Electrodermal activity (EDA) is a widely used physiological signal for assessing sympathetic nervous activity, such as arousal, stress, and pain. However, reliable decomposition into tonic and phasic components remains challenging, particularly in noisy environments and across individuals with varying signal morphologies and stimulus responses. We propose ospEDA, a novel Orthogonal Subspace Projection (OSP) based method for EDA decomposition. The method integrates (1) tonic estimation via physiologically motivated valley detection for noise robustness; (2) phasic extraction using OSP to accommodate inter subject variability; and (3) phasic driver estimation through non-negative least squares (NNLS) deconvolution with ridge regularization. We evaluated ospEDA on five real-world datasets and one simulated EDA dataset with ground-truth components, comparing its performance against six existing methods. In simulations with a 20 dB signal to noise ratio (SNR), ospEDA achieved the lowest root mean square error (RMSE) for estimated tonic (0.131) and phasic (0.132) components. Under noisier conditions (10 dB SNR), it maintained superior phasic RMSE (0.293), Pearson correlation (0.782), and R^2 (0.979) values. Furthermore, ospEDA consistently provided the highest F1 scores (0.573, 0.617, 0.638) for sympathetic nerve activity detection across 10, 20, and 30 dB SNR levels, respectively, compared to existing methods. On the real world datasets, ospEDA achieved a stimulus classification AUROC of 0.766 and consistently maintained strong effect sizes (ω^2>0.14) across all five datasets. Overall, ospEDA represents a promising framework for EDA decomposition, showing generally consistent performance and reliable phasic driver estimation under the varying noise conditions, with potential utility for real world physiological monitoring applications.

We construct an explicit normal singular affine toric variety X of dimension five over an algebraically closed field of characteristic three such that the normalized Nash blowup of X already contains an open affine subset isomorphic to X. Combined with previously known examples, this yields one-step counterexamples in every dimension greater than or equal to five and every characteristic. The characteristic-three case is the most delicate: the previously known counterexample in dimension four requires a two-step iteration of the normalized Nash blowup, and our example demonstrates that in dimension five and higher the minimal number of iterations needed to produce a loop is one.

Let $\mathrm{G}$ be a symplectic or a split orthogonal group over a local non-archimedean field $\mathrm{F}$. A prime $\ell$ is called banal with respect to $\mathrm{G}$ if it does not divide the cardinality of the $k$-points of $\mathrm{G}$, where $k$ is the residue field of $\mathrm{F}$. In this paper we show that for every banal prime $\ell$, any smooth irreducible $\overline{\mathbb{F}}_\ell$-representation of $\mathrm{G}(\mathrm{F})$ admits a lift to $\overline{\mathbb{Q}}_\ell$. We also state similar results for more general classical groups of symplectic, orthogonal or unitary type. As an application we prove Howe-duality in the strongly banal case for symplectic-orthogonal or unitary dual pairs.

We develop the first theoretically-efficient algorithm for maintaining the maximal independent set (MIS) of a graph in the parallel batch-dynamic setting. In this setting, a graph is updated with batches of edge insertions/deletions, and for each batch a parallel algorithm updates the maximal independent set to agree with the new graph. A batch-dynamic algorithm is considered efficient if it is work efficient (i.e., does no more asymptotic work than applying the updates sequentially) and has polylogarithmic depth (parallel time). In the sequential setting, the best known dynamic algorithms for MIS, by Chechik and Zhang (CZ) [FOCS19] and Behnezhad et al. (BDHSS) [FOCS19], take $O(\log^4 n)$ time per update in expectation. For a batch of $b$ updates, our algorithm has $O(b \log^3 n)$ expected work and polylogarithmic depth with high probability (whp). It therefore outperforms the best algorithm even in the sequential dynamic case ($b = 1)$. As with the sequential dynamic MIS algorithms of CZ and BDHSS, our solution maintains a lexicographically first MIS based on a random ordering of the vertices. Their analysis relied on a result of Censor-Hillel, Haramaty and Karnin [PODC16] that bounded the ``influence set" for a single update, but surprisingly, the influence of a batch is not simply the union of the influence of each update therein. We therefore develop a new approach to analyze the influence set for a batch of updates. Our construction of the batch influence set is natural and leads to an arguably simpler analysis than prior work. We then instrument this construction to bound the work of our algorithm. To argue our depth is polylogarithmic, we prove that the number of subrounds our algorithm takes is the same as depth bounds on parallel static MIS.

Drone delivery is rapidly emerging as a cost-effective and energy efficient alternative for last-mile delivery. Unlike ground vehicles, a drone's energy consumption depends on its payload in addition to travel distance. This creates a unique environmental challenge for multi-stop delivery tours, as the drone's total weight, and therefore its energy consumption rate, dynamically changes after each delivery. This paper investigates a novel green drone routing problem focused on maximizing energy efficiency. Through a series of motivating examples and numerical experiments, we demonstrate that energy-aware routing leads to several counter-intuitive routing strategies that contradict traditional distance-minimization delivery: a longer route may actually consume less energy than a shorter one; separate single-customer tours can be superior to a multi-stop tour; and a heterogeneous fleet, with drones of varying sizes, can achieve greater efficiency by matching drone capacity to specific delivery demands. In the numerical study, the green routing strategy shows energy savings in 67% of the instances. For these cases, the average energy saving is 2.17%, with a maximum saving of 5.97%, compared to minimum distance routing. These findings highlight the potential for green drone routing strategies to improve the sustainability of last-mile delivery.

The electrophoresis of charged colloidal particles in fluids exhibiting odd viscosity represents a fundamental challenge in understanding transport phenomena within charge-stabilized chiral active suspensions. Here, we provide the first concept of a charged chiral active fluid, where electrokinetics is coupled to odd Stokes flow, to explore how classical results from electrophoresis in Newtonian fluids generalize in the presence of odd viscosity. In particular, we derive a general expression for the electrophoretic mobility for particles of any shape under weak external electric fields using the Lorentz reciprocal theorem for odd fluids. By applying this result to a conducting charged sphere at low zeta potentials, we obtain an exact, closed-form analytical expression for the electrophoretic mobility, valid for arbitrary values of the Debye screening length and the odd-viscosity coefficient. Similar to Newtonian fluids, we find that the electrophoretic mobility is proportional to the translational mobility of an uncharged sphere, modulated by the Henry function. However, unlike in Newtonian fluids, odd viscosity leads to directional asymmetries in the electrophoretic mobility tensor that persist even for thin electric double layers. This case contrasts significantly with a charged anisotropic particle suspended in an isotropic Newtonian fluid, where anisotropic effects would vanish under the same electrostatic-screening conditions.

In this paper, we present the results for the forward trijet production differential cross section in the gluon initiated channel at leading order in proton-nucleus collisions. The calculations are carried out within the Color Glass Condensate (CGC) effective theory, and in the dilute-dense approximation, using effective vertices for the quark and gluon propagators interacting with the small-$x$ background gluon field. We employ the covariant perturbation theory approach and disentangle the amplitudes into regular and instantaneous contributions. Our results are expressed as convolutions of multiparton color correlators of light-like Wilson lines and perturbative impact factors, organized in compact expressions in terms of the ``bare" topologies of the contributing diagrams. The gluon initiated channel receives contributions from a $q\bar{q}g$ and a $ggg$ final state. Interestingly, when considering the $ggg$ final state, we observe, for the first time, that the four-gluon vertex topology follows a structure similar to the instantaneous contributions. Furthermore, when integrating (one of) the real gluon(s) in the final state, we identify that: i) the rapidity divergence contributes to the real part of JIMWLK of the leading-order color correlator; and ii) the collinear divergence contribute to the evolution of initial-state gluon parton distribution function, and final state fragmentation functions. These results validate the dilute-dense hybrid formalism at one-loop order, and are key ingredients towards the complete next-to-leading order calculation of dijet/dihadron production in proton--nucleus collisions.

In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of a spacetime symmetry, the Weyl gauge theory (of dilatations and Poincaré symmetry). The initial physical interpretation of his theory was however short-lived and led to the downfall of Weyl geometry as a physical theory. We review how this action was re-born into a physical Weyl gauge theory of gravity. This is the only gauge theory of a spacetime symmetry with a physical gauge boson, is Weyl anomaly-free, has {\it exact} geometric interpretation, with all scales of geometric origin, and generates Einstein-Hilbert action and a positive cosmological constant in its spontaneously broken phase. A more fundamental Weyl-Dirac-Born-Infeld gauge theory action exists in Weyl geometry, that does not need a UV regularisation, of which the (geometrically regularised) Weyl gauge theory is the leading order.

Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order $\mathcal{O}((np)^3)$. In many applications, however, not all cross-dependencies between variables are relevant, suggesting that sparse covariance structures may be both statistically advantageous and practically necessary. We propose a LASSO-penalized estimation framework that induces sparsity in the Cholesky factor of the multivariate Matérn correlation matrix, enabling automatic identification of uncorrelated variable pairs while preserving positive semidefiniteness. Estimation is carried out via a projected block coordinate descent algorithm that decomposes the optimization into tractable subproblems, with constraints enforced at each iteration through appropriate projections. Regularization parameter selection is discussed for both the likelihood and composite likelihood approaches. We conduct a simulation study demonstrating the ability of the method to recover sparse correlation structures and reduce estimation error relative to unpenalized approaches. We illustrate our procedure through an application to a geochemical dataset with $p = 36$ variables and $n = 3998$ spatial locations, showing the practical impact of the method and making spatial prediction feasible in a setting where standard approaches fail entirely.

We study ballistic transport in bilayer graphene junctions and show how electrostatic gating, interlayer bias, and homogeneous strain provide complementary control over electron transmission. In the absence of strain, transport is governed by symmetry constraints that suppress transmission at specific incidence angles despite the availability of states. An interlayer bias lifts this suppression through mode mixing and opens a tunable transport gap. Within a full four-band description, we identify a distinct conductance threshold that marks the onset of propagation of the upper band inside the barrier. This produces a clear change in the slope of the conductance and serves as an experimentally accessible transport fingerprint of the multiband structure and interlayer coupling. Homogeneous in-plane strain acts as a geometric control mechanism. By reshaping the band structure in momentum space, it redistributes the angular transmission window and suppresses conductance without introducing disorder. Importantly, strain preserves the underlying symmetry-based decoupling responsible for transmission suppression while shifting its condition away from normal incidence. These results provide a unified framework for interpreting angle-resolved transport in bilayer graphene and establish multiband ballistic transport as a practical probe of band-structure geometry.

We construct a Super-Grassmannian for $n-$point functions in $\mathcal{N}=2$ to $4$ SCFT$_3$. The constraints imposed by super-conformal invariance and $R-$symmetry are completely manifest in this formalism through (operator-valued) delta functions. We test our formalism in $\mathcal{N}=2$ and $\mathcal{N}=4$ AdS$_4$ super Yang-Mills theories. In the $\mathcal{N}=2$ case, for instance, we reproduce the four-gluon correlator using the four-point scalar correlator as input. For $\mathcal{N}=4$, we construct the super-operator in two distinct ways. In one approach, the super-operator has a lowest component of spin zero and includes all states up to spin two. In the other approach, we build the super-operator in a CPT self-conjugate manner, which contains only operators with spin zero, spin half, and spin one mimicking flat space $\mathcal{N}=4$ SYM super-field constructions. The latter construction is particularly interesting, as it matches directly with the $\mathcal{N}=4$ SYM amplitudes in the flat space limit, thereby demonstrating the non-triviality and usefulness of our framework. It is interesting to note that the $R-$symmetry group enhances from $SO(\mathcal{N})$ to $SU(\mathcal{N})$ in the flat space limit.

We compute the excitation function of the global $Λ$ polarization in semicentral heavy-ion collisions within a Core--Corona framework, where the interaction region is described as a dense core and a dilute corona separated by a critical value of the participant density. An important ingredient in the model are the intrinsic polarization functions in each of the two regions. These are computed from a field-theoretical approach where the vortical motion of the medium is included in an effective fermion propagator, which we derive explicitly. The interactions in the core and the corona are transmitted by suitable mediators at finite temperature and baryon chemical potential; gluons for the former and $σ$-mesons for the latter. The temperatures and baryon chemical potentials are related to the collision energies along the chemical freeze-out curve. By allowing the cross section for $Λ$ production in the nuclear environment to take on values below the nucleon-nucleon threshold cross section, the calculation describes the lowest energy polarization data point. For the centralities corresponding to the experimental data, we find that the contribution from the corona is the dominant one and that a lifetime, and correspondingly a volume of this region, which becomes larger for the smaller energies due to stopping, is an essential ingredient in the calculation. Overall, the model provides a good description of the excitation function across the full experimental range and predicts a robust maximum near $\sqrt{s_{NN}}\sim$ 3 GeV that remains stable under reasonable variations of the freeze-out curve and the proton-proton $Λ$ production threshold to account for subthreshold production in a nuclear environment.

The Dirac quantization of spherically symmetric gravity coupled to a scalar field in Loop Quantum Gravity remains unresolved, mainly because of the difficulty in maintaining a consistent constraint algebra at the quantum level. One possible way to overcome this obstruction is to fix the gauge by coupling the system to a physical clock. However, this approach requires careful control of the consistency of the gauge-fixed theory and factor-ordering ambiguities. Here, we address these issues by analyzing whether the gauge-fixed quantization reproduces the well-known results for the quantization of a black hole in vacuum using the Dirac method. This requires a treatment valid throughout the outer region of the black hole, where the asymptotic approximations considered in previous studies do not hold true.

Observations of temperate sub-Neptunes suggest active chemical environments, finding evidence of both water vapor and photochemical hazes in their atmospheres. Hazes formed in water-rich atmospheres are chemically complex, containing molecules relevant to prebiotic chemistry, and their strong optical opacity obscures sought-after gaseous molecular absorption features. While many studies have investigated haze formation and properties across diverse atmospheric conditions, little is known about the evolution of these hazes in their environment once formed. In particular, interactions with water can drive hydrolysis reactions that alter haze composition and optical behavior, affecting our interpretations of habitability and observational spectroscopy. Here, we perform hydrolysis experiments on haze analogs of temperate water-rich exoplanets and measure their optical properties. Transmittance measurements from 0.4 to 28.5 $μ$m reveal changes in key functional groups after hydrolysis, along with an overall increase in sample absorbance. We report the derived optical constants for use in observational and modeling studies. Through synthetic atmospheric spectra, we demonstrate the need for physically informed haze optical properties in models, consistent with expected planetary conditions. The increased absorptivity and high imaginary refractive index of hydrolyzed hazes almost completely flatten features in model spectra, presenting critical consequences for atmospheric characterization of water-rich sub-Neptunes.

We study the three-dimensional stochastic electron magnetohydrodynamics (EMHD) system with fractional dissipation on the torus, driven by Stratonovich transport noise acting through divergence-free first-order operators. The noise generates an Itô correction while preserving the transport structure of the Hall nonlinearity. Since the Hall term contains one more derivative, in the stochastic setting it must be controlled together with commutators arising from the transport operators. We develop a high-order Sobolev energy method based on Littlewood--Paley analysis and refined commutator estimates, which yields uniform bounds for Galerkin approximations in $H^s$ with $s > \tfrac{5}{2}$ together with suitable time regularity. Using stochastic compactness and identification of limits, we construct martingale solutions for initial data in $L^2(Ω; H^s)$. Pathwise uniqueness follows from cancellations in the Hall term combined with a stochastic Grönwall argument. An application of a Yamada--Watanabe type result then yields local pathwise well-posedness and the existence of maximal pathwise solutions.

The theory of uninterpreted functions is a key modeling tool for systems with unknown or abstracted components. Some domains such as systems biology impose further restrictions regarding monotonicity on these components, requiring specific inputs to have a consistently positive or negative effect on the output. In this paper, we tackle the model inference problem for biological systems by applying the theory of uninterpreted functions with monotonicity constraints. We compare the performance of naive quantified encodings of the problem and the performance of the existing approach based on eager quantifier instantiation, which is based on the fact that a finite set of quantifier-free monotonicity lemmas is sufficient to encode the monotonicity of uninterpreted functions. Additionally, we consider a lazy variant of the approach that introduces the monotonicity lemmas on demand. We evaluate the SMT-based approach to model inference using a large collection of systems biology benchmarks. The results demonstrate that the instantiation-based encodings significantly outperform quantified encodings, which typically struggle with large function arities and complex instances. As the key result, we show that our approach based on SMT with uninterpreted functions and monotonicity constraints significantly outperforms state-of-the-art domain-specific tools used in systems biology, such as the ASP-based Bonesis and the BDD-based AEON.

Multifunctional materials can exhibit emergent behavior from the coupling of two or more different properties. For example, coupling between magnetic and ferroelectric order enables electrical control of the magnetic state, enabling for example magnetoelectric memory or logic devices that combine the nonvolatility of magnetic order with the energy efficiency of voltage control. Magnetic iron garnets have outstanding magnonic and magnetooptical properties making them valuable in a range of technologies, but they have not been successfully incorporated into thin film two-phase magnetoelectric nanocomposites. Taking advantage of heterogeneously patterned substrates, this work demonstrates the engineering of garnet-perovskite composites in which both phases are polymorphs with the same composition but dramatically different structures and properties. Applying an electric field to the perovskite phase modulates the magnon dispersion and magnetooptical response of the garnet, opening a path to voltage-controlled garnet devices.

Free-space optical communications (FSOC) are a key enabling technology for future high-capacity space-based networks. Particularly, the backbone of global communication relies on intersatellite optical links. In a previous study, the authors proposed a method to mitigate the impact of transmitter pointing jitter by using a superposition of orthogonally polarized Gaussian and higher-order Laguerre-Gaussian (LG) beams. In this study, we experimentally characterize the proposed system using a spiral phase plate (SPP) to generate higher-order annular beams. We demonstrate that such superpositions can be reliably generated in a realistic optical setup, quantify the associated beam-shaping errors and losses, and assess their impact on intersatellite optical communication performance. It is found that the proposed beam-shaping approach can still yield power savings on the order of 20% compared to a conventional Gaussian beam under the considered conditions.

In this article, we study nonlinear nonlocal equations with coercive gradient nonlinearity of the form \[ (-Δ_p)^s u(x) + H(x, \nabla u) = f, \] where $f$ is Lipschitz continuous. We show that any viscosity solution $u$ is locally Lipschitz continuous, provided \[ p \in \left(1, \frac{2}{1-s}\right) \cup (1, m+1). \] We also establish Hölder continuity of subsolutions. Furthermore, in the case $f=0$ and $H$ is independent of $x$, we prove that the equation admits only the trivial solution in the class of bounded solutions, for all $m, p \in (1,\infty)$.

This paper establishes (set) identification results in a dynamic dyadic network formation model with time-varying observed covariates, lagged local network statistics, and unobserved heterogeneity in the form of fixed effects. Our framework accommodates observed-covariate homophily, transitivity through common friends, second-order or indirect-friend effects, and more general local subgraph statistics within a single dynamic index model. The analysis combines two complementary ways of handling fixed effects: inequalities that integrate out time-invariant dyad heterogeneity by treating each dyad as a short panel, and signed-subgraph comparisons that difference out fixed effects algebraically through intertemporal variation within each dyad. We show that the semiparametric identifying restrictions can be sharpened using either or both of the following assumptions: (i) error distribution is serially independent with a known distribution, (ii) pairwise fixed effect takes the form of additive individual fixed effects. Combining (i) and (ii) under i.i.d. logit shocks, we obtain an exact conditional logit representation and provide sufficient conditions for point identification.

We have simulated a one dimensional capillary fiber bundle model with fracking events while acted between a pressure gradient across the system. The hydraulic fractures are incorporated through a decreasing nature of capillary thresholds for each tube that replicates an increment in pore spaces due to fracking. An increment in flow rate is evident through the evolved rheology we observe in our study. Analytical approaches for certain limits are adopted to understand the rheology which matches well with the numerical results. The overall hydraulic power increases with pressure gradient as well as with the percentage decrease in capillary threshold due to a single event, defines as the fracking amplitude. This combined with the early onset of linear Darcy flow increases the quality of the fluid extraction. We successfully point towards an optimum pressure gradient at which the fracking events are most effective - maximum change in fluid extracting with a maximum rate. We observed that it is possible to extract the information regarding the change from non-linear to Darcy flow due to fracking as well as the optimum pressure for fluid extraction through local flow profile, something which in much superior from the point of view of computational cost. The former is done by correlating the maximum fluctuation in local flow profile to the onset of Darcy flow. The later is done through the relative change in Shannon entropy with respect to the fracking amplitude that points towards the pressure associated with the maximum fluid extraction criterion.

This study evaluates the dissolution of the supported electrocatalysts Pd/C, PdSn/C, PdNb/C, and PdFe3O4/C during ethanol oxidation reaction for ADLFC applications. A scanning flow cell (SFC) coupled to an inductively coupled mass spectrometry (online ICP-MS) is used to assess the dissolution stability in a broad potential window. Accelerated stress tests with and without ethanol are developed using a rotating disk electrode (RDE) with dissolution products analysis by ex-situ ICP-MS. Potential profiles simulating those experienced by the catalyst during regular fuel cell operation were used. Sn and Fe catalysts demonstrate improved activity and stability compared with the material with Pd alone. For these reasons, PdSn/C and PdFe3O4/C are suitable for ADLFC applications. Severe Nb dissolution destabilizes Pd, increasing its leaching. This work demonstrates that while additional metals and oxides can improve the alcohol oxidation kinetics of Pd, these additives' dissolution stability must already be considered at the catalyst design stage.

Motivated by increasing wireless capacity demands and 6G advancements, the newly defined Frequency Range 3 (FR3, 7.125-24.25 GHz), also known as the upper mid-band, has emerged as a promising spectrum candidate. It offers a balance between the large bandwidth potential of millimeter-wave bands and the favorable propagation characteristics of sub-6 GHz bands. As a result, the upper mid-band presents a strong opportunity to enhance both coverage and capacity, particularly for 6G systems and Cellular Vehicle-to-Base Station (C-V2B) communications. Harnessing this potential, however, requires addressing key technical challenges through accurate and realistic channel modeling across diverse urban environments, including Suburban, Urban, and HighRise Urban scenarios. To this end, we employ a ray-tracing tool to characterize downlink propagation and enable detailed channel modeling for reliable C-V2B links. We evaluate data rate performance across FR1 (sub-6 GHz), FR3, and FR2 (mmWave) bands using antenna array configurations designed for different urban environments. The results show that, under equal aperture sizes, FR3 achieves higher data rates than FR2 for cell-edge User Equipment (UEs) in both interference-free and full-interference scenarios, indicating that the additional array gain at mmWave is insufficient to fully compensate for the severe experienced path loss. Integrating one-hand-grip pedestrian UEs model into ray tracer shows that transitioning from vehicular to pedestrian UEs results in negligible differences in coverage probability (about 1\%--3\%) across all frequencies, with the minimum differences observed in FR3, particularly at 8.2 GHz.

We explore the potential of the Mu2e experiment to probe the lepton-flavor-violating process $μ^- e^- \to e^- e^-$ in a muonic atom within a simplified axion-like particle (ALP) framework featuring flavor-violating $e$-$μ$ couplings and a flavor-diagonal pseudoscalar coupling to electrons, which also allows for possible invisible ALP decays into a dark sector. We compute the ALP-mediated contribution to the transition rate and show that, at fixed couplings, the branching ratio increases for lighter mediators and scales as $(Z-1)^3$, favoring heavier nuclei. We compare the model against constraints from $μ\to eγ$, $μ\to 3e$, $μ\to eγγ$, $μ\to e+\mathrm{inv}$, and muonium-antimuonium conversion, as well as from the anomalous magnetic moments of the electron and muon. Additional astrophysical and beam-dump limits on the electron coupling are also discussed. A key result is that $Δa_e$ provides one of the most stringent probes of the parameter space and, in the global scan, excludes the largest fraction of sampled points. After applying the laboratory constraints used in the scan, the viable branching ratio for $μ^- e^- \to e^- e^-$ in aluminum drops to at most $\mathcal{O}(10^{-20})$, while the resonant region $2m_e<m_a<m_μ-m_e$ is much more heavily suppressed. The highest achievable values are closely tied to $\mathcal{B}(μ\to 3e)$ near its current limit, indicating that the upcoming Mu3e experiment will explore the most promising region relevant for this muonic-atom signal. Our analysis shows that, although a light ALP can parametrically enhance $μ^- e^- \to e^- e^-$ at fixed couplings, existing bounds -- especially $Δa_e$, $μ\to 3e$, $μ\to eγ$, and muonium oscillations -- severely limit the observable rate.

This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning game utilizing the cross-log-likelihood ratio to naturally model multi-agent spatial conflicts, such as congestion avoidance. By applying a generalized multivariate Cole-Hopf transformation, we decouple the associated non-linear Hamilton-Jacobi-Bellman (HJB) equations into a system of linear partial differential equations. This reduction enables the efficient, grid-free computation of feedback Nash equilibrium strategies via the Feynman-Kac path integral method, effectively overcoming the curse of dimensionality.

We study the mixing time of the Rook's Walk Markov chain on a $d$-dimensional chess board of side length $n\geq 3$, where a rook moves by first selecting an axis uniformly at random and then selecting a new position along that axis uniformly from among the $n-1$ unoccupied alternatives. Our method is to lump the state space of the Rook's Walk by Hamming distance, yielding a birth-death Markov chain. We prove that this lumped birth-death chain has the same mixing time as the Rook's Walk and identify all eigenvalues and eigenfunctions of the projected chain. We then combine the eigenfunction lower bound approach of Wilson (2004) with an $L^2$ upper bound to obtain new sharpened bounds on the mixing time of the Rook's Walk. As a consequence, we show that the Rook's Walk Markov chain exhibits cutoff.

We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing preferences onto analogous quantities in statistical physics, we define an effective free energy which is minimized in the grand canonical ensemble. Using a mean field approximation, we observe phase transitions in the model from disordered events in time to orderings that closely reproduce those seen in music. We then compare the range of rhythmic characteristics predicted by the model to a dataset drawn from compositions by Johann Sebastian Bach, finding generally good quantitative agreement. The results provide a new lens through which to study musical rhythm, and a method for generatively producing rhythms.

Spatial time series (STS) data are fundamental to climate science, yet conventional approaches often conflate temporal co-evolution with genuine spatial dependence, obscuring subtle but critical climatic anomalies. We introduce a Random Matrix Theory (RMT)-based framework to isolate "core spatial association" by suitably trimming out strong but routine temporal signals while preserving spatial signals. Our pipeline introduces Hilbert space filling curve technique and Bergsma's correlation measure of statistical dependence, to climate modelling. Applied to the diurnal temperature range (DTR) data of India (1951-2022), the method reveals distinct spatial anomalies shaped by topography, mesoclimate, and urbanization. The approach uncovers temporal evolution in spatial dependence and demonstrates how regional climate variability is structured by both physical geography and anthropogenic influences. Beyond the Indian application, the framework is broadly applicable to diverse spatio-temporal datasets, offering a robust statistical foundation for predictive modelling, resilience planning, and policy design in the context of accelerating climate change.

In this article, we address the lower bounds for the sums $a_f(p)+a_g(p)$ of the $p$-th Fourier coefficients of two twist-inequivalent, non-CM normalized newforms $f$ and $g$. Our main result shows that for such forms with integer Fourier coefficients, the largest prime factor of $a_f(p)+a_g(p)$ satisfies $P(a_f(p)+a_g(p)) > (\log p)^{1/14} (\log \log p)^{3/7-ε}$ for almost all primes $p$ and for any $ε> 0$. Beyond primes, we apply Brun's sieve to show that a similar phenomenon holds for a set of positive integers with natural density one. The main result is further strengthened under the Generalized Riemann Hypothesis, where we establish exponential growth for the absolute value of $a_f(p)+a_g(p)$ in terms of $p$.Additionally, we derive an interesting result related to the multiplicity one theorem, demonstrating that if the sum $a_f(p)+a_g(p)$ is small for a positive-density subset of primes, then $f$ and $g$ must be twist-equivalent by a quadratic character.

A foundational result in relativistic quantum information theory due to Peres, Scudo, and Terno, is that von Neumann entropy is not Lorentz invariant. Motivated by the "It from Qubit" paradigm, here we show that Lorentzian symmetries of quantum information emerge naturally in a pre-spacetime setting, without any reference to external variables such as position or momentum. In particular, we derive the natural action of the restricted Lorentz group $\text{SO}^+(1,3)$ on the internal degrees of freedom of a single qubit from a simple, information-theoretic principle we refer to as preservation of linear entropy. It is then shown that the Lorentz invariance of the linear entropy of a relativistic qubit is a special case of a much more general phenomenon, namely, that any spectral invariant of an operator we term the '$W$-matrix' is an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant scalar. Consequently, the linear $n$-partite quantum mutual information is shown to be an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant for all $n$-qubit states. Finally, we show that the correlation function associated with a pair of qubits in the singlet state yields the Minkowski metric on the space of qubit observables, whose symmetry group is the full Lorentz group $\text{SO}(1,3)$. In accordance with the "It from Qubit" paradigm, our results thus establish the natural emergence of relativistic spacetime structure from intrinsic properties of quantum information.