We study the aggregate hazard rate of a heterogeneous population whose individual event intensities are modeled as Cox (doubly stochastic) processes. In the deterministic hazard setting, the observed pool hazard is the survival weighted mean of the individual hazards, and its time derivative equals the mean individual hazard drift minus a variance term. This yields a transparent structural explanation of burnout in mortgage pools. We extend this perspective to stochastic intensity models. The observed pool hazard remains a survival-weighted mean, but now evolves as an Ito process whose drift contains the mean drift of the individual hazards and a negative selection term driven by cross-sectional dispersion, together with a diffusion term inherited from the common factor. We formulate the general identity and discuss special cases relevant to mortgage prepayment modeling.

The particle nature of dark matter (DM) remains one of the central open problems in modern physics. Among the most extensively studied candidates are weakly interacting massive particles, whose parameter space is now under strong pressure from direct detection, indirect detection, and collider searches. In this work we revisit the Higgs-portal scenario with vector DM, first in an effective-field-theory description and then in a renormalizable UV-complete realization. We show that the effective Higgs-portal model with a Proca vector coupled quadratically to the Standard Model Higgs is essentially excluded over almost all of its parameter space by current direct-detection limits, with only a narrow region near the Higgs resonance surviving with a required fine tuning of the DM to Higgs mass that should at the permille level. We then consider a UV completion based on an additional gauged $U(1)_X$ symmetry, in which the DM candidate is a massive vector boson $V$ and the scalar sector is extended by a dark Higgs that mixes with the Standard Model Higgs. In this framework, the presence of a second scalar mediator opens an additional resonant annihilation channel and can substantially weaken the direct-detection constraints. In particular, when the DM mass lies sufficiently close to the heavy-scalar resonance, $m_V \simeq m_{H_2}/2$, the coupling required to reproduce the observed relic abundance can lie up to about two orders of magnitude below current direct-detection bounds, thereby opening viable parameter space that is absent in the effective description. Our results highlight the importance of going beyond the effective-field-theory approximation in Higgs-portal vector DM models and show that UV-complete realizations can qualitatively change the phenomenological conclusions.

Measurements of the kinematic cosmic dipole continue to show an intriguing tension between the value inferred from the CMB and that obtained from high-redshift source number counts. While the measured dipole direction appears consistent, the amplitude, set by the observer's peculiar velocity $v_{o}$, remains in significant disagreement. In this paper, we propose using strong gravitational lenses with well-measured Einstein radii to estimate the kinematic cosmic dipole, through the relativistic aberration of the Einstein angle induced by the observer's motion. We show that this effect could be detected solely from measurements of the Einstein radius in wide, high-resolution imaging surveys such as Euclid. However, the precision achievable using Einstein-radius measurements alone, without redshift or lens-galaxy mass information, appears insufficient to discriminate between the CMB value of $v_{o}$ and that derived from source number counts at high statistical significance. Nevertheless, we demonstrate that including a large sample of lenses with available kinematic information, either via the Fundamental Plane relation or, ideally, through spectroscopic velocity-dispersion measurements, drastically reduces the noise and substantially improves the constraining power of this method. We show that, for a realistic sample of strong lenses detected by Euclid and complemented with spectroscopic velocity dispersion measurements from 4MOST or DESI, it is possible to discriminate between the CMB- and source-number-counts-inferred values at the $\sim 5σ$ level using a new, fully independent method. We further demonstrate that this technique is only weakly sensitive to strong-lensing selection effects, with selection biases and threshold effects estimated to be well below the 1% level.

While Large Language Models (LLMs) have achieved remarkable success in code generation, they often struggle with the deep, long-horizon reasoning required for complex software engineering. We attribute this limitation to the nature of standard pre-training data: static software repositories represent only the terminal state of an intricate intellectual process, abstracting away the intermediate planning, debugging, and iterative refinement. To bridge this gap, we propose a novel paradigm: understanding via reconstruction. We hypothesize that reverse-engineering the latent agentic trajectories -- the planning, reasoning, and debugging steps -- behind static repositories provides a far richer supervision signal than raw code alone. To operationalize this, we introduce a framework that synthesizes these trajectories using a multi-agent simulation. This process is grounded in the structural realities of the source repositories (e.g., dependency graphs and file hierarchies) to ensure fidelity. Furthermore, to guarantee the logical rigor of the synthetic data, we employ a search-based optimization technique that iteratively refines the Chain-of-Thought (CoT) reasoning to maximize the likelihood of the ground-truth code. Empirical results demonstrate that continuous pre-training on these reconstructed trajectories significantly enhances Llama-3-8B's performance across diverse benchmarks, including long-context understanding, coding proficiency, and agentic capabilities.

This is the first paper that provides a systematic treatment of the $r$-dimensional PTE problem in additive number theory, abbreviated by PTE$_r$, through its connection with combinatorial design theory, the branch of combinatorial mathematics that deals with finite set systems or arrangements with the ^^ balancedness' conditions. We first propose a combinatorial reconsideration of the definition of nontrivial solution introduced by Alpers and Tijdeman (2007), and then prove a fundamental lower bound for the size of such solutions. We exhibit high-dimensional minimal solutions with respect to the fundamental bound, which inherently have the structure of distinctive block designs or orthogonal arrays (OAs). Next, we develop a powerful method for constructing PTE$_r$ solutions via various classes of combinatorial designs such as block designs and OAs. Furthermore, we explore two dimension-lifting methods for constructing PTE$_r$ solutions: one is a combinatorial composition that produces PTE$_r$ solutions by embedding lower-dimensional solutions into OAs with $r$ columns, and the other is a recursive technique in which a PET$_r$ solution is constructed by taking the Cartesian product of two lower-dimensional solutions. It is emphasized that our results generalize many previous works, including a measure-theoretic construction by Lorentz (1949) and its geometric analog by Alpers and Tijdeman (2007), a key lemma in Jacroux's work (1995) on the construction of sets of integers with equal power sums, and the famous Borwein solution and its two-dimensional extension by Matsumura and Sawa (2025). In addition, we prove a characterization theorem for ideal solutions of the PTE$_1$ and discuss the connection with a curious phenomenon, called half-integer design, that is rarely reported in the combinatorial design theory or spherical design theory.

We propose a model independent framework for generating SPX and VIX risk scenarios based on a joint optimal transport calibration of their market smiles. Starting from the entropic martingale optimal transport formulation of Guyon, we introduce a perturbation methodology that computes sensitivities of the calibrated coupling using a Fisher information linearization. This allows risk to be generated without performing a full recalibration after market shocks. We further introduce a dimension reduction method based on perturbed optimal transport that produces fast and stable risk estimates while preserving the structural properties of the calibrated model. The approach is combined with Skew Stickiness Ratio(SSR) dynamics to translate SPX shocks into perturbations of forward variance and VIX distributions. Numerical experiments show that the proposed method produces accurate risk estimates relative to full recalibration while being computationally much faster. A backtesting study also demonstrates improved hedging performance compared with stochastic local volatility models.

High-entropy alloys (HEAs) combine compositional disorder with exceptional functional tunability, yet their inherently high-density limits use in lightweight systems. Here, we introduce entropy-architected nanowire metamaterials, a class of materials that couple configurational entropy with structural porosity to achieve metal-like functionality at ultralow density. FeCoNiCrCu HEA nanowires were electrodeposited into porous templates and freeze-cast into three-dimensional ``bird`s-nest`` scaffolds with densities below 1 $\%$ of the bulk metal. The resulting architectures retain a disordered face-centered-cubic phase, exhibit Curie temperatures exceeding 1000 K, and deliver thermal diffusivity ($\approx0.211$ mm$^2$ s$^{-1}$) comparable to titanium alloys. Structural and spectroscopic analyses reveal nanoscale Cu segregation that enhances magnetic ordering and thermal stability. These findings demonstrate that configurational entropy and architectural hierarchy can be co-engineered to yield lightweight, high-temperature functional materials for extreme-environment applications.

Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often extremely challenging, particularly in more than one spatial dimension. Analog simulation using tunable synthetic quantum systems can both verify existing theoretical predictions and lead to new physical insights. Here, we realize quantum simulation of massive relativistic fields in $2+1$ dimensions (two spatial dimensions and time), using two coherently coupled spin components in a uniform two-dimensional Bose-Einstein condensate. Specifically, we encode the paradigmatic sine-Gordon model in the field describing the relative phase, $ϕ$, of the two components. We show that, in the perturbative regime, collective field excitations exhibit a relativistic dispersion with a tuneable mass gap. We also observe explicitly non-perturbative phenomena, including the existence of topological domain walls across which $ϕ$ rapidly winds by $2π$. Our work opens possibilities for studies of cosmologically relevant phenomena including preheating, dynamics of topological defects, and relativistic false-vacuum decay.

This paper introduces a method for detecting, estimating, and localising a soft fault in wired communication networks. The proposed method is based on analysing the transmission coefficients (TC) in the time domain under both fault-free and faulty situations. An orthogonal frequency-division multiplexing (OFDM)-based scheme is used to estimate the TC. A fault-severity ratio is derived to estimate the fault intensity, while a residual-based function is proposed to determine its location. Experimental validation is carried out on a Y-shaped test setup to demonstrate the efficiency of the proposed approach.

SDSS~J143016.05+230344.4 ($z=0.08105$) has been proposed as a candidate pre-coalescence supermassive black hole binary and shows remarkable multiwavelength variability. Its radio evolution provides a direct probe of the compact emitting region and of the physical origin of the late-time activity. We aim to localize the variable radio emission, characterize its spectral evolution, and constrain whether the radio brightening is produced by a newly emerging compact component, external absorption, or dissipation in a structured circumnuclear environment. At all epochs, the radio emission is dominated by a single unresolved milliarcsecond core with $T_{\rm B} \gtrsim 10^{7}$ K, constraining the variable emission to $\lesssim 0.3$ pc. The broadband spectra require two synchrotron self-absorbed components: a persistent low-frequency component with $ν_{\rm p,steady} \approx 0.74$ GHz and $S_{\rm p,steady} \approx 1.22$ mJy, and a flare component whose turnover evolves from $(6.35 {\rm GHz}, 0.18 {\rm mJy})$ in 2022 February-May to $(8.61 {\rm GHz}, 0.38 {\rm mJy})$ in 2022 December, and then to $(5.83 {\rm GHz}, 0.25 {\rm mJy})$ in 2023 March-April. The flare contribution at 15 GHz reaches $\sim 80\%$ and matches the near-epoch VLBI recovery fraction, showing that the high-frequency brightening arises from a newly formed compact synchrotron component. A second brightening of the 15.2 GHz VLBI core is detected between 2023 September and 2024 February, while the source remains unresolved. Equipartition scalings imply characteristic radii of $\sim 5 \times 10^{-4}$ pc for the flare and $\sim 9 \times 10^{-3}$ pc for the steady component, and indicate a steep inner circumnuclear density profile, $n \propto R^{-1.7}$. The delayed radio flare is best explained by dissipation in an outflow or jet-base disturbance propagating through a structured circumnuclear medium.

We discuss the general covariance of operator product expansion in D-dimensional Euclidean conformal field theories. We propose to organise the expansion in powers of geodesic distance between two insertion points and to use the tangent vector to the geodesic for contractions with tensor operators. For conformally flat manifolds we show by explicit calculation that certain curvature terms arise in the OPE. For example for D>2 the leading term of this type in the identity channel of OPE of two scalar primaries is proportional to the Schouten tensor. We further argue that the terms we found are present for a general metric and are thus universal but there may be curvature terms at higher order in the expansion whose coefficients are not determined by the flat space OPE. The curvature terms we discuss are of practical interest in conformal perturbation theory calculations on curved spaces.

Despite the success of Landau-level theory and edge-state transport formalisms, a direct microscopic link between bulk quantization and the observed hierarchy of quantum Hall plateaus has not been established. In particular, no unified microscopic mechanism accounting simultaneously for integer and fractional sequences has been derived within standard quantum mechanics. Here we show that boundary-induced quantization of edge states provides this missing bridge. Starting from the Landau problem in laterally confined two-dimensional electron systems, we demonstrate that the imposition of Dirichlet, Neumann, and mixed (Robin) boundary conditions discretizes both the guiding-center coordinate and the longitudinal momentum of chiral edge states. The resulting boundary-dependent spectra generate families of edge channels with well-defined multiplicities that couple to electronic transport. When incorporated into an edge-state transport description, this boundary quantization reproduces the integer Hall sequence and simultaneously yields a structured hierarchy of fractional filling factors without invoking separate microscopic mechanisms. We further show that a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum while leaving the bulk Landau levels intact. This controlled symmetry breaking enhances edge-state multiplicities at small Landau indices and stabilizes the fractional plateaus observed at strong magnetic fields. The quantized Hall response thus emerges from the interplay between Landau quantization and boundary-induced guiding-center discretization, which together determine the spectrum and occupation of chiral edge channels. These results establish boundary-induced quantization as the microscopic origin of quantum Hall transport and provide a unified description of both integer and fractional regimes within conventional quantum mechanics.

The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty parameter $λ=\log n$ and $λ=2$ are too small, leading to many false discoveries, and their inherent (best subset) discrete optimization is infeasible in high dimension. We alleviate these issues with the pivotal information criterion: PIC is defined as a continuous optimization problem, and the PIC penalty parameter $λ$ is selected at the detection boundary (under pure noise). PIC's choice of $λ$ is the quantile of a statistic that we prove to be (asymptotically) pivotal, provided the loss function is appropriately transformed. As a result, simulations show a phase transition in the probability of exact support recovery with PIC, a phenomenon studied with no noise in compressed sensing. Applied on real data, for similar predictive performances, PIC selects the least complex model among state-of-the-art learners.

We classify rotary (orientably-regular) maps whose underlying graphs are multicycles. For the multicycle $\mathrm{C}_n^{(λ)}$ of length $n$ and edge-multiplicity $λ$, we determine all rotary embeddings for $n\geqslant 3$ and $λ\geqslant 2$. When $n$ is odd, there is a unique isomorphism class; when $n$ is even, the embeddings form a family $\mathcal{M}_n^{(λ)}(i,j)$ parameterized by integer pairs $(i,j)$ satisfying explicit congruence conditions.

High-brightness X-ray Free Electron Lasers (FELs) produce spatially and temporally coherent pulses on attosecond to femtosecond timescales, providing a transformative tool for discovery across biology, chemistry, physics, and materials science. This paper proposes a compact accelerator that enables a high-repetition-rate (MHz) 1 nm soft X-ray FEL with a footprint of less than 100 meters. Such an FEL is suitable for installation within research institution settings where space is limited. The accelerator leverages a multi-turn recirculating linear accelerator that integrates state-of-theart superconducting accelerator technology with recent advances in diffraction-limited storage rings. We present the conceptual layout and analyze the impact of two most challenging factors for such a compact accelerator, incoherent and coherent synchrotron radiation. We have systematically studied both effects for different multi-bend achromat lattices and electron beam peak currents. For a peak current of 60 Ampere before final compression and using 11-bending magnets, the horizontal emittance growth after the 90-degree arc can be kept below 10%, demonstrating that these effects are not limiting factors for achieving high-quality electron beams. Such a compact X-ray FEL facility would substantially reduce both construction and operational costs, greatly expanding access to these powerful research tools. Furthermore, this concept provides a potential upgrade path to generating hard X-ray radiation by incorporating high accelerating gradient structures to further accelerate a portion of the MHz electron beam.

We derive a thermodynamic uncertainty relation (TUR) under quantum continuous measurement and feedback control. By incorporating the quantum-classical-transfer entropy, which quantifies the information gained by continuous measurement, we show that the precision of currents is constrained by information-thermodynamic costs such as the entropy production and information gain. Our result shows that information gain has the potential to enhance the precision of currents beyond the bounds set by the conventional TUR. We illustrate the bound with a driven two-level system under continuous measurement and feedback, demonstrating that feedback achieves higher precision of currents while suppressing the entropy production.

Black holes are some of the most interesting objects in the universe. While they first arise in the complicated behavior of general relativity, the physical laws ruling their behavior are surprisingly simple. For example, one of the core facts about black holes is that their area never decreases, much like the entropy in thermodynamics. In this note directed at introductory physics students and their instructors, we use this similarity to understand properties of black hole physics using standard techniques from an undergraduate course in thermal physics. We explore the never-decreasing nature of black hole area to obtain bounds on the energy emitted in a black hole merger (a calculation originally done by Hawking). We show how this allows us to think of black holes in manners very similar to heat engines, and how these ideas have been used in modern gravitational wave observatories to test general relativity. This allows a research-level topic to be discussed in introductory physics lectures.

This paper investigates the potential of near-field (NF) indoor communications in the FR2 frequency bands using fully dielectric structures to generate orbital angular momentum (OAM) waves. All-dielectric platforms based on distributions of T-shaped unit cells are employed for this purpose. The unit cell design is based on a circuital approach and analytical formulations, where phase shifts necessary for OAM generation are achieved by varying the dielectric-to-air ratio within the structure. Based on this unit cell, a set of transmitarrays (TAs) are designed to produce specific OAM modes. These TAs are fabricated in-house using stereolithographic 3D printing and experimentally tested. The tests evaluate two key features of OAM beams: the orthogonality of distinct vortex modes, as characterized by their electric field distributions, and their object-avoidance capability, enabled by the central null characteristic of the wavefront. In addition, a field-test within an indoor environment is conducted emulating a real wireless system. A bit error rate lower than 10\textsuperscript{$-$6} is observed for solidary modes in Tx and Rx, whereas orthogonal modes produces an increment in 4 order of magnitude. The obtained results reveals that the prototype is suitable for short-range scenarios, enabling techniques such as OAM-multiplexation or physical-layer security thanks to the effective orthogonality beteween modes.

The dielectric properties of proteins, particularly in their hydrated state, have been extensively studied. Numerous theoretical and experimental investigations have reported values of both the permittivity and the intrinsic dipole moments of specific proteins under well-defined hydration conditions. Since even approximate estimates of these properties are relevant from both fundamental and applied perspectives, we propose a easy-to-use method to calculate the relative permittivity that can be readily integrated into proteotronics workflows. To validate the proposed approach, we compare the results with those obtained using a classical macroscopic method. The outcomes are consistent and contribute further insight into this long-debated issue.

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the prior and likelihood densities. Particular emphasis is placed on the hyperparameter controlling the prior smoothness and regularity, which is critical in ensuring well-posedness, shaping posterior structure, and determining predictive uncertainty. Commonly it is assumed to be known and fixed a priori; however in this paper we will adopt a hierarchical Bayesian framework in which smoothness and other hyperparameters are treated as unknown and assigned hyperpriors. Posterior inference is performed using Metropolis-within-Gibbs sampling suitable to high dimensions, for which hyperparameter estimation involves little computational overhead. The methodology is demonstrated on inverse problems for the Navier-Stokes equations and the stochastic advection-diffusion equation, under sparse and dense observation regimes, using Gaussian priors with different covariance structure. Numerical results show that jointly estimating the smoothness substantially reduces the errors in uncertainty quantification and parameter estimation induced by smoothness misspecification, by achieving performance comparable to scenarios in which the true smoothness is known.

In South Korea, age-disaggregated tuberculosis (TB) data at the district level are not publicly available due to privacy constraints, limiting fine-scale analyses of healthcare accessibility. To address this limitation, we present a high-resolution, district-level dataset on tuberculosis (TB) fatalities and hospital accessibility in South Korea, covering the years 2014 to 2022 across 228 districts. The dataset is constructed using a reconstruction method that infers age-disaggregated TB cases and fatalities at the district level by integrating province-level age-specific statistics with district-level spatial and demographic data, enabling analyses that account for both spatial heterogeneity and age structure. Building on an existing hospital allocation framework, we extend the objective function to an age-weighted formulation and apply it to the reconstructed dataset to minimize TB fatalities under different age-weighting schemes. We demonstrate that incorporating age structure can give rise to distinct optimized hospital allocation patterns, even when the total number of minimized fatalities is similar, revealing trade-offs between efficiency and demographic targeting. In addition, the dataset supports temporal analyses of TB burden, hospital availability, and demographic variation over time, and provides a testbed for spatial epidemiology and optimization studies that require high-resolution demographic and healthcare data.

We present the results of observations of the radio halo in the Coma galaxy cluster at 4.8 GHz performed with the Sardinia Radio Telescope. The radio halo in this cluster is detected for the first time at this frequency with a statistical significance higher than $3σ$. After the removal of the Radio Frequency Interference and of the discrete sources contribution, and after the correction for the Sunyaev-Zel'dovich effect, we estimate a flux density of $61\pm11$ mJy, higher than the value previously reported in literature at this frequency. By using the value we obtained, it is possible to estimate an integrated spectral index between 4.8 and 6.6 GHz of $α\sim1.17$, where $F(ν)\propto ν^{-α}$, indicating a possible higher-frequency slowdown of the spectral steepening observed between 1.4 and 4.8 GHz. Such a spectral behavior is compatible with turbulent re-acceleration if the seed electrons have a spectrum extending up to high energies, as in the case of continuous injection by hadronic interactions or dark matter annihilation. We also report the detection at 4.8 GHz of a polarized spot inside the halo, without an evident counterpart, already detected at 6.6 GHz.

We establish a geometric inequality relating the Dirichlet energy $E_1(f)$ and the bienergy $E_2(f)$ of smooth maps \[ f : (M,g) \to (\overline{M},\overline{g}) \] between Riemannian manifolds. Assume that $(M,g)$ is a compact, connected Riemannian manifold whose Ricci curvature has global minimum $\operatorname{Ric}_{\min}$, and that the target manifold $(\overline{M},\overline{g})$ has non-positive sectional curvature along $f(M)$. We prove that \[ E_2(f) \ge \operatorname{Ric}_{\min}\, E_1(f). \] We further analyze the equality case and obtain rigidity results: equality holds if and only if $f$ is totally geodesic and of constant rank. Applications to maps into Hadamard manifolds are also presented. To the best of our knowledge, this is the first geometric inequality directly relating the Dirichlet energy and the bienergy of smooth maps. This result establishes a direct connection between the Ricci curvature of the domain and higher-order variational energies.

Pauli channels are widely used to describe errors in quantum computers, particularly when noise is shaped via Pauli twirling. A common assumption is that such channels admit a Markovian generator, namely a Pauli-Lindblad model with non-negative rates, but the validity of this assumption has not been systematically examined. Here, using CP-indivisibility as our criterion for non-Markovianity, we study multi-qubit Pauli channels from a single snapshot of the dynamics. We find that while the generator always has the same structure as the standard Pauli-Lindblad model, the rates may be negative or complex. We show that random Pauli channels are almost always non-Markovian, with the probability of encountering a negative rate converging doubly exponentially to unity with the number of qubits. For physically motivated noise models shaped by Pauli twirling, including single-qubit over-rotations and two-qubit amplitude damping errors, we find that negative rates are generic, even when the underlying physical noise is Markovian. We generalize probabilistic error amplification and cancellation to non-Markovian generators, and quantify the sampling overhead introduced by negative and complex rates. Experiments on superconducting qubits confirm that allowing negative rates in the learned noise model yields more accurate predictions than restricting to non-negative rates.

We present a fully Bayesian framework for time delay inference and stationarity tests in quasar light curves using marginalised Gaussian processes. The model separates a deterministic, non-stationary drift (piecewise linear mean) from stationary stochastic variability (Matérn and Spectral Mixture kernels), and jointly models multiple images with per-image microlensing. Bayesian evidence and parameter posteriors are obtained via nested sampling and marginalised over model choices. Applied to the quasars WFI J2033 - 4723, B 1608 + 656, and HE 0435 - 1223, we find strong evidence for non-stationarity in B 1608 + 656 and HE 0435 - 1223, while WFI J2033 - 4723 is consistent with stationarity. The stochastic component favours an Markovian exponential kernel for B 1608 + 656 and a non-Markovian Matérn-$\frac32$ kernel for WFI J2033 - 4723 and HE 0435 - 1223. Multi-length-scale Spectral Mixture kernels are disfavoured. Time delays are shown to be robust to model assumptions and consistent with prior work within the error. We further identify and mitigate a likelihood pathology which biases toward large delays, providing a practical nested sampling convergence protocol.

An agent chooses an action based on her private information and a recommendation from an informed but potentially misaligned adviser. With a known probability, the adviser truthfully reports his signal; with the remaining probability, he can send any message. We characterize optimal robust decision rules that maximize the agent's worst-case expected payoff. Every optimal rule is equivalent to a trust-region policy in belief space: the adviser's reported beliefs are taken at face value if they fall within the trust region but are otherwise clipped to the trust region's boundary. We derive alignment thresholds above which advice is strictly valuable and fully characterize the solution in both binary-state and binary-action environments.

We investigate how enhanced Koszul properties of Galois cohomology behave under composita of fields. Given fields $K_1$ and $K_2$ containing $μ_p$, with intersection $k$ and compositum $K = K_1K_2$, we formulate an abstract composita stability theorem: under a pro-$p$ amalgam decomposition $G_K \cong G_{K_1} *_{G_k} G_{K_2}$ of maximal pro-$p$ Galois groups, and natural Mayer-Vietoris compatibility assumptions on the mod-$p$ cohomology rings $H^\bullet(G_{K_1},\mathbb F_p)$, $H^\bullet(G_{K_2},\mathbb F_p)$, and $H^\bullet(G_k,\mathbb F_p)$, the quadratic presentation of $H^\bullet(G_K,\mathbb F_p)$ arises from a fiber-product construction on degree-$1$ generators and quadratic relations. Assuming stability of universal Koszulity under this quadratic gluing, we obtain that universal Koszulity of $H^\bullet(G_{K_1},\mathbb F_p)$ and $H^\bullet(G_{K_2},\mathbb F_p)$ implies universal Koszulity of $H^\bullet(G_K,\mathbb F_p)$. As a concrete application, we prove a composita stability theorem for certain Pythagorean fields whose maximal pro-$2$ Galois groups decompose as free pro-$2$ products of Demuškin groups and free factors. For suitable composita $K = K_1K_2$ of such fields, the mod-$2$ Galois cohomology ring $H^\bullet(G_K(2),\mathbb F_2)$ remains quadratic and universally Koszul. This provides large classes of fields, built from local, global, and Pythagorean base fields by admissible extensions and composita, whose maximal pro-$p$ Galois groups have universally Koszul cohomology, and yields inverse Galois obstructions: any finitely generated pro-$p$ group with nonquadratic or non-universally Koszul mod-$p$ cohomology cannot occur as the maximal pro-$p$ Galois group of a field in these families.

The Weakly-Interacting Slim Particle encyclopedia (WISPedia) is a comprehensive reference work dedicated to the systematic compilation of theoretical models, Effective Field Theories, and frameworks involving Weakly Interacting Slim Particles (WISPs): a broad class of light, feebly coupled particles proposed in extensions of the Standard Model. In current times, where the number of models largely surpasses the number of new physics signals, this encyclopedia aims to provide a concise reference of their landscape. The goal is to provide a useful tool to the community to navigate among them. It does not aim to review all the models in detail, but to define their essential characteristics, and point the reader to useful and minimal material such as the original sources, review articles, tools and general compilations of bounds. Hence, the format of this reference resembles the direct style of a model encyclopedia of WISPs.

The leader-following consensus problem for general linear multi-agent systems over jointly connected switching networks has been a challenging problem and the solvability of the problem has been limited to the class of linear multi-agent systems whose system matrix is marginally stable. This condition is restrictive since it even excludes the most commonly used double-integrator system. This paper presents a breakthrough by demonstrating that leader-following exponential consensus is achievable for general linear multi-agent systems over jointly connected switching networks, even when the system matrix is exponentially unstable. The degree of instability can be explicitly characterized by two key quantities that arise from the jointly connected condition on a switching graph. By exploiting duality, we further show that the output-based distributed observer design problem for a general leader system is solvable over jointly connected switching networks, even when the system matrix is exponentially unstable. This is also in sharp contrast to the existing distributed observers, which rely on the assumption that the leader system is marginally stable.

The establishment of the Wilson-Fisher fixed point (WFP) for $O(n)$ spin models in $d=4-ε$ dimensions stands as a cornerstone of the renormalization group (RG) theory for critical phenomena. However, when long-range (LR) interactions, algebraically decaying as $\propto 1/r^{d+σ}$, are introduced, the fate of the short-range WFP (SR-WFP) has remained a subject of intense debate since the 1970s. We employ two complementary techniques -- the standard field-theoretic RG and a perturbative bootstrap scheme, and perform the $ε$-expansion calculations up to the two-loop level. We show that, as long as $σ<2$, the SR-WFP becomes unstable and a stable LR-WFP emerges, and, in the non-classical regime with $d/2 < σ< 2$, the critical exponents, including the anomalous dimension, are functions of $ε$, $δ=2-σ$ and $n$, which reduce to the exact results in the limiting cases $ε\to 0$, $δ\to 0$ or $n \to \infty$. Our $(4-ε)$-expansion calculations support the scenario that the threshold between the LR- and SR-WFP occurs strictly at $σ_*=2$, well consistent with the recent high-precision numerical study while different from the widely accepted Sak's criterion.