We consider the simplest quadratic extension of MacDowell-Mansouri pre-geometric gravity preserving the topological pre-volume form symmetry. After symmetry breaking, it becomes $(\mathrm{Lovelock})^2$ gravity, dual to a Galileon-like Horndeski scalar-tensor theory. The gravitational Higgs mechanism forces the Gauss-Bonnet coupling to be inversely proportional to the bare cosmological constant. The quadratic correction renders the gravitational $θ$-angle dynamical in the form of a gravi-axion, whose effective mass sets the dark energy scale, thus naturally realizing a dynamical dark energy. The model fits DESI's BAO+FS data exceptionally well ($χ^2_{\rm red} = 1.394$), deviating from $Λ\mathrm{CDM}$ by only a few percent in the gravitational slip parameter $γ(z)$ with stable tensor perturbations. This analysis establishes a concrete, testable bridge between pre-geometric gravity and cosmic acceleration.

While it took about a decade for a germanium (Ge) thin film grown on a silicon (Si) substrate to be successfully applied as a detector material for high-speed optical fiber communication application, it took about another decade to further expand its usage as a sensor material for active optical sensing and imaging applications. In this paper, we shall review the progress of a shortwave infrared (SWIR) single-photon detection (SPD) with germanium-silicon (GeSi) single-photon avalanche diode (SPAD), ranging from the first demonstration at cryogenic temperature (Z. Lu et al., 2011) to the recent demonstration at room temperature (N. Na et al, 2024). Potential new applications will also be discussed.

This paper shows the convergence of adele-valued random walks to an adelic Lévy process under scaling limits. We use random walks on the $p$-adic numbers to construct random walks initially on the infinite product space, and use survival time analysis to prove that the random walks are almost surely adelic for all time. The adelic random walks are shown to be small perturbations of processes that are supported on a finite product of path spaces. Weak convergence to an adelic Lévy process is established in the $J_1$ Skorokhod topology.

As modern cyber systems scale to include large populations of heterogeneous IoT devices, securing them against impersonation and forgery is a critical cybersecurity challenge. Physical Unclonable Functions (PUFs) offer a lightweight, hardware-rooted trust anchor for IoT security. However, different PUF architectures possess distinct challenge-response spaces and raw response reliabilities, making existing authentication protocols PUF-type specific. To bridge this interoperability bottleneck, this paper proposes a scalable, helper-data-free, open-set PUF authentication framework that leverages an OpenGAN-based classifier to manage heterogeneous fleets of IoT devices. Our method addresses the limitations of traditional database-centric and digital-twin modeling methods by encoding raw responses from diverse PUF types, including strong, weak and hybrid PUFs, into a unified image representation. This enables robust, single-pass classification and impostor rejection. We integrate the classifier into a generic protocol employing hybrid encryption and Bloom filter-based replay detection. Evaluated across four different types of noisy PUF data (Arbiter, SRAM, DRAM, and heterogeneous PUFs), our framework achieves 100% closed-set accuracy and near-zero open-set error rates with up to 45 devices, a significant improvement over the 3 to 5 devices in prior classification-based approaches. Prototyped on a Raspberry Pi, our framework completes one authentication cycle within 0.67 s, approximately 30x faster than the state-of-the-art open-set baselines.

Water adsorption on silicate surfaces is a critical yet poorly understood process relevant to, e.g., mineral weathering and cement hydration. This study investigates the structure of water overlayers on a model calcium silicate, the lowest-energy (100) surface of wollastonite (CaSiO3). It combines atomically resolved non-contact atomic force microscopy (nc-AFM), acquired with qPlus sensors and functionalized tips in ultrahigh vacuum (UHV), with density functional theory (DFT) calculations employing the metaGGA r2SCAN+rVV10 functional. Adding incremental doses of water to the sample at cryogenic temperatures produces distinct structures governed by the competition between water-surface and water-water interactions. With two water molecules per surface unit cell, water-surface interactions dominate: In line with previous theoretical predictions, adsorbates follow the surface lattice. As the coverage increases, intermolecular hydrogen bonding competes with bonding to the surface, leading to the emergence of complex, coexisting patterns. While their small energy differences prevent an unambiguous identification of the most stable structure by DFT, the experimentally observed symmetries help constrain plausible structural models. Above a critical density of four water molecules per unit cell, water-water interactions prevail, and water clusters are formed. The results provide an atomic-scale framework for understanding water interactions with calcium silicate surfaces.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) are promising platforms for low dimensional superconductivity. However, in conventional intercalated systems, achieving a high superconducting transition temperature (Tc) often comes at the expense of reduced interlayer spacing and weakened 2D character. Here, we overcome this long-standing compromise through a unique chain-like intercalation strategy. We report the synthesis and properties of a new polymorph, (BaS)1/3TaS2, in which a distinctive Ba-S-S-Ba chain structure is inserted between TaS2 bilayers. This unique configuration breaks the bulk c axis mirror symmetry while achieving exceptional interlayer decoupling, with an inter-bilayer spacing of 12.75 Å-more than three times that of pristine 2H-TaS2. By suppressing interlayer electronic coupling, this structural evolution allows local inversion symmetry breaking within individual TaS2 layers to dominate. This prevents compensation of the Ising spin-orbit fields typical of centrosymmetric bulk phases, enabling robust 2D Ising superconductivity. Remarkably, the compound exhibits an enhanced Tc without sacrificing its large interlayer spacing, thereby breaking the conventional trade-off between large spacing/high anisotropy and high Tc. Comprehensive transport, magnetic, and thermodynamic measurements confirm its robust superconducting state. Our work establishes a versatile intercalation framework for designing bulk-like 2D Ising superconductors, providing a new route to reconcile competing material demands and expanding the scope of Ising superconductivity research.

Rare-earth-ion-doped crystals has emerged as a promising platform for quantum technologies, owing to their narrow telecom-band optical emission, long spin memory, and compatibility with silicon integrated photonic architectures. However, the realization of scalable quantum devices requires host materials with intrinsically dilute spin environments to suppress decoherence. In this context, erbium (Er$^{3+}$) doped cerium oxide (CeO$_2$) is an attractive candidate due to the ultra-low concentration of nuclear spins in the host matrix and its compatibility with silicon-based technologies. Here we perform a comprehensive investigation of the coherence properties of Er$^{3+}$ electron spin qubit in CeO$_2$ via semiclassical as well as detailed cluster correlation expansion simulations. By systematically exploring magnetic field strength, pulse sequences, erbium concentration, and spin temperature, we identify regimes where decoherence from the spin bath is strongly suppressed. Our investigations illustrate that at dilute doping concentration (of the order of 10 ppb) and sub-Kelvin temperatures, operation near clock transitions enables Hahn-echo coherence times to approach the second timescale even at natural isotopic abundance. Importantly, from a practical standpoint, coherence times on the order of $\sim 10$ ms are expected even at liquid helium temperature (about 2 K) for similar concentrations. Moreover, we demonstrate that an additional enhancement can be obtained with conventional multi-$π$-pulse dynamical decoupling protocols. Thus, our findings establish Er$^{3+}$ doped CeO$_2$ as a front-runner for realizing spin qubits, quantum memories, and integrated quantum networks.

The forthcoming deployment of 6G Integrated Sensing and Communication (ISAC) will transform cellular infrastructure into pervasive, continuous environmental and biometric sensing grids. While current telecom standardization efforts (e.g., 3GPP, ETSI) have formally recognized privacy and trustworthiness as critical pillars for 6G, their proposed mitigations remain overwhelmingly technocentric, relying on cryptographic anonymization and physical layer security. This approach critically underestimates the sociotechnical and legal complexities of the downstream machine learning (ML) models required to interpret raw sensing data, creating a profound collision with existing digital rights legislation. This position paper argues that technical security is insufficient. ISAC trustworthiness must be redefined as mandatory regulatory and sociotechnical compliance. We identify the specific legal friction points between continuous ISAC surveillance and the mandates of emerging global digital rights regimes, using the stringent requirements of the EU AI Act and GDPR as our primary regulatory baselines. To bridge this gap, we propose a governance framework centered on three pillars: Purpose-bound sensing activation, citizen transparency mechanisms, and algorithmic accountability for ISAC-driven ML models. Ultimately, this paper provides a regulatory roadmap to prevent the illegal deployment of 6G sensing infrastructures and ensure they remain viable before physical deployment.

The odd-Ramsey number $r_{\text{odd}}(n,H)$ of a graph $H$ is the minimum number of colors needed to edge-color $K_n$ so that in every copy of $H$ some color occurs an odd number of times, and the unique-Ramsey number $r_{\text{u}}(n,H)$ is the corresponding notion in which some color is required to occur not only an odd number of times but exactly once. In this paper, we address three questions from previous papers. We show $r_{\text{odd}}(n,K_{s,t})> n^{1/\left(\frac s2+\frac 1{2\lfloor t/8 \rfloor}\right)}$ when $s\leq t$ and $s$ is odd and $t$ is even, which is log-asymptotically tight when $s$ is fixed and $t\to\infty$. Next, we consider the odd-Ramsey number when the host graph to be edge-colored is a super-Dirac graph, and show that in any host graph with minimum degree at least $n/2+2$, the odd-Ramsey number of Hamilton cycles is non-trivial. Finally, we show that $r_\text{u}(n,C_n)> n/4$, which leads to a polynomial gap between $r_\text{odd}(n,C_n)$ and $r_\text{u}(n,C_n)$.

This work presents TREA, a low-precision time-multiplexed and resource-efficient edge-AI accelerator for object detection and classification, targeting stringent area-power-latency constraints of edge vision platforms. The proposed architecture integrates a dual-precision (4/8-bit) SIMD multiply-accumulate (DQ-MAC) unit based on most-significant-digit-first (MSDF) shift-and-add computation with run-time bit truncation, eliminating conventional multiplier overhead and reducing accumulator bit-width. The DQ-MAC supports 4x FxP4 or 1x FxP8 operations per cycle, achieving up to 4x throughput improvement without hardware duplication. A structured hardware-aware reductive pruning (SHARP) strategy is co-designed with the SIMD datapath, enabling near 50% structured sparsity while maintaining full MAC utilization. This allows a 3x3 convolution kernel to be computed in 1 cycle in FxP4 mode compared to 9 cycles in FxP8, and a 5x5 kernel in 3 cycles versus 25 cycles, yielding up to 9x latency reduction at the kernel level. The accelerator further incorporates a reconfigurable CORDIC-based nonlinear activation function (RQ-NAF) core with a 9-stage pipeline, supporting Sigmoid, Tanh, and ReLU at one output per cycle after pipeline fill, while enabling (N-1) hardware reuse through time-multiplexing. The complete TREA architecture employs a 1D array of 100 SIMD DQ-MAC units with layer-wise hardware reuse, significantly reducing area and control complexity. Experimental results demonstrate substantial improvements in latency, hardware utilization, and energy efficiency compared to conventional fixed-precision and non-reconfigurable accelerators, validating TREA as an effective solution for real-time edge vision workloads.

In agile software development, breaking down user stories into actionable tasks is a critical yet time-consuming process. This paper investigates the potential of Generative AI tools to assist in task splitting, aiming to enhance planning efficiency. We conducted a controlled experiment comparing traditional task-splitting methods with AI-assisted approaches using GitLab Duo. Our findings indicate that while current AI tools are not yet mature enough to replace developers, they can aid in generating more granular task lists and ensuring no important tasks are overlooked. Participants favored a hybrid approach, combining AI tools with conventional methods to maintain high accuracy in planning. This study highlights the potential benefits and limitations of integrating Generative AI into agile development processes, suggesting that AI tools can serve as valuable aids in task splitting, provided there is human oversight to filter out irrelevant tasks.

This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation capability for nonlinear dynamics, certifying observer convergence under model mismatch and measurement noise has remained a largely open problem. To resolve this, we establish a structural correspondence between the error dynamics of a Koopman latent-space observer and the class of generalized Persidskii systems, which admits diagonal Lyapunov functions and incremental sector characterizations. Exploiting this connection, we design a nonlinear correction term whose gain is computed via a linear matrix inequality (LMI) that simultaneously certifies input-to-state stability (ISS) of the estimation error with respect to both lifting residuals and external disturbances. Exponential convergence in the nominal case and ultimate boundedness under bounded perturbations are established analytically. Numerical validation on the Van~der~Pol oscillator and a nonlinear robotic arm with friction uncertainty demonstrates that the proposed observer substantially outperforms both the Extended Kalman Filter and a linear Koopman observer in terms of estimation accuracy and robustness, achieving up to a 42\% reduction in steady-state RMSE under lifting mismatch.

Clinical prediction models must be developed using sufficiently large datasets to minimise overfitting and ensure robust predictive performance. Existing sample size calculations assume complete predictor data for all included participants, yet missing values are common and may increase required sample sizes. This study aimed to quantify how missing predictor data and different imputation methods affect overfitting and model degradation, within datasets that adhere to current sample size criteria. We also aimed to explore how a general sample size framework based on anticipated posterior (sampling) distributions can be adapted to incorporate missing data assumptions and handling strategies. Using a simulation study, we found that in development data meeting current minimum sample size requirements, missing data reduced predictive performance, with expected calibration slopes frequently falling below the targeted value of 0.9. Increasing the required sample size to account for missing data reduced overfitting concerns, but the necessary inflation factor was context specific. In some scenarios, up to twice the minimum sample size was needed to achieve performance comparable to models developed using fully observed data. Expected value of perfect information calculations allowed quantification of the expected loss due to finite samples and missingness. Through two applied examples, we illustrate how embedding missing data assumptions and handling within the posterior sampling approach provides a principled way to determine required minimum sample sizes under missing data. Overall, missing predictor data increases minimum sample size requirements to develop stable and well-calibrated models. Our adaptations to recent posterior (sampling) sample size calculations offer a practical approach for incorporating missing data directly into sample size calculations.

This paper presents the design, fabrication, and experimental validation of a reconfigurable intelligent surface (RIS) employing electrically actuated vanadium dioxide (VO2) switches for millimeter wave beam steering. The proposed RIS is realized using a multilayer microfabrication process on an alumina substrate, enabling monolithic integration of hundreds of sub-4 micrometer VO2 switching elements within deeply subwavelength unit cells, approximately one-fifth of the wavelength. The switching-induced modulation of surface impedance is analyzed through full-wave simulations, and the resulting phase and amplitude responses are experimentally characterized using a custom WR-28 waveguide measurement setup. Based on the validated unit-cell design, a 10 x 20 RIS array integrating 200 VO2 switches is fabricated. The switches within each column are serially biased using integrated routing lines, allowing programmable control of the spatial phase distribution across the surface. Synthesized phase profiles enable dynamic beam steering, resulting in measured far-field gain enhancement of 10-20 dB over an 18 percent fractional bandwidth centered at 33 GHz, with steering angles up to 60 degrees. The measured radiation patterns are in good agreement with semi-numerical channel modeling predictions. By combining thin-film PCM switching with an integration-aware unit-cell design, this work demonstrates a scalable RIS architecture that mitigates packaging parasitics and footprint limitations inherent to conventional semiconductor-based implementations, providing a practical pathway toward higher-frequency reconfigurable surfaces.

This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown function.This is a non-trivial business comparing to the analogous results with time-derivative type semilinear terms, especially for the proof to obtain the sharp upper bound of the lifespan as we have to deal with space dependent weights among iteration procedures of the weighted functional of the solution. Also it is surprising that a part of them reaches to the same ordinary differential inequality for classical semilinear damped wave equations introduced by Li and Zhou (Discrete Contin. Dynam. Systems, 1995, 1(4): 503-520), and we show a simple proof for blow up result from this ordinary differential inequality by iteration argument and slicing method in more general situation.

This paper presents a new derivation of the variational Poisson multi-Bernoulli (V-PMB) filter for multi-target estimation proposed in [#Williams15]. The proposed derivation is based on considering an augmented space that includes the set of target states with their track indices and the global hypothesis variable. Then, we show that the V-PMB projection performs a coordinate descent Kullback-Leibler divergence (KLD) minimisation on this augmented space to fit the best possible PMB density to the Poisson multi-Bernoulli mixture (PMBM) posterior. We also show that this V-PMB projection keeps the probability hypothesis density of the posterior. The paper also includes a comparison with the PMBM filter and other PMB filter variants, including a track-oriented Murty-based implementation, a track-oriented loopy belief propagation implementation and a global nearest neighbour implementation, showing the benefits of the V-PMB filter compared to the other PMB filters when targets get in close proximity and then separate.

The inert two-Higgs doublet model (IDM) is a compelling framework for weakly interacting massive particles (WIMPs) linked to electroweak symmetry breaking. It can account for both the Galactic Center gamma-ray excess (GCE) and the AMS-02 antiproton anomaly while also satisfying relic density and direct detection constraints for dark matter (DM) masses in the $55-75$ GeV range. Three specific DM annihilation channels can be identified: Higgs resonance, $SA$ co-annihilation, and $SS\to WW^{\ast}$ annihilation. Among these, the DM mass range of $70-75$ GeV with dominant $SS\to WW^{\ast}$ annihilation has received less attention in collider searches. To validate this parameter space, we combine LHC searches for mono-$W/Z$ signatures. In particular, we develop a channel-separation strategy to disentangle the contributions of charged mass splitting ($Δ^{\pm}$) and neutral mass splitting ($Δ^0$) in the inert scalar sector at the LHC. Our results indicate that most of the parameter space consistent with these astrophysical anomalies in the $SS\to WW^{\ast}$ annihilation regime will be testable at the High-Luminosity LHC. Specifically, from the leptonic channel we obtain a $2σ$ exclusion limit of $80 \lesssim Δ^0 \lesssim 260$ GeV, while the hadronic channel yields $30 \lesssim Δ^0 \lesssim 150$ GeV and $70 \lesssim Δ^{\pm} \lesssim 230$ GeV for $m_S = 70$ GeV.

We propose a hidden Markov model for univariate proportion time series taking values in (0,1), where regime switching captures latent structural changes and the emission distribution belongs to the Beta family. In each latent state, the Beta mean is linked to covariates through a generalized additive model (GAM) with spline-based smooth functions, while the Beta precision is state-specific, enabling flexible modeling of both nonlinear covariate effects and regime-dependent variability. Estimation is carried out via a penalized expectation--maximization algorithm, combining smoothing with numerical maximization of the penalized emission likelihood. To select the number of latent states and the smoothing penalty, we implement a grid search guided by standard information criteria (Akaike Information Criterion/Bayesian Information Criterion/Integrated Completed Likelihood) with a diagnostic filter that removes degenerate solutions characterized by explosive precision estimates. Uncertainty is quantified through a parametric bootstrap procedure for transition probabilities and state-dependent parameters. Simulation results demonstrate accurate recovery of transition dynamics, state precisions, and latent-state decoding. A motivating application to Russian age-specific mortality data (1960--2014, ages 0--40) illustrates how the proposed model summarizes smooth age patterns in female-to-total mortality ratios while identifying two persistent latent regimes that admit a substantive demographic interpretation in light of the country's well-documented mortality shocks that occurred over the second half of the twentieth century.

We solve a conjecture by Becker et al. (arXiv:2404.05963) on the topic of zero forcing regarding the number of minimal forts of a tree. They conjectured and we prove $\mathcal{F}_{T_n} \le \binom{n}{2} \mathcal{F}_{P_n}$ where $\mathcal{F}_{T_n}$ is the maximum number of minimal forts on a tree on $n$ vertices and $\mathcal{F}_{P_n}$ is the number of minimal forts of the path graph on $n$ vertices. Our solution relies on both a computational and theoretical approach. Computationally, we introduce and implement an efficient algorithm to compute the exact number of minimal forts for small trees; this is used to establish the large base case required for our strong induction. Theoretically, we provide an adaptation of the recursion relation that defines $\mathcal{F}_{P_n}$ that applies for all forests; this is used in the induction step to establish the result.

E-commerce search systems rely on modeling user behavior to estimate item relevance and user preference, which are typically assumed to be stable and independently learnable signals. However, in practice, user interactions are jointly shaped by exposure mechanisms, feedback loops, and semantic matching, leading to entangled and dynamically drifting behavioral signals. As a result, both preference estimation and relevance modeling suffer from confounding effects and semantic misalignment, which limits the robustness of downstream ranking models. To address this issue, we propose PRISM, a Preference-Relevance Interaction Semantic Modeling framework for e-commerce search behavior prediction. PRISM explicitly models the interaction between user preference and item relevance rather than treating them as independent components. Specifically, it introduces a preference rectification module to iteratively refine user preference under relevance-aware constraints, improving robustness against behavioral confounding. To ensure semantic consistency, we further incorporate a large language model (LLM)-driven semantic anchoring mechanism that leverages positive and negative prototypes to calibrate relevance representations. Finally, a preference-conditioned evidence routing module adaptively aggregates multi-source behavioral signals, enabling context-aware and preference-aligned relevance estimation. Extensive experiments on two public e-commerce benchmarks demonstrate that PRISM consistently outperforms strong baselines, validating the effectiveness of explicitly modeling preference-relevance interaction for robust and semantically grounded search behavior modeling.

With the advent of the construction and deployment of entanglement-based quantum networks, the efficient use of network resources will become a critical challenge for the scalable operation of such a system. Recently, architectures that incorporate memoryless optical switches have gained attention for forwarding entangled photons. By leveraging these architectures, costly resources such as high efficiency Bell State Analyzers (BSAs) can be shared across the network. Nevertheless, the introduction of switching substantially complicates the process of multiplexing and resource allocation compared to an individual link. In this work, we propose a switching protocol for unbuffered, multidrop quantum networks in a photonic synchronization domain that establishes a link between two end nodes using a shared BSA in the switched network. To achieve this, two end nodes cooperatively select the target BSA node with the lowest path cost and independently reserve each path within the network. Bi-path reservations are performed to allocate resources in a distributed manner. The proposed protocol is evaluated through simulation on Q-Fly network topologies under varying traffic conditions. The results demonstrate high link establishment success with stable performance even under increased network load. These capabilities which are driven by our proposed protocol are an essential way to realize large-scale, managed, and automated quantum networks.

LLM-based SOC log classifiers are commonly evaluated using regular-expression pipelines that extract structured fields from free-form model output. We demonstrate that this practice introduces a class of silent, systematic evaluation errors, which we term parsing-induced suppression that can cause a fully functional model to appear completely non-functional. Using OpenSOC-AI, a LoRA fine-tuned TinyLlama-1.1B system for security log threat classification, as a reproducible case study, we show that a strict regex parser reported 0% threat accuracy while a corrected fuzzy parser recovered 76% threat accuracy on the same model outputs and the same evaluation set. A gap of 76 percentage points attributable entirely to evaluation methodology. Severity accuracy remained constant at 58% under both parsers, providing a built-in control that isolates field name format mismatch as the causal mechanism rather than model degradation. For external reference, Claude Sonnet evaluated zero-shot on the same 50 example set achieved 88% threat accuracy and 58% severity accuracy under the same fuzzy protocol. Residual errors under fuzzy evaluation concentrate in three categories including reconnaissance, brute force, and credential stuffing, each contributing all 4 misclassifications, a pattern that reflects class-boundary difficulty among behaviorally adjacent log types rather than global model failure. We propose SOC-Bench v0, a benchmark framework comprising a standardized 13 category threat taxonomy, minimum statistical power requirements, fuzzy field extraction specification, and a public scoring script intended to prevent parser specific accuracy distortion in future SOC LLM research.

The evaluation of voice anonymisation remains challenging. Current practice relies on automatic speaker verification metrics such as the equal error rate (EER). Performance estimates dependent on the classifier and operating point provide an incomplete or even misleading characterisation of privacy risk. We investigate the use of similarity rank disclosure (SRD), an information-theoretic metric, which operates on feature representations rather than classifier decisions, providing a threshold-independent assessment of privacy and analysis of both average and worst-case disclosure. We report its application to speaker embeddings, fundamental frequency, and phone embeddings using 2024 VoicePrivacy Challenge systems. The SRD reveals privacy leaks and system-specific weaknesses missed by EER-based evaluation. Findings highlight the merit of representation-level metrics and demonstrate the potential of SRD as a flexible and interpretable tool for the evaluation of voice anonymisation.

In this paper, we are focusing on proofs of a blow-up result for a quadratic semilinear wave equation in two space dimensions. There is a logarithmic loss in estimating the lifespan of a classical solution if the 0th moment of the initial speed does not vanish. This result is already known with almost sharp constants. But in order to have a direct application to the numerical analysis, we show a simple proof by iteration argument for a point-wise estimate of the solution with a slicing technique. Such a research direction can be found in the case of critical nonlinearity.

We prove the existence, uniqueness, and sharp bilateral pointwise estimates for positive bounded solutions to the Lane--Emden type problem \[ \begin{cases} L u = \sum\limits_{i=1}^{m}σ_{i} u^{q_{i}}+σ_0, \quad u\geq0 & \text{in } Ω, \liminf \limits_{x \rightarrow y} u(x) = f(y), & y \in \partial^\inftyΩ, \end{cases} \] where $0 < q_{i} < 1$. Here $Lu = - \text{div}(A \nabla u)$ is a uniformly elliptic operator with bounded coefficients, $σ_{i}$ is a nonnegative locally finite Borel measure on an $A$-regular domain $Ω\subset \mathbb{R}^n$ which possesses a positive Green function associated with $L$, and $f$ is a nonnegative continuous function on the boundary $\partial^\inftyΩ$. An analogous result for positive continuous solutions to the problem is also illustrated. Our method can be adapted to address related sublinear problems with zero boundary conditions involving the fractional Laplace operator $(-Δ)^α$ for $0< α< n/2$, in place of $L$, in $\mathbb{R}^n$ as well.

Integrated quantum photonics requires compact, efficient, and low-power phase modulators. While silicon nitride (SiN) is a promising platform, existing modulators suffer from high power consumption, thermal crosstalk, or high driving voltages. Liquid crystal (LC) offers a compelling alternative because of the large index changes and industrial maturity. However, their suitability for supporting various applications in the photonic quantum system has not been experimentally confirmed.Here, we report the first experimental demonstration that LC-based phase modulators integrated on a SiN platform show highly visible quantum interference. We fabricated a liquid-crystal integrated Mach-Zehnder interferometer (LC-MZI) that achieved CMOS-compatible performance with V_pi * L < 1 V-mm. In two-photon interference experiments, the devices exhibited high-visibility quantum interference (~98.5%) with voltage-tunable phase control. Furthermore, we validated the scalability of our approach by demonstrating wafer-scale fabrication using stepper lithography. This work establishes LC-integrated SiN photonics as a scalable, reconfigurable, and energy-efficient platform for quantum photonic circuits.

Phase-field simulations provide mechanistic descriptions of microstructure evolution, but repeated high-fidelity integration over long horizons and broad parameter spaces remains computationally expensive. We present PFNet, a physics-informed neural operator framework that advances microstructural states by learning conditional evolution operators rather than direct correlations. PFNet combines a diffusion-inspired U-Net with periodic padding, entropy-based state conditioning and thermodynamic-parameter modulation to encode boundary consistency, instantaneous ordering state and changes in the free-energy landscape. For Cahn-Hilliard coarsening, PFNet achieves accurate one-step prediction and stable autoregressive rollouts across composition, gradient-energy coefficient, coarsening stage and morphology class, with errors concentrated near diffuse interfaces and topology-changing regions. The same framework extends to a four-channel martensitic-transformation benchmark without martensite-specific redesign. These results indicate that physics-informed operator learning can provide transferable surrogates for phase-field dynamics and broader energy-dissipative dynamical systems.

This paper investigates the asymptotic behavior of path-dependent multivalued McKean-Vlasov stochastic differential equations perturbed by small noise. Specifically, we first establish a large deviation principle for such equations under non-Lipschitz coefficients by the weak convergence approach. Subsequently, we introduce an auxiliary equation and apply it to derive the moderate deviation principle. Finally, we construct another auxiliary equation and a limit equation, and prove the central limit theorem.

Everywhere-$δ$-dense graphs are defined as graphs on $n$ vertices in which every vertex has degree at least $δn$ for some constant $δ> 0$. Approximation schemes are vital for handling NP-hard optimization problems, but for many graph cut problems, existing PTAS algorithms often suffer from running times of $n^{f(1/\varepsilon)}$. In this paper, we bring PTASs down to EPTASs for several fundamental minimization problems on everywhere-$Ω(1)$-dense graphs. Specifically, we present the first Efficient Polynomial-Time Approximation Scheme (EPTAS), running in time $f(1/\varepsilon)n^{O(1)}$, for the ConstrainedMinCut problem under a global constraint on vertex weights, a problem that captures BalancedSeparator and SmallSetExpansion. Moreover, we give the first EPTASs for MinQuotientCut and ProductSparsestCut on everywhere-$δ$-dense graphs with integer-valued dense vertex weights; these problems generalize the four well-known problems UniformSparsestCut, EdgeExpansion, Conductance, and NormalizedCut. Our main technical contribution is an EPTAS for ConstrainedMinCut, based on the weak regularity lemma and sampling and estimation techniques. We then obtain EPTASs for MinQuotientCut and ProductSparsestCut via a unified reduction that invokes this algorithm as a subroutine. In contrast, previous works giving PTASs for these problems on everywhere-$δ$-dense graphs typically rely on powerful tools such as the Lasserre hierarchy or specific integer programming technique, which we avoid.

We demonstrate that conditional Masked Autoregressive Flows constitute a flexible interpolation tool for lattice QCD observables, conditioned on bare lattice parameters. As a benchmark, we use the chiral phase structure of QCD with five degenerate light quark flavours, which on coarse lattices exhibits a region of first-order chiral transitions terminating in a critical quark mass. The method successfully reproduces standard reweighting in the gauge coupling, and naturally extends to interpolation in quark mass and spatial volume, for which reweighting is computationally prohibitive or inapplicable, respectively. Once trained, the model generates samples across the full parameter space in minutes, which can be used to obtain consistent first estimates of the critical quark mass without simulating all intermediate parameter values. This offers a concrete reduction in the number of lattice ensembles required. Precision on the critical mass from learned distributions is so far prohibited by the mode-covering effect inherent to maximum-likelihood-based training, which introduces a systematic bias near first-order transitions. At the current stage, the method is well-suited for a range of practical applications: localising phase boundaries, identifying the universal scaling axes at a critical point, and accelerating informed determinations of parameter values ahead of high-precision Monte Carlo campaigns.