In Scalar-Tensor-Vector Gravity (STVG, also known as MOG), a massive vector field $ϕ_μ$ generates a repulsive fifth force that endows rotating black holes with a gravitational charge $Q \propto \sqrtα\,M$, modifying the near-horizon geometry through a single deformation parameter $α$. We investigate how this vector-field coupling imprints itself on the thermal continuum emission of geometrically thin, optically thick accretion disks in the Kerr-MOG black hole. By re-deriving the innermost stable circular orbit (ISCO), the Novikov-Thorne radiative flux, the relativistic energy shift, and the null geodesic structure for the Kerr-MOG spacetime, we compute fully relativistic disk spectra across a broad range of spins, inclinations, and fifth-force strengths using a dedicated \textsc{xspec} spectral model (\texttt{kmspec}). We find that the fifth-force charge pushes the ISCO outward, lowers the peak disk temperature, and systematically softens the thermal continuum relative to its Kerr black hole counterpart at the same spin, with the deviation amplified at high observer inclinations. The resulting spectral modification closely mimics a reduction of spin in the pure Kerr black hole framework, indicating that independent spin measurements from, e.g., iron-line reflection spectroscopy are indispensable for disentangling the vector-field contribution. All results recover the standard Kerr black hole predictions when $α= 0$, and the model is validated against independent analytic and numerical benchmarks to machine precision. Application to a 69.6~ks \textit{XMM-Newton} observation of LMC~X-1 yields $α< 0.044$ at 90\% confidence, consistent with the Kerr metric and general relativity.

We prove that the Gromov--Witten invariants of the elliptic orbifold lines $\mathbf{P}^1_{3,3,3}$, $\mathbf{P}^1_{2,4,4}$, and $\mathbf{P}^1_{2,3,6}$ satisfy a certain system of Hirota Quadratic (or Bilinear) Equations. Our result is the analogue of the so-called Toda conjecture in the Gromov-Witten theory of $\mathbf{P}^1$ or more precisely its non-extended version. A new feature in our constructions is a certain bilinear operator whose principal symbol can be expressed in terms of elliptic theta functions.

Gaussian quantum channels constitute a pivotal physical framework for characterizing the dynamics of Gaussian quantum states. Extensive scholarly attention has been devoted to the estimation of parameters associated with Gaussian channels. However, while previous research has predominantly focused on parameter estimation within inertial frames, the noninertial scenario, particularly in the context of the Unruh effect, remains largely unexplored. In this paper, we analyze the impact of the Unruh effect on the estimation precision of Gaussian channel parameters, with a specific focus on thermal attenuator and thermal amplifier channels. Our findings reveal that the Unruh effect significantly degrades the precision of single-parameter estimation for Gaussian channel parameters when employing both the input coherent state and squeezed vacuum state. For the two-parameter estimation, we further demonstrate that the quantum Cramér-Rao bound serves as an asymptotically achievable precision limit. Consistent with the single-parameter case, the Unruh effect exerts a detrimental impact on the precision of two-parameter estimation. Notably, heterodyne measurement is near-optimal for both single- and two-parameter estimation in the limit of high acceleration or large thermal mean numbers. These results provide crucial theoretical insights and practical guidance for advancing quantum parameter estimation in a relativistic context.

We present a Lean 4/Mathlib formalization of the additive representation theory behind Classical Lottery in Action and the Wakker-Debreu-Koopmans (WDK) layer it relies on. Our central result is a machine-checked proof that the cross-pair Thomsen / double-cancellation (hexagon) condition is irreducible from the ordinal axioms of additive conjoint measurement (weak order, restricted solvability, Archimedean condition, and tradeoff consistency). We exhibit an explicit verified counter-model (additiveRealBoolPref) satisfying all ordinal axioms yet failing the cross-pair condition, with every strict standard sequence being an arithmetic progression and hence non-dense. Around this boundary we mechanize the full derivable construction: continuous Debreu/Eilenberg utility from separability, standard-sequence grids, bisection methods from connectedness, and global additive gluing. All public theorems are sorry-free conditional wrappers over this single irreducible structural input. The development is kernel-clean, depending only on standard Lean foundations (propext, Classical.choice, Quot.sound). The companion file ClassicalLotteryInAction.lean formalizes local classical-lottery constructions, average-utility results, matching-frequency lemmas, and ambiguity-attitude statements used by the Management Science paper. This draws a precise, machine-certified line between what additive conjoint measurement can prove and what it must assume.

The two-dimensional border-collision normal form is a four-parameter family of continuous, piecewise-linear maps. When this form has a zero determinant, all of its nonlinear dynamics are captured a one-dimensional first return map. The first return map is discontinuous and piecewise-linear, where each piece of the map corresponds to a constant return time. We show that when the normal form has a repelling focus fixed point, the configuration of the first return map is dictated by a rational rotation number whereby the set of return times and ordering of the pieces of the map are given by the denominators of the left and right sequences of Farey parents of this number. The result is proved by characterising polygons formed from preimages of the switching manifold, and employing an inductive argument on the Farey web. Several surfaces in parameter space where the configuration changes are bifurcations from chaotic to quasiperiodic or mode-locked dynamics.

For the 1D generalized Coulomb problems--a family that includes the quantizations of the 1D generalized Kepler problems of Ma-Meng-Xiao \cite{MMX2025}--we construct two explicit unitary intertwiners $\hatι_{\pm}$, the quantum analogs of the classical symmetry regularization maps $ι_{\pm}$ of \cite{MMX2025}, that unitarily identify each $H_κ$-energy-definite portion of the Hilbert space $L^{2}(\mathbb{R}_{>0},\mathrm{d}q)$ with a unitary lowest-weight representation of $\widetilde{\mathrm{SL}}(2,\mathbb{R})$.

Future space-borne gravitational-wave (GW) detectors, such as LISA and DECIGO, are expected to detect a large number of GW events, a fraction of which may be strongly lensed by intervening galaxies or galaxy clusters. In this work, we develop a comprehensive framework to simulate strongly lensed GWs in the context of space-borne detectors. Based on realistic astrophysical models for both the source population and the lens distribution, we construct mock catalogs of lensed GW events, referred to as \textbf{GW-LMC-Space}. Our results show that, for a four-year LISA observation, the expected number of lensed events ranges from $0$ to $131$, depending on the adopted formation model of massive black hole binaries (MBHBs). The corresponding lensing probability for MBHBs can reach up to $\sim 0.3\%$. For DECIGO, we find that the number of lensed events in a one-year observation is expected to lie in the range of $0$--$44$, with a lensing probability of $\sim 0.15\%$ for stellar-mass binary black holes (BBHs), binary neutron stars (BNSs), and neutron star--black hole binaries (NSBHs). We further show that the overlap of lensed signals is a common feature in space-borne detectors, which can significantly affect both the signal-to-noise ratio (SNR) estimation and event identification. These results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future space-borne GW observations.

We study finite-state finite-action Bayesian statistical decision problems. While exact error-exponent characterizations are known for several special cases, including hypothesis testing and hypothesis exclusion, the asymptotic behavior of the optimal Bayes regret is largely unknown for general decision problems. In this paper, we show that the optimal regret always decays exponentially fast and characterize its exact exponent for arbitrary loss functions. The exponent is given by the minimum multivariate Chernoff information over the minimal incompatible subsets of states, where an incompatible subset is a collection of states for which no single action is optimal for all states in the subset. Our result recovers the classical pairwise-minimum Chernoff exponent for symmetric multiple hypothesis testing and the multivariate Chernoff exponent for hypothesis exclusion, while also yielding, to the best of our knowledge, the first exact exponent characterization for list hypothesis testing.

Large language models are increasingly deployed on edge devices with tight power and area budgets. While mixed-precision GEMM reduces arithmetic complexity, quantized inference is often dominated by dequantization and nonlinear operators. Lookup Table (LUT)-based method mitigates these costs by precomputing outputs and replacing repeated arithmetic with table lookups, but existing designs incur significant capacity and lookup-latency overheads. This paper presents PALUTE, a LUT-based Processing-In-Memory accelerator built on Monolithic 3D DRAM for efficient edge LLM inference. PALUTE enables in-DRAM LUT queries that exploit the vertical organization of M3D DRAM memory array tiles to achieve high parallelism with low area overhead. A near-memory LUT generator supports low-latency LUT generation for both GEMM and element-wise unary nonlinear operators, while a system-level tiering and scheduling strategy minimizes data movement across memory tiers. Evaluation using cycle-accurate simulation and RTL synthesis shows that PALUTE achieves 1,264 TPS end-to-end throughput at 0.16 W, improving energy efficiency by 12.8$\times$ over CHIME and 1.6$\times$ over FIGLUT, improving area efficiency by 2.0$\times$ over PIMPAL under W4A4 across Qwen3-4B models.

Recently there has been some progress in understanding the density of a subset of $[N]^2$ that avoids polynomial patterns. Kravitz, Kuca, and Leng showed that if $P\in\mathbb{Z}[z]$ satisfies certain conditions, then any set $A\subseteq[N]^2$ does not contain $(x,y),(x+P(z),y),(x,y+P(z))$, we must have \[ |A|\ll_P\frac{N^2}{(\log\log\log N)^c} \] for some small constant $c$. In this article, we show a similar result in $(\mathbb{F}_p)^2$ where we get a better bound on the density of a set $A\subseteq (\mathbb{F}_p)^2$ not containing $(x,y),(x+P(z),y),(x,y+P(z))$ with some conditions on $P\in \mathbb{F}_p[z]$.

We construct an exact rotating vacuum of the NS--NS sector, equivalently a Double Field Theory vacuum. The construction applies compact $\mathbf{SO}(2)$ S-duality to a rotating Einstein--scalar seed. The solution has four independent parameters $\{\mathfrak{m},j,\mathfrak{q},ζ\}$. To our knowledge, this is the first explicit rotating solution of the pure NS--NS vacuum equations with all three NS--NS fields $\{g,B,ϕ\}$ determined analytically, independent dilaton and $H$-flux charges, and no Maxwell sector. The static limit is obtained by taking the rotation parameter $j\to 0$. In this limit the geometry is not the spherical Burgess--Myers--Quevedo solution. Instead, it is an axial Zipoy--Voorhees branch carrying $H$-flux, so an oblate deformation remains after rotation is switched off. This geometric memory is absent in pure general relativity and in Einstein--Maxwell--dilaton--axion. The two static branches nevertheless share the same $\ell=0$ parametrized post-Newtonian data $\{MG,β_{\mathrm{PPN}},γ_{\mathrm{PPN}},h\}$. They give two inequivalent NS--NS geometries at identical monopole charges, with the degeneracy lifted at $\ell=2$. At the Kerr horizon locus the outer shell is generically singular in curvature. Above the threshold $|\mathfrak{q}|>\sqrt{\mathfrak{m}^{2}-j^{2}}$, polar geodesics are repelled outward and the rotation axis becomes regular in curvature at the shell. On that axis the inverse metric $g^{μν}$ stays finite while the lower-index Riemannian metric components diverge, whereas off the axis the inverse metric itself diverges. This axis-local degeneracy may offer a setting for non-Riemannian geometry in Double Field Theory, where $g_{μν}$ is not fundamental and the $\mathbf{O}(D,D)$ variables $\{d,\mathcal{H}_{AB}\}$ remain well defined.

Let $X$ be an $n$-dimensional Alexandrov space with curvature $\ge -1$, and let $η> 0$. Define $\mathcal{S}^{k}_η(X)$ as the set of $(k,η)$-singular points in $X$ whose tangent cones are $η$-away from splitting off $\mathbb{R}^{k+1}$ isometrically. For a point $p \in X$, assume that $M = B_2(p) \setminus (\mathcal{S}^{n-2}_η(X) \cup \partial X)$ is a smooth manifold equipped with the Riemannian metric induced by $X$. We prove that the integral of the scalar curvature of $M$ over $B_1(p)$ is bounded from above by a constant depending only on $n$ and $η$. As a special case, this extends Petrunin's bounded curvature integral result for complete manifolds with lower sectional curvature bound to the setting of open manifolds and smooth manifolds with boundary, provided that these manifolds are Alexandrov spaces.

Internet censorship affects over four billion people, and deployed circumvention systems share a common weakness: their endpoints are fixed and discoverable, so a patient censor can enumerate and block them. Moving-target circumvention systems instead rotate endpoints across commercial cloud address space faster than censors can react, but the field lacks a theory of when rotation works, leaving rotation intervals and pool sizes to intuition. We give the first formal account of moving-target censorship resistance by modeling the censor-defender interaction as a continuous-time timing game over a combinatorial address-domain space, generalizing FlipIt to a collateral-bounded adversary. We prove a sustainability frontier separating configurations a censor can defeat from those it cannot, and show that under the Great Firewall's 2024 shift to blocking QUIC and TLS by domain, raw rotation speed is not the binding constraint. Instead, availability is governed by the domain burn rate, $β=λ_{\mathrm{disc}}/λ_{\mathrm{intro}}$, the ratio between how quickly the censor blocks defender domains and how quickly the defender introduces fresh ones. We derive a closed-form availability law, prove that address rotation alone cannot sustain high availability when $β>1$ regardless of endpoint rotation speed, and characterize the frontier $β^\star$. We validate the analysis with an open, model-level censor-defender simulator requiring no privileged access or cloud deployment. The simulator reproduces the predicted phase transition at $β^\star$ under adversary profiles representative of the GFW, Russia's TSPU, and Iran, and shows robustness to state-dependent discovery and bursty, provider-correlated burns. The result replaces the heuristic of ``rotate faster'' with a precise operating condition: keeping the domain economy ahead of the censor.

This paper proposes a design-for-test (DFT) methodology and architecture for testing and validation of silicon photonic integrated circuits. We describe the design of silicon photonic circuits and components that comprise the proposed DFT architecture. The designs are extensively simulated and validated as test-access and fault-detection circuitry. We demonstrate how the DFT approach can be deployed on photonic integrated circuits and how they can be tested for correct operation, in terms of signal power and phase. The application is demonstrated on two distinct types of designs -- an optical neural network comprising optical devices in a feed-forward topology, and on an optical logic circuit with feedback loops.

We study the long-time behaviour of a coninuous time one-dimensional elephant random walk with an absorbing boundary. By analyzing the associated evolution equation, we identify a proper limiting operator and establish a Poincaré inequality with spectral gap of order $N^{-2}$. As a consequence, we obtain matching exponential upper and lower bounds for the survival probability, showing that it decays at rate $e^{-ct/N^2}$. The proof relies on a decomposition of the generator into a limiting operator and a time-dependent perturbation, together with spectral estimates.

We propose a matrix-free right-preconditioning strategy for the Generalized Minimal Residual (GMRES) method based on the Multiscale Robin Coupled Method with oversampling (MRCM-OS) for the numerical solution of elliptic problems arising in subsurface flow. The resulting preconditioner is constructed through local subdomain solves with oversampling and smoothing, and can be applied without explicit assembly of the global operator. After a careful presentation of the new procedure, it is used in extensive numerical experiments. Our results demonstrate that the proposed approach substantially reduces iteration counts across a range of challenging, high-contrast subsurface flow problems. In many cases, convergence is obtained in one or two GMRES iterations when oversampling and smoothing are employed. The results indicate that combining GMRES with multiscale Robin-based operators is a promising direction for the construction of rapidly convergent preconditioning strategies.

Let $f: X \to S$ be a quasi-projective family of varieties defined over $\overline{\mathbb{Q}} \subset \mathbb{C}$. We show that the points of $S(\overline{\mathbb{Q}})$ that are Hodge generic for the variation of Hodge structures associated to $f$ are analytically dense in $S(\mathbb{C})$. In fact, in the spirit of the Grothendieck period conjecture and under a large monodromy assumption, we prove the density of the points of $S(\overline{\mathbb{Q}})$ where the periods of the fibre do not satisfy extra relations 'up to degree $δ$'. As a by-product, we also establish new instances of the Mumford-Tate conjecture, beyond the realm of abelian motives. When the base $S$ is a curve, we provide quantitative estimates for points satisfying these properties. The main technical contribution is a new result on relations satisfied by solutions of $G$-operators, which relies on height estimates due to Bombieri and André.

Improving energy efficiency in the transportation sector is critical for achieving sustainable mobility, with eco-driving emerging as a key strategy. However, implementing effective eco-driving for connected and automated vehicles (CAVs) in mixed traffic presents a significant control challenge due to the heterogeneous, uncertain behavior of human-driven vehicles (HDVs). Data-enabled Predictive Control (DeePC) offers a promising model-free approach but is often hindered by a high computational burden, limiting its real-time feasibility. This paper introduces a novel Direct Data-driven Predictive Control (D3PC) framework to address this limitation. By reformulating the data-driven prediction mechanism, the D3PC significantly reduces computational complexity, making its computation time nearly invariant to historical data size. This computational efficiency directly enables the formulation of a sophisticated eco-driving controller that can solve the complex energy optimization problem in real time, even within diverse and stochastic mixed-traffic environments. Comprehensive simulations demonstrate that the D3PC is orders of magnitude faster than existing DeePC-based methods while achieving superior energy efficiency. Specifically, it reduces total platoon energy consumption by up to 10.71% compared to rule-based cruise control baselines and 3.80% compared to the original DeePC, confirming its effectiveness for real-time, energy-efficient control.

Infrared divergences in QED cancel in inclusive observables through the Bloch--Nordsieck and KLN mechanisms. However, this cancellation removes only the unphysical infrared regulator. The detector resolution scale $ω_{\max}$, which specifies the maximum energy of unresolved soft photons, remains in the observable cross section. We emphasize that this surviving scale has a natural interpretation as a coarse-graining scale in the reduced density matrix of the hard sector. Soft photons below $ω_{\max}$ are not observed and are effectively traced over. The corresponding soft-sector overlap therefore becomes resolution dependent, $D_{ij}=D_{ij}(ω_{\max})$. Observable infrared memory is consequently defined not only by the asymptotic soft sector itself, but also by the resolution scale separating observed and unobserved infrared degrees of freedom. This provides a bridge between the traditional infrared-safe cross-section formulation and the modern interpretation of soft photons as carriers of infrared memory and quantum information.

In this paper, we investigate the well-posedness of the three-dimensional stationary incompressible resistive-viscous Hall magnetohydrodynamic (Hall-MHD) system within the framework of scale-invariant Besov-Morrey spaces. A key component of our analysis is the derivation of product estimates in these spaces, which are instrumental in handling the system's nonlinear terms. As an application, we also establish a well-posedness result for the stationary Navier-Stokes equations in this setting, thereby broadening the admissible classes of external forces and solutions.

Public elevation data can support landscape research, environmental interpretation, planning, education, and public engagement, but their practical reuse is often limited by fragmented delivery and specialist processing requirements. This paper presents RO-LiDAR GeoQuickView, an independent, voluntary, and non-commercial Web-GIS initiative for exploring and reusing publicly accessible elevation data in Romania. The platform integrates LiDAR-derived digital terrain models (DTMs) and complementary elevation models of different resolutions, publishes standardized hillshade visualizations for immediate browser access, supports participatory landscape documentation, and provides a spatial index for direct raster retrieval. Its most detailed currently integrated component is the 0.5 m LAKI III Zone A DTM coverage for Caras-Severin, Gorj, Mehedinti, and Dolj counties. LAKI III Zone B, comprising Suceava, Neamt, Bacau, and Vrancea counties, is the next scheduled high-resolution extension. It will be integrated after the public products become available and pass through the same harmonization and quality-control workflow. The platform also incorporates LAKI II and additional public altimetric sources through a source-aware processing workflow that accommodates different acquisition units, including one-kilometre cells and larger raster blocks. The paper documents the data architecture, harmonization steps, quality-control procedures, access modes, application range, and limitations. The platform is conceived as an accessibility layer over public data infrastructures: it supports rapid discovery and preliminary interpretation, but it does not replace official products, specialist modelling, expert review, or field verification.

Quantum computers offer a route to outperform classical methods in tasks such as molecular simulation, motivating hybrid algorithms like the Variational Quantum Eigensolver (VQE) for near-term devices. Silicon spin qubits are a promising platform for scalable quantum computation, but their performance is limited by hardware imperfections -- most notably charge-noise-induced potential fluctuations and static miscalibration of gate-electrode voltages -- which degrade quantum gate fidelities and, ultimately, algorithmic accuracy. Here we develop a hardware-algorithm co-simulation framework for silicon quantum-dot processors that links 3D electrostatics to effective $g$-factors and exchange couplings, and propagates voltage-level noise through realistic control pulses. Using VQE for $\mathrm{H}_2$ ground-state energy estimation as a circuit-level testbed, we study both static scaling/offset errors on the gate-electrode voltages and stochastic fluctuations modeled as random-telegraph noise with tunable amplitudes and switching times. At the gate level, we show that exchange-based two-qubit gates are roughly an order of magnitude more sensitive to these types of noise than ESR-driven single-qubit rotations. Quantum process tomography and Kraus-operator analysis further distinguish coherent and incoherent contributions and quantify the fraction of error that is, in principle, correctable by a compensating unitary. Embedding these noise models into the VQE circuit, we identify regimes of miscalibration strength and noise switching time compatible with chemically accurate energy estimates, and discuss how statistical post-processing based on the full distribution of noisy energy estimates could further improve accuracy.

As quantum networks evolve from experimental testbeds to fault-tolerant systems, the primary performance metric shifts from physical link fidelity to end-to-end logical error rate. However, current control planes remain ill-equipped for this transition: routing decisions are typically decoupled from Quantum Error Correction (QEC) strategies, relying on topology or scalar fidelity metrics that fail to predict how specific physical noise structures interact with logical codes. Optimizing this coupled route-and-code performance requires precise, real-time visibility into network error biases, yet traditional active tomography is operationally prohibitive due to throughput collapse and service interruption. We present SCOPE (Syndrome-based COntrol PlanE), a network-layer architecture that enables joint routing and coding optimization using purely passive telemetry. Instead of injecting probes, SCOPE harvests error syndromes -- the parity-check outcomes naturally generated by QEC decoders during user service. By aggregating these signals, SCOPE's inference engine reconstructs the network's time-varying error map, capturing complex, context-dependent noise correlations. This visibility drives a decision engine that proactively pushes optimal route-and-code configurations to source nodes. NetSquid and IBM-calibrated simulations show that SCOPE reduces estimation error by more than 60% relative to a standard EM baseline. In large-scale networks, this precision reduces logical error rates by 30-35% (up to 65%) against topology-aware baselines.

We consider the fair division problem of indivisible chores and resolve the long-standing open problem for the existence of EFX allocations with additive cost functions. We show that, even for tri-valued additive cost functions, for every $n\geq 4$, there exists an instance with $n$ agents where no EFX allocation exists. Our counterexample only uses three types of chores, which is also tight on the number of types, as an EFX allocation is known to exist for two types of chores. We then consider bi-valued instances. We show that, for every $n\geq 4$, there exists an instance with $n$ agents where every EFX allocation is not Pareto-optimal. This is also the first example showing the incompatibility of EFX and Pareto-optimality when the costs of items are positive: existing examples showing the incompatibility of EFX and Pareto-optimal exploit items with $0$ costs. Our result shows such an example exists even for bi-valued instances. The number of agents $n$ is also tight: for $n\leq 3$, it is known that EFX is compatible with Pareto-optimality. Finally, we also show that an EFX allocation is guaranteed to exist for $n=4$.

Atomic clocks have made time and frequency the most precisely measured quantities in physics, progressing from microwave standards that realize the SI second to optical clocks that now reach unprecedented levels of precision. A nuclear clock would shift the frequency reference from an electronic transition to the uniquely low-lying, laser-accessible isomeric transition in the $^{229}$Th nucleus, offering a route to compact, robust timekeeping and sensitive tests of fundamental physics. However, turning recent advances in spectroscopy of the $^{229}$Th nuclear resonance into clock operation requires the nuclear transition to serve as a stable discriminator for steering a traceable oscillator. Here we demonstrate the operation of a $^{229}$Th nuclear clock by stabilizing a continuous-wave narrow-linewidth 148.4 nm vacuum-ultraviolet (VUV) laser to a resolved nuclear transition in a solid-state host. This clock operation is enabled by fast frequency discrimination based on phototube photocurrent readout of the transmitted VUV power. The 10 $μ$W VUV laser, generated by four-wave mixing in cadmium vapour, provides a high-signal-to-noise absorption signal from a home-grown $^{229}$Th:CaF$_2$ crystal, allowing the laser to be locked to a weakly temperature-sensitive nuclear transition. The clock reaches a fractional frequency instability of $2\times10^{-12}/\sqrt{τ/s} $, where $τ$ is the averaging time. Remarkably, nuclear-clock frequencies measured with two distinct crystals agree at the $10^{-13}$ level, demonstrating the reproducibility of solid-state nuclear frequency references. By making a laser-addressed atomic nucleus an operational clock reference, this work extends quantum metrology from electronic to nuclear transitions, and opens a new platform for compact clocks, solid-state nuclear quantum sensors and precision tests of fundamental physics.

Closed-loop network monitoring and orchestration increasingly require semantic interpretations of live telemetry beyond raw counter collection. However, dynamic cloud-edge environments change both the active node set and the monitoring query at runtime, while control loops demand bounded millisecond-scale responses. We introduce a latent predictive state estimator (LPSE) for dynamic network monitoring and orchestration, built on latent predictive learning over streaming telemetry. The framework converts variable-cardinality node telemetry into topology-adaptive temporal representations, fuses them with monitoring questions, and returns bounded answers from a semantic codebook instead of autoregressive text generation. This design enables fixed-cost, single-pass inference while preserving semantic interpretability. By operating on permutation-invariant, slot-routed node representations keyed by stable identity, the model maintains a fixed input space and generalizes to node addition, removal, and reordering without retraining. Experimental results on a multi-node Kubernetes cluster show semantic prediction accuracy of 82.42% at approximately 41$\times$ lower mean inference latency and 15$\times$ smaller memory footprint compared with a deployable 4B LLM endpoint.

We prove that the one-dimensional Dirichlet spectrum with respect to approximation in $L_1$ norm $\mathbb{D}^{[1]}$ satisfies $$ \mathbb{D}^{[1]}=\left[\frac12,1\right]. $$ This is equivalent to the fact that the Minkowski spectrum $\mathbb M$, associated with the Minkowski diagonal continued fraction, satisfies $$ \mathbb M=\left[\frac14,\frac12\right]. $$ Further, we show that level sets $$ Θ_m=\{α\in(0,1)\setminus\mathbb Q:\mathfrak m(α)=m\}, $$ where $\mathfrak{m}(α)$ is the Minkowski constant of $α$, have Hausdorff dimension strictly greater than $1/2$ for any $m\in(1/4,1/2]$, while $\dim_H Θ_{1/4}=\frac{1}{2}$.

The notions of provisional, negative, and apparent convergence to 0 are introduced. It is then shown that Markov's principle is equivalent, in Bishop-style constructive mathematics, to the statement `every decreasing sequence of real numbers provisionally convergent to 0 actually converges to 0', and that this equivalence holds with `provisionally' replaced by `negatively'. Finally, apparent convergence and convergence are related by means of the anti-Specker principle.

We present an X-ray spectro-polarimetric study of the nearby type-1 active galactic nucleus NGC 4151 using two long IXPE observations obtained in 2022 and 2024, supported by simultaneous XMM-Newton and NuSTAR spectroscopy. IXPE measures a polarization degree of $\sim 6-7\%$ above 4 keV, with a polarization angle parallel to the radio jet, and a distinct low-energy component with a different angle, indicating at least two polarized components in the $2-8$ keV band. Previous work interpreted the hard X-ray polarization as evidence for a radially extended slab-like corona. Here we test an alternative scenario in which the observed polarization is produced predominantly by relativistic reflection from an accretion disk illuminated by a compact, lamp-post-like corona. Using recently developed models, we fit the IXPE Stokes spectra with a lamp-post plus distant-torus geometry, including partial-covering absorption and an additional soft polarized power-law component. We find that the data require a low coronal height ($h<9\,R_{\rm g}$ at $3σ$) and a relatively large torus opening angle ($>45^\circ$ at 3$σ$), while the disk reflection contributes $\sim 20\%$ of the 2-8 keV flux. The soft polarized component carries only $\sim 1-5\%$ of the flux but has a high polarization degree ($>10\%$) and a polarization angle around $20^\circ$. The same configuration provides acceptable fits to the $0.4-79$ keV XMM-Newton and NuSTAR spectra, demonstrating that disk reprocessing by a compact corona can simultaneously account for both the polarization and broadband spectral properties of NGC 4151.

We consider the following quasilinear reaction-diffusion equation $$ \partial_tu=Δu^m+(1+|x|)^σu^p, \quad (x,t)\in\mathbb{R}^N\times(0,\infty), $$ in dimension $N\geq3$ and in the range of exponents $1<p<m$ and $-\infty<σ<-2$. We prove that, for initial conditions $u_0$ satisfying $$ u_0\geq0, \quad u_0\not\equiv0, \quad \lim\limits_{|x|\to\infty}|x|^{-(σ+2)/(m-p)}u_0(x)=0, $$ the solution $u$ to the corresponding Cauchy problem remains uniformly bounded from above and below: $$ C_1\leq \|u(t)\|_{\infty}\leq C_2, \quad t\in(0,\infty), $$ for some positive constants $C_1$ and $C_2$. Under suitable conditions on $p$, we also establish the rate of expansion of the upper limit $R(t)$ of the positivity set for compactly supported data, that is, $$ At^β\leq R(t)\leq Bt^β, \quad β=-\frac{m-p}{σ(m-1)+2(p-1)}, $$ and a \emph{different time scale in outer sets}, that is $$ D_1t^{-α}\leq u(x,t)\leq D_2t^{-α}, \quad α=\frac{σ+2}{σ(m-1)+2(p-1)}, \quad {\rm if} \ |x|\geq Ct^β. $$ The boundedness is in striking contrast with the property of grow-up as $t\to\infty$ established in previous works by the authors for $σ>-2$, illustrating the character of threshold of the exponent $σ=-2$.