Predictive Bayesian inference (PBI) represents a model-and prior-agnostic approach to standard Bayesian inference which allows users to quantify uncertainty for a functional of interest only by specifying a forward predictive model for future unobserved data. The flexibility and generality of this framework have led to a host of novel algorithms for implementing this approach, and many empirical applications, yet the reliability of the resulting inferences for the underlying statistical functional of interest remains unclear. Herein, we demonstrate that when using PBI for a population functional of interest, the resulting posterior concentrates onto a well-defined quantity that explicitly depends on the forward predictive model used to implement the predictive recursion underlying the method. Furthermore, the forward predictive model entirely determines the uncertainty quantification produced in PBI. Consequently, our results show that if the predictive model does not capture all relevant features of the data, and, even in very simple examples, the coverage of predictive Bayes credible sets for the population value of the functional of interest can be arbitrarily close to zero. We carefully explain why this occurs, and show that this behavior is directly tied to the inaccuracy of the forward predictive model used to produce future observations within the PBI framework. As a consequence, our results imply that in order for PBI to deliver calibrated posterior inferences, the resulting predictive engine used to generate posterior samples must contain, in a well-defined sense, the true DGP, else inferences generated under this framework will not be calibrated.

We study exclusive vector meson production in ultra-peripheral collisions (UPCs) of a wide range of nuclei, and assess the potential of measurements to constrain the small-$x$ structure of oxygen and neon nuclei. We employ an impact-parameter-dependent color glass condensate framework incorporating JIMWLK evolution, with parameters constrained by a recent global Bayesian analysis of $γ+p$ and $γ+\mathrm{Pb}$ data. We present predictions for coherent and incoherent $\mathrm{J}/ψ$ production in $\mathrm{O}+\mathrm{O}$ and $\mathrm{Ne}+\mathrm{Ne}$ UPCs at LHC energies, and quantify theoretical uncertainties using posterior samples from the calibration. We employ several nuclear structure models and find that $t$-differential observables are sensitive to the chosen model. We further study the mass-number dependence of saturation effects through nuclear suppression factors for coherent and incoherent vector meson production. Saturation-induced suppression increases systematically with both nuclear mass number and energy. Our results provide a unified framework for the systematic study of the onset of gluon saturation and nuclear structure at high energy, accessible in future UPC measurements at the LHC and at the Electron-Ion Collider.

Urban to rural migration is a less-researched phenomenon compared to its counterpart: rural to urban migration. In parts of Europe, an increasing number of people living in big urban centers within the country, or moving from other countries decide to relocate to rural areas. In this paper, we examine this phenomenon by analysing content posted on TikTok that documents this transition. We collected a corpus of 901 videos posted until late 2025, documenting urban to rural migration in Romania, under three hashtags, which have collectively been played a total of 24 million times at the time when we gathered the dataset. We analyse this corpus both quantitatively and qualitatively and discuss our findings through the lens of digital rurality - a theory based on Harvey's and Soja's spatial triad, applied to rural spaces, and based on the role of digital technologies as (re-)mediators of everyday lived experience. Specifically, we analyze the corpus as: (a) digital rural localities, (b) formal representations of the digital rural, and (c) everyday lives of the digital rural. We find that (a) Social media platforms enable new forms of paid labor that sometimes involve the commodification of the self in rural areas, although many of the creators we analyze do not explicitly acknowledge this with their audiences. (b) The digital rural gains new forms of representation, and rural areas in remote Romania are highly data-rich across TikTok. (c) The everyday lives represented through the digital rural are sometimes idealized or romanticised. However, they serve as promoters for tourism and are used as sites to document and discuss a variety of topics including giving ample health advice, typically by non-specialists and sometimes criticizing Western medicine, expressing and promoting religious and political views but also acting as forms of general self-expression.

This work establishes rigorous mathematical foundations connecting spectral graph theory, algebraic geometry, and string theory. We construct a canonical mapping whereby any finite graph \(G\) defines a compact Riemann surface \(X_{G}\) (the spectral curve) whose period matrix \(Ω_{G}\) encodes the graph's coarse-grained spectral information. We demonstrate that in the continuum limit of graph sequences converging to Riemannian manifolds, these spectral curves converge in the Deligne-Mumford compactification sense to the classical stable curves associated with the manifold. We establish connections to the topological recursion framework of Eynard-Orantin, showing that under appropriate conditions the spectral curve satisfies the loop equations of multi-cut matrix models. The spectral memory field \(Φ_{G}(u)\) is introduced and shown to provide a discrete regularization of minimal string partition functions. We construct quantum scattering operators on spectral curves and prove that their unitarity is equivalent to a positivity condition on the spectral memory field. Furthermore, we apply this framework to resolve spacelike singularities in general relativity, proving that the Belinski-Khalatnikov-Lifshitz (BKL) chaotic regime is isospectral to a critical random graph ensemble. The classical singularity is replaced by an infinite nodal chain of rational curves, and the Bekenstein-Hawking entropy emerges from the automorphism group of the spectral curve. This work provides rigorous mathematical underpinnings for discrete approaches to quantum gravity and establishes new connections between graph theory, algebraic geometry, and theoretical physics.

Detailed-balance limits for transition-metal dichalcogenide (TMD) solar cells have been reported, but existing TMD-specific limits do not simultaneously resolve thickness-dependent optics, carrier multiplication (CM), hot-carrier (HC) extraction, and finite cooling leakage. Here, we develop a generalized detailed-balance theory that provides an upper-bound framework. The model combines energy- and thickness-dependent absorptance a(E,d), exciton-resolved monolayer absorbance, an experimentally available CM quantum-yield limit (eta_CM <= 0.97), and an endoreversible HC engine with ideal energy-selective contacts and finite heat-leak coefficient kappa. The framework shows that CM and HC draw on the same above-gap photon-energy reservoir; therefore, CM does not raise the reversible HC thermodynamic limit. Instead, CM can protect finite-kappa performance only by shifting excess-energy utilization from a cooling-sensitive voltage channel into collected current. For optically thick TMDs under AM1.5G illumination, the SQ optimum lies near E_g = 1.3 eV, whereas the CM/HC-favored envelope shifts toward E_g = 1.0 eV with reversible efficiencies above 50%. For monolayer TMDs such as WSe2 (E_g = 1.63 eV), CM is essentially inactive because only about 3.7% of above-gap AM1.5G photons satisfy E > 2E_g, giving an idealized short-circuit-current gain of only about 0.6% before device nonidealities. Bulk-like TMDs can show large HC-related gains at d = 10-50 nm, but even kappa = 0.2 W m^-2 K^-1 implies about 100 W m^-2 heat leak for Delta T = 500 K. Thus, high-E_g monolayer TMDs are not promising one-sun CM candidates, whereas narrow-E_g, bulk-like TMD absorbers remain plausible beyond-SQ candidates only if energy-selective extraction and phonon-engineered cooling suppression are realized together.

The large-scale clustering of galaxies encodes both geometric and dynamical information about the Universe. The Baryon Acoustic Oscillations (BAO) phenomenon provides a standard ruler that constrains the cosmic expansion history, while Redshift Space Distortions (RSD) probe the growth of structure through the peculiar velocity field. In this work, we present a joint analysis of BAO and growth rate parameter, $fσ_{8}$, in the Local Universe out to $z = 0.1$, using the $65,331$ galaxy distances of CosmicFlows-4++ database. A distinctive property of this catalogue is the availability of real space galaxy positions in addition to the redshift space coordinates. Fitting an empirical model to the measurements we obtain $r_{\rm{BAO}}^{\rm{real}} = 132\pm 8\,h^{-1}\,{\rm Mpc}$ in real space, and $r_{\rm{BAO}}^{z} = 139 \pm 7\,h^{-1}\,{\rm Mpc}$ in redshift space, at redshift $z = 0.07$. Modeling the enhancement of the correlation function within the Kaiser formalism, we derive a constraint on the growth rate parameter $fσ_8 = 0.344 \pm 0.105$. This analysis demonstrates how the combination of real and redshift space clustering measurements enables a simultaneous probe of important observables of the large-scale structure. Their joint detection in the same dataset, therefore, provides a self consistent view of the structure and evolution of the Local Universe. This study may be used for consistency analyses of upcoming surveys, as DESI and 4MOST, that will also provide data in both real and redshift space.

Linking issue reports to the commits that resolve them is essential for software traceability, maintenance, and evolution. Accurate issue-commit links help developers to understand system changes and the rationale behind them. While numerous automated techniques have been proposed, ranging from heuristic and feature-based approaches to modern deep learning and large language model approaches, our goal is to evaluate these techniques to determine which are most effective and efficient. In this study, we revisit several established issue-commit link recovery techniques, including BTLink, EasyLink, FRLink, RCLinker, and Hybrid-Linker, and assess their performance for reranking issue-commit links. We first evaluate different retrieval methods (BM25, BM25L, SBERT-Semantic Search, ANNOY, LSH, HNSW) for their ability to efficiently retrieve relevant commits, reducing the candidate set that must be considered by more computationally expensive models. Using the best retrieval methods, we then investigate the reranking effectiveness of different machine learning-based techniques, including traditional machine learning models, a cross-encoder, and large language models (ChatGPT, Qwen, Gemma, Llama), to refine the reranking of candidate commits and improve precision. Finally, we compare the effectiveness of these techniques. Our results show that dense retrieval methods outperform sparse retrieval approaches in identifying relevant commits and that combining dense and sparse retrieval can improve recall. Additionally, we find that traditional machine learning-based reranking techniques achieve higher performance than LLM-based approaches. Our results highlight that retrieval-based pipelines remain a practical and effective solution for large-scale issue-commit linking, and that simpler models should be carefully considered before adopting computationally expensive LLM-based approaches.

Quantum-memory models often reduce complex level structures to an idealized $Λ$ system, potentially missing nearby levels and unwanted couplings that can qualitatively alter the predicted performance. Here, we study an extension of a cavity-based $Λ$-type ensemble memory, a four-level model with unwanted couplings from both the control field and signal, using a fully quantum treatment. We derive explicit expressions for the single-photon storage efficiency, retrieval efficiency, and fidelity, and on this basis identify three distinct dynamical regimes: stable, threshold, and unstable. Within the stable regime, we additionally discriminate between two qualitatively different sub-regimes. Applying the theory to warm-vapor-inspired parameters, we determine the conditions under which the system can still operate as a high-quality quantum memory. More generally, our results provide a practical framework for distinguishing genuine memory operation from amplification and for optimizing realistic quantum memories beyond idealized models.

In this work, we construct a novel two-dimensional discrete neuron map by incorporating a cosine-based memristor into the reduced Chialvo neuron map to examine the dynamical analysis of electromagnetic modulation. The nonlinear current-voltage characteristics of the memristor enrich the neuron map's behavior, leading to diverse firing regimes, stability behaviors, and chaotic attractors. This study begins to establish the equilibrium points using both analytical and numerical methods. Additionally, we determine the conditions on parameters under which the proposed map exhibits a Neimark-Sacker bifurcation. Further, the numerical study reveals the antimonotonicity structure through the forward and backward bifurcation diagrams. The model exhibits a wide range of codimension-one and codimension-two bifurcation patterns, including Neimark-Sacker, period-doubling, saddle-node, generalized period-doubling, cusp-point, fold-flip, and various resonance structures (1:1, 1:2, 1:3, and 1:4). We also observe that the coexistence of multistable attractors including a stable limit cycle, a period-five attractor, and a chaotic attractor, along with their respective basins of attraction. Furthermore, we extend this analysis to the network of neurons under the ring-star configuration and discuss several spatiotemporal patterns. This network investigation reveals complex collective patterns, including imperfect synchronization, clustered patterns, and multi-chimera state phenomena, which have not been previously observed in existing Chialvo-based studies. These results highlight the potential of the discrete memristor-based neuron map for advancing theoretical neurodynamics and offer a robust framework for investigating low-dimensional yet dynamically rich neuron systems.

We develop a thermodynamic description of accumulation-layer heterostructures in which the induced sheet density is partitioned between the near-interface accumulation-layer charge and a complementary screening charge in the surrounding structure. Treating this partition as the central state variable yields a complete Helmholtz free energy, a corrected locked-branch chemical potential, and a shifted release potential that separates energetic path selection from geometric capacitance. The physical path is selected spectrally: compressible segments remain fully screened, whereas incompressible segments evolve along a locked branch until release is triggered by the relevant gap. Differential capacitance, tunnel current and plateau width then emerge as different projections of the same coupled thermodynamic structure. A canonical two-stage self-consistent Poisson--Schrödinger reduction supplies universal master functions for the isolated accumulation layer and master surfaces for its finite-buffer extension, making the theory calculable across density and geometry. Comparison with magnetocapacitance and magnetotunneling data supports a picture in which nearby extended charge refills the accumulation layer and the effective screening depth grows with magnetic field.

We investigate constraints on the high-density equation of state (EOS) of neutron star matter by analyzing the probability distributions of the endpoints of mass-radius M(R) sequences within a Bayesian weighting framework. Starting from two representative hadronic baseline EOSs, SFHo and DD2, matched at higher densities to an extended linear sigma model description and constrained to approach perturbative QCD (pQCD) results, we construct families of causal hybrid EOSs spanning a broad range of stiffness at supranuclear densities. Observational constraints from the binary neutron-star merger GW170817, mass-radius measurements from the Neutron Star Interior Composition Explorer (NICER), and candidate low-mass and mass-gap compact objects are incorporated through Bayesian likelihood weighting. This approach allows us to determine probability distributions for the maximum neutron-star mass M$_{\rm TOV}$ and the corresponding radius R$_{\rm TOV}$, i.e., the endpoints of the M(R) sequences. We find that the maximum-mass distributions are largely determined by observational constraints and show only weak sensitivity to the choice of baseline EOS, favoring values around 2.2-2.3 M$_\odot$ when the most robust constraints are applied. In contrast, the corresponding radius distributions exhibit a stronger dependence on the underlying hadronic EOS, with typical preferred values near $12\pm 1$ km. Additional tidal-deformability constraints further restrict the allowed parameter space and disfavor very stiff EOS realizations when interpreted together with the possible mass-gap neutron-star candidate. Our results demonstrate that endpoint distributions of M(R) sequences provide a sensitive and complementary diagnostic for constraining the high-density behavior of the neutron-star EOS within a multimessenger Bayesian framework.

In a spin-1 hadron, tensor-polarized parton distribution functions (PDFs) exist. The twist-2 function is $f_{1LL}$ and a twist-3 one is $f_{LT}$. Because an experiment is under preparation at the Thomas Jefferson National Accelerator Facility (JLab) to measure the cross section of electron-deuteron deep inelastic scattering with the tensor-polarized deuteron target, these PDFs need to be understood theoretically. Especially, measurements will be done in a relatively low-$Q^2$ region at JLab, so that twist-3 contributions could become sizable in the cross section. In a previous work, a twist-2 relation was derived for $f_{LT}$ in terms of $f_{1LL}$ by using a nonlocal operator, and it corresponds to the Wandzura-Wilczek (WW) relation between $g_1$ and $g_2$. In addition, another relation similar to the Burkhardt-Cottingham (BC) sum rule was obtained. It is known that a formal way to derive the WW relation and the BC sum rule is to use the operator product expansion (OPE) with local operators. In this work, the WW-like relation and the BC-like sum rule for $f_{LT}$ are derived by using the local OPE method as a reliable independent way to establish these relations.

Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs. Its iterative Voronoi sweep for interference detection leads to redundant predicate evaluations and scales poorly on rotationally symmetric structures (e.g., spheres, cones or cylinders), where candidate counts grow quadratically. We propose P2M++ to address these limitations through three key contributions. First, we adaptively augment the set of mesh vertices with auxiliary sites in regions of high Voronoi vertex density to localize complex interference within minimal spatial regions. Second, we reformulate interference detection as a series of sphere-triangle collision tests centered at Voronoi cell corners, which are efficiently resolved using the base mesh's BVH. Finally, we enhance runtime performance by replacing the standard kd-tree search with a faster recursive dynamic programming implementation. Experimental results demonstrate that P2M++ is 3x-10x faster than the original P2M during preprocessing and 1.5x faster in queries, with even more pronounced gains on rotationally symmetric geometries.

Strong experimental papers in electrical and computer engineering and computer science (ECE/CS), especially in systems, networking, and applied machine learning, rest on more than a single impressive number. They rest on a chain of design, measurement, analysis, and validation choices that, taken together, make a result believable. This tutorial is a compact, example-driven guide to that chain for beginning researchers. We organize it as an evaluation workflow: claim, hypothesis, unit of analysis, baseline, regime sweep, uncertainty estimate, validation check, and reporting. Within that workflow we cover the classical statistical foundations (descriptive statistics, the central limit theorem, normal- and $t$-based confidence intervals, Student's $t$-test, ANOVA, chi-squared and Pearson correlation, linear regression) alongside the modern, distribution-free techniques (the bootstrap, Wilcoxon and Mann--Whitney tests, Cliff's delta) that are usually preferred for ECE/CS data. We also discuss factorial design, randomization and blocking, multiple-comparison correction, latency-specific pitfalls, simulation verification and validation, equivalence-style claims, and reproducibility. A running example, a comparison of two job-scheduling algorithms on simulated workloads with truncated heavy-tailed job sizes, threads through the tutorial, with Python snippets the reader can paste and adapt. The paper closes with a pre-submission checklist; companion student-facing material (project-type translation tables, an evaluation-plan worksheet, exercises, and a worked ``bad evaluation autopsy'') is collected in a separate workbook released alongside this paper.

Understanding HPC facilities users' behaviors and how computational resources are requested and utilized is not only crucial for the cluster productivity but also essential for designing and constructing future exascale HPC systems. This paper tackles Challenge 4, 'Analyzing Resource Utilization and User Behavior on Titan Supercomputer', of the 2021 Smoky Mountains Conference Data Challenge. Specifically, we dig deeper inside the records of Titan to discover patterns and extract relationships. This paper explores the workload distribution and usage patterns from resource manager system logs, GPU traces, and scientific areas information collected from the Titan supercomputer. Furthermore, we want to know how resource utilization and user behaviors change over time. Using data science methods, such as correlations, clustering, or neural networks, our findings allow us to investigate how projects, jobs, nodes, GPUs and memory are related. We provide insights about seasonality usage of resources and a predictive model for forecasting utilization of Titan Supercomputer. In addition, the described methodology can be easily adopted in other HPC clusters.

For each $i \geq 0$, we study the trace ideal of the $i$-th exterior power of the module of differentials. We show that these ideals characterize the polynomial rank of graded rings and the formal power series rank of complete local rings, namely the maximal number of variables for a polynomial or formal power series extension over a subring. For the top exterior power, we introduce the top differential trace and prove that it precisely defines the singular locus of reduced equidimensional local or graded rings. Motivated by this, we introduce and investigate nearly regular rings, which are Noetherian rings whose top differential trace contains the maximal ideal.

The paper analyzes and characterizes the algebraic and logical structure of the multiset semantics for SPARQL patterns involving AND, UNION, FILTER, EXCEPT, and SELECT. To do this, we align SPARQL with two well-established query languages: Datalog and Relational Algebra. Specifically, we study (i) a version of non-recursive Datalog with safe negation extended to support multisets, and (ii) a multiset relational algebra comprising projection, selection, natural join, arithmetic union, and except. We prove that these three formalisms are expressively equivalent under multiset semantics.

The anomalous behavior of liquid water is widely associated with a liquid-liquid phase transition between high- and low-density states in the supercooled regime. At the microscopic level, tetrahedral hydrogen-bond networks govern these properties, motivating structural descriptors that characterize local molecular environments. These structural descriptors quantify features such as tetrahedral order, local density, and the separation between the first and second coordination shells; however, they have largely been proposed independently, with limited systematic comparison. Here we evaluate 16 previously proposed descriptors using a neural-network-based temperature classification framework, enabling an objective assessment of their ability to distinguish temperature-dependent structural changes in supercooled water. We further apply an explainable artificial intelligence method that identifies the structural features responsible for the model predictions. This approach reveals how different descriptors encode local structural information and establishes a data-driven framework for benchmarking structural descriptors in liquid water.

Ensuring the reliability of the Rust compiler is of paramount importance, given increasing adoption of Rust for critical systems development, due to its emphasis on memory and thread safety. However, generating valid test programs for the Rust compiler poses significant challenges, given Rust's complex syntax and strict requirements. With the growing popularity of large language models (LLMs), much research in software testing has explored using LLMs to generate test cases. Still, directly using LLMs to generate Rust programs often results in a large number of invalid test cases. Existing studies have indicated that test cases triggering historical compiler bugs can assist in software testing. Our investigation into Rust compiler bug issues supports this observation. Inspired by existing work and our empirical research, we introduce a bracket-based masking and filling strategy called clozeMask. The clozeMask strategy involves extracting test code from historical issue reports, identifying and masking code snippets with specific structures, and using an LLM to fill in the masked portions for synthesizing new test programs. This approach harnesses the generative capabilities of LLMs while retaining the ability to trigger Rust compiler bugs. It enables comprehensive testing of the compiler's behavior, particularly exploring edge cases. We implemented our approach as a prototype CLOZEMASTER. CLOZEMASTER has identified 27 confirmed bugs for rustc and mrustc, of which 10 have been fixed by developers. Furthermore, our experimental results indicate that CLOZEMASTER outperforms existing fuzzers in terms of code coverage and effectiveness.

Budget-feasible procurement auctions play a pivotal role in various AI-driven marketplaces, such as data acquisition and crowdsourcing, where a buyer with a limited budget seeks to procure services from strategic sellers with private costs. While numerous budget-feasible mechanisms have been proposed for the classic objective of maximizing the buyer's valuation, the more challenging and economically significant objective of social welfare maximization has only recently been studied, and existing approaches still sacrifice budget feasibility, thereby limiting their practical applicability. In this paper, we bridge this gap by proposing BFM-SWM, the first budget-feasible mechanism with provable approximation guarantees for submodular welfare maximization in procurement auctions. Our mechanism satisfies standard economic properties, including truthfulness, individual rationality, and non-negative auctioneer surplus. As a by-product, we develop BFM-VM, a variant tailored for valuation maximization, which achieves a deterministic approximation ratio of $1/(12+4\sqrt{3})$ for general submodular functions, substantially improving upon the best-known deterministic ratio of $1/64$ established by [Balkanski et al., SODA 2022], while reducing the running time from $\mathcal{O}(n^2\log n)$ to $\mathcal{O}(n\log n)$. Extensive experiments demonstrate the efficiency and effectiveness of our mechanisms.

We propose a numerical procedure to solve an inverse problem that estimates the state of a magma reservoir from observed surface displacement of a volcano. Our variational approach aims to find the minimizer of a cost function consisting of a norm concerning both data and derivative, which evaluates the misfit between the estimated and observed displacement. The extremal of the cost function leads to a linear system, to find the stress distribution on the reservoir surface, has very high condition number, but it is feasible to get appropriate solution by using high precision arithmetic.

We consider the isentropic compressible Euler equations in the half-line which govern the motion of gaseous fluids in contact with stationary vacuum boundary. We construct a large class of solutions that are initially smooth and square-integrable, and which, in finite time, transition to $C^{1-μ}$ regularity for $μ\in [1/2,1)$ near the boundary, leading to the gradient blowup at the boundary. It is based on stability analysis of self-similar waiting time solutions \cite{JLN2025} recently constructed by the authors.

Selection artefacts are common in science. A method of selecting samples from a larger population may produce bias, in either direction. It may induce correlations between variables independent in the full population, or mask correlations between variables dependent in the full population. Here we propose a surprising application of these familiar ideas. We argue that they are relevant to puzzling correlations uncovered in quantum theory by John Stewart Bell (Bell 1964). In the light of Bell's work and subsequent experiments it is widely believed that the quantum world is 'nonlocal', in apparent tension with relativity. Many hold that the only alternative is to abandon 'realism', the view that there is an objective world independent of measurement. We propose instead that Bell correlations are selection artefacts, in tension neither with relativity nor realism.

Recent advances in precise phasor measurement units are enabling new approaches to estimate distribution and transmission grid parameters in real-time. In this paper, we investigate voltage and current phasor measurement requirements to estimate the electric grid topology and admittance parameters. We show necessary and sufficient conditions for the number of independent operating points (measurements) required to determine the topology and admittance of a completely unknown electric grid. With prior topology information, we also show that there is a minimum number of measurements required to uniquely determine the admittance matrix and corresponding grid topology. In the presence of noisy phasor measurements, we show that the admittance matrix can be estimated using a structured total least squares approach. By means of numerical simulations on the IEEE 13-node distribution feeder, the IEEE 14-node transmission network, and the IEEE 123-node distribution feeder, we demonstrate our approach is suitable for applications in radial and mesh grid topologies in the presence of measurement noise.

Modern package designs make use of technologies such as backside power delivery (BSPD) and 3D stacked chiplets that require accounting for the heterogeneity in back end of the line (BEOL) structures in hot-spot prediction. Multiscale homogenization strategies have been demonstrated to be effective for steady-state simulations, however accurate 3D transient simulations that include BEOL structures remain an open challenge. In this work, we demonstrate a transient thermal workflow that accounts for the 3D heterogeneous structures in the BEOL for problems with strong- and weak- temporal scale separation under the assumption of temperature independent constitutive properties. Our workflow, based on Bloomfield et. al. 2025, automatically extracts, meshes, and homogenizes thermal properties from GDSII and OASIS files to construct thermal property maps. Property maps (heat capacity and conductivity) have been generated for a 1 mm by 1 mm SoC-style model die that was constructed with LibreLane for 100 by 100 grids with 5 micron by 5 micron representative volume elements (RVEs), and 50 by 50 grids with 10 micron by 10 micron RVEs. The expressions for a transient effective conductivity are provided and a demonstration of the impact of the transient effects are provided for a single RVE. Finally, transient conductivity maps have been provided for a time integration timestep of dt=0.001.

In Riemannian optimization, it is well known that the condition number of the Riemannian Hessian at an optimum strongly influences the asymptotic convergence behavior of optimization algorithms. On the manifold of symmetric positive definite (SPD) matrices, several commonly used metrics for optimization, such as the Affine-Invariant (AI) and Bures--Wasserstein (BW) metrics, tend to become ill-conditioned as the underlying SPD matrix becomes ill-conditioned. As a result, even when the Euclidean Hessian remains uniformly well-conditioned on the SPD manifold, optimization may still become difficult near an optimum associated with an ill-conditioned SPD matrix. In this paper, we address this issue through the Alpha-Procrustes (AP) geometry on the SPD manifold. This geometry generalizes several well-known metrics, including the Log-Euclidean (LE) metric for \(α=0\) and the BW metric for \(α=1/2\). We first show that, when \(α=1\), all eigenvalues of the Riemannian metric operator induced by the AP geometry are uniformly bounded independently of the underlying SPD matrix. Therefore, under the assumption that the Euclidean Hessian satisfies the uniform spectral bounds, all the eigenvalues of the corresponding Riemannian Hessian are uniformly bounded independently of the underlying SPD matrix. Consequently, the case \(α=1\) provides a robust geometric framework for several Riemannian optimization problems involving ill-conditioned SPD matrices. Finally, we validate our theoretical findings through extensive numerical experiments across a range of applications.

Classical flocking models demonstrate how local interactions generate emergent order, but real-world multi-agent deployments are bound by severe constraints: limited actuator availability, heterogeneous communication latencies, and environmental noise. In this talk, we present a unified finite-N framework that tackles the interplay of these exact mechanisms. We study a delayed stochastic leader-follower particle system featuring topological communication, singular repulsion, and bounded sparse leader actuation. A central challenge in such systems is mathematical well-posedness, as discontinuous communication laws and singular repulsions clash with standard strong Ito frameworks. We resolve this by introducing an augmented Lyapunov functional that simultaneously enforces a strict collision barrier and closes a uniform Gronwall estimate. Building on this rigorous foundation, we formulate a free-terminal-time, chance-constrained optimal control problem. We show that temporally sparse, bang-off-bang leader actuation not only drastically reduces control effort compared to continuous baselines, but also reveals non-monotone sensitivities to leader density. Ultimately, we demonstrate that in delayed stochastic swarms, adding more direct actuation is not strictly optimal -- highlighting a highly non-trivial resource allocation paradox in cooperative control.

The physics governing the boundary between the most massive neutron stars (NSs) and the least massive black holes (BHs) is currently uncertain, but could potentially be constrained with new observations. While NSs have been observed with masses up to $\sim2~M_{\odot}$, there is a dearth of electromagnetic observations of compact objects in the $\sim2-5~M_{\odot}$ range, known as the lower mass gap. Recent observations of gravitational-wave (GW) signals from binary mergers detected by the LIGO-Virgo-KAGRA (LVK) collaboration indicate that this gap is likely not empty. Rapidly distinguishing whether a candidate GW event has components in this purported mass gap can indicate the likelihood of a detectable electromagnetic counterpart, and thus inform decisions for follow-up observations. In this work we train a neural network model, GWSkyNet-MassGap, that simultaneously predicts the probability that a candidate merger has a component in the lower mass gap ($P_{\mathrm{MassGap}}$) and the probability that it involves a NS ($P_{\mathrm{NS}}$). We find that the model is able to infer information about the source chirp mass to predict $P_{\mathrm{MassGap}}$ and $P_{\mathrm{NS}}$, leading to correct predictions for high-mass mergers with $\mathcal{M}_c\gtrsim15~M_{\odot}$, but less accurate predictions for lower-mass systems which require knowledge of the binary mass ratio to break the mass degeneracy. For candidate events in the first part of LVK's fourth observing run (O4a), the model has a mean prediction error of 9% for $P_{\mathrm{MassGap}}$ and 6% for $P_{\mathrm{NS}}$. The model could be further developed to rapidly predict the source chirp mass for candidate events in future observing runs.

We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First, we explain why a direct application of standard optimality conditions -- based on reformulating MPECs via KKT systems or differentiable exact penalty functions -- is often inadequate, as such approaches typically require strong and restrictive assumptions, including nondegeneracy and smoothness conditions. Second, we develop a first-principles framework for analyzing MPECs by focusing on the geometric structure of the feasible region. In particular, we study stationarity concepts and provide a detailed characterization of the tangent cone at feasible points, which leads to appropriate constraint qualifications tailored to MPECs. These results form the foundation for rigorous first-order analysis and clarify the relationship between the original MPEC formulation and its KKT-based representation, offering practical guidance for handling these inherently challenging optimization problems.

We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to modern error bound theory. The goal is twofold. First, we explain how classical optimality conditions can be interpreted through exact penalization, and why such results typically rely on constraint regularity conditions that can be understood as error bounds on perturbations of feasible sets. We then highlight how recent developments based on subanalytic geometry and Lojasiewicz-type inequalities extend this framework beyond classical regularity assumptions, enabling exact penalization under broader analytic conditions. Second, we demonstrate how this theory can be applied in practice to MPECs by reformulating them via KKT systems and constructing exact penalty functions based on residual mappings. Particular attention is given to fractional-order penalties arising from Lojasiewicz error bounds, as well as to improved formulations for special problem classes where sharper exponents can be obtained. These developments provide both theoretical insight and practical guidance for analyzing and solving challenging constrained optimization problems.