u$ in weighted tent spaces, showing at the same time maximal regularity. Uniqueness follows from a different strategy using interior representation for weak solutions and boundary behavior.

The possibility of searching for right-handed neutrinos at the MoEDAL's Apparatus for Penetrating Particles (MAPP) detector is investigated in this work. In particular, pair-production of right-handed (RH) neutrinos $N$ from either a $B-L$ gauge boson $Z'$, as well as Standard Model (SM) $Z$ boson are considered. Under a no-background assumption, we show that the MAPP detector can be sensitive to active-sterile neutrino mixing strengths as low as $V_{μN}^2 \approx 10^{-12}$ for multiple choices of $m_N / m_{Z'}$ values, when taking the $B-L$ gauge coupling $g_{B-L} = 10^{-3}$ near its current limit. The SM $Z$ boson portal can reach a similar sensitivity, when the effective mixing between the $B-L$ and SM gauge boson is $α\approx 0.002$.

Model-independent theoretical upper bound on the thermal dark matter (DM) mass can be derived from the maximum inelastic DM cross-section featuring the whole observed DM abundance. We deploy partial-wave unitarity of the scattering matrix to derive the maximal thermally-averaged cross section for general number-changing processes $r\to 2$ (with $r\ge 2$), which may involve standard model particles or occur solely within the dark sector. The usual upper limit on the DM mass for $s$-wave annihilation is around 130 TeV (1 GeV) for $r=2$ (3), only applies in the case of a freeze-out occurring in the standard cosmological scenario. We consider the effects of two nonstandard cosmological evolutions, characterized by low-temperature reheating: $i)$ a kination-like scenario and $ii)$ an early matter-dominated scenario. In the first case, early freeze-out strengthens the unitarity bound to a few TeVs for WIMPs; while in the second case, the WIMP DM can be as heavy as $\sim 10^{10}$ GeV due to a large entropy dilution.

Identifying signals that replicate across multiple studies is essential for establishing robust scientific evidence, yet existing methods for high-dimensional replicability analysis either rely on restrictive modeling assumptions, are limited to two-study settings, or lack statistical power. We propose a general empirical Bayes framework for multi-study replicability analysis that jointly models summary-level $p$-values while explicitly accounting for between-study heterogeneity. Within each study, non-null $p$-value densities are estimated nonparametrically under monotonicity constraints, enabling flexible and tuning-free inference. For two studies, we develop a local false discovery rate (Lfdr) statistic for the composite null of non-replicability and establish identifiability, consistency, and a cubic-rate convergence of the nonparametric MLE, along with minimax optimality. Extending replicability analysis to $n$ studies typically requires estimating $2^n$ latent configurations, which is computationally infeasible. To address this challenge, we introduce a scalable pairwise rejection strategy that decomposes the exponentially large composite null into disjoint components, yielding linear complexity in the number of studies. We prove asymptotic FDR control under mild regularity conditions and show that Lfdr-based thresholding is power-optimal. Extensive simulations demonstrate that our method provides substantial power gains while maintaining valid FDR control, outperforming state-of-the-art alternatives across a wide range of scenarios. Applying our framework to East Asian- and European-ancestry genome-wide association studies of type 2 diabetes reveals replicable genetic associations that competing approaches fail to detect, illustrating the method's practical utility in large-scale biomedical research.

We provide criteria for Itô integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probability. The results are novel in the M1 setting and unify existing theories in the J1 case. Beyond sufficient criteria, we present an example of uniformly convergent martingale integrators for which the continuity breaks down. Moreover, we show that, for families of local martingales, M1 tightness in fact implies J1 tightness under a mild localised uniform integrability condition. Finally, we apply our results to study scaling limits of models of anomalous diffusion driven by continuous-time random walks. This yields new results on weak M1 and J1 convergence to stochastic integrals against subordinated stable processes. In the case of superdiffusive scaling, an interesting counterexample is obtained.

The Jiangmen Underground Neutrino Observatory is building the world's largest liquid scintillator detector with a 20 kt target mass and about 700 m overburden. The total underground space of civil construction is about 300,000 m$^3$ with the main hall volume of about 120,000 m$^3$, which is the biggest laboratory in the world. Radon concentration in the underground air is quite important for not only human beings' health but also the background of experiments with rare decay detection, such as neutrino and dark matter experiments. The radon concentration is the main hall is required to be around 100 Bq/m$^3$. Optimization of the ventilation with fresh air is effective to control the radon underground. To find the radon sources in the underground laboratory, we made a benchmark experiment in the refuge room near the main hall. The result shows that the radon emanating from underground water is one of the main radon sources in the underground air. The total underground ventilation rate is about 160,000 m$^3$/h fresh air with about 30 Bq/m$^3$ $^{222}$Rn from the bottom of the vertical tunnel after optimization, and 55,000 m$^3$/h is used for the ventilation in the main hall. Finally, the radon concentration inside the main hall decreased from 1600 Bq/m$^3$ to around 100 Bq/m$^3$. The suggested strategies for controlling radon concentration in the underground air are described in this paper.

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is presented which corrects this and is shown to conserve energy. New theoretical predictions are supported by numerical results which use averaging of simulations of wave scattering over finite sections of random bathymetry for which transfer matrix eigenvalues are used to accurately measure decay. The model of wave propagation used in this paper is derived from a linearised long wavelength assumption whereby depth averaging leads to time harmonic waves being represented as solutions to a simple ordinary differential equation. In this paper it is shown how this can be adapted to incorporate a model of a continuous covering of the surface by fragmented floating ice. Attenuation of waves through broken ice of random thickness is then analysed in a similar manner as bed variations previously and some comparisons are made with published field data for attenuation of waves in the marginal ice zones. Key features of the data are reproduced by theory including the attenuation being proportional to a power of frequency between 2 and 4 as well as capturing the "roll-over effect" at high frequencies.

We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit is not a minimizer of the fixed-time action, for any conormal boundary condition. Under an orbit-cylinder hypothesis, its Morse index strictly increases in the free-time setting. As a consequence, strongly nondegenerate brake orbits fail to be linearly stable under a dimensional condition; in dimension at least three, nondegenerate mountain-pass brake orbits are spectrally unstable when the monodromy is semisimple. The key ingredient is a local index contribution at each brake instant. Using Seifert collar coordinates near the Hill boundary, we reduce the normal dynamics to a one-dimensional model, exhibiting a degeneracy inherent to brake symmetry. We illustrate the results by explicit Morse index computations for the planar anisotropic oscillator, the planar pendulum, and the planar Kepler problem; in the Kepler case, the ejection--collision orbit is treated via cotangent-lift Levi--Civita--Lissajous regularization.

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there have been remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 10^8 at room temperature, the highest value achieved among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

We study Kähler manifolds that are (weak) relatives, that is, Kähler manifolds which share a (locally isometric) submanifold. In particular, we prove that if two Kähler manifolds are weak relatives and one of them is projective, then they are relatives. Moreover, we introduce the notion of strict relatives Kähler manifolds and provide several nontrivial examples.

Arm introduced the Confidential Compute Architecture (CCA) in the upcoming Armv9-A architecture, enabling the support of confidential virtual machines (CVMs) in a separate world called the Realm world, providing protection from untrusted normal world. While CCA offers a promising future for confidential computing, the widespread commercial CCA hardware is not available in the near future. To fill this gap, we present virtCCA, an architecture that facilitates virtualized CCA using TrustZone, a mature hardware feature on existing Arm platforms. Notably, virtCCA can be implemented on platforms equipped with the Secure EL2 (S-EL2) extension from ARMv8.4 onwards, as well as on earlier platforms that lack S-EL2 support. virtCCA provides strong compatibility with the CCA specifications at the API level. We developed the entire CCA software and firmware stack on top of virtCCA, including the enhancements to the normal world's KVM to support CVMs, and the TrustZone Management Monitor (TMM) that enforces isolation among CVMs and provides CVM lifecycle management. We have implemented virtCCA on real Arm servers, both with and without S-EL2 support. Our evaluation on micro-benchmarks and macrobenchmarks demonstrates that the overhead of running CVMs is acceptable compared to running normal-world VMs. Specifically, in a set of real-world workloads, the overhead of virtCCA-SEL2 is less than 29.7% for I/O intensive workloads, while virtCCA-EL3 outperforms the baseline in most cases.

Molecular mechanisms that enable collective and upconverted energy transfer from multiple photoacceptors to a non-absorbing spectator reaction center are highly desirable for efficient light-energy utilization. Here, we show that intermolecular Coulombic decay (ICD), a nonlocal energy relaxation channel in photoexcited molecules, offers an avenue for such a novel energy transfer mechanism. On irradiation of pyridine-argon gas mixture at 266 nm and at low laser intensities, we observed a surprisingly dominant formation of argon cations. Measurements of the laser power dependence, together with systematic studies of Ar$^+$ yield versus laser intensity and molecular density, reveal that ICD mediates the collective funneling of excitation energy from multiple photoexcited pyridine molecules to a non-photoabsorbing argon atom, leading to its ionization. The density of the reaction center offers an efficient handle to optimize this collective energy transfer. This mechanism opens new avenues in light harvesting design and may help explain the remarkable resistance of biomolecules to photodamage.

Sparse Code Multiple Access (SCMA) and Blind Interference Alignment (BIA) are key enablers for multi-user communication, yet each suffers from distinct limitations: SCMA faces high complexity and limited multiplexing gain, while BIA requires a long temporal channel pattern and incurs significant decoding delay. This paper proposes SBMA (Sparsecode-and-BIA-based Multiple Access), a novel framework that synergizes SCMA's diversity and BIA's multiplexing while addressing their drawbacks. We design two decoders: a low-complexity two-stage decoder (Zero-forcing + Message Passing Algorithm (MPA)) and a Joint MPA (JMPA) decoder leveraging a virtual factor graph for improved BER. Theoretical analysis derives closed-form BER expressions for a 6-user 2x1 MISO system, validated by simulations. Compared to existing schemes, SBMA with JMPA achieves a diversity gain equivalent to STBC-SCMA and a multiplexing gain comparable to BIA, while simultaneously offering enhanced privacy (relative to STBC-SCMA) and reduced reliance on channel coherence time (compared to BIA). These advancements position SBMA as a compelling solution for next-generation wireless communication systems, particularly in IoT applications demanding high throughput, robust data privacy, and adaptability to dynamic channel conditions.

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear convergence near the minimizer. We introduce an adaptive multilevel Newton-type method with a principled automatic switch to full Newton once its quadratic phase is reached. The local quadratic convergence for strongly convex functions with Lipschitz continuous Hessians and for self-concordant functions is established and confirmed empirically. Although per-iteration cost can exceed that of classical multilevel schemes, the method is efficient and consistently outperforms Newton's method, Gradient Descent, and the multilevel Newton method, indicating that second-order methods can outperform first-order methods even when Newton's method is initially slow. The promising empirical results open new avenues for designing reduced-cost second- and high-order methods with extremely fast convergence rates.

We find the optimal function norm on the left-hand side of the $m$th order Sobolev type inequality $\|u\|_{Y(\mathbb{H}^n)} \leq C \|\nabla_g^m u\|_{X(\mathbb{H}^n)}$ in the $n$-dimensional hyperbolic space $\mathbb{H}^n$, $1\leq m < n$. The optimal function norm in the inequality among all rearrangement-invariant function norms is completely characterized. A variety of concrete examples of optimal function norms is provided. The examples include delicate limiting cases, and especially when $m\geq3$, seem to provide new, improved inequalities in these limiting cases.

We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.

We report the experimental observation of the spin-wave moiré edge and cavity modes using Brillouin light scattering spectro-microscopy in a nanostructured magnetic moiré lattice consisting of two twisted triangle antidot lattices based on an yttrium iron garnet thin film. Spin-wave moiré edge modes are detected at an optimal twist angle and with a selective excitation frequency. At a given twist angle, the magnetic field acts as an additional degree of freedom for tuning the chiral behavior of the magnon edge modes. Micromagnetic simulations indicate that the edge modes emerge within the original magnonic band gap and at the intersection between a mini-flatband and a propagation magnon branch. Our theoretical estimate for the Berry curvature of the magnon-magnon coupling suggests a non-trivial topology for the chiral edge modes and confirms the key role played by the dipolar interaction. Our findings shed light on the topological nature of the magnon edge mode for emergent moiré magnonics.

The John-Nirenberg spaces $JN_p$ are generalizations of the space of bounded mean oscillation $BMO$ with $JN_{\infty}=BMO$. Their vanishing subspaces $VJN_p$ and $CJN_p$ are defined in similar ways as $VMO$ and $CMO$, which are subspaces of $BMO$. As our main result, we prove that $VJN_p$ and $CJN_p$ coincide by showing that certain Morrey type integrals of $JN_p$ functions tend to zero for small and large cubes. We also show that $JN_{p,q}(\mathbb{R}^n) = L^p(\mathbb{R}^n) / \mathbb{R}$, if $p = q$.

We construct a series of finite-dimensional quantum groups as braided Drinfeld doubles of Nichols algebras of type Super A, for an even root of unity, and classify ribbon structures for these quantum groups. Ribbon structures exist if and only if the rank is even and all simple roots are odd. In this case, the quantum groups have a unique ribbon structure which comes from a non-semisimple spherical structure on the negative Borel Hopf subalgebra. Hence, the categories of finite-dimensional modules over these quantum groups provide examples of non-semisimple modular categories. In the rank-two case, we explicitly describe all simple modules of these quantum groups. We finish by computing link invariants, based on generalized traces, associated to a four-dimensional simple module of the rank-two quantum group. These knot invariants distinguish certain knots indistinguishable by the Jones or HOMFLYPT polynomials and are related to a specialization of the Links-Gould invariant.

The field of gravitational waves is rapidly progressing due to the noticeable advancements in the sensitivity of gravitational-wave detectors that has enabled the detection prospects of binary black hole mergers. Extreme mass ratio inspiral (EMRI) is one of the most compelling and captivating binary systems in this direction, with the detection possibility by the future space-based gravitational wave detector. In this article, we consider an EMRI system where the primary or the central object is a spherically symmetric static braneworld black hole that carries a \textit{tidal charge} $Q$. We estimate the effect of the tidal charge on total gravitational wave flux and orbital phase due to a non-spinning secondary inspiralling the primary. We further highlight the observational implications of the tidal charge in EMRI waveforms. We show that LISA (Laser Interferometer Space Antenna) observations can put a much stronger constraint on this parameter than black hole shadow and ground-based gravitational wave observations, which can potentially probe the existence of extra dimensions.

A geometric graph associated with a set of points $P= \{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$ and a fixed kernel function $\mathsf{K}:\mathbb{R}^d\times \mathbb{R}^d\to\mathbb{R}_{\geq 0}$ is a complete graph on $P$ such that the weight of edge $(x_i, x_j)$ is $\mathsf{K}(x_i, x_j)$. We present a fully-dynamic data structure that maintains a spectral sparsifier of a geometric graph under updates that change the locations of points in $P$ one at a time. The update time of our data structure is $n^{o(1)}$ with high probability, and the initialization time is $n^{1+o(1)}$. Under certain assumption, our data structure can be made robust against adaptive adversaries, which makes our sparsifier applicable in iterative optimization algorithms. We further show that the Laplacian matrices corresponding to geometric graphs admit a randomized sketch for maintaining matrix-vector multiplication and projection in $n^{o(1)}$ time, under sparse updates to the query vectors, or under modification of points in $P$.

We report on coherent propagation of antiferromagnetic (AFM) spin waves over a long distance ($\sim$10 $μ$m) at room temperature in a canted AFM $α$-Fe$_2$O$_3$ with the Dzyaloshinskii-Moriya interaction (DMI). Unprecedented high group velocities (up to 22.5 km/s) are characterized by microwave transmission using all-electrical spin wave spectroscopy. We derive analytically AFM spin-wave dispersion in the presence of the DMI which accounts for our experimental results. The AFM spin waves excited by nanometric coplanar waveguides with large wavevectors enter the exchange regime and follow a quasi-linear dispersion relation. Fitting of experimental data with our theoretical model yields an AFM exchange stiffness length of 1.7 angstrom. Our results provide key insights on AFM spin dynamics and demonstrate high-speed functionality for AFM magnonics.