We consider the multilinear polytope, defined as the convex hull of the feasible region of a lifted binary polynomial optimization problem. We define a relaxation in an extended space for this polytope, which we call the complete edge relaxation. The complete edge relaxation is stronger than several well-known relaxations of the multilinear polytope, including the standard linearization, the flower relaxation, and the intersection of all possible recursive McCormick relaxations. In addition, for fixed-degree binary polynomial optimization problems, the case of primary practical interest, the complete edge relaxation is of polynomial size and is computationally efficient in practice. We prove that the complete edge relaxation is an extension of the multilinear polytope if and only if the corresponding hypergraph is alpha-acyclic, the most general type of hypergraph acyclicity. This is in stark contrast with the widely-used standard linearization, which describes the multilinear polytope if and only if the hypergraph is Berge-acyclic, the most restrictive type of hypergraph acyclicity. Finally, we introduce a new class of facet-defining inequalities for the multilinear polytope of alpha-cycles of length three, which serve as the generalization of the well-known triangle inequalities for the Boolean quadric polytope.

Affective polarization and political sorting drive public antagonism around climate change and other issues at the science-policy nexus. We study cross-domain spillover of incivility in public engagements with climate change and public health on Twitter and Reddit using the COVID-19 period as a case study. We find strong evidence of the signatures of affective polarization surrounding COVID-19 spilling into the climate change domain. Across different social media systems, COVID-19 content is associated with incivility in climate discussions. These patterns of increased antagonism were responsive to pandemic events that made the link between science and public policy more salient. The observed spillover activated along pre-pandemic political cleavages, specifically anti-internationalist populist beliefs, that linked climate policy opposition to vaccine hesitancy. Our findings show how affective polarization in public engagement with science becomes entrenched across policy domains, which has implications for how the public engages with and communicates about issues such as climate change and public health.

A fundamental problem in multivariate analysis is testing general linear hypotheses for regression coefficients in a multivariate linear model. This framework encompasses a wide range of well-studied tasks, including MANOVA, joint significance testing of predictors, and detection of trends or seasonal effects. Among classical approaches, Roy's largest root test is particularly effective for detecting concentrated signals, relying on the largest eigenvalue of an F matrix constructed from residual covariance matrices. However, in high-dimensional settings, these matrices often become ill-conditioned or singular, rendering the test infeasible. To address this, we propose a ridge-regularized Roy's test that stabilizes the covariance estimation via a ridge term. We establish the asymptotic Tracy-Widom distribution of the largest eigenvalue of the regularized F-matrix under a high-dimensional regime, where both the dimension and hypotheses are comparable to the sample size, assuming only finite-moment conditions. A computationally efficient procedure is developed to estimate the associated centering and scaling parameters. We further analyze the power of the test under a class of low-rank alternatives and examine the influence of the regularization parameter. The method demonstrates strong performance in simulations and is applied to data from the Human Connectome Project to assess associations between volumetric brain measurements and behavioral variables.

Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of non-commutative observables. In this work, we propose a resolution to this dilemma for quantum spin chains, by introducing an exact representation of their dynamics in terms of classical continuous-time Markov chains (CTMCs). These CTMCs effectively model the creation, annihilation, and propagation of pairs of classical particles and antiparticles. The quantum dynamics then emerges by averaging over various realizations of this classical process.

In this paper, we investigate the production of a $Ξ^0 \barΞ^0$ using $e^+e^-$ collision data at ten center-of-mass energies between 3.51 and 4.95 GeV collected with the BESIII detector at the BEPCII collider and corresponding to an integrated luminosity of 30 $\rm{fb}^{-1}$ to study the structure of baryons. The data collected by the BESIII detector are useful for the study of XYZ states, and this collaboration continues the exploration of these exotic charmonium-like states. We explore a hyperon pair produced in the electron-positron annihilation reactions. In the present paper we present the phenomenological results of our studies on the production of $Ξ^0 \barΞ^0$ in $e^+e^-$ annihilation at the BESIII detector at the BEPCII Collider. In the reaction $e^+e^- \to Ξ^0 \barΞ^0$, we consider two different contributions: one from the $D$ meson loop and the ofther from the three-gluon charmonium annihilation. We compute the total cross section of the process $e^+e^- \to Ξ^0 \barΞ^0$ including the contributions of the $D$-meson loop and three-gluon loops as well as the interference of all diagrams. As for the purely electromagnetic mechanism, large relative phases are generated for these contributions. For a large momentum transferred region we get as a byproduct a fit of the electromagnetic form factor of the $Ξ^0$ - hyperon. In this paper, in addition to the $ψ(3770)$ charmonium, we also take into account the contributions of other charmonium (-like) states, such as $ψ(4040)$, $ψ(4160)$, $Y(4230)$, $Y(4360)$, $ψ(4415)$, and $Y(4660)$. On the whole our results are in good agreement with the available experimental data.

Redundancy elimination is a key optimization direction, and loop nests are the main optimization target in modern compilers. Previous work on redundancy elimination of array computations in loop nests either targets specific computation patterns or fails to recognize redundancies with complex structures. This paper proposes RACE (Redundant Array Computation Elimination), a hash-based technique that utilizes a novel two-level scheme to identify the data reuse between array references and the computation redundancies between expressions, enabling hierarchical redundancy detection beyond pattern-specific methods. It traverses the expression trees in loop nests to detect redundancies hierarchically in linear time and generates efficient code with optimized auxiliary arrays that store redundant computation results. Furthermore, RACE supports the expression reassociation with various aggressive strategies to improve the redundancy opportunities. Experimental results demonstrate the effectiveness of RACE.

Polynomial factorisation is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity theory classifies polynomials into complexity classes based on their computational hardness. This raises a natural question: Are these complexity classes closed under factorisation? In this survey, we revisit pivotal techniques in polynomial factorisation: Hensel lifting, Newton iteration, and Lagrange inversion. These techniques have played an essential role in resolving key factoring questions in algebraic complexity for more than half a century. We examine and organise the known results through the lens of these techniques, discussing their underlying mathematical equivalence while reflecting on how their applications vary depending on the problem context. We focus on prominent algebraic complexity classes, including $\text{VP}$ (circuits of polynomial size and degree), its closure $\overline{\text{VP}}$, the class $\text{VNP}$ (verifier circuits of polynomial size and degree), $\text{VBP}$ (polynomial-size branching programs), $\text{VF}$ (polynomial-size formulas), and $\text{VP}_{\text{nb}}$ (circuits of polynomial size and exponential degree). We also discuss bounded-depth circuits and sparse polynomials. Along the way, we highlight several unresolved open problems.

Decision-making is the process of selecting an action among alternatives, allowing biological and artificial systems to navigate complex environments and optimize behavior. While neural systems rely on neuron-based sensory processing and evaluation, decision-making also occurs in organisms without a centralized organizing unit, such as the unicellular slime mold \textit{Physarum polycephalum}. Unlike neural systems, P. polycephalum relies on rhythmic peristaltic contractions to drive internal flows and redistribute mass, allowing it to adapt to its environment. However, while previous studies have focused on the outcomes of these decisions, the underlying mechanical principles that govern this mass relocation remain unknown. Here, we investigate the exploration process of P. polycephalum confined by blue light into polygonal shapes up to its escape. While the escape occurs along the longest axis of the polygones, independent of confinement shape, the exploration process prior to escape extends protrusions almost everywhere around a shape boundary. We find protrusions to align with the direction of peristaltic contraction waves driving mass relocation. Mapping out contraction modes during exploration in detail we observe an ongoing switching between different dominant principle contraction modes. Only over the course of time does the organism ultimately settle on the contraction mode most efficient for transport, which coincides with the escape. Thus, we find that only harsh environmental confinement triggers optimal behaviour which is reached by long time re-organization of the flow patterns. Our findings provide insights into the mechanics of decision-making in non-neuronal organisms, shedding light on how decentralized systems process environmental constraints to drive adaptive behavior.

This article establishes a Riemann-Hilbert correspondence in rigid-analytic geometry. We construct an explicit solution functor and prove that it is fully faithful on Ardakov-Wadsley's coadmissible D-cap-modules. For vector bundles with flat connection, our functor is canonically identified with Scholze's horizontal sections functor.

Motivated by the theory of p-adic differential equations and p-adic geometric representation theory, we introduce overconvergent variants of Fontaine's classical period rings. In particular, we study the positive overconvergent de Rham period ring, which is the stalk of the structure sheaf of the analytic Fargues-Fontaine curve at infinity. Our main results include the computation of the Galois cohomology of these overconvergent period rings, as well as the cohomology of the associated period sheaves and period structure sheaves.

Exhaustively identifying all loopholes in the Bell test is demanding for interpreting the results of the relevant experiments, since any loophole if not closed can be catastrophic to our understanding of the nonlocal structure of quantum mechanics. Despite a series of recent Bell experiments that claim to be free of loopholes, a united framework with a sound base is still missing to fully recognize all potential loopholes in these experiments, as verified by a recent experiment that has pinned down a detection loophole of a new type in Bell analysis. Here, we reveal another loophole previously unknown in the Bell test through a local theory developed here on the basis of a new mathematical concept of high-dimensional vectorial probability, quantified as a vector with interesting but hidden geometry in the probability space. We show that the statistical property of the stochastic events generated for the Bell test can be well described by the local theory, and, in particular, the correlations of these events that violate Bell's theorem can be closely connected to the geometry of the vectorial probability. To close the loophole, theoretical investigations are highly recommended to search for the statistical nature of the stochastic events in quantum measurements that can distinguish the predictions of quantum mechanics and those of the local theory.

We prove the existence of infinite-volume IDLA forests in $\mathbb{Z}^d$ , with $d \geq 2$, based on a multi-source IDLA protocol. Unlike IDLA aggregates, the laws of the IDLA forests studied here depend on the trajectories of particles, and then do not satisfy the famous Abelian property. Their existence is due to a stabilization result (Theorem 1.1, our main result) that we establish using percolation tools. Although the sources are infinitely many, we also prove that each of them play the same role in the building procedure, which results in an ergodicity property for the IDLA forests (Theorem 1.2).

The Release-Acquire (RA) semantics and its variants are some of the most fundamental models of concurrent semantics for architectures, programming languages, and distributed systems. Several steps have been taken in the direction of testing such semantics, where one is interested in whether a single program execution is consistent with a memory model. The more general verification problem, i.e., checking whether any allowed program run is consistent with a memory model, has still not been studied as much. The purpose of this work is to bridge this gap. We tackle the verification problem, where, given an implementation described as a register machine, we check if any of its runs violates the RA semantics or its Strong (SRA) and Weak (WRA) variants. We show that verifying WRA in this setup is in O(n5 ), while verifying the RA and SRA is PSPACE complete. This both answers some fundamental questions about the complexity of these problems, but also provides insights on the expressive power of register machines as a model.

It is assumed that superheavy dark matter particles (SHDM, $ϕ$) with $\mathcal{O}$(ZeV) mass may decay to relativistic milli-charged particles (MCPs, $χ$) via a channel $ϕ\toχ\barχ$. The downward-going MCPs passing through the atmosphere can be searched for at the Pierre Auger observatory (Auger). The massless hidden photon model is taken for MCPs to interact with nuclei, so that we evaluated the numbers and fluxes of expected MCPs at Auger assuming 14 years of Auger data. The hybrid data of Auger was fitted with the flux of UHE MCPs exceeding GZK-cutoff energy. Then the corresponding upper limits on $ε^2$ are calculated at 90\% C. L.. These results indicate that MCPs can be searched for with $ε^2\gtrsim 3.73\times10^{-5}$ at Auger, when $m_ϕ=2\times10^{21}$ eV and $τ_ϕ=10^{27}$ s. And a new region of 10$^{10}$ eV < $m_{MCP}$ < 10$^{11.6}$ eV and $ε$ > $2.02\times10^{-2}$ is ruled out in the $m_{MCP}$-$ε$ plane with 14 years of Auger data. These results indicate potential existence of MCPs and SHDM in the Universe.

The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP). However, the number of variables and constraints in such a formulation grows exponentially with the number of measurements, rendering it intractable for large measurement sets. In this work, we circumvent this problem by transforming the SDP into a hierarchy of linear programs that compute upper and lower bounds on the incompatibility robustness with a complexity that grows polynomially in the number of measurements. The hierarchy is guaranteed to converge and it can be applied to arbitrary measurements -- including non-projective POVMs (Positive Operator-Valued Measures) -- in arbitrary dimensions. While convergence becomes impractical in high dimensions, in the case of qubits our method reliably provides accurate upper and lower bounds for the incompatibility robustness of sets with several hundred measurements in a short time using a standard laptop. We also apply our methods to qutrits, obtaining non-trivial upper and lower bounds in scenarios that are otherwise intractable using the standard SDP approach, although such bounds are significantly looser than the ones obtained in the qubit case. Finally, we show how our methods can be used to construct local hidden state models for states (i.e., to prove that a state cannot lead to steering under any possible local measurements), or conversely, to certify that a given state exhibits steering; for two-qubit quantum states, our approach is comparable to, and in some cases outperforms, the current best methods.

Lévy processes, known for their ability to model complex dynamics with skewness, heavy tails, and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most Lévy processes, whether in parametric or non-parametric settings, remains a significant challenge. In this work, we present a novel Bayesian non-parametric inference framework for inferring the Lévy measures of subordinators and normal variance-mean (NVM) processes within a linear state space model. A flexible random measure, the Independent Gamma-scaled Dirichlet Process (IGSDP), is introduced, for which the well-known Gamma process is a special case, leading to tractable conditional distributions for inference about both Lévy measures. We further show that in the Gamma process special case, conjugacy can be achieved for hyper-parameter inference. An explicit characterization of the parameter contour for NVM processes is provided, enabling an identifiable parameterization of the model for effective Markov Chain Monte Carlo algorithms in posterior inference. The method is demonstrated on both synthetic and tick-level (high-frequency) financial datasets.

We investigate exact solutions of the Einstein-Maxwell equations with the cosmological constant where the source of the gravitational field consists of a magnetic field and dust. In particular, we restrict our study to the case of Bianchi type III models. All these solutions either start with a singularity and then expand, or they are initially collapsing and end at a singularity. We discuss the physical meaning of the parameters appearing in the metrics and examine the possible subcases and the relative importance of the dust and the magnetic field as we approach the singularity.

Using Hamiltonian encoding to inject an input into parameterized quantum circuits (PQCs), the output of the PQC can be written as truncated Fourier series. In recent years, the expressivity of PQCs was established as the number of frequencies contained in this Fourier series. While this concept has also been applied to other quantum machine learning (QML) paradigms, a clear notion of expressivity for temporal information processing with quantum systems is still lacking. Here, we introduce such a notion to the field of quantum reservoir computing (QRC). We analytically derive an expression for the readouts showing that the output of a QRC can be interpreted as a multi-dimensional Fourier series. We give a formula for the growth of expressivity induced by the sequential information injection, which we corroborate with numerical simulations, calculating explicitly the number of multi-dimensional output functions which can be generated from the readouts. Our results show that the specific interplay between system size, input encoding, and memory time gives rise to a boundary on the system size beyond which it is obstructive to further increase the reservoir size in extreme scrambling systems. We propose a recipe for determining this maximal system size for a given QRC setup.

The halide double perovskite Cs$_2$AgBiBr$_6$ has been proposed as a potential replacement for organic halide perovskites for photovoltaic applications. Further investigation of its dielectric response, optical properties and structural stability is thus warranted. Cs$_2$AgBiBr$_6$ exhibits a well-documented structural phase transition at 120 K but indications for an additional lower temperature ($\sim$40 K) phase transition have also been reported. On the basis of measurements of the specific heat capacity, temperature dependent powder X-ray diffraction, low frequency capacitance, and infrared reflectivity we clarify the previously reported splitting of phonon modes in the Raman spectrum at $\sim$40 K as due to a subtle structural phase transition from the tetragonal I4/m structure to a monoclinic $P12_1$/$n1$ crystal structure. The infrared active vibrational modes are experimentally investigated in the three structural regimes. In the cubic structure at room temperature the four IR active modes are observed at 135,$\sim$95, 55, and $\sim$25 cm$^{-1}$, as the symmetry reduces to tetragonal a minute splitting of these modes is expected, however below 40 K an additional mode is observed indicating a further reduction in symmetry.

Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally obtained solutions and compare them to numerically exact calculations in quantum critical systems. We demonstrate that interpreting the cost functional as an integral permits the deployment of iterative quadrature schemes, thereby reducing the required number of measurements by more than an order of magnitude even in the presence of noise. We further show that a modified ansatz captures deviations from the Bisognano-Wichmann form in lattice models, improves convergence, improves trainability and provides a cost-function-level diagnostic for quantum phase transitions. Finally, we establish that a low cost value does not by itself guarantee convergence in trace distance. Nevertheless, it faithfully reproduces degeneracies and spectral gaps, which are essential for applications to topological phases.

Integrated plasmonics is advancing rapidly, enabling a wide range of functionalities to be incorporated onto a single chip. Applications span information processing, computation, quantum sensing, and dark-matter detection. This progress has driven the development of integrated non-reciprocal devices, which are essential for preventing unwanted feedback that can degrade system performance. While non-reciprocal devices have been realized in edge magnetoplasmon materials via classical interference effects, their operation is often limited by the input power range. Here, we demonstrate that topological circulators utilizing asymmetric coupling offer improved input power range, isolation, and insertion loss. In this configuration, we demonstrate the coupling between a chiral edge magnetoplasmonic resonator and a pair of LC resonators is well described by an effective non-Hermitian two-site Hatano-Nelson model with asymmetric directional couplings, resulting in nonreciprocal behavior. The coherent photon-plasmon interaction enables a circulator with up to 50 dB of isolation across a broad range of excitation power. These results suggest that magnetic topological insulators provide a promising platform for realizing asymmetric non-Hermitian couplings at radio frequencies and for exploring regimes of strong directional suppression and possible exceptional-point physics. More broadly, they highlight the potential of topological-material-based microwave devices for future integration with superconducting quantum information platforms.

The global energy landscape is undergoing a transformative shift towards renewable energy and advanced storage solutions, driven by the urgent need for sustainable and resilient power systems. Isolated offshore communities, such as islands and offshore platforms, which traditionally rely on mainland grids or diesel generators, stand to gain significantly from renewable energy integration. Promising offshore renewable technologies include wind turbines, wave and tidal energy converters, and floating photovoltaic systems, paired with a storage solution like battery energy storage systems. This paper introduces a renewable energy microgrid optimizer (REMO), a tool designed to identify the optimal sizes of renewable generation and storage resources for offshore microgrids. A key challenge in such models is accurately accounting for battery degradation costs. To address this, the REMO model integrates a deep neural network-based battery degradation (DNN-BD) module, which factors in variables like ambient temperature, charge/discharge rates, state of charge, depth of discharge and battery health. Simulations on six test regions demonstrate that the REMO-DNN-BD approach minimizes lifetime energy costs while maintaining high reliability and sustainability, making it a viable design solution for offshore microgrid systems.

We consider twisted eigenvalues $λ_{1}^{g}(Ω)$, defined as the minimum of the Rayleigh quotient of functions in $H^1_{0}(Ω)$ that are orthogonal to a given function $g\in L^2_\text{loc}(\mathbb R^d)$. We prove an isoperimetric inequality for $λ_1^g(Ω)$, which provides a uniform bound on twisted eigenvalues -- not only with respect to the set $Ω$ (an open bounded set of $\mathbb R^d$) -- but also in relation to the orthogonality function $g$. Remarkably, the lower bound is uniquely attained when $Ω$ is the union of two disjoint balls of specific radii, and when the function $g$ in the orthogonality constraint is of bang-bang type, i.e., constant on each ball. As a consequence, we obtain a continuous 1-parameter family of optimal sets -- each being the union of two disjoint balls -- that interpolates between the optimal shapes of the first two Dirichlet eigenvalues of the Laplacian. This new isoperimetric inequality offers fresh perspectives on well-established results, such as the Hong-Krahn-Szeg{o} and the Freitas-Henrot inequalities. Notably, only for these two particular inequalities our proof avoids reliance on Bessel functions, suggesting potential extensions to nonlinear settings. However, extending the inequalities to the general case requires proof strategies that rely on properties of Bessel functions.

The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant franchise metaphor. The latent tables simplify the expression of the posterior and allow for the implementation of Gibbs sampling algorithms to approximately draw posterior samples. However, managing their assignments can become computationally expensive, especially as the size of the dataset and the number of levels increase. In this work, we identify a prior for the concentration parameter of the hierarchical Dirichlet process that (i) induces a quasi-conjugate posterior distribution, and (ii) removes the need for tables, leading to more interpretable expressions for the posterior, with both a scalable and an exact algorithm to sample from it. Remarkably, this construction extends beyond the Dirichlet process, leading to a new framework for defining normalized hierarchical random measures and a new class of algorithms to sample from their posteriors. The key analytical tool is the independence of multivariate increments, that is, their representation as completely random vectors.

Building on the techniques behind the recent progress on the 3-term arithmetic progression problem \cite{KelleyM2023strong}, Kelley, Lovett, and Meka \cite{KelleyLM2024-nof} constructed the first explicit 3-player function $f:[N]^3 \rightarrow \{0,1\}$ that demonstrates a strong separation between randomized and (non-)deterministic NOF communication complexity. Specifically, their hard function can be solved by a randomized protocol sending $O(1)$ bits, but requires $Ω(\log^{1/3}(N))$ bits of communication with a deterministic (or non-deterministic) protocol. We show a stronger $Ω(\log^{1/2}(N))$ lower bound for their construction. To achieve this, the key technical advancement is an improvement to the sifting argument for grid norms of (somewhat dense) bipartite graphs. In addition to quantitative improvement, we qualitatively improve over \cite{KelleyLM2024-nof} by relaxing the hardness condition: while \cite{KelleyLM2024-nof} proved their lower bound for any function $f$ that satisfies a strong two-sided pseudorandom condition, we show that a weak one-sided condition suffices. This is achieved by a new structural result for cylinder intersections (or, in graph-theoretic language, the set of triangles induced from a tripartite graph), showing that any small cylinder intersection can be efficiently covered by a sum of simple ``slice'' functions.

For a positive integer $k$ and an ordered set of $n$ points in the plane, define its \textit{k-sector ordered Yao graphs} as follows. Divide the plane around each point into $k$ equal sectors and draw an edge from each point to its closest predecessor in each of the $k$ sectors. We analyze several natural parameters of these graphs. Our main results are as follows: I Let $d_k(n)$ be the maximum integer so that for every $n$-element point set in the plane, there exists an order such that the corresponding $k$-sector ordered Yao graph has maximum degree at least $d_k(n)$. We show that $d_k(n)=n-1$ if $k=4$ or $k \ge 6$, and provide some estimates for the remaining values of $k$. Namely, we show that $d_1(n) = Θ( \log {n} )$; $\frac{1}{2}(n-1) \le d_3(n) \le 5\left\lceil\frac{n}{6}\right\rceil-1$; $\frac{2}{3}(n-1) \le d_5(n) \le n-1$; II Let $e_k(n)$ be the minimum integer so that for every $n$-element point set in the plane, there exists an order such that the corresponding $k$-sector ordered Yao graph has at most $e_k(n)$ edges. Then $e_k(n)=\left\lceil\frac{k}{2}\right\rceil\cdot n-o(n)$. III Let $w_k$ be the minimum integer so that for every point set in the plane, there exists an order such that the corresponding $k$-sector ordered Yao graph has clique number at most $w_k$. Then $\lceil\frac{k}{2}\rceil \le w_k\le \lceil\frac{k}{2}\rceil+1$. All the orders mentioned above can be constructed effectively.

We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.

This paper develops a scalable min-max multi-gradient descent framework for multi-objective transportation problems with competing objectives and high-dimensional constraints. Unlike linear scalarization, which may conceal trade-offs behind pre-specified weights, and evolutionary heuristics, which can be inefficient in highly constrained feasible regions, the proposed method directly uses gradient information to construct a balanced common descent direction. At each iteration, it solves a constrained min-max problem that minimizes the worst directional derivative across all objectives, thereby prioritizing the least-improved objective and promoting robust progress. With linear constraints, the direction-finding problem reduces to a linear program. We prove the existence of the proposed direction, establish its relationship with Pareto criticality, and analyze convergence for a fixed-step update. Under a dense worst-case interior-point model, the linear-programming formulation has the same asymptotic complexity order as classical quadratic-programming-based steepest descent, while providing a distinct and more balanced direction-selection mechanism. Experiments on two transportation applications demonstrate its effectiveness. For a physics-informed car-following model, the method removes the need for manually fixed loss weights, achieves the best average predictive accuracy, reduces average RMSE by approximately /(5.81/%/) relative to the baseline, and substantially lowers variability across random seeds. For a multi-criteria traffic assignment problem balancing user equilibrium and system optimum, it produces stable common descent directions and performs favorably on large networks. Overall, the framework provides a robust, scalable, and theoretically grounded gradient-based approach to multi-objective transportation optimization.

Organizations often rely on statistical algorithms to make socially and economically impactful decisions. We must address the fairness issues in these important automated decisions. On the other hand, economic efficiency remains instrumental in organizations' survival and success. Therefore, a proper dual focus on fairness and efficiency is essential in promoting fairness in real-world data science solutions. Among the first efforts towards this dual focus, we incorporate the equal opportunity (EO) constraint into the Neyman-Pearson (NP) classification paradigm. Under this new NP-EO framework, we (a) derive the oracle classifier, (b) propose finite-sample based classifiers that satisfy population-level fairness and efficiency constraints with high probability, and (c) demonstrate statistical and social effectiveness of our algorithms on simulated and real datasets.

We present a novel methodology for analyzing the optimal promotion in the Bass model for the spreading of new products on networks. For general networks with $M$ nodes, the optimal promotion is the solution of $2^M-1$ nonlinearly-coupled boundary-value problems. On structured networks, however, the number of equations can be reduced to a manageable size which is amendable to simulations and analysis. This enables us to gain insight into the effect of the network structure on optimal promotions. We find that the optimal advertising strategy decreases with time, whereas the optimal boosting of peer effects increases from zero and then decreases. In low-degree networks, it is optimal to prioritize advertising over boosting peer effects, but this relation is flipped in high-degree networks. When the planning horizon is finite, the optimal promotion continues until the last minute, as opposed to an infinite planning horizon where the optimal promotion decays to zero. Finally, promotions with short planning horizons can yield an order of magnitude higher increase of profits, compared to those with long planning horizons.