Papers

We discuss the quench dynamics of an isolated system composed of a single spinful impurity in the transverse Rabi field and bath of non-interacting three- and two-dimensional bosons. Specifically, we consider the evolution of bosons and a spin-$\frac{1}{2}$ particle, initially prepared in a Bose-Einstein condensate state and a magnetic ground state, respectively, with the spin-dependent contact boson-impurity interaction switched on. Applying an original mean-field-like approximation, which naturally reflects the statistical effects of the bosonic bath, we calculate time-dependent components of the average impurity spin and the overlap of the wave function between initial and arbitrary time moments. A key prediction is a substantial speed-up in the decoherence (thermalization) dynamics of the spin degree of freedom compared to results obtained with the Chevy-like ansatz.

GPU robotics lacks the reusable numerical infrastructure of mature CPU stacks, instead relying on compiler frameworks that introduce overhead or repeatedly reimplementing numerical libraries. To address this, we introduce GLASS (GPU Linear Algebra Simple Subroutines), a header-only CUDA C++ library that provides thread-, warp-, block-, and NVIDIA-backed implementations of robotics-scale linear algebra and geometric computations under one composable device API. GLASS treats implementation choice, execution scope, and launch packing as architecture-specific placement decisions determined by offline measurement and resolved statically at compile time. This is critical as the best and worst placements differ by a median of 4.9x (max 81x), with 145 of 396 recommended placements changing between a Jetson AGX Orin and an RTX 5090, and 162 of 396 versus an AGX Xavier. These stakes are highest at the edge as GLASS's advantage over the best of PyTorch and JAX is as much as 73x on the Orin versus 12x on the RTX 5090. GLASS is released open source with independent numerical oracles and source-bound local-GPU test attestation. Finally, integrating GLASS with published robotics systems both exposed a pre-existing numerical bug and improved embedded runtimes by up to 1.5x.

We formulate a complete-information two-player strategic timing game that we refer to as the reverse war of attrition (RWoA). Waiting yields a strictly positive current rent, and the player that outwaits its rival may earn an even higher flow. However, remaining in the waiting state when the rival has moved triggers a discrete late-mover penalty. The distinctive primitive is a player-owned productive buffer which enables the rent-generating activity while waiting, but is degraded by this activity. A rival's move can raise the waiting rent and accelerate depletion. We characterize a unique symmetric equilibrium. We apply RWoA to Bertrand competition in a homogeneous-good market, where vintage inventory serves as the buffer clock for timing repricing. We also discuss competitive maintenance. As an extension, we replicate the bilateral game across a continuum of disjoint heterogeneous local markets and, via the exact law of large numbers, derive deterministic aggregate state shares.

LLM leaderboard gains can reflect selection among privately evaluated model variants, yet neither the number of variants nor their dependence is public. We ask how many hidden variants a published margin can support while retaining statistical evidence of a provider's advantage over a fixed comparator. For a fixed candidate family under a Gaussian margin model, we derive a sensitivity curve that reports this maximum count as a function of a lower bound on within-family correlation. The relevant correlation must match the score used for ranking and the sampling model: in a controlled family, pooled item correlation is 0.90, whereas composite-score correlation is 0.46 under item resampling and 0.92 when MMLU subjects are resampled. An item-based audit of 394 adjacent-rank claims on the Open LLM Leaderboard finds that 391 lack statistical support even before accounting for selection. Among claims that pass the uncorrected test, certification can depend on assumptions about the hidden family's correlation. The resulting curves make these assumptions explicit without estimating the unobserved search size.

Increasing numbers of people now routinely interact with large language models (LLMs) across many aspects of life, including in the workplace, educational settings, and for personal activities. The pace at which these tools have been adopted across society in recent years has led to substantial shifts in the ways in which people approach tasks and access information and advice. As a result, it is important for researchers and policymakers to gain up-to-date evidence on how the public engages with these technologies, including what people typically use them for, the extent to which users trust the information and advice that LLMs provide, and how the public perceives the potential benefits and risks associated with their use. We surveyed a nationally representative sample of 2,002 adults in the UK. Participants were asked about their use of LLMs, including both practical applications and more personal and social forms of engagement, their trust in the information provided by these systems across a range of topics and compared with other common sources, and their attitudes towards the potential societal benefits and risks associated with these tools. Results show that while practical tasks remain the most common type of LLM use, many people now engage with these tools for personal support. Almost one third of regular users (31%) say they use LLMs for personal and emotional support, such as talking through problems and asking for help with decisions, while one quarter report interacting with LLMs for meaningful conversation. We also find that trust in LLM-generated information is relatively high, but that public attitudes towards LLMs are characterised by both optimism and concern. While over three quarters of our sample report feeling enthusiastic about the potential benefits of LLMs (77%), a majority also express concern about their potential risks (70%).

Humanoid soccer contact skills require more than producing high-impact foot-ball contacts: the robot must close the loop over perception, approach, alignment, impact, and recovery while its own motion induces substantial viewpoint changes, frequent loss of the ball from view, and uncertain contact outcomes. In this work, we ask a compact yet stricter question: can a humanoid learn soccer contact skills using only a head-mounted depth image, proprioceptive history, and an optional low-dimensional task command, and directly output 25-DoF joint PD targets without extra runtime perception or planning modules? To this end, we propose DAVIS, a depth-only end-to-end framework for humanoid soccer skills that learns visibility-aware auxiliary geometry during training, and combines GT-to-prediction annealing, task curricula, and AMP-style motion priors to smoothly bridge privileged supervision and real deployment. Built on this framework, we instantiate representative soccer contact skills, including goal-directed shooting and directional dribbling, through task-specific definitions of objects, commands, rewards, and curricula, and validate them through simulation, Noetix E1 real-robot experiments, and ablations.

Matching theory has largely evolved around two canonical rules: deferred acceptance (DA) in the marriage problem and top trading cycles (TTC) in the object reallocation problem. Although the two rules operate through different procedures, we show that they rest on a common axiomatic foundation. In the marriage problem, stability decomposes into individual rationality and pair rationality, and a classic result characterizes DA by these two axioms together with strategy-proofness for the proposing side. We show that individual rationality, pair rationality, and strategy-proofness likewise characterize TTC. More strongly, three weak rationality axioms concerning individuals and pairs, together with strategy-proofness, uniquely determine TTC. Even weak rationality requirements therefore rule out strategy-proof implementation when there is a cap on the size of exchange cycles.

We present a review of results concerning the properties of scales larger than the forcing scale in turbulent flows. In three-dimensional turbulence, when the power driving the flow is injected at a well-defined scale, the injection scale separates the small-scale range, where the Kolmogorov cascade takes place, from the large-scale range across which the mean energy flux is zero, suggesting that these modes are in equilibrium. We show that, in the case of spatially periodic forcing involving only a few modes, an equipartition energy spectrum is generated at large scales, and we discuss the deviations from equipartition observed with more complex forcings. In two-dimensional turbulence, the injection scale separates the direct enstrophy cascade toward small scales from the inverse energy cascade toward large scales. Because of the inverse cascade, one would not expect equilibrium statistical physics tools to be suitable for describing the large-scale structures. Yet this is precisely the situation in which such tools have been most widely used. We indeed show that the bifurcations observed between different largescale regimes of two-dimensional turbulence, both in experiments and in direct numerical simulations, can be qualitatively described by the Truncated Euler equations, whose solutions satisfy statistical equilibrium.

Robots in a LiDAR-equipped swarm mutually interfere when their optical ranging codes collide. Existing mitigations either assign codes statically – requiring $L=N$ distinguishable codes for $N$ robots – or react to detected interference without a scalable, coordinated assignment rule beneath them; prior work explicitly identifies the code-assignment scaling problem as unsolved. We propose a decentralized protocol in which robots dynamically reassign spatial reuse codes based on a live, beacon-maintained interference-neighborhood graph, and prove that the number of codes required grows as $O(\log N/\log\log N)$ under constant robot density – an unbounded improvement over the $\Theta(N)$ growth of static assignment. We validate this result under conditions substantially beyond the idealized proof – robot mobility, imperfect beacon-based detection, and reactive reassignment – via Monte Carlo simulation (30 seeds per condition, 95% confidence intervals): the advantage over static assignment widens from roughly $2\times$ at 15 robots to $12\times$ at 120. Against a structurally faithful, fairly constructed model of an existing coordination-free approach, our protocol achieves both substantially greater code-reuse efficiency and 30–40% lower collision risk under an identical, constrained code budget, demonstrating that coordination – not merely reactivity – is what closes the scaling gap.

Gravitational-wave (GW) observations offer a promising probe of new physics associated with a strong first-order electroweak phase transition. Null results from direct searches and constraints from precision measurements, together with the comparatively weak constraints on Higgs self-interactions, motivate scenarios in which non-decoupling effects in the Higgs potential coexist with additional decoupling new physics. Previous Fisher matrix studies within the Standard Model effective field theory (SMEFT) have explored the sensitivity of future GW observations to new physics, focusing on transitions driven by the dimension-six operator $(H^\dagger H)^3$. However, the validity of the truncated EFT expansion can become questionable in the parameter regions relevant to such transitions. We instead consider transitions driven by non-decoupling effects described by the nearly aligned Higgs effective field theory (naHEFT). We investigate whether GW observations can probe small corrections to the Higgs effective potential induced by decoupling effects in interactions other than Higgs self-interactions. As a representative benchmark for additional decoupling effects, we consider the dimension-six SMEFT operator $(H^\dagger H)(\overline{q}_3 t_R\widetilde{H})$ with Wilson coefficient $C_{uH}$. Although we focus on this benchmark, the same framework can be applied to other dimension-six SMEFT operators. We perform two-parameter Fisher matrix analyses for DECIGO and BBO to quantify their expected sensitivity to $C_{uH}$ and the naHEFT mass scale $\Lambda$. For the benchmark configurations considered, the non-decoupling dynamics generates a detectable GW signal. We find that these small corrections can produce potentially measurable changes in the GW spectrum, even after accounting for the correlation between $C_{uH}$ and $\Lambda$.

Zero Trust (ZT) replaces the implicit trust of perimeter-based security with explicit, continuous, context-aware authorization. This shift is particularly relevant to IoT and cyber-physical systems, whose heterogeneous, long-lived, and remotely connected components make persistent trust untenable. Yet their physical coupling complicates ZT adoption: restricting a suspicious component can reduce cyber exposure while removing telemetry or control capabilities required for operation. Existing work mainly models physical harm caused by attacks, with less attention to consequences introduced by enforcement itself. We introduce Safety-Aware Zero Trust (SA-ZT), which treats restriction-induced physical consequences as policy inputs. We map the NIST ZT tenets to nine IoT/CPS convergence strains, distinguish IoT-amplified challenges from those specific to cyber-physical coupling, and derive corresponding operational requirements. SA-ZT extends the NIST ZT Architecture with a Safety Engine and a Telemetry Broker. The Safety Engine selects among admissible responses by jointly considering residual cyber risk and restriction-induced consequences, while the Telemetry Broker mediates raw telemetry visibility and estimator influence. With command-side enforcement, these entities separate raw visibility, automated influence, and state-changing authority, preserving observations for monitoring while constraining their influence on automated control. An IEEE 30-bus case study under false-data-injection attack illustrates how SA-ZT makes cyber containment, telemetry visibility and influence, physical consequences, and authorization timing explicit, providing an implementable and inspectable representation of cyber-physical enforcement trade-offs.

We disprove the Reiner–Shimozono conjecture that products of key polynomials have nonnegative expansions in Demazure atoms. By relaxing the defining relations of Demazure modules, we obtain an exact coefficient-extraction formula that yields an explicit infinite family of counterexamples, including negative coefficients in twenty-eight variables. These examples answer van der Kallen's long-standing open question on relative Schubert filtrations negatively, already for tensor products of two dual Joseph modules. For individual atom coefficients, we give a sufficient criterion for positivity that is checkable in polynomial time in the binary input length, uniformly in rank. For each fixed rank $n\ge4$, this criterion recognizes a nonvanishing proportion of the positive atom coefficients as the bound on the composition entries tends to infinity.

The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

Nonadiabatic Matsubara dynamics has been proposed in both the Meyer-Miller-Stock-Thoss (MMST) and spin-mapping representations, whereby the dynamics are truncated in the higher path-integral normal modes of the nuclear degrees of freedom, but no truncation is performed in the electronic variables. In contrast to single-surface Matsubara dynamics, these methods do not appear to conserve the Quantum Boltzmann Distribution (QBD) for general systems. Recently, it was shown that truncating in the electronic path-integral normal modes of the MMST representation does not lead to conservation of the QBD for a single trajectory or accurate computation of a correlation function. Here, the electronic path-integral normal modes in the spin-mapping representation are investigated. We focus on a two-level system although we expect our findings to be applicable to any number of electronic states. We find, perhaps surprisingly, that the higher normal modes of the spin-vector $z$-component, the difference in state populations, are constrained by the QBD, that the time-evolved state population observable is a function of only the spin-mapping centroid, and that the full $N$-bead computational results are replicated using only the spin-mapping centroid, leading to accurate, QBD conserving dynamics. While at present these results are not a generally-applicable method, we believe this may explain the recent success of spin-mapping approaches compared to MMST approaches, %To our knowledge, this is the first method obtaining conservation of the QBD when truncating in electronic normal modes and should aid the future derivation of highly accurate and Quantum Boltzmann conserving nonadiabatic dynamics methods.

The optical properties (scattering phase function SPF; degree of linear polarization DoLP; reflectance) of the dust particles orbiting in debris disks can be retrieved through scattered light imaging and are linked to the physicochemical properties of the dust (size, shape, composition...). Among debris disks, the bright, narrow disk surrounding HR 4796A presents several peculiarities, in particular unusually high DoLP values at small scattering angles. We aim at improving the constraints on the properties of the dust particles orbiting in HR 4796. We use new observational data (SPHERE/ZIMPOL and IRDIS) in scattered light of HR 4796, for lambda = 0.63 um; 0.79 um and 1.25 um. We modeled the disk at each of these wavelengths and found geometric parameters consistent with previous results. We obtained the parametrized SPF and DoLP over the whole range of scattering angles (13 degrees to 167 degrees) and extracted the DoLP and spectral reflectance at 90 degrees (without any parametrization) from the visible to the NIR wavelength range. We compared the reflectance and polarimetric properties of HR 4796 to those measured on a laboratory dust sample and find that the sample providing the best match appears to be large iron sulfides particles. We confirm that the DoLP of HR 4796 peaks at high values (> 45 percent) and for small scattering angles (< 55 degrees). At a 90 degrees scattering angle, we observe a red spectral slope in the visible and NIR wavelength range, as well as a blue polarimetric slope. These results are compatible with large (a few um to 100 um) absorbents being the main scatterers in the disk. We show that the DoLP of HR 4796 is notably different from that of Solar System comets and seems closer to that of some more processed near-Earth orbit asteroids, possibly indicating devolatilization and/or melting induced by space weathering on the dust particles of HR 4796.

Multimodal learning (MML) falls into the optimization dilemma due to the modality imbalance phenomenon, leading to suboptimal overall performance in practice. While many attempts primarily focus on balancing the optimization dynamics across modalities to address this issue, we identify a subtle yet critical flaw: optimization yields asymmetric gains in predictive certainty, with the strong modality more confident than the weak one, driving imbalanced modality contributions. In this paper, our analysis reveals that this flaw stems from unimodal characteristics rather than multimodal learning, and this confidence discrepancy can be corrected by positive cross-modal intervention. Based on this insight, we propose multimodal Max Confidence Regularization (MaxCR) to dynamically intervene in modality semantic confidence. Specifically, the semantic confidence of each modality is tracked using a nonlinear sparsity measure. We then design max suppression and max excitation based on this measure to regularize strong and weak modalities, respectively. They penalize and encourage the top-1 confidence, thereby constraining multimodal prediction. To this end, strong and weak modalities are expected to make calibrated confidence, thereby improving the overall performance. Empirical experiments on widely used datasets reveal the superiority of our method through comparison with various state-of-the-art (SOTA) multimodal learning baselines.

The Large Magellanic Cloud (LMC), a satellite galaxy of our Milky Way, is considered to be a very good target for investigations of diffuse gamma-ray emission. Observations have shown that diffuse emissions are related to the large- and small-scale structures of the LMC. Particularly, it has been suggested that some of the small-scale bright diffuse emissions coincide with supergiant shells (SGSs) previously identified based on H$\alpha$ images. We analyzed the gamma-ray emission from the LMC using more than 15 years of observations with the Fermi Large Area Telescope in the energy range of 300$\,$MeV-300$\,$GeV. A dedicated spatial and spectral analysis was made for diffuse emission components of the LMC. Particularly, we evaluated the emissions from SGSs in detail using phenomenological approaches, and we established their corresponding spatial templates for gamma-ray emission. In the analysis of small-scale extended emissions, we detected seven H$\alpha$-selected SGSs at a significance of more than $5\sigma$. The emission structure nested inside the SGSs appears to be a non-Gaussian feature and is very likely due to a modulated cosmic-ray distribution by an ensemble of supernova remnant shocks. The spectra of the gamma-ray emission for most SGS regions favor a hadronic origin. For the large-scale diffuse emission from the LMC disk, our results suggest an interplay of hadron- and lepton-induced emission. The cosmic-ray proton energy density derived for bright SGSs is 3-10 times higher than that in the LMC disk. SGS$\,2$ was detected to be the most significant emission region among all SGSs. Based on the gamma-ray excess emission we detected in H$\alpha$-selected SGSs in the LMC, we estimate that their contribution to the total diffuse gamma-ray emission in the LMC is at a non-negligible 41% level.

We study the high-dimensional recovery of a signal vector $\mathbf{x}$ in the presence of sparse Wishart-like noise. We define an $N \times N$ matrix $A = J+(\theta/N)\mathbf{xx}^{\top}$, where $\mathbf{xx}^{\top}$ is the rank-one deformation of the random noise matrix $J$. We consider a Wishart-like matrix $J={X}^{\top} X$, where $X$ is a sparse $M \times N$ random matrix with entries $X_{ij} = c_{ij}W_{ij}$, with $c_{ij}$ regulating the density of non-zero elements, and $W_{ij}$ the bond weights. Using the replica method, we compute analytically the top eigenpair statistics of $A$, and their dependence on the signal strength $\theta$, the rectangularity ratio $\alpha=\sqrt{M/N}$, and the average connectivity of the noise. The spectral observables are expressed in terms of a system of Recursive Distributional Equations, which are efficiently solved via a Population Dynamics algorithm. They allow us to compute the average largest eigenvalue $\langle\lambda_1\rangle_{A}$, the average top eigenvector component density, and the average overlap between the top eigenvector of $A$ and $\mathbf{x}$. We identify a critical threshold $\theta_{\mathrm{crit}}$–depending on the average connectivity of the noise–that marks a BBP-like phase transition: below this value, $\langle\lambda_1\rangle_{A}$ is unaffected by the signal, and the overlap vanishes. Thus, the signal is not recoverable from the top eigenvector of $A$. For $\theta>\theta_{\mathrm{crit}}$, the signal-related outlier eigenvalue becomes $\langle\lambda_1\rangle_{A}$ and the overlap is nonzero, allowing for recovery of the signal. The results are in excellent agreement with numerical diagonalisation. We show that in the dense limit, the recovery threshold and eigen-statistics converge to the results predicted by the classical BBP transition for additive rank-one deformations of dense Wishart matrices.

In the compressible liquid drop model (CLDM), the curvature energy term has been included in many works in the literature, and its effects on the presence of pasta phases have also been extensively investigated. However, the analytical part of the inclusion used to cease once a 4-order algebraic equation for the optimized size of the nucleus was written. In this paper, an optimization is suggested to the analytical part of the solution of the CLDM equations. Solving analytically the 4-order algebraic equation proves to be helpful for a straightforward identification of the denied parameter ranges in which the CLDM has no real-root solutions. Using a particular nuclear force derived from the chiral effective field theory, I investigate effects on the ground state of the nucleus curvature. Surprisingly, the inclusion has lead to a significant modification of the range of baryon density in which the bubble phases are found, disfavoring the bubble phases from the ground state. This shows a strong difference between the predictions of the CLDM with the nucleus size obtained when including the curvature term and that obtained from the $w_\mathrm{s} = 2w_{\mathrm{C+L}}$ approximation. The importance of the curvature energy in the CLDM is linked with its ability to change qualitatively the ground state. This paper presents an analytical extension to the CLDM solution, which is ready to be used with any other nuclear model in the future, in order to optimize the inclusion of the nuclear curvature energy, and is not limited to one nuclear model.

Advantage-guided reinforcement learning provides a practical way to post-train vision-language-action (VLA) policies using limited robot data. However, its performance depends on several coupled choices, including how critic-derived advantages are constructed, calibrated, and used for policy training. Existing recipes often combine these choices into a single end-to-end procedure, making their individual effects difficult to identify. In this work, we dissect advantage-guided VLA post-training through a controlled empirical study that separates these design choices while accounting for their distinct estimands. We develop stage-specific offline evaluation methods to screen alternative choices efficiently, without requiring extensive real-robot policy evaluations for every possible combination. The staged evaluation identifies a modular recipe that combines temporal-difference advantage construction, group-wise calibration, and continuous advantage weighting. Across four real-world bimanual tasks, the resulting recipe improves mean task progress and success over the SFT initialization by 0.42 and 0.63, respectively. Moreover, the proposed evaluation diagnostics show an overall alignment with downstream real-world performance, supporting their use for interpreting empirical outcomes and selecting advantage-guided post-training designs in practice.

Existing link-based combinatorial preprocessing methods speed up the computation of persistent homology by removing a vertex or edge only when its link remains a cone. We replace this condition with a quantitative homological certificate. The reduced homology of the filtered link of a generator (a vertex or edge) defines a local obstruction module whose future part describes the effect of deleting that generator. Its barcode certifies either exact deletion or an explicit bound on the bottleneck error, and a conflict colouring extends this guarantee to families of generators. Our implementation, HomTrim, removes an additional 13% to 41% of the input edges beyond domination-only preprocessing and reduces backend persistence time by factors ranging from 1.55 to 4.61 on weighted flag filtrations. The same module also yields regularity diagrams that measure how far a generator can move before becoming visible to homology, together with a multiscale stability result.

Standard contrastive learning frameworks are mainly designed from a semantic perspective, yet learning 2D visual representations that preserve 3D spatial structure is also important for scene understanding. In this work, we propose Depth-Guided Contrastive Learning (DGCL), a simple auxiliary objective that injects 3D spatial awareness into 2D contrastive representation learning. Our key idea is to use depth to convert local 3D proximity into contrastive similarity: pixels that are closer in 3D space are encouraged to have more similar representations than pixels that are farther apart. Instead of relying on absolute depth values, DGCL formulates supervision through relative 3D distance comparisons among randomly sampled pixels, making the objective invariant to depth scale, efficient to compute, and easy to integrate into existing contrastive frameworks. Experiments across different datasets and models show that DGCL consistently improves 2D representation learning and benefits semantic downstream tasks by stronger spatial and geometric understanding. The code is available on https://github.com/LeungTsang/DGCL.

We derive an analytic black-hole family in three-dimensional scalar–tensor Einstein–Gauss–Bonnet gravity with positive coupling. A single implicit equation determines the static circular metric and a scalar linear in time. We show that these solutions exhaust regular nonextremal exteriors with the stated AdS boundary conditions and a fixed nonzero coefficient of time in the scalar. The coupled metric and scalar perturbations have one propagating degree of freedom. On one branch, its kinetic coefficient is positive, its equation is hyperbolic throughout the exterior, and its bulk spatial energy is positive for perturbations of compact support. Scalar signals can cross the metric horizon outward, so exterior evolution needs information from the interior. For linear perturbations with the original metric and scalar boundary values fixed, nonzero compact initial master displacements with zero velocity can evolve only until their first contact with the AdS boundary. We derive this restriction from the original metric and scalar equations.

We construct forward discretely self-similar (DSS) solutions of two-dimensional Navier-Stokes equations with arbitrarily large data in $L^2_{loc}(\mathbb{R}^2\setminus\{0\})$. For such rough initial data, we first establish a sharp linear estimate under the discrete scaling, which identifies the \(L^2\)-norm of the initial datum on a fundamental annulus with the Dirichlet energy of its caloric lift over one period in logarithmic time. This, together with a structural cancellation between the linear profile and the nonlinear remainder over one period in logarithmic time, yields a uniform \(\dot{H}^1\)-bound for the remainder, where the natural $L^2_{loc}$-regularity of the initial data seems to be sharp. Since the two-dimensional Leray operator has no \(L^2\)-coercivity, we recover uniform energy control for the remainder by exploiting \(L^p\)-estimates ($1<p<2)$, together with a key bootstrap argument and periodicity. We then first construct smooth DSS solutions using further weighted estimates and a fixed-point argument as long as the initial data belong to $C^2_{loc}(\mathbb{R}^2\setminus\{0\})$. These stronger weighted bounds are not uniform under approximation of rough data. Instead, the passage to \(L^2_{\rm loc}\) data relies only on the unweighted energy estimates. Finally, we use strong time continuity of the limiting periodic profile to recover the uniform spatial tightness needed to verify the initial data.

Downlink channel state information (CSI) feedback is essential for frequency-division duplex massive MIMO, yet the feedback overhead grows rapidly with the numbers of antennas and subcarriers. To reduce this overhead, most deep learning approaches compress CSI by treating it as a generic image, leaving its low-rank multipath structure unexploited. In contrast, model-driven alternatives explicitly embed this structure in iterative recovery, but at the cost of high computational complexity and latency. To overcome these limitations, we propose a low-rank prior-guided (LRP) framework that performs learnable rank-one sensing at the user equipment to compress CSI into low-dimensional codewords, and reconstructs CSI by direct rank-one synthesis at the base station. Both compression and reconstruction are jointly optimized, and fully exploit the low-rank structure of CSI. We further develop DCRNetV2, which preserves LRP as its backbone and uses gated dilated-convolutional residual paths to compensate for finite-rank errors. Experimental results show that LRP outperforms iterative model-based methods with lower complexity, and DCRNetV2 achieves a better accuracy-complexity tradeoff than existing learning-based methods.

The decoupling of phonon and electron transport remains a central challenge in the development of high-performance TE materials. Configurational-entropy maximization is widely invoked as a design principle for decoupling phonon and electron transport. This study investigates compositionally engineered LaCoO$_3$-based high-entropy perovskites to determine whether thermoelectric transport can be improved by tuning cation identity and concentration rather than maximizing configurational entropy. La$_{1-x}$Sr$_x$(CoFeMnCrNi)O$_3$ ($x=0.0$–$0.2$) and selected non-equimolar A- and B-site perovskite compositions were prepared by solid-state reaction. The obtained samples are predominantly single-phase, as confirmed by X-ray diffraction and Rietveld refinement, consistent with the calculated size-disorder parameters. Multication disorder introduces substantial mass and strain-field fluctuations that promote phonon scattering. All samples exhibit p-type, thermally activated electrical transport consistent with adiabatic SPH. Sr substitution progressively reduces the hopping barrier and $\rho$, whereas non-equimolar B-site engineering partially recovers electrical transport while retaining low k. La$_{0.9}$Sr$_{0.1}$Co$_{0.4}$Cr$_{0.3}$Ni$_{0.1}$Fe$_{0.1}$Mn$_{0.1}$O$_3$, featuring a Co-rich and Cr-rich B-site composition, combines Co-associated mixed valence and spin-state degeneracy that sustain a large alpha with Cr-mediated control of carrier concentration and a reduced polaron hopping barrier of 0.19eV. This composition achieves a power factor of 40–43 $\mu$W/(m K$^2$) and a $zT\sim0.072$ at 1100K, approximately 2.7 times that of its equimolar analogue. These results demonstrate that targeted cation chemistry and mass contrast, rather than configurational-entropy maximization alone, provide an effective strategy for balancing electronic and phonon transport in multicomponent oxide TE.

Global building and settlement products increasingly support population mapping, exposure assessment, and urban monitoring, yet comparative evidence remains fragmented across representations, geographic contexts, and evaluation methods. We benchmark seven global or near-global products against harmonized reference building footprints across 135 study areas. Our representation-aware framework integrates complementary measures of detection, geometric agreement, and aggregate quantity accuracy with stratified analyses of settlement characteristics, evaluation resolution, reference provenance, and temporal alignment. Overture Maps achieved the highest median city-level vector F1 (0.786), while 3D-GloBFP showed the closest aggregate building-area agreement despite weaker detection performance. Raster rankings were scale-dependent: Google Open Buildings Temporal (OBT) performed best at 10\,m (F1 = 0.680), whereas WSF Tracker led at 100\,m (F1 = 0.904) but substantially overestimated reference building area (relative bias = 1.845). Raster accuracy increased with building density ($\rho=0.58$–$0.75$), while smaller candidate footprints were disproportionately associated with vector false positives. Temporal alignment improved WSF Tracker mean city-level F1 by 0.060. These findings demonstrate that product reliability depends on representation, spatial scale, and settlement context, providing a reproducible framework for assessing the suitability of EO-derived urban information for different applications.

Biorthogonality plays a central role in the analysis of non-Hermitian photonic systems, where modal expansions generally require both right and left eigenstates. While these concepts are straightforward within scalar and coupled-mode descriptions, their interpretation in the full vectorial Maxwell framework is less transparent. In particular, the standard electromagnetic modal orthogonality relation derived from unconjugated Lorentz reciprocity involves both electric and magnetic fields and differs in form from the biorthogonality relations obtained from conventional adjoint-operator arguments. Here, we establish the connection between these two formulations for non-Hermitian waveguiding systems with gain and loss. Starting from the full vectorial electric-field wave equation, we formulate the guided-mode problem as a quadratic eigenvalue problem in the propagation constant, construct its adjoint, and identify the corresponding left eigenmodes. We show that the left eigenmode is related to the complex conjugate of the backward-propagating electric-field mode and demonstrate that the resulting electric-field biorthogonal pairing is equivalent to the mixed electric–magnetic field relation obtained from unconjugated Lorentz reciprocity. The framework also clarifies the electromagnetic meaning of modal normalization, its connection to self-orthogonality at exceptional points, and the recovery of conventional conjugated modal orthogonality in the lossless limit. These results provide a unified operator-theoretic interpretation of electromagnetic biorthogonality and Lorentz reciprocity and establish a direct connection between the left/right eigenstate language of non-Hermitian physics and the reciprocity-based modal framework of classical electromagnetism.

We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence of the Sobolev constant on the Lebesgue exponents and allow us to recover the asymptotics of the continuous case. As a consequence we derive a discrete version of the Trudinger inequality and variants. We extend our results to broken Sobolev spaces and discuss implications of these new or refined discrete functional inequalities in the numerical analysis of non-conforming numerical methods.

Finite corner curvature is commonly omitted when rarefied cavity flows are represented using idealised geometries. This study examines how downstream corner rounding affects lid-driven cavity flow over 0.5 $\le$ Kn $\le$ 5. Direct simulation Monte Carlo calculations were performed for normalised corner radii of Rc = 0, 0.10 and 0.20. The model was assessed through published benchmark data and a local grid-sensitivity test. Velocity fields, centreline profiles, area-averaged speed, translational temperature, number density and temperature anisotropy were analysed. A single primary vortex persisted across all cases. Corner rounding modified the local turning of the downstream return flow but caused little change in the wider circulation. The root-mean-square differences between the rounded and sharp-cornered centreline velocity profiles remained below 0.007. The area-averaged normalised speed increased in all rounded configurations, with a maximum change of approximately 2.5%. The thermodynamic response showed a stronger dependence on rarefaction. Corner rounding reduced the mean temperature non-uniformity at Kn = 0.5 and 1, but increased it at Kn = 2 and 5. Changes in the mean density deviation remained within approximately 1.3%, while the mean translational-temperature anisotropy varied from about -3% to 2.4%. The results show that the sharp-corner approximation captures the global velocity structure under the conditions studied, but can omit local flow changes and small thermodynamic responses associated with finite corner curvature.