We present an explicit family of hypergraphs with arbitrarily large uniformity and chromatic number that admit realizations in both geometric and number-theoretic settings. As an application, we give a new proof of a theorem of Chen, Pach, Szegedy, and Tardos. They showed that for any constants $c,k\ge1$, there exists a finite point set $P$ in the plane with the following property: for every coloring of $P$ with $c$ colors, there is an axis-parallel rectangle containing at least $k$ points, all of the same color. Their original proof is probabilistic; we present an explicit construction. Moreover, in the case $k=2$, we show that one can even realize a graph that has arbitrarily large girth and chromatic number simultaneously. We also answer a question of Pálvölgyi on coloring sets of integers with respect to certain finite arithmetic progressions. Finally, we give an application to coloring partially ordered sets.

For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first result is a weak convergence rate for the discretised rough Ornstein-Uhlenbeck process, that is essentially in $\min(3α-1,1)$, where $\frac{t^{α-1}}{Γ(α)} $ is the fractional convolution kernel with $α\in (1/2,1)$. Then, our main result is to obtain the same convergence rate for the corresponding stochastic rough volatility model with polynomial test functions.

Double parton distributions at small distances between the two partons are dominated by a mechanism in which the two observed partons originate from the splitting of a single parton. This contribution can be computed in terms of single-parton distributions and perturbative splitting kernels. We demonstrate that two-loop corrections to these kernels can have a substantial quantitative impact and considerably improve the stability of predictions for double parton scattering. We also consider the impact of heavy quark masses in the two-loop splitting kernels in an approximate manner.

The pressurized Shastry-Sutherland Mott insulator SrCu2(BO3)2 has been found to host a plaquette-singlet phase and an antiferromagnetic phase that break different symmetries spontaneously.The recent experiment showed that their transition is of a first order nature, which seems against the pursuit of exotic and deconfined degrees of freedom in this famous frustrated quantum magnet. We found a new direction in this study. By applying a magnetic field to the material, we discover that SrCu2(BO3)2 exhibits a universal and metallic T-linear specific heat behavior in a large magnetitic field range close to the pressure of zero-field first order transition between plaquette-singlet and antiferromagnetic phases. Such an unexpected gapless response from an electronically gapped Mott insulator could be attributed to magnetized Dirac spinons liberated by the combined effect of magnetic field and pressure, consistently seen from our quantum many-body thermal tensor network computation of the Shastry-Sutherland model under magnetic field. Such a robust and universal T-linear specific heat phase points out the richness of the phase diagram of the material expanded by the axes of pressure and magnetic field and is calling for new theoretical frameworks to its full explanation.

We investigate how controlled foaming alters the mechanical dissipation of liquid crystalline elastomers (LCEs). Using thermal expandable microspheres, we generate homogeneous foams with precisely tuned bubble volume fractions up to 13% and compare their behaviour with non-mesogenic silicon analogues. We show that microsphere expansion induces a particle-centred mesogenic interphase arising from local elastic distortion and preferential alignment of mesogenic units at the inclusion surface. At low bubble volume fraction (0.5 to 5%), these interfaces remain spatially isolated and produce a pronounced no-monotonic enhancement of damping, with the loss factor reaching tan-delta=0.2 even in the isotropic regime. At higher loading, interphase overlaps and mechanical constraints suppress this effect, and the dissipation returns towards baseline elastomeric values. Large-strain tensile tests and impact experiments exhibit the same non-monotonic trend, demonstrating that low density LCE forms achieve the highest mechanical energy absorption per unit mass. Compared with conventional high porosity polymer foams used for acoustic damping, these materials retain sufficient mechanical integrity to sustain impact loads, establishing a microstructural route to engineer high-performance damping in soft solids.

A search is performed for a new resonance X decaying into either a pair of Higgs bosons (HH) or into a Higgs boson and a new scalar boson Y (HY), using proton-proton collision data collected at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. This study performs a comprehensive exploitation of the bbZZ events, encompassing the following decay topologies. One H candidate is identified through its decay into a bottom quark-antiquark pair, while the other H or the Y candidate is selected through its decay into a pair of Z bosons. One Z boson is required to decay leptonically and the other, to decay into a pair of quarks or neutrinos. Events of interest are categorized based on the Lorentz boosts of the hadronically decaying H and Z bosons. Machine-learning-based discriminants, together with the reconstructed resonance mass, are employed across the different categories to separate signal from backgrounds, and their corresponding distributions are included in a simultaneous fit. No significant deviations from the standard model predictions are observed. Upper limits at the 95% confidence level are set on the HH and HY production cross sections. For resonant HH production, the upper limit on the cross section of pp $\to$ HH production is 1 pb for a high-mass resonance. For HY production, the upper limit on the cross section of the process pp $\to$ X $\to$ bbZZ is approximately 5 fb for a high-mass resonance. This is comparable to the sensitivity achieved in other analyses, which focus on H decays to $γγ$ or $ττ$ and Y decays into a pair of bottom quarks or massive vector bosons.

Swift electrons from highly focused beams produced in aberration-corrected scanning transmission electron microscopes offer a powerful route for probing and manipulating matter at the nanoscale. Although linear momentum transfer from swift electrons to nanoparticles has been investigated theoretically and experimentally, subsequent analyzes revealed that several earlier predictions relied on non-causal dielectric functions or insufficient numerical convergence, leading to spurious sign reversals in the transferred momentum. Here, we derive analytical expressions and develop a numerically efficient electrodynamic framework to compute the linear momentum transferred from a swift electron to an isolated spherical nanoparticle described by a fully causal, local dielectric response. We apply our framework to large nanoparticles with 50 nm radius and explicitly resolve the spectral density of linear momentum transfer across the full frequency domain. Using causal dielectric functions for aluminum and bismuth, we analyze the role of electron velocity, impact parameter, and material-specific resonances. We find that, when causality and full multipolar convergence are enforced, the net transverse linear momentum transferred to spherical nanoparticles remains attractive toward the electron trajectory for all nanoparticles considered, despite the presence of material-dependent sign changes in individual electric and magnetic contributions. These results contrast with earlier theoretical predictions of net repulsive behavior and indicate that additional physical mechanisms beyond the present isolated, local description are required to account for experimentally observed repulsion. Our work establishes a robust reference framework for momentum transfer calculations and provides quantitative benchmarks relevant for electron-beam-based nanoscale manipulation.

This paper is devoted to the study of the falsification by fellow-traveller property (FFTP) in Dyer groups. We exhibit a finite generating set for which the associated Cayley graph is a locally finite mediangle graph, and leverage its properties to prove that Dyer groups have the FFTP. It follows that Dyer groups have finitely many cone types, emphasising their role in providing a unified approach to Coxeter groups and graph products of cyclic groups.

In this article we prove existence and symmetry properties of periodic surfaces of revolution with constant anisotropic nonlocal mean curvature, generalizing a classical result of Delaunay to the anisotropic nonlocal setting. First, by studying the corresponding periodic isoperimetric problem, under natural assumptions on the kernel, we use rearrangement inequalities to extend a periodic version of the Wulff inequality to the nonlocal setting. This leads to the existence and symmetry properties of minimizers for every given volume in each period, thus generalizing the results of Cabré, Csató, and Mas to the anisotropic case. Second, under the same hypotheses on the kernel, we prove the existence of a one-parameter family of Delaunay near-cylinders in $\mathbb{R}^2$ bifurcating from a straight cylinder and having each constant anisotropic mean curvature. This extends the results of Cabré, Fall, Solà-Morales, and Weth to the anisotropic case. The stability of these near-cylinders will be studied in a forthcoming paper.

In this paper, we study planar nonlocal Delaunay sets. That is, open sets in $\mathbb{R}^2$ with constant nonlocal mean curvature that are periodic in $x_1$, and even in $x_1$ and in $x_2$. Using bifurcation analysis and fine explicit computations, we prove that every sufficiently $C^{1,β}$-flat nonlocal Delaunay set in $\mathbb{R}^2$ that is not a straight band is unstable with respect to volume-preserving periodic variations. Our results support the conjecture that, as in the local case, in the range of large areas, minimizers of the periodic nonlocal isoperimetric problem -- also known as the nonlocal liquid drop problem with prescribed area between two parallel hyperplanes -- are all straight bands.

The integrated density of states (IDS) is a fundamental spectral quantity for quantum Hamiltonians modeling condensed matter systems, describing how densely energy levels are distributed. It can be interpreted as a volume-averaged spectral distribution. Hence, there are two equivalent definitions of the IDS related by the Pastur-Shubin formula: an operator-theoretic trace formula and a limit of normalized eigenvalue counting functions on finite volumes. We study a discrete random Schrödinger operator with bounded random potentials of finite-range correlations and prove a quantitative concentration inequality ensuring, with explicit high probability, that the empirical IDS (normalized eigenvalue counting function) uniformly approximates the abstract IDS trace formula within a prescribed error, thereby implying confidence regions for the IDS.

We address the problem of uncertainty quantification for the deconvolution model \(Z = X + Y\), where \(X\) and \(Y\) are nonnegative random variables and the goal is to estimate the signal's distribution of \(X \sim F_0\) supported on~\([0,\infty)\), from observations where the noise distribution is known. Existing frequentist methods often produce confidence intervals for $F_0(x)$ that depend on unknown nuisance parameters, such as the density of \(X\) and its derivative, which are difficult to estimate in practice. This paper introduces a novel and computationally efficient nonparametric Bayesian approach, based on projecting the posterior, to overcome this limitation. Our method leverages the solution \(p\) to a specific Volterra integral equation as in \cite{74}, which relates the cumulative distribution function (CDF) of the signal, \(F_0\), to the distribution of the observables. We place a Dirichlet Process prior directly on the distribution of the observed data $Z$, yielding a simple, conjugate posterior. To ensure the resulting estimates for \(F_0\) are valid CDFs, we isotonize posterior draws taking the Greatest Convex Majorant of the primitive of the posterior draws and defining what we term the Isotonic Inverse Posterior. We show that this framework yields posterior credible sets for \(F_0\) that are not only computationally fast to generate but also possess asymptotically correct frequentist coverage after a straightforward recalibration technique for the so-called Bayes Chernoff distribution introduced in \cite{54}. Our approach thus does not require the estimation of nuisance parameters to deliver uncertainty quantification for the parameter of interest $F_0(x)$. The practical effectiveness and robustness of the method are demonstrated through a simulation study with various noise distributions for $Y$.

Vehicular Ad Hoc Networks (VANETs) support the information dissemination among vehicles, Roadside Units (RSUs), and a Trust Authority (TA). A trust model evaluates an entity or data or both to determine truthfulness. A security model confirms authentication, integrity, availability, non repudiation issues. With these aspects in mind, many models have been proposed in literature. Furthermore, many information dissemination approaches are proposed. However, the lack of a model that can manage traffic incidents completely inspires this work. This paper details how and when a message needs to be generated and relayed so that the incidents can be reported and managed in a timely manner. This paper addresses this challenge by providing a traffic incident management model to manage several traffic incidents efficiently. Additionally, we simulate this model using the VEINS simulator with vehicles, RSUs, and a TA. From the experiments, we measure the average number of transmissions required for reporting a single traffic incident while varying the vehicle density and relaying considerations. We consider two types of relaying. In one series of experiments, messages from regular vehicles and RSUs are relayed up to four hops. In another series of experiments, messages from the regular vehicles and RSUs are relayed until their generation time reaches sixty seconds. Additionally, messages from the official vehicles are relayed when they approach an incident or when the incident is cleared. Results from the simulations show that more vehicles are informed with four-hop relaying than sixty-second relaying in both cases.

DMPP is a radial-velocity survey that aims to detect planets around stars exhibiting anomalous activity signatures, consistent with the presence of close-in evaporating planets. Here, we report the discovery of 7 new planetary signals in 5 different systems: DMPP-2c & d, HD67200/DMPP-6b & c, HD118006/DMPP-7b, HD191122/DMPP-8b, and HD200133/DMPP-9b. We update the orbital parameters of the DMPP-1, DMPP-2, and DMPP-3 systems, along with those of the planetary systems orbiting HD181433, HD39194, and HD89839. We derive detection limits for all 24 targets in our sample with adequate observational coverage, and test the DMPP hypothesis by calculating the occurrence rates for planets in this configuration. We find that the occurrence rates of planets in our sample with orbital periods shorter than $50~\mathrm{d}$ and masses in the range $3$-$10$ M$_\oplus$ are $83.0^{+27.1}_{-24.4}\%$, for $10$-$30$ M$_\oplus$ are $27.0^{+15.0}_{-11.2}\%$, and for $30$-$100$ M$_\oplus$ are $13.9^{+11.8}_{-7.5}\%$. This is significantly higher than the occurrence rates reported by other radial velocity surveys, providing strong support for the DMPP hypothesis.

Most implicit collaborative filtering (CF) models are trained with negative sampling, where existing work designs sophisticated strategies for high-quality negatives while largely overlooking the exploration of positive samples. Although some denoising recommendation methods can be applied to implicit CF for denoising positive samples, they often sparsify positive supervision. Moreover, these approaches generally overlook user activity bias during training, leading to insufficient learning for inactive users. To address these issues, we propose a simple yet effective negative sampling plugin, PSP-NS, from the perspective of enhancing positive supervision signals. It builds a user-item bipartite graph with edge weights indicating interaction confidence inferred from global and local patterns, generates positive sample pairs via replication-based reweighting to strengthen positive signals, and adopts an activity-aware weighting scheme to effectively learn inactive users' preferences. We provide theoretical insights from a margin-improvement perspective, explaining why PSP-NS tends to improve ranking quality (e.g., Precision@k/Recall@k), and conduct extensive experiments on four real-world datasets to demonstrate its superiority. For instance, PSP-NS boosts Recall@30 and Precision@30 by 32.11% and 22.90% on Yelp over the strongest baselines. PSP-NS can be integrated with various implicit CF recommenders or negative sampling methods to enhance their performance.

One of the longest standing open problems in science is how life arises from non-living matter. If it is possible to measure this transition in the lab, then it might be possible to understand the physical mechanisms by which the emergence of life occurs, which so far have evaded scientific understanding. A significant hurdle is the lack of standards or a framework for cross comparison across different experimental contexts and planetary environments. In this essay, I review current challenges in experimental approaches to origin of life chemistry, focusing on those associated with quantifying experimental selectivity versus de novo generation of molecular complexity, and I highlight new methods using molecular assembly theory to measure molecular complexity. This metrology-centered approach can enable rigorous testing of hypotheses about the cascade of major transitions in molecular order marking the emergence of life, while potentially bridging traditional divides between metabolism-first and genetics-first scenarios. Grounding the study of life's origins in measurable complexity has significant implications for the search for life beyond Earth, suggesting paths toward theory-driven detection of biological complexity in diverse planetary contexts. As the field moves forward, standardized measurements of molecular complexity may help unify currently disparate approaches to understanding how matter transforms to life. Much remains to be done in this exciting frontier.

In this paper, I take the cultural effects of generative artificial intelligence (generative AI) as a context for examining a broader perspective of AI's impact on contemporary art notions. After the introductory overview of generative AI, I summarize the distinct but often confused aspects of art notions and review the principal lines in which AI influences them: the strategic normalization of AI through art, the representation of AI art in the artworld, academia, and AI research, and the mutual permeability of art and kitsch in the digital culture. I connect these notional factors with the conceptual and ideological substrate of the computer science and AI industry, which blends the machinic agency fetishism, the equalization of computers and humans, the sociotechnical blindness, and cyberlibertarianism. The overtones of alienation, sociopathy, and misanthropy in the disparate but somehow coalescing philosophical premises, technical ideas, and political views in this substrate remain underexposed in AI studies so, in the closing discussion, I outline their manifestations in generative AI and introduce several viewpoints for a further critique of AI's cultural zeitgeist. They add a touch of skepticism to pondering how technological trends change our understanding of art and in which directions they stir its social, economic, and political roles.

Organic crystalline materials are potential candidates for photocatalytic overall water splitting (OWS). Although organic crystals have been heavily investigated for application in organic electronics, such as organic light-emitting diodes (OLEDs) and solar cells, there have been comparatively fewer studies into OWS in these materials. A major challenge is the large number of electronic and structural criteria that must be met for a material to make a viable OWS photocatalyst. Optical absorption, reduction and oxidation potentials and charge-transport properties are among the key considerations, and these are influenced both by molecular properties and the solid-state packing arrangement, making computational modelling challenging. Here, we investigate a series of known organic electronic materials that have published crystal structures using periodic density functional theory (DFT) and compare their calculated electronic properties of optical absorption and reduction and oxidation potentials with literature experimental data. Furthermore we perform a series of gas-phase molecular calculations which show a good agreement with literature data and periodic DFT for the optoelectronic properties of the organic molecular crystals studied, showing that gas-phase molecular calculations could be used to screen organic crystals for OWS at a reduced computational cost.

Adaptive coupling in networks of interacting neurons has gained recent attention due to the many applications both in biological and in artificial neural networks, where adaptive coupling or synaptic plasticity is considered as a key factor in learning processes. In the present study, we apply adaptive connectivity rules in networks of interacting FitzHugh-Nagumo oscillators. Adaptive coupling, here, is realized via Hebbian learning adjusted by the Oja rule to prevent the network link weights from growing without bounds. Numerical investigations demonstrate that during the adaptation process the FitzHugh-Nagumo network undergoes adaptive transitions realizing traveling waves, synchronized states and chimera states transiting through various multiplicities. These transitions become more evident when the time scales governing the coupling dynamics are much slower than the ones governing the nodal dynamics (nodal potentials). Namely, when the coupling time scales are slow, the network has the time to realize and demonstrate different synchronization regimes before reaching the final steady state. The transitions can be observed not only in the spacetime plots but also in the abrupt changes of the average coupling weights as the network evolves in time. Regarding the asymptotic coupling distributions, we show that the limiting average coupling strength follows an inverse power law with respect to the Oja parameter (also called "forgetting" parameter) which balances the learning growth. We also report abrupt transitions in the asymptotic coupling strengths when the parameter related to adaptive coupling crosses from fast to slow time scales. These findings are in line with previous studies on spiking neural networks.

Rubin's theorem asserts that if $Γ\curvearrowright X$ and $Δ\curvearrowright Y$ are Rubin actions, then any group isomorphism $Γ\cong Δ$ induces an equivariant homeomorphism $Y\cong X$. We provide an embedding version of Rubin's theorem highlighting group embeddings that induce a spatial equivariant map of a certain form. We further showcase instances of such embeddings between generalized Brin-Thompson groups.

The existence of a distinct mass boundary between the heaviest neutron stars and the lightest black holes remains in question. It is an artefact of our ignorance of the properties of matter at supra-nuclear densities, which exist in the cores of neutron stars. The study addresses these problems with a physics-informed machine learning approach, guided by astrophysical observations. The Transformer model is trained on an agnostically generated ensemble of equations of state. Two geometric parameters are defined on the mass-radius sequence of a neutron star--the front bending and the back bending. The transformer provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters. Second, it predicts the square of the sound speed profile, completing the inverse mapping. The prediction is that massive neutron stars form when the sound speed peaks at low density, leading to strong back-bending and an early phase transition to quark matter. Massive stars favour a stiff equation of state at low density, and the density of matter at the star's core is sufficiently small. The maximum mass for a neutron star predicted by the astrophysical constrained transformer model is $2.477$ solar masses, and a minimum radius of about $11.498$ km for a neutron star of $1.4$ solar masses.

The adoption of Generative AI (GenAI) suggests major changes for software engineering, including technical aspects but also human aspects of the professionals involved. One of these aspects is how individuals perceive themselves regarding their work, i.e., their work identity, and the processes they perform to form, adapt and reject these identities, i.e., identity work. Existent studies provide evidence of such identity work of software professionals triggered by the adoption of GenAI, however they do not consider differences among diverse roles, such as developers and testers. In this paper, we argue the need for considering the role as a factor defining the identity work of software professionals. To support our claim, we review some studies regarding different roles and also recent studies on how to adopt GenAI in software engineering. Then, we propose a research agenda to better understand how the role influences identity work of software professionals triggered by the adoption of GenAI, and, based on that, to propose new artifacts to support this adoption. We also discuss the potential implications for practice of the results to be obtained.

AI art comprises a spectrum of creative endeavors that emerge from and respond to the development of artificial intelligence (AI), the expansion of AI-powered economies, and their influence on culture and society. Within this repertoire, the relationship between the cognitive value of human vision and the wide application range of computer vision (CV) technologies opens a sizeable space for exploring the problematic sociopolitical aspects of automated inference and decision-making in modern AI. In this paper, I examine the art practices critically engaged with the notions and protocols of CV. After identifying and contextualizing the CV-related tactical AI art, I discuss the features of exemplar artworks in four interrelated subject areas. Their topical imbrications, common critical points, and shared pitfalls plot a wider landscape of tactical AI art, allowing me to detect factors that affect its poetic cogency, social responsibility, and political impact, some of which exist in the theoretical premises of digital art activism. Along these lines, I outline the routes for addressing the challenges and advancing the field.

Phase-only computer-generated holography (CGH) seeks a phase pattern for a spatial light modulator (SLM) whose propagated optical field reproduces a desired intensity distribution. In the far-field (Fraunhofer) regime, optical propagation reduces to a Fourier transform, such that each hologram pixel contributes to the entire reconstructed intensity distribution. When restricted to phase-only modulation, intensity must be shaped through global phase interference effects, making the inverse mapping from target intensity to phase highly non-linear and sensitive to local minima. We present a proof-of-concept physics-in-the-loop approach in which a transformer maps a target intensity image to a phase-only SLM field and is trained end-to-end through exact FFT-based propagation embedded directly within optimization. We further observe that patch tokenization strongly shapes the optimization geometry: coarse tokenization acts as an implicit spectral regularizer that stabilizes training and suppresses checkerboard-like attractors, while finer tokenization increases spatial degrees of freedom but benefits from curriculum or hierarchical refinement. Despite training on limited primitives and a single digit class (only digit 6), the learned generator exhibits out-of-distribution (OOD) generalization to unseen digits and hand-drawn target patterns. These results suggest that transformer architectures, whose self-attention enables global token interactions, are a natural fit for far-field holography and provide a viable foundation for scalable physics-grounded hologram generation.

Moiré systems have emerged as an exciting tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moire potential at a filling factor of $ν_m =1/4$ (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form a singlet-like valence bond state which restores local $C_6$ symmetry in hexagonal molecules each spanning $6$ moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems, and opportunities to engineer exotic properties.

We perform a new global QCD analysis of unpolarized parton distribution functions (PDFs) in the nucleon from proton, deuteron and $A=3$ data, including recent measurements of $^3$He/$D$ and $^3$H/$D$ cross section ratios from the MARATHON experiment at Jefferson Lab. Simultaneously inferring the PDFs and nucleon off-shell corrections allows both to be determined consistently, without theoretical assumptions about the isospin dependence of nuclear effects. The analysis provides strong evidence for the need of nucleon off-shell corrections to describe the $A=3$ data, and suggests the presence of both isoscalar and isovector nuclear effects in $A \leq 3$ nuclei. We find that the extracted EMC ratios of nuclear to nucleon structure functions for $A=2$ and 3 differ from those naively extrapolated from heavy nuclei down to low $A$.

The empirical literature on the relationship between income inequality and economic growth has produced highly heterogeneous and often conflicting results. This paper investigates the sources of this heterogeneity using a meta-analytic approach that systematically combines and analyzes evidence from relevant studies published between 1994 and 2025. We find an economically small but statistically significant negative average effect of income inequality on subsequent economic growth, together with strong evidence of substantial heterogeneity and selective publication based on statistical significance, but no evidence of systematic directional bias. To explain the observed heterogeneity, we estimate a meta-regression. The results indicate that both real-world characteristics and research design choices shape reported effect sizes. In particular, inequality measured net of taxes and transfers is associated with more negative growth effects, and the adverse impact of inequality is weaker - or even reversed - in high-income economies relative to developing countries. Methodological choices also matter: cross-sectional studies tend to report more negative estimates, while fixed-effects, instrumental-variable, and GMM estimators are associated with more positive estimates in panel settings.

Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in which local noise, geometry, and forces are held fixed while global constraints are varied. Trajectories are generated for particles evolving toward a central attractor, and entropy production is quantified using both a continuum probability-current estimator and coarse-grained Markov transition statistics across multiple spatial and temporal resolutions. Across systematic sweeps of timestep size, domain extent, and boundary topology, entropy production is governed primarily by constraint-induced probability flow rather than local stochastic variability. Periodic domains that permit sustained circulation yield substantially higher entropy production than reflecting domains despite identical local stochastic structure, with the magnitude of the separation depending on domain extent. In contrast, coarse-grained estimates decrease as temporal resolution increases and rise with finer spatial binning, demonstrating that discrete estimates depend strongly on observation scale and may fail to resolve topology-induced irreversible structure. Ergo, entropy production is not a direct measure of environmental roughness or randomness. Instead, it quantifies how strongly system dynamics are driven away from reversibility by global constraints, geometry, and the space of allowed trajectories. Interpreted in this way, entropy production maps function as diagnostics of organized probability flow and provide a principled method for detecting hidden dynamical constraints from trajectory data alone.

Persistent homology maps a simplicial complex filtered by elements in $\mathbb R$ to finite formal sums of elements of $\mathbb R_{\leq}^{2} = \{ (b,d) \in \mathbb R^2 \cup \{ \infty \} \mid b < d \}$ called (finite) persistence diagrams. This map is stable with respect to the $p$--Wasserstein distance for all $p \in \left[1, + \infty \right]$. Bubenik and Elchesen extend the free translation-invariant commutative Lipschitz monoid of finite persistence diagrams $D(X,A) = D(X)/D(A)$ on arbitrary metric pairs $(X,d,A)$ with $A \subset X$ onto the free translation-invariant abelian Lipschitz group of virtual persistence diagrams $K(X,A) = K(X)/K(A)$ as an isometric embedding $D(X,A) \hookrightarrow K(X,A)$ via the Grothendieck group completion. They prove that the $p$-Wasserstein distance is translation invariant on $D(X,A)$ if and only if $p=1$ and define the unique translation-invariant embedding of $W_1[d]$ into $K(X,A)$ as $ρ.$ When $K(X,A)$ is locally compact abelian, translation-invariant kernels can be constructed via positive-definite functions and Bochner's theorem on the Pontryagin dual. We prove that, for the metric topology induced by $ρ$, the group $(K(X,A),ρ)$ is locally compact if and only if it is discrete, equivalently when the pointed metric space $(X/A,d_1,[A])$ is uniformly discrete, and hence this approach fails outside that case. Assuming instead that $(X/A,d_1,[A])$ is separable and not uniformly discrete, we develop a translation-invariant kernel theory for non--locally compact virtual persistence diagram groups. The group $K(X,A)$ embeds isometrically into its canonical Banach-space linearization $B=\widehat V(X,A)\cong\mathcal F(X/A,d_1)$, and each bounded symmetric positive operator $Q\colon B\to B^\ast$ determines a translation-invariant Gaussian kernel $k(x,y)=\exp\!\left(-\tfrac12\,\langle Q(x-y),x-y\rangle_{B,B^\ast}\right).$

We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight while enhancing computational performance, we consider a broad class of facility location problems. In particular, the expressions are used within a Benders decomposition framework to derive novel formulations for the Discrete Ordered Median Problem with non-increasing weights. Numerical experiments validate that the resulting formulations achieve state-of-the-art performance and exhibit strong robustness across a wide range of instances.