An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting convex body is given by an explicit representation formula in terms of the measure. More generally, existence problems for mixed area measures are addressed. The approach relies on constructing explicit convex solutions to mixed Monge-Ampère equations on $\mathbb{R}^n$ under the assumption of radial symmetry, with the conditions on the measure being expressed through its values on open balls. As a special case, the Dirichlet problem for $k$-Hessian equations on $\mathbb{R}^n$ is treated.

Soft X-ray tomography provides detailed structural insight into whole cells but is hindered by experimental artifacts such as the missing wedge and by limited availability of annotated datasets. We present SimAQ, a simulation pipeline that generates realistic yeast phantoms and applies synthetic imaging artifacts to produce paired noisy volumes, sinograms, and reconstructions. We validate our approach by training a neural network primarily on synthetic data and demonstrate effective few-shot and zero-shot transfer learning on real X-ray tomograms. Our model delivers accurate segmentations, enabling quantitative analysis of noisy tomograms without relying on large labeled datasets.

Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $Γ< G$ an irreducible lattice. Consider the group measure space von Neumann algebra $\mathscr M = \operatorname{L}(Γ\curvearrowright G/H)$ associated with the nonsingular action $Γ\curvearrowright G/H$ and regard the group von Neumann algebra $M = \operatorname{L}(Γ)$ as a von Neumann subalgebra $M \subset \mathscr M$. We show that the group $\operatorname{Aut}_M(\mathscr M)$ of all unital normal $\ast$-automorphisms of $\mathscr M$ acting identically on $M$ is isomorphic to the Weyl group $\mathscr W_G$ of the semisimple algebraic group $G$. Our main theorem is a noncommutative analogue of a rigidity result of Bader-Furman-Gorodnik-Weiss for group actions on algebraic homogeneous spaces and moreover gives new insight towards Connes' rigidity conjecture for higher rank lattices.

Multi-agent systems (MAS) have demonstrated significant effectiveness in addressing complex problems through coordinated collaboration among heterogeneous agents. However, real-world environments and task specifications are inherently dynamic, characterized by frequent changes, uncertainty, and variability. Despite this, most existing MAS frameworks rely on static architectures with fixed agent capabilities and rigid task allocation strategies, which greatly limits their adaptability to evolving conditions. This inflexibility poses substantial challenges for sustaining robust and efficient multi-agent cooperation in dynamic and unpredictable scenarios. To address these limitations, we propose DRAMA: a Dynamic and Robust Allocation-based Multi-Agent System designed to facilitate resilient collaboration in rapidly changing environments. DRAMA features a modular architecture with a clear separation between the control plane and the worker plane. Both agents and tasks are abstracted as resource objects with well-defined lifecycles, while task allocation is achieved via an affinity-based, loosely coupled mechanism. The control plane enables real-time monitoring and centralized planning, allowing flexible and efficient task reassignment as agents join, depart, or become unavailable, thereby ensuring continuous and robust task execution. The worker plane comprises a cluster of autonomous agents, each with local reasoning, task execution, the ability to collaborate, and the capability to take over unfinished tasks from other agents when needed.

Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information measured from its neighbors. Although this problem has been extensively investigated, existing approaches are mostly limited to uniform scaling transformations. This article proposes a new type of local matrix-valued constraints, via which non-uniform scaling control of position formation can be achieved by tuning the positions of only two agents (i.e., leaders). Here, the non-uniform scaling transformation refers to global scaling the position formation with different ratios along different orthogonal coordinate directions. Moreover, by defining scaling and translation of attitudes, we propose a distributed control scheme for scaling and translation maneuver control of joint position-attitude formations. It is proven that the proposed controller achieves global convergence, provided that the sensing graph among agents is a 2-rooted bidirectional graph. Compared with the affine formation maneuver control approach, the proposed approach leverages a sparser sensing graph, requires fewer leaders, and additionally enables scaling transformations of the attitude formation. A simulation example demonstrates our theoretical results.

While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the statistics of pairwise distances $r_H$ between configurations. Focusing on the concrete example of Ising spins, we establish crucial analytical links between this geometry and fundamental real-space observables, i.e., the magnetization and two-point spin correlation functions. This link unveils the universal scaling law in the configuration space: the standard deviation of the normalized distances exhibits universal criticality as $\sqrt{\mathrm{Var}(r_H)}\sim L^{-2β/ν}$, provided that the system possesses zero magnetization and satisfies $4β/ν< d$. We validate this scaling with stochastic series expansion quantum Monte Carlo simulations of the transverse-field Ising model(TFIM). Furthermore, we propose configuration-space diagnostics that go beyond local real-space observables. First, the distribution probability $P(r_H)$ parameterized by the transverse field $h$ forms a one-dimensional manifold. Information-geometric analyses, particularly the Fisher information defined on this manifold, successfully pinpoint the TFIM phase transition, regardless of the measurement basis. Second, for the Su-Schrieffer-Heeger Heisenberg model, a parity index derived from $P(r_H)$ successfully characterizes the symmetry-protected topological phase and its transition. Our work establishes configuration space geometry as a novel perspective on quantum criticality, revealing how macroscopic universal phenomena are encoded within its global statistical features.

In this work we study a scale invariant gravity theory containing two scalar fields, dust particles and a measure defined from degrees of freedom independent of the metric. The integration of the degrees of freedom that define the measure spontaneously break the scale symmetry, leaving us in the Einstein frame with an effective potential that is dependent on the density of the particles. The potential contains three flat regions, one for inflation, another for early dark energy and the third for late dark energy. At a certain point, as the matter dilutes, tunneling from the early dark energy to the late dark energy can start efficiently. This mechanism naturally alleviated the observed Hubble tension by modifying the sound horizon prior to recombination while preserving late-time cosmology. Moreover, the model predictions are consistent with observations from the reduced CMB, BAO, and local measurement of $H_0$, providing a coherent and unified description of the universe. In this context, the Bayesian analysis of these datasets confirms the viability of our scenario, with the best-fit parameters indicating an early dark energy fraction of $f_{\rm NEDE}\approx 0.3$ at a redshift of $z^{\prime}=5000$. This preliminary estimate, obtained using the reduced CMB dataset, is expected to be tightened once the full CMB likelihood is considered.

Measurements of galaxy distributions at large cosmic distances capture clustering from the past. In this study, we use a cosmological model to translate these observations into the present-day galaxy distribution. Specifically, we reconstruct the 3D matter power spectrum at redshift $ z = 0 $ using Dark Energy Spectroscopic Instrument (DESI) Year 1 (DR1) galaxy clustering data and Cosmic Microwave Background (CMB) observations, assuming the $ Λ\text{CDM} $ model, and compare it to the result assuming the $ w_0w_a \text{CDM} $ model. Building on previous state-of-the-art methods, we apply Effective Field Theory (EFT) modelling of the galaxy power spectrum to account for small-scale effects in the 2-point statistics of galaxy data. The EFT approach offers a more robust methodology than traditional methods for modelling the galaxy power spectrum from galaxy clustering data, which can be used to test the consistency of the assumed cosmological model. By incorporating both CMB and galaxy clustering data across a range of redshifts, we can identify discrepancies between the datasets, which would indicate potential inaccuracies in the assumed expansion history. While previous studies have shown consistency with $ Λ\text{CDM} $, this work extends the analysis with higher-quality data to further test the expansion histories of both $ Λ\text{CDM} $ and $ w_0w_a \text{CDM} $. Our findings show that both $ Λ\text{CDM} $ and $ w_0w_a \text{CDM} $ provide consistent fits to the matter power spectrum recovered from DESI DR1 data.

We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group $K$ on a manifold $M$ descends to an integrable system on a dense open subset of the quotient Poisson space $M/K$. The higher dimensional phase space $M$ carries a bivector $P_M$ yielding a bracket on $C^\infty(M)$ such that $C^\infty(M)^K$ is a Poisson algebra. The unreduced system on $M$ is supposed to possess `action variables' that generate a proper, effective action of a group of the form $\mathrm{U}(1)^{\ell_1} \times \mathbb{R}^{\ell_2}$ and descend to action variables of the reduced system. In view of the form of the group and since $P_M$ could be a quasi-Poisson bivector, we say that we work with a generalized Hamiltonian torus action. The reduced systems are in general superintegrable owing to the large set of invariants of the proper Hamiltonian action of $\mathrm{U}(1)^{\ell_1} \times \mathbb{R}^{\ell_2}$. We present several examples and apply our construction for solving open problems regarding the integrability of systems obtained previously by reductions of master systems on doubles of compact Lie groups: the cotangent bundle, the Heisenberg double and the quasi-Poisson double. Furthermore, we offer numerous applications to integrable systems living on moduli spaces of flat connections, using the quasi-Poisson approach.

Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the $X$ and $Y$ bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.

Head impacts can cause concussion, but the precise biomechanical conditions that produce injury remain uncertain. Rotational acceleration has long been posited as the primary cause and has guided concussion prevention strategies. Using instrumented mouthguards to record head kinematics of diagnosed concussions, we directly tested this hypothesis and found that linear acceleration predicted injury with greater precision than rotational acceleration, while rotational velocity provided additional predictive value. Injury risk functions derived from these measurements indicated substantial predicted concussion risk during typical impacts to an American football helmet. Introducing a liquid-filled helmet pad designed to attenuate linear acceleration reduced predicted risk by up to 52%. These results indicate that effective concussion prevention requires targeting linear acceleration.

High altitude platform stations (HAPS) offer a promising solution for achieving ubiquitous connectivity in next-generation wireless networks (xG). Integrating HAPS with terrestrial networks, creating HAPS-empowered vertical heterogeneous networks (vHetNets), significantly improves coverage and capacity and supports emerging novel use cases. In HAPS-empowered vHetNets, HAPS and terrestrial network tiers can share the same spectrum, forming harmonized spectrum vHetNets that enhance spectral efficiency (SE). However, harmonized spectrum vHetNets face major challenges, including severe co-channel interference and scalability in large-scale deployments. To address the first challenge, we adopt a cell-free multiple-input multiple-output (MIMO) network architecture in which users are simultaneously served by multiple base stations using beamforming. However, beamforming weight design leads to a nonconvex, high-dimensional optimization problem, highlighting the scalability challenge. To address this second challenge, we develop a two-level distributed proportional fairness beamforming weight design (PFBWD) algorithm. This algorithm combines the augmented Lagrangian method (ALM) with a three-block ADMM framework. Simulation results demonstrate the performance improvements achieved by integrating HAPS with standalone terrestrial networks, as well as the reduced complexity and signaling overhead of the distributed algorithm compared to centralized algorithms.

Spatiotemporal data are being produced in continuously growing volumes by a variety of data sources and a variety of application fields rely on rapid analysis of such data. Existing systems such as PostGIS or MobilityDB usually build on relational database systems, thus, inheriting their scale-out characteristics. As a consequence, big spatiotemporal data scenarios still have limited support even though many query types can easily be parallelized. In this paper, we propose our vision of a native serverless data processing approach for spatiotemporal data: We break down queries into small subqueries which then leverage the near-instant scaling of Function-as-a-Service platforms to execute them in parallel. With this, we partially solve the scalability needs of big spatiotemporal data processing.

We study horizontal differentiation when the set of feasible products is a structured subset of the Lancasterian characteristics space. Modeling this set as a compact Riemannian manifold, we show that intrinsic geometry governs substitutability and thereby determines market outcomes. We establish that production constraints induce sectional curvature, which controls the elasticity of technological substitution. Negative curvature amplifies technological divergence and attenuates competitive pressure, whereas positive curvature compresses technological distances and intensifies competition. This mapping yields a characterization of spatial competition in which equilibrium existence and stability are determined by geometric primitives. In particular, we show that sufficiently negative curvature and high dimensionality stabilize minimum differentiation, while continuous symmetries preclude it. The analysis provides a microfoundation linking technological constraints, through the geometry of the feasible set, to endogenous regimes of market power.

The paper is devoted to the study of the boundary behavior of mappings. We consider mappings that satisfy inverse moduli inequalities of Poletskii type, under which the images of the domain under the mappings may change. It is proved that a classes of such mappings are equicontinuous with respect to prime ends of some domain if the majorant in the indicated modulus inequality is integrable.

Spin mixtures of degenerate fermions are a cornerstone of quantum many-body physics, enabling superfluidity, polarons, and rich spin dynamics through $s$-wave scattering resonances. Combining them with strong, long-range dipolar interactions provides highly flexible control schemes promising even more exotic quantum phases. Recently, microwave shielding gave access to spin-polarized degenerate samples of dipolar fermionic molecules, where tunable $p$-wave interactions were enabled by field-linked resonances available only by compromising the shielding. Here, we study the scattering properties of a fermionic dipolar spin mixture and show that a universal $s$-wave resonance is readily accessible without compromising the shielding. We develop a universal description of the tunable $s$-wave interaction and weakly bound tetratomic states based on the microwave-field parameters. The $s$-wave resonance paves the way to stable, controllable and strongly-interacting dipolar spin mixtures of deeply degenerate fermions and supports favorable conditions to reach this regime via evaporative cooling.

In this paper, we investigate equivalent characterizations of the condition that every acyclic complex of projective, injective, or flat modules is totally acyclic over a general ring R. We provide examples to illustrate relationships among these conditions and show that several are closely tied to the homological invariants silp(R), spli(R) and sfli(R). We also give sufficient conditions for the equality spli(R) = silp(R), thereby refining results due to Ballas-Chatzistavridis and Wang-Yang. Further, we extend a result of Christensen-Foxby-Holm on characterizations of Iwanaga-Gorenstein rings to the non-commutative setting. This generalizes a theorem of Estrada-Fu-Iacob, offering additional equivalent characterizations under a general assumption while also yielding characterizations of the Nakayama conjecture.

A hypergraph is \textit{bipartite with bipartition $(A, B)$} if every edge has exactly one vertex in $A$, and a matching in such a hypergraph is \textit{$A$-perfect} if it saturates every vertex in $A$. We prove an upper bound on the number of $A$-perfect matchings in uniform hypergraphs with small maximum codegree. Using this result, we prove that there exist order-$n$ Latin squares with at most $(n/e^{2.117})^n$ transversals when $n$ is odd and $n \equiv 0\pmod 3$. We also show that $k$-uniform $D$-regular hypergraphs on $n$ vertices have at most $((1+o(1))q/e^k)^{Dn/k}$ proper $q$-edge-colorings when $q = (1+o(1))D$ and the maximum codegree is $o(q)$.

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. This work develops the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the \textit{M3D-C1} https://m3dc1.pppl.gov fusion energy science code. The semi-implicit time integrator in \textit{M3D-C1} is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in \textit{M3D-C1} is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in \textit{M3D-C1} is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC https://cfs.energy/technology/sparc disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

In collaborative inference (CI), transmitting intermediate representations $Z$ from edge devices enables model inversion attacks (MIA) that reconstruct the original inputs $X$, while existing defenses mainly perturb shallow-layer $Z$ at the cost of utility. We instead ask where an edge-cloud model should be partitioned to obtain intrinsic resistance to MIA. We challenge the intuition that depth is the driver of MIA resistance, and show that depth is sufficient only insofar as it enables a representational transition; this transition is necessary for intrinsic resistance and is marked by an abrupt rise in the lower bound of $H(X|Z)$. Correspondingly, the decisive variance term in the entropy bound shifts from a global variance to the intra-class mean-squared radius $R_c^2$ rather than dimensionality alone, yielding an $R_c^2$-based criterion to locate the transition zone, or identify it post hoc from MIA outcomes, which we term the Golden Partition Zone (GPZ). We further explain how $R_c^2$ evolves during training and show that it can be controlled through the label distribution; we refer to this controllable dynamic behavior as the Neural Vortex, an analysis-backed explanatory concept. Across four representative deep vision models, partitioning at the GPZ yields more than 4x higher reconstruction MSE compared to shallow splits; under entropy and inversion-model enhancements, decision-level representations provide 66 percent stronger resistance than feature-level ones, and we further observe that data type affects both the transition boundary and reconstruction.

We give a description of prepositive cones -- a notion of ordering on algebras with involution introduced by Astier and Unger -- in the specific context of quaternion algebras with involution. Our main result establishes that, for a broad class of quaternion algebras with involution, every prepositive cone is maximal.

Recently, Rodriguez-Lopez, Wang, and Antezza [Phys. Rev. B v.111, 115428 (2025)] compared the theoretical descriptions of electric conductivity of graphene given by the Kubo model and quantum field theory in terms of the polarization tensor. According to this article, in the spatially nonlocal case, the quantum field theoretical description contains ``hard inconsistencies". By modifying the equality, which relates the conductivity and polarization expressions, the predictions of quantum field theory were revised and brought in agreement with those following from the nonrelativistic Kubo model. Here, it is shown that this modification violates the requirement of gauge invariance and, thus, is unacceptable. By comparing both theoretical approaches, we demonstrate that all the results obtained within quantum field theory are physically well justified whereas an application of the modified expression for the conductivity of graphene leads to the consequences of nonphysical character.

The effective string tension ($κ$) in the Schwinger mechanism and the effective temperature ($T$) in Bose-Einstein statistics are extracted from the transverse momentum ($p_T$) spectra of heavy quarkonia produced in proton-proton (p+p) collisions at the Large Hadron Collider (LHC). Here, $T$ derived from the heavy quarkonium $p_T$ spectra also serves as the initial effective temperature (effective temperature at the initial stage) of small collision systems. This is because, despite the absence of quark-gluon plasma (QGP) formation during the collisions, which leaves $T$ largely unaffected by QGP-related effects, the initial geometric asymmetry and local partonic thermalization still induce radial and transverse flows, thereby contributing to an increase in $T$. The effective parameters ($κ$ and $T$) are obtained by fitting the experimental $p_T$ spectra of $J/ψ$ and $Υ(nS)$ ($n=1$, 2, and 3) within various rapidity intervals, produced in p+p collisions at center-of-mass energies of $\sqrt{s}=13$ and 8 TeV, as measured by the LHCb Collaboration. It is found that the multi-component distribution structured within the framework of the Schwinger mechanism or Bose-Einstein statistics can effectively describe the heavy quarkonium $p_T$ spectra in small collision systems. With decreasing rapidity in the forward region, both $κ$ and $T$ increase, indicating a directly proportional relationship between them. Based on $κ$, the average minimum strong force radius of participant quarks is determined.

The discovery of the superconducting diode effect (SDE) has been cherished as a milestone in developing superconducting electronics. Tremendous efforts are being dedicated to realizing SDE in a wide variety of material platforms. Despite the diversity in the hosting materials and device designs, SDE is usually operated in a single mode which is enabled by either out-of-plane or in-plane magnetic field/magnetization. In this work, we report the realization of a dual-mode SDE in 2H-$\mathrm{NbS_2}$/2H-$\mathrm{NbSe_2}$ heterostructures where both the out-of-plane magnetic field $B_{\perp}$ and in-plane magnetic field $B_{||}$ can independently generate and manipulate SDE. The two modes share similar diode efficiency but differ in two aspects: 1. $B_{\perp}$-induced SDE is activated by a field on the order of 1 mT while $B_{||}$-induced SDE requires a field on the order of 100 mT; 2. $η$ of $B_{\perp}$-induced SDE exhibits a square-root like temperature dependence while $η$ of $B_{||}$-induced SDE takes a more linear-like one. We demonstrate that the dual-mode SDE is most likely a result of mirror symmetry breaking along multiple orientations. Thanks to the two orders difference in the operational field for the two modes, we propose a dual-functionality device scheme to showcase the potential of the dual-mode SDE in realizing advanced superconducting architecture, where fast polarity-switching functionality is implemented with $B_{\perp}$-induced SDE and high-fidelity functionality is enabled with $B_{\perp}$-induced SDE.

We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual Dynamic Programming (SDDP) method replacing affine cuts by quadratic cuts. We provide conditions ensuring strong convexity of the recourse functions and prove the convergence of SQDP. In the special case of a single stage deterministic problem, we call QCSC (Quadratic Cuts for Strongly Convex optimization) the method and prove its complexity. Numerical experiments illustrate the performance and correctness of SQDP, with SQDP being much quicker than SDDP for large values of the constants of strong convexity both for a multistage problem and a two-stage assembly recourse model. We also present the results of numerical experiments on deterministic problems where QCSC is much quicker than several popular competing optimizers for solving 6 strongly convex optimization problems from the literature.

We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight convergence guarantees together with an optimal face identification property. Furthermore, we propose two highly efficient corrective steps for convex quadratic objectives based on linear optimization or linear system solving, akin to Wolfe's minimum-norm point, and show that they converge in finite time under suitable conditions. Beyond optimization problems that are directly quadratic, we revisit two algorithms - split conditional gradient and second-order conditional gradient sliding - which can leverage quadratic corrections to accelerate their quadratic subproblems. We demonstrate improved convergence rates for the first and broader applicability for the second, which may be of independent interest. Finally, we show substantial computational speedups for Frank-Wolfe-based algorithms with quadratic corrections across the considered problem classes.

We develop a class of regular black holes by prescribing finite curvature invariants and reconstructing the corresponding spacetime geometry. Two distinct approaches are employed: one based on the Ricci scalar and the other on the Weyl scalar. In each case, we explore a variety of analytic profiles for the curvature functions, including Gaussian, hyperbolic secant, and rational forms, ensuring regularity, asymptotic flatness, and compatibility with dominant energy conditions. The resulting mass functions yield spacetime geometries free from curvature singularities and exhibit horizons depending on model parameters. To assess the stability of these solutions, we perform a detailed analysis of quasinormal modes (QNMs) under axial gravitational perturbations. We show that the shape of the effective potential, particularly its width and the presence of potential valleys, plays a critical role in determining the QNMs. Models with a large peak-to-valley ratio in the potential barrier exhibit stable, exponentially decaying waveforms, while a small ratio may induce late-time instabilities. Our results highlight the significance of potential design in constructing physically viable and dynamically stable regular black holes, offering potential observational implications in modified gravity and quantum gravity scenarios.

Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural approach based on sequential elimination: elements of the group are removed one by one, and their assessments are aggregated. We study this approach in the context of coalitional games and show that, for almost all semivalues, it does not depend on the order of players. In particular, we introduce a new group value, called the Union Shapley Value, and investigate its axiomatic properties. Our results build on a comprehensive analysis of group values in coalitional games. Specifically, we define a class of group (weak consistent) semivalues - a variant of semivalues satisfying a weak form of monotonicity. This framework allows us to clarify the differences between existing notions in the literature. We show that existing group values either assess the total worth of a group or measure its synergy. We distinguish these two approaches axiomatically and uncover a connection between the corresponding values. In particular, we show that the well-known Interaction Index is a synergistic counterpart of the value introduced by Marichal et al., which corresponds to the merge approach. The analysis also yields new synergistic group values associated with the Union Shapley Value, which we call the Intersection Shapley Value. Our results demonstrate that the sequential extension - and the Union Shapley value in particular - constitute one of the most natural extensions of player values to groups in coalitional games.

We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number of mathematical properties specific to the proposed method that is well-balanced, mass-conserving and positivity-preserving under a mild CFL condition also in the presence of wet-dry fronts. The method includes a consistent conservative discretization for passive tracers. We use a high-order Discontinuous Galerkin (DG) method as implemented in the deal.II library. This environment provides efficient and native parallelization techniques and automatically handles non-conforming meshes to implement adaptive strategies which are tested in a coastal environment. Idealized test cases show the robustness in presence of irregular bathymetries also with under-resolved features at the grid scale. A benchmark with realistic bathymetry and a complex domain shows the potential of the proposed discretization for adaptive simulations of coastal flows.

Quantitative metrics derived from software repositories and package ecosystems are widely used to assess the impact, popularity, maintenance, and criticality of free and open source software (FOSS) projects. However, these metrics are often assumed to be reliable despite their potential susceptibility to manipulation. Prior empirical software engineering and security research deployed these in a variety of ways which assume they indeed capture project impact and popularity. Yet, the extent to which these underlying signals can be spoofed in practice, and the consequences this has for downstream uses of the metrics, has received little focused attention. To address this gap, the paper decomposes existing combined metrics into atomic metric categories, analyzes their spoofing effort under a maintainer-centered threat model, and investigates a real-world sybil attack on npm connected to an impact-based reward mechanism. The analysis finds that many metric categories, especially commit data, issue-tracker activity, downloads, repository contents, and dependency relations, are manipulable with low to moderate effort, and it identifies a sybil attack comprising more than 70,000 spam packages on npm. These results imply that quantitative FOSS metrics should be used with much greater caution in software engineering research and practice, particularly for ranking, dataset construction, and any allocation or evaluation process that turns metrics into optimization targets.