This study examines whether engagement with social robots translates into improved human-directed social abilities in autistic children. We conducted an 8-week home-based randomized controlled trial with 40 children aged 5--9 using a commercial social robot (Qrobot). Families were assigned to either continued robot access or robot withdrawal. Quantitative measures and caregiver interviews assessed anxiety, social motivation, emotion inference, and empathy. Results showed that continued robot access significantly reduced anxiety, confirming strong affective benefits and high usability. However, children in the withdrawal group demonstrated greater improvements in social motivation, emotion understanding, and empathic behaviors toward caregivers and peers. Qualitative findings revealed a "handoff versus siloing" pattern: withdrawal promoted reorientation toward human social interaction, while continued access concentrated engagement within the child--robot dyad and limited transfer to real-world contexts. We interpret these results as evidence that high engagement does not guarantee social transfer.

Electrical readout of 180$^\circ$ switching in strictly compensated collinear antiferromagnets remains a major challenge in antiferromagnetic spintronics. Electrical writing of perpendicularly magnetized ferromagnets by out-of-plane orbital torque remains an important challenge in orbitronics. In this work, we propose a second-order nonlinear magnetic orbital Hall effect in the source antiferromagnet as a simultaneous recipe for both difficulties. This orbitronics effect is induced by spin-orbit coupling and is odd in the Néel vector, thus is a unique effect that integrates both functionalities via electric control of the Néel vector in the source antiferromagnet. Our first-principles calculations in CuMnAs predict significant non-perturbative orbital effects from spin-orbit coupling, with a orbital Berry-curvature dipole mechanism. These findings unveil new possibilities opened by topological antiferromagnetic orbitronics.

Within a unified framework, we reveal that the seemingly disparate control approaches for classical and quantum continuous-variable systems are interconnected via differential manifolds of the ancillary representations. For classical systems, the ancillary representation is defined by the time-dependent ancillary canonical variables resulting from a symplectic transformation over the original canonical variables. Under the conditions of the Hamilton-Jacobi equation, the ancillary canonical variables act as dynamical invariants to guide the system nonadiabatically through the entire phase space. The second quantization of the Liouville equation for the canonical variables leads to the Heisenberg equation for the relevant ancillary operators, which is found to be a sufficient condition to yield nonadiabatic passages towards arbitrary target states in both Hermitian and non-Hermitian systems and constrained exact solutions of the time-dependent Schroedinger equation. Using the non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation, our theory is exemplified by the generation of single-mode squeezed states with a squeezing level of 29.3 dB and double-mode squeezed states with 20.5 dB, respectively.

Distributed integrated sensing and communication (D-ISAC) enables multiple spatially distributed nodes to cooperatively perform sensing and communication. However, achieving coherent cooperation across distributed nodes is challenging due to practical impairments. In particular, residual phase synchronization errors result in imperfect channel state information (CSI), while angle-of-arrival (AoA) uncertainties induce radar cross-section (RCS) variations. These impairments jointly degrade target detection performance in D-ISAC systems. To address these challenges jointly, this paper proposes a robust beamforming design for coherent D-ISAC systems. Multiple distributed nodes coordinated by a central unit (CU) jointly perform joint transmission coordinated multipoint (JT-CoMP) communication and multi-input multi-output (MIMO) radar sensing to detect a target while serving multiple user equipments (UEs). We formulate a robust beamforming problem that maximizes the expected Kullback-Leibler divergence (KLD) under statistical RCS variations while satisfying system power and per-user minimum signal-to-interference-plus-noise ratio (SINR) constraints under imperfect CSI to ensure the communication quality of service (QoS). The problem is solved using semidefinite relaxation (SDR) and successive convex approximation (SCA), and numerical results show that the proposed method achieves up to 3 dB signal-to-clutter-plus-noise ratio (SCNR) gain over the conventional beamforming schemes for target detection while maintaining the required communication QoS.

In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent characterization of the problem, namely, the solution to the Calabi flow exists globally in time and converges if and only if there exists a weight function that realizes the prescribed curvature. In particular, for constant curvature weights, we prove that the solution to the Calabi flow exists globally in time and converges under certain topological conditions.

We numerically construct a five-dimensional Proca-Maxwell system coupled to an infinite tower of higher-derivative gravity, parameterized by the correction order and coupling constant. While the first-order correction case recovers standard Einstein gravity results, and the second-order correction (Gauss-Bonnet) case fails to resolve the central singularity in the vanishing frequency limit, we demonstrate that higher-order corrections effectively regularize the spacetime, yielding globally regular solutions. A key finding is the emergence of a ``frozen state'' in the supercritical regime: as the field frequency approaches zero, matter concentrates entirely within a critical radius, creating a regular core that externally mimics an extremal black hole. We further reveal that introducing the electric charge fundamentally alters this behavior; the electrostatic repulsion counteracts the gravitational collapse, effectively ``unfreezing'' the system and preventing the formation of the critical core. Significantly, unlike models relying on exotic matter, our solutions satisfy all standard energy conditions across the entire parameter space, establishing a physically viable pathway for constructing regular black hole mimickers.

Dirac materials have been a unique solid state platform for exploring relativistic quantum phenomena including supercritical atomic collapse, which leads to emergent discrete scale symmetry and logperiodic quantum oscillations. In the relativistic regime, the fundamental effect in quantum electrodynamics, vacuum polarization, can further modulate the atomic collapselike state by screening bare charges but is rarely harnessed in condensed matter system. Here, we report a continuous progression from low field Shubnikov de Haas oscillations to high field log periodic oscillations in the Dirac material HfTe5, with both phenomena modulated by Fermi surface anisotropy. This maps the transition from single particle Landau levels to an interaction-driven, discrete scale invariant energy spectrum of quasi-bound states. Crucially, our findings suggest vacuum polarization provides a compelling mechanism for renormalizing the effective impurity charge, quantitatively explaining the carrier-density dependent scale factor. By revealing the intricate interplay between Landau quantization, many body electronic screening, and scale-symmetry breaking, our results establish Dirac solids as a controllable platform for exploring relativistic vacuum effects and emergent novel symmetry.

In this paper we initiate the study of higher Chow cycles on holomorphic symplectic manifolds. Our concrete central result is construction of explicit indecomposable (2,1)- and (4,1)-cycles on the Fano varieties of lines on cyclic cubic fourfolds. This is the first explicit example of such cycles on holomorphic symplectic manifolds. The proof of indecomposability is done by degeneration to cuspidal cubic fourfolds. Along the way, we develop a method of inducing (p,1)-cycles on Hilbert squares of K3 surfaces. Finally, we study restriction of (2,1)-cycles to Lagrangian subvarieties, and observe the phenomenon that the restricted cycles are always decomposable in the examples in our hand.

We propose the notion of Frobenius quotients between Frobenius exact categories. It turns out that any Frobenius quotient induces Frobenius quotients between the corresponding inflation categories. We obtain an explicit Frobenius quotient from the category of vector bundles on weighted projective lines with three weights to a certain category consisting of monomorphism grids.

This paper studies deterministic data-driven reachability analysis for dynamical systems with unknown dynamics and nonconvex reachable sets. Existing deterministic data-driven approaches typically employ zonotopic set representations, for which the multiplication between a zonotopic model set and a zonotopic state set cannot be represented algebraically exactly, thereby necessitating over-approximation steps in reachable-set propagation. To remove this structural source of conservatism, we introduce constrained polynomial matrix zonotopes (CPMZs) to represent data-consistent model sets, and show that the multiplication between a CPMZ model set and a constrained polynomial zonotope (CPZ) state set admits an algebraically exact CPZ representation. This property enables set propagation entirely within the CPZ representation, thereby avoiding propagation-induced over-approximation and even retaining the ability to represent nonconvex reachable sets. Moreover, we develop set-theoretic results that enable the intersection of data-consistent model sets as new data become available, yielding the proposed online refinement scheme that progressively tightens the data-consistent model set and, in turn, the resulting reachable set. Beyond linear systems, we extend the proposed framework to polynomial dynamics and develop additional set-theoretic results that enable both model-based and data-driven reachability analysis within the same algebraic representation. By deriving algebraically exact CPZ representations for monomials and their compositions, reachable-set propagation can be carried out directly at the set level without resorting to interval arithmetic or relaxation-based bounding techniques. Numerical examples for both linear and polynomial systems demonstrate a significant reduction in conservatism compared to state-of-the-art deterministic data-driven reachability methods.

Large-scale integration of inverter-based resources into power grids worldwide is challenging their stability and security. This paper takes a closer look at synchronous condensers as a solution to mitigate stability challenges caused by the preponderance of grid-following inverters. It finds that while they are not grid-forming assets themselves, they could enhance grid stability. Throughout this paper, different facets of power system stability and their underlying phenomena are discussed. In addition, instances of instability and mitigation strategies using synchronous condenser are demonstrated using electromagnetic transient simulations. The analysis in this paper highlights the underlying mechanism by which synchronous condensers enhance angular stability, frequency response, and voltage stability. Moreover, it underscores the criticality of their choice of location by demonstrating the destabilizing behavior that could be initiated by the interactions of synchronous condensers.

The importance of simulating pinning arrays in superconducting samples for the increase of critical currents has been increasing in the last few years. Since the Time Dependent Ginzburg Landau (TDGL) can be more accurate than alternative methodologies, the simulation procedures involving it are critical to design devices that can sustain higher critical currents and, therefore, to the field of applied superconductivity. In this article, a simple novel algorithm is presented for the reduction of bias and optimisation of execution time in iterative time dependent simulations, applied to TDGL solutions of superconducting samples. Taking a time series approach to the magnetic response of the sample, stationary solutions are found for each step in the evolution of the applied external field, leading to bias reduction and minimisation of iterations needed to be spent at each step in the applied field. The results are presented for a pure superconductor, in a framework of simulations via link variable technique, with simple Euler algorithm for the solution in time, but the implementation can be adapted easily to deal with adaptive step size solutions or semi-implicit methods, which are not exempt from the bias and iterations tradeoff.

In this paper, we present an online learning approach for two-player zero-sum linear quadratic games with unknown dynamics. We develop a framework combining regularized least squares model estimation, high probability confidence sets, and surrogate model selection to maintain a regular model for policy updates. We apply a shrinkage step at each episode to identify a surrogate model in the region where the generalized algebraic Riccati equation admits a stabilizing saddle point solution. We then establish regret analysis on algorithm convergence, followed by a numerical example to illustrate the convergence performance and verify the regret analysis.

We obtain explicit estimates for the mixed character sum $S= S(χ,g,f,p^m) = \sum_{x=1}^{p^m} χ(g(x)) e_{p^m}(f(x))$, where $p^m$ is a prime power, $χ$ is a multiplicative character mod $p^m$ and $f,g$ are rational functions over $\mathbb Q$. Let $f=f_+/f_-$, $g=g_+/g_-$ in reduced form, and set $D=\text{deg}(f)+Z-1$ where $Z$ is the number of distinct complex zeros of $f_-g_+g_-$, and $Δ= \text{deg}(f)+\text{deg}(g)$ for polynomial $f,g$, $Δ=2(\text{deg}(f)+\text{deg}(g))$ otherwise. We show for example that for odd $p$, any non-degenerate sum has $|S|\le 3^{4/3}\, p^{m(1-\frac 1D)}$ if $\text{deg}_p(f) \ge 1$, and $|S| \le 3^{4/3}\, p^{m(1-\frac 1Δ)}$ if $\text{deg}_p(g) \ge 1$. Analogous bounds are given for degenerate sums.

We study the Stochastic Boolean Function Certification (SBFC) problem, where we are given $n$ Bernoulli random variables $\{X_e: e \in U\}$ on a ground set $U$ of $n$ elements with joint distribution $p$, a Boolean function $f: 2^U \to \{0, 1\}$, and an (unknown) scenario $S = \{e \in U: X_e = 1\}$ of active elements sampled from $p$. We seek to probe the elements one-at-a-time to reveal if they are active until we can certify $f(S) = 1$, while minimizing the expected number of probes. Unlike most previous results that assume independence, we study correlated distributions $p$ and give approximation algorithms for several classes of functions $f$. When $f(S)$ is the indicator function for whether $S$ is the spanning set of a given matroid, our problem reduces to finding a basis of active elements of a matroid by probing elements. We give a non-adaptive $O(\log n)$-approximation algorithm for arbitrary distributions $p$, and show that this is tight up to constants unless P $=$ NP, even for partition matroids. For uniform matroids, we give constant factor $4.642$-approximation ([BBFT20]) that can be further improved to a $2$-approximation if additionally the random variables are negatively correlated for the case of $1$-uniform matroid. We also give an adaptive $O(\log k)$-approximation algorithm for SBFC for $k$-uniform matroids for the Graph Probing problem, where we seek to probe the edges of a graph one-at-a-time until we find $k$ active edges. The underlying distribution on edges arises from (hidden) independent vertex random variables, with an edge being active if at least one of its endpoints is active. This significantly improves over the information-theoretic lower bound on $Ω(\mathrm{poly}(n))$ ([JGM19]) for adaptive algorithms for $k$-uniform matroids with arbitrary distributions.

The persistent absence of signals in traditional dark matter searches has intensified interest in scenarios beyond the canonical weakly interacting massive particle paradigm. In this work, we investigate the collider phenomenology of feebly interacting dark matter produced via the freeze-in mechanism through a spin-2 portal. We consider a framework in which a massive graviton-like mediator couples minimally and universally to the energy--momentum tensor of both the Standard Model (SM) and the dark sector. Such interactions arise naturally in extra-dimensional constructions and effective theories of gravity, providing a theoretically well-motivated and predictive setup. We systematically connect early-Universe cosmology with collider observables by identifying regions of parameter space consistent with freeze-in conditions and the observed dark matter relic abundance, and examining their testability at the Large Hadron Collider (LHC). Focusing on bosonic fusion production channels, which are particularly sensitive to spin-2 interactions, we analyze invisible mediator decay signatures and assess current and projected experimental sensitivities. To enhance sensitivity in this challenging regime of feeble couplings, we develop a search strategy based on machine-learning algorithms. Our results demonstrate that collider searches can probe substantial regions of the cosmologically viable freeze-in parameter space, highlighting the high-luminosity LHC as a powerful laboratory for feebly interacting dark sectors. This study establishes a concrete and complementary pathway to test freeze-in dark matter scenarios through spin-2 portals, thereby bridging gravitationally motivated new physics, cosmology, and high-energy collider experiments.

Angle-selective optical devices are of importance to several applications such as photovoltaics, high-sensitivity photodetectors and displays. There are several approaches to realizing angular selectivity, but it remains challenging to obtain isotropic responses over large spectral bandwidths in optically thin structures. We introduce a dispersion engineering approach coupled with topology optimization to design 2D metastructures, leveraging guided-mode resonances (GMRs), that exhibit isotropic angular selectivity over relative bandwidths of approximately 20%. We experimentally demonstrate metastructures with complementary angular selectivities, either scattering light strongly near normal incidence and transmitting efficiently at higher incident angles, or vice versa. A key finding is that these designs enable operation over spectral bandwidths greater than the GMR linewidths would suggest, a result of carefully tailored interactions between the Fabry-Perot background and resonantly scattered light. This work marks a significant step forward for the realization of broadband, angle-selective scattering in readily fabricated structures of subwavelength thickness, and enables new possibilities in sensing, analog information processing, high-efficiency photovoltaics, and displays.

This paper is Part II of a series on global existence and asymptotic behavior of positive solutions to \begin{equation*} \begin{cases} \displaystyle u_t=Δu-χ_0\nabla\cdot\left(\frac{u^m}{(1+v)^β}\nabla v\right)+au-bu^{1+α}, & x\inΩ, \cr \displaystyle 0=Δv-μv+νu^γ, & x\inΩ, \cr \displaystyle \frac{\partial u}{\partial n}=\frac{\partial v}{\partial n}=0, & x\in\partialΩ, \end{cases} \end{equation*} where $Ω\subset\mathbb{R}^N$ is a bounded and smooth domain. The parameters $α,γ,m,μ,ν$ are positive, $χ_0$ is real, and $a,b,β$ are nonnegative. In Part I, we established boundedness and global existence. Here, we study persistence and stabilization, quantifying how $β$ and $χ_0$ influence long-time dynamics. First, we prove uniform persistence if $m\ge 1$. Next, for $a,b>0$, the unique positive equilibrium is $(u^*,v^*) = \left((\tfrac{a}{b})^{1/α},(\tfracνμ)(\tfrac{a}{b})^{γ/α}\right)$. We identify a threshold $χ^*(u^*)$: $(u^*,v^*)$ is linearly stable if $χ_0<χ^*(u^*)$, with local exponential decay, unstable if $χ_0>χ^*(u^*)$. We also give conditions ensuring every bounded solution converges exponentially to $(u^*,v^*)$. For $a=b=0$, we study stability of the constant equilibria under mass constraint, obtaining a linear stability threshold and global stabilization. We extend the Lyapunov method from $m=1$ to $m>1$ and the rectangle/ODE method from $β=0$ to $β>0$. For $m\ge 1$, signal saturation (large $β$) or repulsion ($χ_0<0$) prevents aggregation and promotes relaxation. In Part III, we study bifurcation and pattern formation when $χ_0$ passes through critical thresholds.

Academic institutions have been challenged to adapt as data science and AI have rapidly evolved into disciplines, degrees and careers. Efforts to provide students with learning experiences have led to the development of novel credentials, renamed departments, new schools and even additional colleges within universities. Generally, these approaches are siloed in some way, perhaps separating STEM students from those in the humanities or separating faculty assigned to these courses from their colleagues in their home departments. NC State University decided to take a novel approach by creating a new type of entity called an Academy that would reach across all disciplines, departments, colleges, centers and institutes to catalyze work in data science and AI in all points of the university's mission: teaching, research and engagement.

To address the multidimensional nature of health-related questions, advances in health research often require integrating information from various data sources within statistical analyses. When complementary information pertaining to the same set of individuals are distributed across different institutions, vertical methods make it possible to obtain analysis results without sharing or pooling individual-level data. To guide stakeholders toward a transparent use of vertical methods, this study aims to (1) Identify existing vertical methods enabling statistical inference; and (2) Characterize the methodological properties of these methods and the current extent of their use with health data. We conducted a scoping review using four interdisciplinary databases. We then systematically extracted the characteristics of identified vertical methods with respect to comparability with the pooled analysis, efficiency of communication schemes and confidentiality. We additionally screened studies that cited included articles to identify applications on vertically partitioned real-world health data. Among 2887 articles initially screened, 30 were included in the review. Inference for the linear and the logistic regression framework were the most frequent statistical inference tasks undertaken in proposed methods. Equivalence with the pooled analyses was not systematically addressed and most methods required multiple communications between participating parties. Almost all articles described their approach as privacy-preserving, although a minority provided privacy assessments. The scope of existing approaches enabling statistical inference for vertically partitioned data is still relatively limited. Most existing methods do not concurrently achieve results equivalent to centralized analyses, high communication efficiency, and guaranteed protection of individual-level data.

Evidence of the production of two Z bosons and a photon in proton-proton collisions is reported for the first time in CMS. The analysis uses data collected by the CMS experiment between 2016 and 2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The first evidence for the process pp $\to$ ZZ$γ$ $\to$ 4$\ellγ$ ($\ell$ = e, $μ$), with an observed (expected) significance of 3.7 (3.1) standard deviations in a fiducial region defined by $p_\mathrm{T}^γ$ $\gt$ 20 GeV, $\lvertη^γ\rvert$ $\lt$ 2.4, $ΔR(\ell,γ)$ $\gt$ 0.5, $m_\text{Z}$ between 60 and 120 GeV, and the invariant mass of either of the two Z bosons combined with the photon ($m_{\text{Z}γ}$) larger than 100 GeV, is reported. The measured (predicted) fiducial cross section is 60$^{+27}_{-22}$ ab (47.56 $\pm$ 0.04 ab). Additionally, the inclusive production of pp $\to$ 4$\ellγ$ is studied by removing the $m_{\text{Z}γ}$ requirement to include final state radiation where one Z boson decays to 2$\ellγ$, yielding an observed (expected) significance of 5.0 (4.2) standard deviations and a measured (predicted) fiducial cross section of 156$^{+39}_{-35}$ ab (99.97 $\pm$ 0.09 ab).

Fusion reactors can permanently remediate mercury by using it as a neutron multiplier: each (n,2n) reaction reduces the neutron number towards ${}^{197}$Hg which quickly decays into stable gold, irreversibly removing it from the environment while generating substantial economic value. Fusion energy is therefore not merely environmentally benign, but anti-polluting through the continuous consumption of an environmental pollutant. The history of nuclear fission demonstrates that environmental concerns can be decisive obstacles to low-carbon power deployment, suggesting that integrated pollution remediation fundamentally improves the policy calculus for fusion energy. We show that at high neutron flux (achievable in muon-catalyzed and inertial confinement fusion), nuclear reactions make all mercury isotopes eligible for gold transmutation, incentivizing mercury recovery and valuing the world mercury extractable stock at ${\sim}\$200$ trillion, exceeding all in-ground gold reserves. Co-producing gold alongside electricity can triple a fusion plant's revenue, aligning economic incentives with complete, permanent mercury remediation.

Carroy, Miller, Schrittesser, and Vidnyánszky established the $L_0$ dichotomy: there is a Borel graph of Borel chromatic number three that admits a continuous homomorphism to every analytic graph of Borel chromatic number at least three. Their proof relies on a transfinite analysis of terminal approximations over a decreasing $ω_1$-sequence of analytic sets. I give a new, substantially shorter proof of this result by adapting the graph-theoretic framework recently introduced by Bernshteyn for the $G_0$ dichotomy. The central device is a $σ$-ideal of \emph{small} sets of homomorphisms from finite path approximations into the target graph, where smallness is witnessed by a bounded odd-walk condition on vertex projections. The key lemma that largeness is preserved under the doubling operation is established via the First Reflection Theorem, replacing the original transfinite construction with a single Borel reflection argument. The continuous homomorphism from the canonical graph $\mathbb{L}_c$ into the target is then obtained as a limit of shrinking families of copies, in direct analogy with Bernshteyn's proof for $G_0$.

We investigate the descriptive complexity of order convergence in separable Banach lattices. While uniform convergence is Borel and $σ$-order convergence is known to be ${\bf Δ}^1_2$, it is unclear in general when $σ$-order convergence is analytic. We introduce a transfinite hierarchy of weakenings of the classical Fatou property, indexed by countable ordinals, and show that it provides a complete structural classification of this definability problem. For a separable Banach lattice $X$, we prove that the following are equivalent: (i) the set of decreasing positive sequences with infimum zero is Borel; (ii) $σ$-order convergence is analytic; and (iii) $X$ satisfies the $α$-Fatou property for some countable ordinal $α$. We further establish that the hierarchy is proper: for every countable ordinal $α$ there exists a separable Banach lattice with a countable $π$-basis that fails to be $α$-Fatou, but is $β$-Fatou for some $β>α$. Thus the Borel definability of order convergence is governed by a canonical ordinal invariant intrinsic to the lattice, and the descriptive complexity can be arbitrarily high below $ω_1$. These results identify projective complexity as a genuine structural invariant in Banach lattice theory.

We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge reductions of games to arrive at smaller, solved sub-games for closed subspaces of the positions. This process makes it much easier to prove that there are moves from N-positions to P-positions, and can also be used in some cases to show that there are no moves between P-positions. This process is suitable for all variations of the game Nim whose rule sets form a simplicial complex. We rephrase Simplicial Nim as Set Nim SN($n,A$) and derive results on the structure of the P-positions in terms of invariant vectors, without needing the background and notation of simplicial complexes. We also show that invariant vectors differ from the circuits used to describe the P-positions in Simplicial Nim and that invariant vectors have wider applicability compared to circuits. We apply the Invariance Reduction Process to derive results on the P-positions of the family of Path Nim games where play is allowed on at least half the stacks, as well as for the Circular Nim games CN($n,k$) with $n=7, k=3$ and $n=8,k=3$.

Minimum dominating set is a basic local covering problem and a core task in distributed computing. Despite extensive study, in the classic LOCAL model there exist significant gaps between known algorithms and lower bounds. Chang and Li prove an $Ω(\log n)$-locality lower bound for a constant factor approximation, while Kuhn--Moscibroda--Wattenhofer gave an algorithm beating this bound beyond $\log Δ$-approximation, along with a weaker lower bound for this degree-dependent setting scaling roughly with $\min\{\log Δ/\log\log Δ,\sqrt{\log n/\log\log n}\}$. Unfortunately, this latter bound is weak for small $Δ$, and never recovers the Chang--Li bound, leaving central questions: does $O(\log Δ)$-approximation require $Ω(\log n)$ locality, and do such bounds extend beyond LOCAL? In this work, we take a major step toward answering these questions in the non-signaling model, which strictly subsumes the LOCAL, quantum-LOCAL, and bounded-dependence settings. We prove every $O(\logΔ)$-approximate non-signaling distribution for dominating set requires locality $Ω(\log n/(\logΔ\cdot \mathrm{poly}\log\logΔ))$. Further, we show for some $β\in (0,1)$, every $O(\log^βΔ)$-approximate non-signaling distribution requires locality $Ω(\log n/\logΔ)$, which combined with the KMW bound yields a degree-independent $Ω(\sqrt{\log n/\log\log n})$ quantum-LOCAL lower bound for $O(\log^βΔ)$-approximation algorithms. The proof is based on two new low-soundness sensitivity lower bounds for label cover, one via Impagliazzo--Kabanets--Wigderson-style parallel repetition with degree reduction and one from a sensitivity-preserving reworking of the Dinur--Harsha framework, together with the reductions from label cover to set cover to dominating set and the sensitivity-to-locality transfer theorem of Fleming and Yoshida.

We analyze the scaling limits (hydrodynamic limit/propagation of local equilibrium) of two particle systems in the discrete one-dimensional segment where the left boundary is in contact with a reservoir, which may stow any (finite) number of particles. These two particle systems are independent random walks and the symmetric exclusion process. At rate one a particle (if there is one there) jumps from site $1$ to a finite reservoir, and at rate $αη(0)N^{-θ}$ a particle jumps from the finite reservoir to the site $1$ (if the site $1$ is empty in the exclusion case), where $η(0)$ is the total number of particles in the reservoir at that moment and $θ\geq 0$ is a parameter whose tuning leads to a dynamical phase transition. For all values of $θ$, the hydrodynamic equation is the heat equation with Neumann b.c. at the right boundary for both systems. On the other hand, the left boundary condition depends on the chosen value of $θ$. For $θ\in [0,1)$, it is given by the Neumann b.c., which means that the deposit is asymptotically empty, acting as a barrier. For $θ\in (1,\infty)$, in the random walk scenario, it is given by a non-homogeneous Dirichlet boundary condition, which means that the reservoir becomes asymptotically infinite, acting as a heat bath, while in the exclusion scenario it is given by a homogeneous Dirichlet boundary condition, meaning that the reservoir behaves as a sink. Finally, at the critical value $θ=1$, we obtain a non-local Dirichlet boundary condition relating the value at zero to the total mass of the system, which is additionally non-linear in the exclusion scenario. As a by-product of these results, we find an equivalence between solutions to the heat equation with Wentzell boundary conditions and solutions to the heat equation with certain non-local Dirichlet boundary conditions related to the total mass of the system.

The increasing frequency and intensity of wildfires poses severe threats to the secure and stable operation of power grids, particularly one that is interspersed with renewable generation. Unlike conventional contingencies, wildfires affect multiple assets, leading to cascading outages and rapid degradation of system operability and stability. At the same time, the usual precursors of large wildfires, namely dry and windy conditions, are known with high confidence at least a day in advance. Thus, a coordinated decision-making scheme employing both day-ahead and real-time information has a significant potential to mitigate dynamic wildfire risks in renewable-rich power systems. Such a scheme is developed in this paper through a novel stochastic preventive-corrective cut-set and stability-constrained unit commitment and optimal power flow formulation that also accounts for the variability of renewable generation. The results obtained using a reduced 240-bus system of the US Western Interconnection demonstrate that the proposed approach increases the resilience of power systems across multiple levels of wildfire risks while maintaining economic viability.

The increasing, high-risk interactions between vehicles and vulnerable micromobility users, such as e-scooter riders, challenge vehicular safety functions and Automated Driving (AD) techniques, often resulting in severe consequences due to the dynamic uncertainty of e-scooter motion. Despite advances in data-driven AD methods, traffic data addressing the e-scooter interaction problem, particularly for safety-critical moments, remains underdeveloped. This paper proposes a pipeline that utilizes collected on-road traffic data and creates configurable synthetic interactions for validating vehicle motion planning algorithms. A Social Force Model (SFM) is applied to offer more dynamic and potentially risky movements for the e-scooter, thereby testing the functionality and reliability of the vehicle collision avoidance systems. A case study based on a real-world interaction scenario was conducted to verify the practicality and effectiveness of the established simulator. Simulation experiments successfully demonstrate the capability of extending the target scenario to more critical interactions that may result in a potential collision.

Even when large-scale, site-specific three-dimensional (3D) subsurface models are used to represent spatial variability, multi-dimensional ground response analyses (GRAs) at downhole array sites continue to exhibit amplitude discrepancies between simulated theoretical transfer functions (TTFs) and recorded empirical transfer functions (ETFs), with ETFs at the Delaney Park Downhole Array (DPDA) showing notably lower amplitudes at the fundamental frequency (f0). This discrepancy suggests greater apparent attenuation from wave scattering and destructive interference than is currently captured in multi-dimensional GRAs. However, most prior studies assume vertically propagating shear-wave input, neglecting inclined and azimuthally varying wavefields. This study evaluates the effects of inclination and azimuth in 2D and 3D GRAs at DPDA to assess whether non-vertical wave incidence improves agreement with observed ETFs. Two approaches for modeling inclined waves, the Input Lag Method (ILM) and the Inclined Domain Method (IDM), are compared, with ILM found to be more effective and computationally efficient for large-scale models. A parametric study using ILM shows that inclination angles up to 15° produce only minor reductions in TTF amplitudes near f0, with limited improvement in ETF agreement. Larger inclination angles reduce amplitudes but introduce systematic shifts in f0 to higher frequencies that are not observed in the ETFs. Azimuthal variation in 3D GRAs has a relatively minor effect, primarily influencing trough amplitudes while leaving f0 and higher-mode peaks largely unchanged.