We study Maschke-type phenomena in the representation theory of generalized digroups. For a generalized digroup $D$, we construct an associative enveloping algebra $A_D$ and prove that $Rep(D)$ is equivalent to the category of left $A_D$-modules. Under a Maschke-type condition on the group component, we show that short exact sequences split on the $ρ$-side, while the obstruction to full splitting is described by cocycles and identified with $Ext^1_{Rep(D)}(Q,W)$. We also derive a spectral sequence with consequences for splitting and non-semisimplicity.

LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we introduce a new framework for estimating ball sizes in the coset graphs of LDPC codes. The key new object is the coset-weight generating function, which encodes the minimum Hamming weights of all cosets of a linear code. Rather than estimating coset balls directly, we upper-bound this generating function through a local growth analysis for codes spanned by low-weight vectors. This framework sharpens the previous ball-size estimate of Iceland and Samorodnitsky. Combined with a general method of Friedman and Tillich that relates balls in coset graphs to sizes of error-correcting codes, it further improves the upper bounds on the rate of LDPC codes for a significant range of relative distances.

We give a complete characterization of generic irreducibility for dispersion polynomials and Bloch varieties of periodic graph operators. More precisely, we prove that for a generic choice of edge weights and potentials, the dispersion polynomial/Bloch variety of a nontrivial periodic graph is irreducible if and only if the quotient graph is connected. Our proof uses a strong dichotomy for parameterized Laurent polynomials: reducibility either occurs for every parameter or fails on a nonempty Zariski-open set. After establishing this dichotomy, we reduce the problem to minimally connected periodic graphs.

We present a unified refractive index (RI) sensing platform that integrates THz-comb-based frequency multiplication with dual-comb active-dummy temperature compensation. In conventional RI-sensing optical frequency combs (OFCs), sensitivity, stability, and measurement speed are fundamentally coupled, limiting overall performance. In the proposed system, RI-induced shifts in the repetition frequency are amplified in the terahertz domain, while temperature-induced fluctuations are suppressed through common-mode rejection in a dual-comb configuration. Experimental results demonstrate a sensitivity of 5.05 * 10^7 Hz/RIU, high linearity (R^2 = 0.9979), improved resolution (1.07 * 10^-4 RIU), and high accuracy (5.50 * 10^-5 RIU). The RI-induced frequency shift is expanded from tens of hertz to hundreds of kilohertz, enabling rapid and precise readout with short gate times. This approach overcomes the conventional trade-off between sensitivity and stability. More fundamentally, it establishes orthogonal control of signal scaling and noise suppression as a design principle for high-performance RI sensing.

Account-based ledgers -- standard externally-owned accounts (EOAs), ERC-4337 smart accounts, post-Pectra EIP-7702 delegated EOAs -- place the holder of the controlling key at the apex of asset authorization. We ask a structural question about ledger access control: under this authorization model, can a protocol enforce the future disposition of an asset without taking custody and without requiring the owner's cooperation at enforcement time? We formalize the target as Non-Custodial Enforced Encumbrance (NCEE), a four-property specification covering self-custody, transition restriction, irrevocability, and permissionless enforcement. We define the Key Sovereignty Axiom (KS) and prove that any ledger satisfying KS cannot realize NCEE; standard EOAs, ERC-4337 smart accounts, and EIP-7702 delegated EOAs satisfy KS for their standard asset paths. We define Asset-Authorization Coupling (AAC) and prove it necessary for NCEE in the transfer-dichotomous asset setting. To witness the positive side, we introduce the envelope, a primitive for commitment-based private-state ledgers that binds a note, a condition tree, and a redistribution intent to protocol-maintained marker sets, separating ordinary spend nullifiers from a new encumbrance-namespace nullifier derived from note randomness rather than the owner key. We prove the envelope realizes NCEE under stated cryptographic assumptions and a deployment assumption that the marker-set registry is immutable; three concrete deployment templates are given. We define games for encumbrance integrity, settlement security, key-compromise resilience, and encumbrance indistinguishability. A reference implementation in Noir and UltraHonk supports the empirical claims, with gas measurements, recursive aggregation benchmarks, and a practical-economics analysis.

Signal Temporal Logic (STL) is a formal language for specifying real-time behaviors of cyber-physical systems (CPS). Automatically transforming natural language requirements into STL specifications has received growing attention. Recent efforts leveraging large language models (LLMs) have demonstrated impressive performance, but some natural language requirements in practice contain vague or ambiguous information, which remains challenging for LLMs to handle. To address these challenges, we propose ClarifySTL, an interactive LLM-agent framework that enhances STL transformation through requirements clarification. ClarifySTL first detects vague expressions that indicate underspecified information in a requirement. If any vagueness is detected, it generates targeted clarification queries to guide users in supplementing the requirement until all necessary details are provided. Subsequently, if ClarifySTL detects ambiguities, it formulates focused ambiguity clarification queries and updates the requirements based on user feedback until all ambiguities are resolved. Finally, the requirements with vagueness and ambiguity clarified are transformed into STL specifications using LLMs. This interactive framework ensures that the resulting STL formulas faithfully capture user intent while reducing the burden on the user. We evaluate ClarifySTL on the representative benchmarks DeepSTL and STL-DivEn, as well as our newly introduced AmbiEval benchmark, which is specifically designed to assess the performance of the agents in handling vagueness and ambiguity, including both detection and query generation. The experimental results show that ClarifySTL is effective.

Blockchain and decentralized finance have revolutionized the financial ecosystem while simultaneously exposing it to cryptocurrency phishing attacks. Existing phishing detection methods primarily rely on graph learning, but they face significant limitations. Static graph learning approaches fail to account for the temporal evolution of phishing patterns, while semi-dynamic methods, such as those combining static GNNs with LSTM, struggle to capture the irregular and bursty nature of blockchain transactions. Moreover, these methods overlook the diversity of Ethereum transactions, treating them as homogeneous graphs, and heavily rely on supervised learning, which requires extensive labeled data that is not readily available. These limitations reduce their adaptability to emerging phishing threats. In this paper, we present PhishEye, a fully dynamic self-supervised system that monitors on-chain transactions to detect phishing activities. PhishEye formulates Ethereum transactions as a heterogeneous temporal attributed multi-graph and incorporates a novel temporal graph contrastive learning model, which captures both temporal patterns and heterogeneous transaction types. The evaluation on a dataset of 161,658 addresses and 416,541 transactions shows that PhishEye outperforms existing methods, achieving an F1 score of 87.23% and an AUC of 98.43% for phishing transaction detection, and an F1 score of 94.19% and an AUC of 98.03% for phishing account detection. In real-world deployment from May 1, 2023 to July 31, 2024, PhishEye identified 1,803 previously unknown phishing addresses, providing early alerts that helped prevent losses exceeding 2 billion USD.

We study the duality between quasi-particle and electron tunneling in point-contact geometries of fractional quantum Hall states. To treat non-Abelian edge operators, we introduce a "phase-shift instanton" that incorporates phase factors from primary fields into the instanton gas framework. Using this method, we reformulate the Moore--Read duality and obtain an explicit dual description for the $k=3$ Read-Rezayi state. Our results clarify how quasi-particle tunneling produces characteristic phase shifts in instantons and how these shifts map strong quasi-particle tunneling to weak electron tunneling. Based on this dual description, we analytically evaluate the non-linear differential conductance in the strong-coupling regime. We reveal that, due to the physical requirement that the tunneling particle across the vacuum gap must be a true fermion, the transport behavior universally converges to a $G \propto V^4$ scaling for both the Moore--Read and Read--Rezayi states. This universal transport signature highlights a fundamental topological constraint underlying non-Abelian fractional quantum Hall edges.

In this paper, we propose a method for privacy-preserving federated learning that uses randomly selected model parameters to update global models. High-quality deep neural networks (DNN) models require a huge amount of training data in general, but model training raises privacy concerns when dealing with sensitive or personal information. Federated learning is a distributed machine learning framework in which multiple clients and a server train a model collaboratively. However, if the shared updates are compromised, an attacker may reconstruct the original training data. In addition, previous methods for improving robustness generally reduce the accuracy. To overcome these issues, in our method called federated learning using randomly selected model parameters (FLRSP), model parameters computed in each local server are randomly selected and shared to update a global model in a central server. In experiments, image classification tasks were carried out on the ResNet34 architecture and the Vision Transformer (ViT) under the use of Federated Stochastic Gradient Descent (FedSGD) and Federated Averaging (FedAvg), and the results demonstrated our method's effectiveness in terms of image classification accuracy and robustness against state-of-the-art attacks compared with previous methods.

We present an exact sampling algorithm for Pfaffian point processes based on a skew-symmetric analogue of the Cholesky factorization. This algorithm enables efficient sampling of a wide range of statistics arising in random matrix theory and combinatorics. For instance, we can sample eigenvalues of the orthogonal and symplectic ensembles ($β= 1,4$). In addition, we introduce a symplectic Arnoldi method for computing skew-orthogonal polynomials associated with a general weight function. This method can be used to efficiently construct the $2 \times 2$ matrix valued skew-symmetric kernels that arise in $β= 1,4$ polynomial ensembles. We illustrate our approach with several numerical examples and experiments, including the symmetric corner growth model, the finite-$N$ Gaussian (Hermite) orthogonal and symplectic ensembles, and the $β= 1,4$ Airy point processes and Tracy-Widom distributions.

Type Ib and Ic supernovae (SNe Ib/Ic) are the bright finale of massive stars that have lost their hydrogen envelopes, making them powerful probes of mass stripping in massive star evolution. The advent of modern large photometric and spectroscopic surveys presents the unique opportunity to investigate systematic differences between these two kinds of SNe. In this study, we analyze a large, homogeneous sample of SNe Ib/Ic light curves from the Zwicky Transient Facility. We find a systematic difference in their optical colors: SNe Ib are, on average, bluer than SNe Ic at a statistically significant level. This difference appears intrinsic, likely reflecting progenitors with different degrees of stripping -- helium-rich for SNe Ib and helium-poor for SNe Ic. In addition, we find that SNe Ib/Ic with narrow lines (SNe Ibn/Icn) are bluer than those without, which might originate from circumstellar matter interaction, with potential connection to fast blue optical transients. We demonstrate that SN colors offer a promising probe of mass stripping in massive stars, potentially providing a useful tool for analyzing large photometric data and improving predictions for the final outcomes of stripped massive stars.

We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo estimates from the constrained chains are then combined with appropriate weights, calculated from the transition probabilities between subsets. In addition to the computational advantages arising from its parallelized structure, this modular MCMC approach enables variance reduction for Monte Carlo estimation in settings where sampling from low-density regions is required. We develop a central limit theorem-type result for the resulting Monte Carlo estimates and propose a method for estimating their standard errors. Furthermore, by applying this modular sampling technique to simulated tempering, we propose a method for Monte Carlo estimation of expectations with respect to multimodal target distributions. This approach effectively addresses a well-known challenge of tempering-based methods: sampling efficiency can be greatly reduced when separated modes of the target distribution have different scales. We demonstrate the efficiency of the proposed methods through numerical examples, including one arising from Bayesian sparse regression with a spike-and-slab prior.

We investigate the influence of interfacial rheology on the motion of a compound particle consisting of a viscous droplet enclosing a translating rigid particle in the Stokes flow regime. The droplet interface is modeled using the Boussinesq-Scriven constitutive law, incorporating both surface shear and dilatational viscosities. An exact analytical solution is derived for the concentric configuration, and the analysis is extended to eccentric geometries using a spectral boundary integral method, enabling a systematic examination of confinement, viscosity contrast, and interfacial properties. For concentric configurations, we show that the induced droplet velocity is independent of surface shear viscosity, while surface dilatational viscosity can either enhance or suppress the droplet motion depending on the interplay between confinement and viscosity ratio. This behavior is rationalized in terms of competing effects between reduced interfacial mobility and increased driving force required to maintain the prescribed particle speed. In contrast, when the particle is eccentrically positioned within the droplet, a dependence on surface shear viscosity emerges, leading to a consistent enhancement of droplet motion that becomes more pronounced with increasing eccentricity. The analytical and numerical results are in excellent agreement and reveal how interfacial rheology, confinement, and symmetry breaking jointly govern the dynamics of compound particle systems. These findings provide mechanistic insight and establish a quantitative benchmark for future studies of active compound particles with complex interfaces.

I report the detection of statistically significant linear alignments and anomalous spatial clustering among high-confidence transient candidates in the VASCO catalog of vanishing sources on Palomar Observatory Sky Survey (POSS-I) photographic plates (1949-1957). A machine learning classifier scores 107,875 candidates by their likelihood of being genuine transients. Searching the 36,215 candidates with probability >= 0.50 for collinear groupings narrower than 3 arcsec, I find 7 plates with alignments of 5-8 sources that exceed Monte Carlo expectations (p < 0.03, 10,000 iterations). The aligned sources are point-like, not streaks, which rules out any continuously luminous object crossing the field during the 45-minute exposures. The implied angular rates (1-15 arcsec/s) overlap with the geosynchronous regime but are inconsistent with low or medium Earth orbits, and no artificial satellites existed during the POSS-I era. When I project each alignment onto Earth's surface assuming a high-altitude object, 6 of 7 maintain constant geographic longitude with sub-degree spread (combined p ~ 3e-10). Four of these cluster near -96 deg longitude (central United States); one falls within 0.3 deg of the longitude of the Hanford nuclear production site on a nuclear test window date. Close pairs (< 30 arcsec) occur at 16.2x the random rate, and the nights with alignments are the same nights with excess close pairs (Fisher exact p < 0.0001). Plate artifacts cluster near the ecliptic plane (26%), but high-confidence transients are depleted there (16%; chi-square test p = 3.3e-82), which rules out asteroids, comets, and zodiacal debris as the dominant source. No transient reappears at the same sky position on a different night. All of these transients predate Sputnik 1.

The rapid expansion of uplink-intensive applications necessitates video coding solutions that balance high Rate-Distortion (RD) efficiency with ultra-low latency. This paper presents a longitudinal performance analysis of NVIDIA hardware encoding (NVENC), spanning from Pascal to the emerging Blackwell generation. We specifically evaluate the operational viability of the new "Ultra High Quality" (UHQ) tuning mode against standard low-latency configurations. Our results demonstrate that while the Blackwell architecture breaks historical efficiency plateaus, achieving a 5.94% BD-Rate gain in standard modes and up to 22.79% in UHQ modes, these gains incur severe system-level penalties. We reveal that UHQ operates as a hybrid pipeline, offloading complexity to CUDA cores and enforcing aggressive temporal structures (up to 7 B-frames) that increase end-to-end latency by over 400% and GPU board power consumption by up to 40%. Consequently, while UHQ successfully bridges the quality gap with software encoders, its prohibitive serialization delay renders it unsuitable for interactive real-time communications, positioning it instead as a specialized solution for Video-on-Demand (VoD) transcoding.

AI-driven penetration testing agents are now capable of autonomously executing attacks within compromised networks. Identifying the model family that controls the active sessions of such agents provides valuable information towards understanding the intent of the attack and further developing attack countermeasures. In this paper, we introduce Trace, a novel multi-stage attribution and forensic framework for AI attack agents using terminal command sequences. Once Trace identifies a model family for the attacker agents, it guides a defensive prompt injection (DPI) strategy to the attacker model via a crafted payload. This is with the aim to exfiltrate system prompts from an attacker model, thus, revealing valuable information to understand the attacker intent and facilitate further forensic investigation. We have implemented our approach revolving around a Linux capture-the-flag (CTF) box. The attacker agents are bolstered via three distinct scaffolds and seven frontier model families. Our evaluation reveals that Trace achieves a macro F1 score of 0.981 in accurately fingerprinting the attacker model family (0.815 when generalizing to unseen scaffolds). Besides, the fingerprinting guides the DPI via a crafted payload to certain model families, resulting in system prompt extraction from 81.9% of non-Claude sessions on average (up to 98.3%) at 0.736 Sentence-BERT fidelity -- 1.88x higher than blind deployment. Finally, to validate the robustness of Trace, we evaluate it with a blackbox and proprietary scaffold employing multiple model families (Gemini and Claude Opus). Our evaluation identified the model family with an average 78% accuracy. Moreover, for the Gemini model family, the DPI employed by Trace revealed the entire system prompt and this has been confirmed by the developers. Trace therefore provides a fundamental first step towards attacker agent forensics.

We study one-dimensional viscoelastic phase transitions modeled by a Ginzburg--Landau energy with a non-convex cubic stress-strain law. Extending the isothermal model, we couple the momentum equation to a heat equation for the temperature field, giving a thermoelastic system with viscous, capillary, and thermal-diffusion terms. We prove global existence and uniqueness of classical smooth solutions for the Cauchy problem, using a traveling-wave decomposition, an exponential transformation of the mechanical perturbation, and coupled energy estimates at successive regularity levels. Under additional integrability and small-data assumptions, the temperature perturbation decays algebraically.

Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial manner across structured categories. In earlier work, we showed that this failure is fundamental and introduced an operadic notion of spectrum that provides a canonical replacement. In this paper, we develop the analytic consequences of this construction and show that the operadic spectrum acts as a control parameter for a calculus of functors. We establish a criterion for polynomial behavior based on higher cross-effects, and prove convergence results for the associated Taylor tower, including explicit exponential error bounds. We further show that the derivatives of a functor form a structured algebraic object with symmetric and operadic features, and satisfy a chain rule governed by a natural composition operation (operadic plethysm). This leads to a reconstruction theorem, showing that analytic functors are completely determined by their derivative data, and hence to a classification in terms of algebraic structures. Compared with classical Goodwillie calculus, which is governed by homotopy-theoretic conditions, the present framework is analytic and quantitative in nature, providing explicit control over convergence and approximation. These results place functor calculus in a setting that combines spectral ideas, analytic methods, and operadic algebra, and suggest further connections with deformation theory and geometry.

Light elements play an important role in influencing the macroscale properties of engineering alloys through grain boundary (GB) segregation phenomena. However, the scarcity and scattered nature of ab initio datasets for light elements in steels makes reproduction and extraction of general trends from the literature difficult. Here, we present a comprehensive ab initio evaluation of the segregation energies and cohesive effects for H, He, B, C, N, O, P, S, extensively sampling both substitutional and interstitial sites in six model coincident site lattice (CSL) ferritic iron GBs using density functional theory (DFT). Cohesive effects are evaluated in both a quantum-chemistry bond-order and rigid Rice-Wang interfacial cohesive strength framework. Our calculations indicate that, compared at the same concentration, B and C enhance GB cohesion, N, P, H are mildly detrimental, and He, O, S as powerful decohesive agents/embrittlers. Sampling both interstitial and substitutional starting positions is necessary to accurately capture segregation spectra. Commonly utilised sampling criteria such as site volumes prove insufficient for identifying deepest GB binding sites. Solutes placed in either kind of site can induce large relaxations to the same final configuration, resulting in site classification ambiguity. The nearest neighbour distance of a solute to its neighbours after relaxation is shown to be a controlling factor for the lower threshold of segregation energies at sites. The freely available DFT dataset and analysis repositories are expected to advance understanding of GB segregation behaviours of light elements in steels and serve as a resource for developing machine learning interatomic potentials.

Political news on social media rarely circulates in isolation: audiences actively engage, react, and clash. Whether these interactions reflect agreement or conflict may depend on the ideological discrepancy between publishers and the news content they share. This study investigates this relationship using Facebook posts linking to political news during a Brazilian presidential election. We analyze five dimensions of engagement: ideological discrepancy between publishers and content, emotional responses, audience consensus, toxicity in posts, and content topics. Our results show that ideological discrepancy is associated with differences in engagement, exhibiting a nonlinear pattern: consensus declines under conditions of very high ideological mismatch and, in our data, also under very high alignment, while toxicity increases primarily under extreme mismatch. A statistical model indicates that emotional valence, toxicity, and ideological discrepancy are the factors most strongly associated with consensus. Among highly partisan publishers, higher toxicity is associated with increased audience consensus, suggesting that hostile discourse may co-occur with in-group agreement in strongly ideological contexts. Overall, these findings highlight how ideological discrepancy, emotional reactions, and interaction dynamics are associated with consensus and polarization in online political engagement.

We introduce a two-parameter continuity path for the J-equation and use it to characterize the solvability of the J-equation for Kähler metrics with Poincaré type singularities along a divisor $D$, allowing simple normal crossings and self-intersections. On Kähler surfaces, we show that the classical subsolution condition in the smooth setting implies solvability in the Poincaré type setting for any smooth divisor $D$. As a consequence, if $X$ contains no curves of negative self-intersections and $K_X[D]$ is ample, then the K-energy is bounded from below on any Poincaré type Kähler class. In the smooth divisor case, we further analyze the asymptotic behavior of solutions near $D$, and show that existence of a Poincaré type solution implies existence of a solution to the J-equation on $D$.

In this paper, we investigate a system of parabolic partial differential equations with unknown-dependent coefficients that integrates two models: an anisotropic orientation-adaptive denoising process in image processing and a phase-field model of grain-boundary motion in materials science. In recent years, several studies have attempted to develop a unified framework for treating these two research areas by considering pseudo-parabolic systems obtained through the introduction of the energy-dissipation operator $ - Δ\partial_t $. However, the mathematical models for image processing and grain-boundary motion are originally formulated as parabolic systems. Therefore, establishing a unified analytical framework for such parabolic models remains an open problem. In this paper, we address this open problem by introducing a notion of solution that reproduces energy dissipation in parabolic systems, which we call an energy dissipative solution. As the main result, we clarify conditions that guarantee the existence of such solutions. The results of this paper establish a unified analytical framework for parabolic models, which has remained unresolved, and provide a solid theoretical foundation for advanced problems spanning both image processing and materials science.

An ample groupoid is said to be AF if it is a directed union of compact open principal subgroupoids. In this paper, we provide a complete homological characterization of these groupoids. Specifically, we prove that an ample groupoid is AF if and only if it has homological dimension zero. More generally, we characterize groupoids of homological dimension zero over a unital ring $R$.

Using the Hill-Hopkins-Ravenel norm, one can produce a $Q_8$-spectrum $N_{C_2}^{Q_8} \text{MU}\mathbb{R}$, where $Q_8$ is the quaternion group. Working towards a computation of the slice spectral sequence for $N_{C_2}^{Q_8} \text{MU}\mathbb{R}$, we compute the zero slice of $N_{C_2}^{Q_8} \text{MU}\mathbb{R}$ and a bigraded subring of the $\text{RO}(Q_8)$-graded homotopy Mackey functors of this slice.

A framework is established that assesses the impact of variations in artificial intelligence (AI) data center (DC) loads on the fatigue damage of steam/gas turbines of the synchronous generators (SGs) from torsional oscillations. Next, a simple three-step process that is supported by frequency-domain analysis is laid out to quantify the limits on fluctuations in AI DC loads. In the first step, the maximum allowable variation in electrical power output at each SG terminal is independently determined from the first principles. This step needs only a lumped multi-mass model of the mechanical side of the SG. In the second step, we propose a new approach that relies on load flow to determine the so-called algebraic `interaction factor' that maps the change in AI DC load at a given bus to the corresponding change in each of the SG power outputs. In the third step, we propose a screening method to rank the candidate buses to site AI DCs and solve an optimization problem to determine the optimal allowable fluctuations in the AI DCs. We demonstrate the applicability of the proposed approach through frequency-domain and time-domain analyses in the modified IEEE 4-machine and IEEE-68 bus systems using a dynamic phasor framework. Finally, we demonstrate the scalability of the proposed approach on the synthetic 2000-bus Texas system.

Extremely large aperture arrays (ELAAs) benefit the dual functions of integrated sensing and communication (ISAC) systems by enabling high-throughput data streams and high angular resolution with near-field spatial diversity. However, near-field spherical wavefront effects and spatial non-stationarity (SNS) bring challenges to both communication and sensing. This paper studies near-field spatially non-stationary channel estimation and environment mapping by jointly accounting for multi-bounce, blockage-induced partial visibility, and hybrid reflection-scattering propagation. We propose a unified parametric sensing channel model that represents the SNS phenomenon (due to partial array blockage, diffraction, and specular reflection) through spatially varying visibility and amplitude of each multipath across the array. To regularize the spatially varying delays caused by propagation mechanisms, we incorporate geometric constraints (GCs) based on environmental interaction points, embedding them into the model as absolute propagation delays. We then develop a GC-space-alternating generalized expectation-maximization (GC-SAGE) algorithm to estimate near-field channel parameters and locate environment scatterers/reflectors. Moreover, the GC-SAGE calculates per antenna path amplitudes based on the delays determined by the coordinates of scatterers/reflectors and transceivers, thereby effectively detecting channel SNS. Both ray-based simulation and field measurement are used to validate the proposed approach.

Developing business-logic-rich microservices requires navigating complex trade-offs between data consistency and distributed coordination. Although patterns like Sagas and Transactional Causal Consistency (TCC) provide mechanisms to manage distributed state, validating their behavior before production is challenging. Current architectural simulators prioritize network metrics over domain semantics, whereas industry frameworks demand full-scale infrastructure deployments, preventing early architectural experimentation. To bridge this gap, we introduce a \textit{Domain-Driven Design} (DDD) microservice simulator that isolates core business logic from communication and transactional infrastructure. By modeling microservice systems around aggregates, the simulator allows developers to evaluate identical application code under varying consistency guarantees and network constraints. It features support for multiple transactional models (Sagas, TCC) and seamless transitions across diverse deployment topologies, ranging from centralized execution to fully distributed environments. We validate the simulator through the implementation and rigorous concurrency testing of a complex, multi-aggregate microservice system. Through empirical benchmarks, we quantify the performance, coordination overhead, and resilience of different transactional models across localized and distributed execution environments. The findings confirm that the simulator minimizes developer effort while providing a powerful, deterministic environment for the shift-left validation and optimization of business logic implementation in microservice architectures.

Modern language model development extends far beyond pretraining, yet environmental reporting remains narrowly focused on the cost of training a single final model. In this work, we provide the first detailed breakdown of the environmental impact of a full model development pipeline, from pretraining through supervised fine-tuning, preference optimization, and reinforcement learning, for Olmo 3, a family of 7 billion and 32 billion parameter models in both instruction-following and reasoning variants. We find that reasoning models are 17x more expensive to post-train than their instruction-tuned counterparts in terms of datacenter energy, driven by reinforcement learning rollout generation. Development costs (including experimentation, failed runs, and ablations) account for 82.2% of total compute, a roughly 65% increase over the ~50% reported for pretraining-focused pipelines in prior work. In total, we estimate our model development process consumed ~12.3 GWh of datacenter energy, emitted 4,251 tCO2eq, and consumed 15,887 kL of water, with water consumption driven entirely by power generation infrastructure rather than data center cooling. These costs, which are almost entirely unreported by model developers, are growing rapidly as post-training pipelines become more complex, and must be accounted for in environmental reporting standards and by the research community working to reduce AI's environmental impact.

Although a recent study suggested that coarse-to-fine learning provides a fast and flexible framework for large-scale spatial process modeling, the method was originally developed for Gaussian responses, limiting its applicability. To address this limitation, we extended the coarse-to-fine spatial modeling (CFSM) framework to accommodate spatial generalized linear mixed models (GLMMs), with a particular focus on count data. The resulting model, referred to as CF-GLMM efficiently addresses the degeneracy problem often encountered in conventional spatial GLMMs. The performance of the proposed CF-GLMMs was evaluated in terms of spatial prediction and multiscale feature extraction via Monte Carlo experiments. Finally, we applied the proposed method to the analysis of coronavirus disease 2019 (COVID-19). The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).

Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and symmetry-theoretic foundations. Spatial covariance requires a strength function to depend on both stress and the corresponding strain measure, so that strength is governed by the pair (stress,strain), not stress alone, and only then can representations based on different stress measures be consistently related, with classical stress-based criteria recovered as a special case. We analyze covariance under spatial diffeomorphisms and relate formulations based on the first Piola--Kirchhoff, second Piola--Kirchhoff, and Cauchy stresses. For stress-based criteria, we define the strength hypersurface as a subset of the constitutively admissible stress manifold and study the associated safe domain. Under standard regularity assumptions and the requirement that sufficiently large stresses are inadmissible, the strength surface is a smooth compact hypersurface of this manifold. For isotropic solids, we show that the safe domain is star-shaped under a proportional-reduction hypothesis. We extend the formulation to anelastic brittle solids, showing that residual stresses and eigenstrains modify the strength surface through the material metric, and discuss anisotropic strength via material symmetry. Finally, in the small-strain limit, the theory reduces to classical stress-based criteria.