Quasi particle based (e.g. Boltzmann equation) studies of spin wave transport often assume that their scattering rates follow the simple form $η=αω$, with the Gilbert damping $α$ and frequency $ω$. In this work, we examine the effective damping $α_{eff,T}=η/ω$ observed in atomistic spin dynamics, when temperature and spin wave interactions are introduced for a 1D spin chain. We extract the dynamical correlation functions from spin trajectories propagated using the stochastic Landau-Lifshitz-Gilbert equation, and fit the dynamical structure factor, yielding the dispersion and scattering rates for a wide range of temperatures. The resulting effective damping can be very different from the initially constant Gilbert value. It exhibits a temperature and crystal momentum scaling which we explain based on interactions with the Gilbert bath and spin wave scattering by changes in local magnetic order.

In this paper we will study the equivalence between super-Poincaré inequality and some log-Sobolev type inequalities, including weak log-Sobolev inequality and super log-Sobolev inequality. The explicit relations between associated rate functions will also be established.

We prove a volume-uniform effective-Hamiltonian theorem for bounded finite-range quantum spin systems on possibly infinite lattices. For any finite target region, we construct an energy-truncated Hamiltonian and prove a volume-uniform spectral-overlap bound controlling the leakage of its low-energy spectral subspace into the high-energy spectral subspace of the original Hamiltonian. The bound may contain non-exponential spectral-window terms, but its cutoff-dependent remainder decays exponentially in the cutoff. In finite volume, this yields stability of low-lying eigenvalues, with eigenvalue errors controlled by the exponentially small cutoff-dependent remainder. In infinite volume, we prove the corresponding spectral-overlap estimate in the GNS representation of an infinite-volume ground state. Thus, for bounded finite-range interactions, we extend and strengthen the effective-Hamiltonian mechanism of Arad, Kuwahara, and Landau by replacing the finite-volume operator-norm formulation with a volume-uniform spectral-overlap formulation applicable in the thermodynamic limit.

In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on the resulting nonlinear systems encounters two potential difficulties: (i) if the graph contains cycles, edge variables are not unique, and (ii) there is no guarantee that the density variables remain positive. To address these challenges, we introduce a finite-difference-type Newton method that eliminates cycle-induced redundancies through a spanning-tree gauge, resulting in a reduced set of independent variables and a well-posed, sparse linear system. For the lattice graph arising from the continuous optimal transport problem, density positivity can also be guaranteed by using an upwind discretization subject to a CFL-type condition. We further demonstrate the versatility of the proposed scheme by applying it to a range of problems, including optimal transport on lattices and random graphs, inverse optimal transport problems, and social network analysis.

In the extreme environments of high-luminosity colliders, traditional planar silicon sensors suffer severe radiation-induced performance degradation and fail to satisfy the stringent demands of high-precision tracking and high-speed timing in particle physics. 3D silicon sensors enhance radiation hardness by shortening charge collection distance, yet conventional designs with columnar or square-cell trench electrodes exhibit non-uniform electric fields, including saddle points and low-field regions, which degrade charge collection efficiency and timing resolution. This work presents a novel racetrack 3D-trench silicon sensor with continuous racetrack electrodes surrounding a long central collection electrode, aiming to eliminate electric field inhomogeneities. For the first time, a 23 $μ$m shallow-etched device was fabricated on an 8-inch platform, which provides a promising basis for its subsequent mass production and engineering applications. The device performance was systematically evaluated through theoretical analysis, 3D TCAD simulations, and characterization using semiconductor parameter analyzers and transient current technique (TCT) measurements. The sensor achieves leakage current below 0.2 nA, breakdown voltage above 110 V, full depletion voltage as low as a few volts, capacitance as low as 650 fF, collected charge of 4 fC, time response of about 640 ps, and time resolution of 50 ps. This large-scale manufacturable, shallow-etched racetrack 3D-trench silicon sensor provides a competitive device solution for portable radiation detection and next-generation 4D tracking under high-radiation and high-event-rate conditions.

Noncommutativity of states and observables is a fundamental signature of quantum theory, and a minimal requirement for nonclassicality. We provide a universal necessary and sufficient condition for pairwise commutativity of quantum states $ρ_1$ and $ρ_2$: they commute if and only if $\mathrm{tr}(ρ_1^2ρ_2^2) = \mathrm{tr}(ρ_1 ρ_2 ρ_1 ρ_2)$. For qubits the identity simplifies to an equality between polynomials of purities and of the two-state overlap $\mathrm{tr}(ρ_1ρ_2)$. These multivariate traces (known as Bargmann invariants) are directly measurable, allowing commutativity tests that bypass full state tomography. We point out possible applications to the analysis of POVM simulability and partial photonic distinguishability.

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process, specifically an adjusted-range normalizer for scalars and a matrix normalizer for vectors, our approach avoids direct estimation of the long-run covariance matrix. Consequently, it eliminates the need for the ad hoc bandwidth, kernel, and lag-truncation choices required by traditional methods. We establish the asymptotic theory for these statistics, deriving pivotal null limiting distributions and proving test consistency. Monte Carlo simulations show that the proposed tests effectively mitigate the finite-sample size distortions associated with traditional heteroskedasticity and autocorrelation consistent (HAC) methods, while retaining strong empirical power against conditional predictability alternatives.

With the rapid evolution of emerging programming language ecosystems, the demand for code translation to low-resource languages continues to grow. As Cangjie emerges as a new programming language, its ecosystem and development toolchains are rapidly expanding. Automated translation from popular programming languages to Cangjie is therefore valuable for practical development. However, constrained by both insufficient Cangjie knowledge and scarce parallel code corpora, general Large Language Models (LLMs) are prone to syntactic errors and semantic as well as structural misalignment in code translation. Existing approaches typically rely on fine-tuning with large-scale parallel data, but they cannot reliably improve compilability or semantic consistency for low-resource Cangjie languages. To tackle these challenges, we propose a multi-stage training framework of LLMs that employs the iterative error repair technique to translate Java code into Cangjie code. This training framework performs training on LLMs, gradually integrating knowledge and achieving semantic alignment as well as structure awareness. During the code translation, we also combine the compiler feedback and error repair case retrieval to repair the incorrect Cangjie code. We construct syntactic knowledge and monolingual instruction datasets to train the LLM. In addition, we also build a Cangjie error repair repository to support error repair in our approach. Experimental results show that, with limited parallel data, our approach improves functional equivalence by 6.06\% compared to the state-of-the-art approaches. Meanwhile, ablation studies confirm that each training stage positively contributes to the final performance.

Applying nonlinear model predictive control (NMPC) to systems with hybrid dynamics or discrete actions typically yields mixed-integer nonlinear programs (MINLPs), whose real-time solution remains a major challenge and limits the applicability of mixed-integer NMPC (MINMPC). This paper proposes a myopic MINMPC framework that incorporates value-function approximation to substantially reduce the online computational burden. Using Bellman's principle of optimality, we shorten the prediction horizon and append a value function learned offline from expert state-action demonstrations via inverse optimization with optimality residual minimization. A central feature is the dual treatment of discrete decisions, whereby integer constraints are relaxed during offline learning to enable KKT-residual-based value function synthesis, while the online controller enforces the true integer constraints to ensure feasibility. The learned value function induces a policy that is approximately policy-consistent with the expert demonstrations. The resulting controller achieves high closed-loop performance with a significantly shorter horizon, enabling real-time MINMPC. The effectiveness of the approach is demonstrated on the Lotka-Volterra fishing problem and a satellite attitude control system with discrete actuators.

Wi-Fi is the dominant wireless access technology, but its widespread use also exposes systems to threats such as rogue access points, deauthentication attacks, and other IEEE 802.11-specific vulnerabilities. Although Cyber Ranges (CRs) have become valuable platforms for cybersecurity training and experimentation, existing wireless-oriented solutions mainly target heterogeneous IoT or mobile-network settings, with Wi-Fi typically treated as one among many. As a result, dedicated CR environments for Wi-Fi-specific security experimentation remain limited. This gap is particularly relevant because wireless attacks often require protocol-aware experimentation that is difficult to reproduce in conventional training environments. This paper introduces a conceptual architecture for a Wi-Fi-focused CR tailored to IEEE 802.11 security scenarios and an open-source prototype. The proposed design is grounded in established CR design principles and organized around core infrastructure, learning management and support, monitoring, management, and access-control zones. Structuring the platform into these distinct zones, the architecture supports modularity, scalability, and future extensibility. Part of the design is realized in a prototype publicly available in a GitHub repository that implements the scenario generation, storage, retrieval, and instantiation workflow, offering an initial practical foundation for the proposed architecture. Overall, the paper provides a structured foundation for the future implementation of Wi-Fi-specialized CR platforms for targeted experimentation.

To complete the analysis of the 2023 KMTNet subprime-field microlensing planetary events identified by its AlertFinder system, we present the analysis of six events, KMT-2023-BLG-(1810, 0084, 1118, 0584, 1697, 2218). We find that the first three events are securely confirmed as planetary, with inferred mass ratios of $\log q \sim -1.9$, $-2.0$, and $-2.6$, respectively. The remaining three events exhibit the well-known degeneracy between binary-lens/single-source (2L1S) and single-lens/binary-source (1L2S) models, and two of these also admit viable stellar binary solutions. A Bayesian analysis indicates that the companions in the confirmed planetary events are likely either super-Jupiters orbiting beyond the snow line of M- or K-dwarf hosts or, for two degenerate solutions of KMT-2023-BLG-1118, Saturn-mass planets orbiting late-type M dwarfs. To date, the 2023 KMTNet sample contains 25 unambiguous planetary events, and its mass-ratio distribution is consistent with that of the KMTNet planetary sample from 2016--2019.

Sparse Matrix-Vector Multiplication (SpMV) is the cornerstone in many iterative workloads, including large-scale graph analytics and sparse iterative solvers. Accelerating SpMV on real-world graphs remains challenging due to highly irregular sparsity patterns. In this paper, we propose MERBIT, a GPU SpMV method designed for repeated SpMV on irregular, graph-like sparse matrices, with PageRank as a representative motivating workload. MERBIT combines two key ideas from existing GPU SpMV methods. At the global level, it uses merge-path partitioning to balance work over nonzeros and row boundaries. At the local level, it encodes each merge-path segment using a compact bit-field descriptor. MERBIT improves workload balance and promotes coalesced memory access for both matrix loading and output writes; moreover, three optimization strategies are incorporated to further enhance performance. Experiments on 50 large irregular datasets demonstrate that MERBIT outperforms competitive baselines, including cuSPARSE, Ginkgo, and academic approaches, achieving average speedups of 1.27 and 1.25 over cuSPARSE COO in single and double precision, respectively.

Transaction selection in parallel or DAG-based distributed ledger technologies (DLTs) is a crucial challenge that directly impacts throughput, fairness, and validator incentives. In these systems, validators independently choose transactions to include in their blocks, often relying on naive heuristics like uniform or proportional selection. This can lead to inefficient outcomes when validators prioritize their own rewards without considering collective impacts. We analyze two fee allocation mechanisms used in practice: Random Fee Allocation (RFA), where transaction fees are randomly assigned to one validator, and Collaborative Fee Sharing (CFS), where fees are distributed equally among all validators. Using a single-shot game-theoretic framework, we derive symmetric Nash equilibria (NE) for selecting transactions for both mechanisms and propose an optimization-based method to compute these equilibria. Numerical simulations demonstrate that the NE of CFS consistently achieves higher throughput and rewards compared to the NE of RFA, particularly under skewed fee distributions. Additionally, we compare these equilibrium strategies to naive benchmarks (uniform and proportional selection), showing that the proportional strategy outperforms the NE of RSA in many situations. These findings may provide actionable insights into the design of transaction selection and incentive mechanisms, enabling more robust and high-performance DAG-based DLTs.

Large-scale online service platforms face severe challenges from organized platform abuse: multiple forms such as credit card fraud and promotion abuse continually emerge, characterized by large numbers of involved accounts, rapid outbreaks, and constantly shifting tactics. Existing mainstream approaches, whether heuristic rules limited in precision, supervised learning with insufficient generalization, or graph models that are engineering-heavy and dependent on seed users, have failed to address such threats effectively. This paper returns to first principles and, starting from the economic constraints of fraudulent behavior, proposes the Fraudster's Trilemma: organized attackers cannot simultaneously achieve scale, low cost, and dispersed cash-out. Building on this theory, we derive a robust structural invariant in organized fraud, namely centralized cash-out, and use a simple statistical method to turn low-precision individual weak signals into high-precision strong decisions. The method requires no labels, is nearly parameter-free, white-box interpretable, has linear complexity O(|E|), avoids cold-start issues, and its detection logic possesses the "open-hand" property: attackers cannot evade it even when fully informed. We validate the approach on two real fraud incidents in backtests. In the promotion abuse case, a single near-zero-cost weak signal (global Precision of only 16%) after structural amplification achieves Precision above 91% and Recall exceeding 99% (z=10.0); at a higher threshold (z=40.0), Precision reaches 93.7%. In the credit card fraud case, an infrastructure-layer weak signal (device spoofing) successfully detects payment-layer attacks without any business-logic linkage, revealing the framework's natural MO-agnostic property: it relies more on the structural invariant than on signal semantics.

Ferroelectricity, a hallmark of spontaneous inversion-symmetry breaking, has been a central concept in condensed matter physics and functional materials research, yet recent discoveries are revealing that switchable polarization can emerge in forms far richer than allowed by the conventional symmetry-based paradigm. Fractional quantum ferroelectricity and ionic-conductor ferroelectricity challenge the long-standing association of ferroelectricity exclusively with polar space groups. In this Review, we reconcile these emerging phenomena within the Berry-phase modern theory of polarization. We emphasize that polarization in insulating periodic crystals is not a single-valued vector, but a multivalued lattice quantity defined modulo a polarization quantum. Consequently, nonpolar crystals may possess nonzero formal polarization, and adiabatic paths connecting symmetry-equivalent structures can produce quantized changes in polarization without violating symmetry principles. The symmetry of this multivalued formal polarization is governed by a generalized Neumann principle. We further show that the large polarization changes induced by long-range ion migration in both fractional quantum ferroelectrics and ionic-conductor ferroelectrics can be naturally understood through the topological definition of oxidation state, which links ionic transport to quantized charge transfer and polarization change. We discuss the physical accessibility of these unconventional polarization states, highlighting the roles of switching pathways, boundary conditions, and domain-wall dynamics, particularly in systems such as $α$-In$_2$Se$_3$. Finally, we suggest that the most promising functionality of these materials may lie not in conventional bulk ferroelectric switching, but in the creation and control of charged interfaces and domain walls arising from discontinuities in formal polarization.

We discuss the problem of counting certain LEGO structures, primarily those comprising parallel $w \times 1$ tiles. These can be combined, as a single LEGO structure, by interlocking the tiles. %Alternatively, if the interlocking condition is relaxed, so that tiles can also be placed end-to-end, a greater number of possible configurations results. We also study the historically earlier problem of counting the number of ways to combine $2 \times 4$ LEGO tiles, which in this case gives a 3-dimensional structure. In all cases the number of configurations is dominated by an exponential growth term, $μ^n$ where $n$ is the number of tiles. We present an algorithm for counting these various LEGO configurations, and use the data to estimate the asymptotics. We analyse the data so generated, and conjecture that, for the two-dimensional structures, the number of possible configurations grows like $A(w)μ(w)^n/n,$ and we give numerical estimates for $A(w)$ and $μ(w)$ for $w < 11,$ while for the three-dimensional structure the number of possible configurations is conjectured to grow like $Aμ^n/n^{3/2},$ where $μ= 117.25 \pm 0.05.$ We also study the sequences that arise when we fix the number of tiles $n,$ and vary the tile size $w.$ We prove that the sequences are polynomials of degree $n-1,$ and we give these explicitly for $n=1 \ldots 14.$

This paper develops a two-period dynastic overlapping-generations (OLG) model in which parents simultaneously choose consumption, savings, fertility, and three distinct dimensions of child quality-education, physical health, and mental health-under a pay-as-you-go (PAYG) pension system. The central innovation is modelling mental health as an independent productivity-enhancing input with its own elasticity $θ$ in a Cobb-Douglas human-capital technology. This yields simple proportional allocation rules and shows how pension policy affects not only the overall level but also the composition of human capital investments. In steady state, higher PAYG contribution rates raise fertility through the Yakita effect but crowd out per-child investments in all quality dimensions, including mental health. An increase in the mental-health elasticity $θ$ shifts resources toward non-cognitive skill development while reducing fertility. These results reveal a fundamental policy tension for developing economies: pension systems that rely on children for old-age support simultaneously increase birth rates while reducing long-term human capital formation, with disproportionate effects on non-cognitive skills. The framework provides theoretical guidance for complementary policies that protect mental-health investments, with particular relevance for countries such as India where children remain a primary source of retirement security and mental-health services are underfunded.

The increasing demand for web applications containing AI-agents, seen as smart web applications, has prompted the need for new techniques to facilitate their creation. Low-code has risen as an approach that reduces the amount of handwritten code by focusing on the abstraction of components in the form of models combined with automated generators to produce applications. Existing low-code platforms are commercial, leading to drawbacks such as the risk of vendor lock-in, limited extensibility, and more. We present the open-source BESSER low-code framework, which allows users to design, generate and deploy their application via a freely accessible web-based editor, while guaranteeing transparency and extensibility.

We analyze the complexity of synthesizing random states and unitary operators in a multi-qudit system in two paradigms. In one case, we consider the situation in which we manipulate the system by applying a sequence of one- and two-qudit quantum gates that constitute the elementary, and universal, gate set. The minimum number of gates required to perform the desired operation represents the computational complexity. In the other case, we consider the situation in which we manipulate the physical system using physical fields with optimized control pulses. The minimum time required to perform the desired operation represents the physical complexity. In both cases, we use analytical arguments in combination with optimal-control-theory numerical calculations to determine the complexity of random operations. We show that the computational complexity of random states or unitary operators scales exponentially with the number of qudits. Our numerical results suggest that the physical complexity of preparing random quantum states and unitary operators scales more slowly than the computational complexity. We discuss various implications of our results, especially concerning the relationship between random and pseudorandom states and unitary operators.

We uncover a new mechanism for realizing three-component quantum droplets in ultracold Bose gases, where only one inter-species interaction is attractive. In this scheme, the inter-species attraction leads to a self-bound binary droplet, and the third component joins through Rabi coupling with one component of the binary droplet. We find that a stronger Rabi coupling leads to a larger fraction of the third component, but also destabilizes the entire droplet due to the involvement of more repulsive forces. Such instability can be remedied by a finite detuning between the Rabi-coupled components. We demonstrate these results in realistic Na-Rb mixtures, using both thermodynamic analyses and numerical simulations based on extended Gross-Pitaevskii equations. Our work outlines a general route for stabilizing multi-component droplets by bridging an existing binary droplet with additional components via suitable single-particle fields.

We propose a method to break the dark mode of two degenerate mechanical resonators (MRs) in optomechanical systems via the Coulomb interaction. Two degenerate MRs can be cooled to their ground-state simultaneously beyond the resolved sideband regime using the Coulomb interaction and an optical parametric amplifier (OPA). We show that strong and robust mechanical squeezing beyond 3 dB can be generated using the OPA and mechanical parametric amplification (MPA) introduced by the Coulomb interaction. Our results manifests that robust bipartite and genuine tripartite entanglement can be produced in a degenerate optomechanical system.

In this paper, we investigate a stochastic approximation procedure $\left(X_n\right)_{n\ge 0}$ taking values in $R$. The process is adapted to a filtration $(F_n)_{n\ge 0}$ and satisfies the recursion $X_{n+1}=X_n+\frac{b}{n+1}\big[g(X_n)+U_{n+1}\big]$, where $b>0$, $g:R \to R$ is a function and $\left(U_n\right)_{n\ge 1}$ is a sequence of bounded martingale differences adapted to the filtration $(F_n)_{n\ge 1}$. We establish the moderate deviation principle for the stochastic process $(X_n)_{n\ge 0}$. As auxiliary results, we also obtain the exponential inequality for $(X_n)_{n\ge 0}$ and the moderate deviation principle for weighted sums of bounded martingale differences.

We study a full-duplex (FD) cell-free massive MIMO system where distributed access points (APs) operate in FD mode while user equipments (UEs) remain half-duplex. Although simultaneous uplink (UL) and downlink (DL) transmissions improve spectral efficiency, they introduce residual self-interference, AP-to-AP coupling, and UE-to-UE cross-link interference. Building on prior over-the-air distributed beamforming frameworks, we develop a fully distributed beamforming design based on iterative UL and DL pilot signaling under a joint UL and DL sum mean-square error criterion that explicitly accounts for these interference components. In FD operation, simultaneous UL and DL pilot transmissions cause UE-to-UE pilot leakage, which contaminates the reconstruction of the cross terms required for AP-specific beamforming design. To mitigate this effect, we introduce a pilot-domain projection of the received signals at the UEs, which suppresses the interference component and enables accurate cross-term reconstruction at the APs. In addition, best-response updates at the UEs are employed within the alternating optimization framework to improve convergence under strong UE-to-UE interference. Numerical results demonstrate faster convergence and higher effective sum rate, with particularly significant gains for strongly interfering UEs, compared with both separate UL and DL distributed OTA beamforming training schemes and designs based solely on local channel state information.

Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods, like the multigrid method, can only efficiently solve the low-frequency components in the error, but not the high-frequency components. In this paper, we apply neural operators to address this issue. By adopting a preconditioning approach, we propose a novel training strategy that trains neural operators to solve the high-frequency components efficiently. Then, we combine the neural operators with some classical iterative solvers, like the weighted Jacobi method, to obtain an efficient hybrid iterative algorithm for the integral equations. We analyze the generalization error of our training strategy and the convergence of the hybrid iterative algorithm. We test our algorithms on large-scale and ill-conditioned linear systems discretized from one- and two-dimensional convolution-type integral equations. Our proposed algorithm significantly outperforms the multigrid method and the preconditioned conjugate gradient method in both iteration numbers and computational time.

This paper presents a unified framework for sufficient dimension reduction (SDR) that generalizes several existing SDR techniques and offers new insights into the connection between inverse conditional moment independence and dimension reduction. The framework is built on two forms of inverse independence between the response vector and predictors: inverse conditional mean independence (ICMI) and inverse conditional variance independence (ICVI). For each form, we develop two general classes of matrices capable of recovering the central subspace, based on projection and kernel techniques respectively. This yields four distinct estimators: projection- and kernel-based variants under both ICMI and ICVI frameworks. Under standard regularity conditions, we establish the theoretical properties of these estimators and derive their convergence rates in high-dimensional settings. The proposed methods exhibit robustness to outliers in the response variable while maintaining computational competitiveness. Simulation studies and real-data analyses demonstrate the practical effectiveness of the proposed methods.

The disposition effect describes investors' irrational behavior of selling profitable assets too soon while holding onto losing assets for too long. This study examines the impact of transparency at the firm level on the disposition effect of individual investors who hold that company's stock. Our results show that an increase in corporate transparency significantly reduces the disposition effect. Further analysis reveals that for companies with greater transparency, when the held stock is profitable, investors' confidence in holding it increases, leading to a reduced bias toward selling profitable stocks. When the stock is held at a loss, investors' confidence in holding it weakens, but they often perceive the loss as temporary and maintain confidence in the company's long-term prospects, thus exacerbating the bias toward holding losing stocks. The effect of increased transparency on the selling behavior of profitable stocks is greater than its effect on the selling behavior of losing stocks. Overall, an increase in corporate transparency significantly reduces the disposition effect.

We study the 1D Brenner-Navier-Stokes-Fourier (BNSF) system, proposed as a refinement of the classical Navier--Stokes--Fourier model through the introduction of the volume velocity, distinct from the mass velocity describing convective transport. When formulated in the Lagrangian mass coordinates with the volume velocity, the discrepancy between the two velocities induces a dissipative structure in the mass conservation law. We prove the global existence of classical solutions for arbitrarily large initial data. More precisely, for initial data in $H^k(\mathbb{R})$ with $k\ge3$, with the specific volume and absolute temperature initially bounded away from zero, we construct global-in-time solutions that remain in the same regularity class. Our result accommodates arbitrarily large initial data. A major difficulty is to establish lower and upper bounds for the specific volume \(v\). The additional dissipation yields an $L_t^2 L_x^2$ bound for $v_x$, which is further improved to an $L_t^\infty L_x^\infty$ bound of $v$ and $1/v$ via the parabolic De Giorgi method. We also apply the maximum principle to obtain a positive lower bound for the absolute temperature.

Recent advances in machine learning have spurred significant interest in learning-augmented algorithms, particularly for online optimization. A growing body of work has studied online bidding in this framework, aiming to characterize the trade-off between robustness and consistency. While this trade-off is fully understood for deterministic algorithms, a gap between upper and lower bounds remains in the randomized setting. In this paper, we close this gap by presenting a Pareto-optimal randomized learning-augmented algorithm for this problem. Our approach introduces the notion of a bidding profile, a novel framework for representing the distribution over bids generated by an algorithm. We show that any bidding algorithm can be reduced, without loss of generality, to one driven by a bidding profile, and we characterize the optimal profile via a system of delayed differential equations. Finally, we demonstrate the broader applicability of our approach by extending it to the linear search problem, yielding a significant improvement over prior learning-augmented algorithms for linear search.

A monopole configuration in the electroweak theory was constructed by Cho and Maison, allowing for a singular behavior at the origin. Since the essential structure of the Cho-Maison monopole is based on an electroweak-type symmetry breaking, similar monopole configurations are expected to arise more generally in gauge theories containing such a structure. In this paper, we explicitly show that Cho-Maison-like monopole configurations can indeed be constructed in a broad class of models. We also show that the Cho-Maison monopole can be embedded into an 't Hooft-Polyakov monopole as its low-energy effective description. In particular, we find that a monopole in the Pati-Salam model behaves as the electroweak Cho-Maison monopole once degrees of freedom which are heavier than the electroweak scale are integrated out.

The Vlasov-Poisson-BGK (VPBGK) model is a kinetic model for describing the dynamics of collisional plasmas. Although various numerical schemes have been developed for it, a corresponding convergence theory has been absent. This paper fills this gap by presenting the first convergence analysis for a non-splitting, finite-difference Eulerian scheme discretized on the full phase-space grid. A major theoretical obstacle is the mixing of velocity indices induced by the electric field, which hinders the derivation of a uniform lower bound for the discrete solution. To overcome this stability challenge, we propose a modified lower bound estimate suitable for ionized systems that incorporates the step-wise degradation. Under a truncated velocity domain with a Neumann boundary condition, we establish error estimates for the distribution function in a weighted $L^{\infty}$ norm and for the electric field in a $L^{\infty}$ norm, respectively.