Directly accessing energy fluctuations in interacting quantum many-body systems remains a long-standing challenge, especially far from equilibrium. Here we show that in scale-invariant quantum gases with SO$(2,1)$ dynamical symmetry, the amplitude of the breathing mode provides a direct and quantitative probe of energy fluctuations. We establish an exact and universal relation between the oscillation amplitude and the energy fluctuation, with a dimensionless ratio fixed solely by the Bargmann index $k$, which labels the irreducible representation of the underlying SU$(1,1)$ algebra and thereby determines the structure of the many-body spectrum and dynamics. As a consequence, this relation is fully dictated by symmetry and remains independent of microscopic details and excitation protocols. Furthermore, we show that the excitation of breathing-mode states follows a universal statistical distribution governed by a single parameter, independent of the specific driving protocol. Our findings demonstrate that energy fluctuations, typically encoded in the many-body spectrum, can be directly accessed through collective dynamics, offering a symmetry-based route to probe nonequilibrium energy statistics in strongly interacting quantum systems.

Integrating renewable generation, hydrogen production, and renewable ammonia (RA) synthesis into power-to-ammonia (P2A) systems creates interactions across electricity and hydrogen markets. Limited operational flexibility, however, places RA at a disadvantage at the Nash equilibrium (NE). Recent advances in ammonia synthesis reactor design enable hot standby (HSB) operation, improving flexibility but introducing integer decision variables that complicate market equilibrium analysis. To address this challenge, we develop a potential game model and derive a convergent ε-approximate equilibrium via an iterative best-response approach. Case studies show that HSB reduces RA's reliance on hydrogen purchases and increases its profit by 20.14%. More importantly, HSB shifts the market equilibrium toward a more mutually beneficial outcome.

We study two conjectures posed in the analysis of Boolean functions $f : \{-1, 1\}^n \to \{-1, 1\}$, in both of which, the Majority function plays a central role: the "Majority is Least Stable" (Benjamini et al., 1999) and the "Non-Interactive Correlation Distillation for Erasures" (Yang, 2004; O'Donnell and Wright, 2012). While both conjectures have been refuted in their originally stated form, we obtain a nearly tight characterization of the noise parameter regime in which each of the conjectures hold, for all $n \ge 5$. Whereas, for $n=3$, both conjectures hold in all noise parameter regimes. We state refined versions of both conjectures that we believe captures the spirit of the original conjectures.

The all-to-all momentum coupling of the Hubbard interaction makes interacting lattice models generically unsolvable. In many settings, however, from Peierls instabilities to Moiré superlattice physics, the low-energy behavior is dominated by scattering at a few characteristic wavevectors. We exploit this by constructing a momentum-space clustering scheme that retains only a chosen subset of interaction channels. Our scheme can be considered a generalization of twist-averaged boundary conditions. In proving this, we also prove that our scheme can be considered as a generalization of Hatsugai-Kohmoto (HK) models, and all versions of the HK model previously considered in the literature arise as special cases. This shows that the surprising phenomenological success of HK models arises from their correspondence to the finite-site Hubbard model. In particular, the recently introduced "Momentum-Mixing HK" model corresponds to a specific choice of clustering limit, which is equal to the original finite-site Hubbard model with twist-averaged boundary conditions. Our scheme becomes particularly powerful when a spatially varying potential selects the dominant momentum channels. We demonstrate this on the one-dimensional analogue of interacting moiré systems: the Aubry-André-Hubbard model. We show that for sufficiently strong onsite potential, clusters as small as two sites can recover the ground state energy to below 1% error relative to DMRG benchmarks. This establishes that physically motivated momentum-space truncations can yield accurate low-energy descriptions at feasible computational cost, opening a path toward tractable interacting models of Moiré systems in two dimensions. Code for reproducing all numerical results is available at https://github.com/chainik1125/decomposing-hubbard.

We develop a numerical scheme for solving the advection equation of $\mathbb{S}^2$-valued functions of real variables, which models the time-evolution of a $\mathbb{S}^2$-valued mapping on the real line by a known velocity field. The idea is to extend the semi-Lagrangian method for the linear scalar advection equation. We first construct the backward flow map between two adjacent time levels and then interpolate the discrete ordered data of $\mathbb{S}^2$. To handle $\mathbb{S}^2$-functions which have kinks or sharp discontinuity in their components, we incorporate the \textit{Spherical Essentially Non-Oscillatory} (SENO) interpolation method, which effectively reduces the spurious oscillations in high-order reconstructions. We will show multiple examples to demonstrate the accuracy and effectiveness of the proposed algorithm for the partial differential equation of $\mathbb{S}^2$-functions.

Gamma-ray bursts (GRBs) have traditionally been classified by their prompt emission duration and spectral hardness, with short GRBs (sGRB; $\lesssim2 \ \rm{s}$) originating from compact object mergers and long GRBs (LGRB; $\gtrsim2 \ \rm{s}$) from massive star core-collapse. Recent kilonova (KN) associations with long-duration GRBs have challenged this standard picture. We analyze the host galaxies of nine GRBs with associated kilonova candidates at $z<0.6$, including five sGRB-KNe and four LGRB-KNe. Using both parametric and non-parametric modeling of the host light distributions, we investigate the progenitor environments of these events and test whether their hosts show evidence for recent galaxy interactions that could favor dynamical formation channels or isolated pathways following merger-driven star formation episodes for neutron star binaries. We find that five of the nine hosts display tidal features that show they have likely undergone recent mergers, suggesting that merger-driven, dynamical formation pathways may contribute in some systems. We find no clear morphological distinction between sGRB-KN and LGRB-KN hosts as both populations span a wide range of morphologies, including ellipticals, spirals, and interacting systems with tidal features. Multi-Sérsic modeling of the host light profiles further shows that host-normalized offsets inferred from single-Sérsic fits can be overestimated when the transient is associated with a specific subcomponent of a complex host light profile. These results highlight the importance of decomposing host morphology into physically relevant components when interpreting GRB environments and galactocentric offsets.

We identify shell-like tidal structures in flattened haloes that appear stream-like under different projections. This projection dependence demonstrates how changes in the host halo directly impact the formation and classification of tidal debris, highlighting the challenges of relying solely on visual inspection. To address this, we employ our clustering-based classification framework to systematically categorise tidally disrupted satellites into stream-like and shell-like structures. Our host consists of a static three-component MW model with flattening introduced along the z-axis NFW dark halo. We consider three halo shapes: spherical q = 1, extremely oblate q = 0.5, and prolate q = 1.5. We evolve three subhalo types: a highly radial massive subhalo favouring shell formation, an eccentric orbit leading to stream formation, and an intermediate orbit. We first classify the tidal structures visually using face-on and edge-on density projections of the 3D position distribution. This reveals shell-like and stream-like formations across face-on projections, while edge-on views lead to contrary classifications in some cases. To resolve these ambiguities, we apply the classification method developed in our earlier work, analysing structures in ordered density, radial, and energy-angle space. We further investigate the spatial dispersion of stream-like structures and the rate at which core density reduces as the flattening parameter varies. Our results demonstrate that halo shape variations affect tidal debris formation and classification, as well as the spatial dispersion and core density evolution of streams. These findings offer new insights into the role of dark matter halo geometry in shaping tidal structure formation and its contribution to hierarchical galaxy formation and evolution.

A particular type of linear optical multiport, the Grover four-port, has previously been shown to couple the spatial symmetry of a photon to its direction of travel. It is shown here that use of a nonstandard choice of qubit, based on symmetry, allows Grover four ports to act as compact, low-resource deterministic linear optical controlledNOTgates, with no post-selection or ancilla measurements required. This approach allows programmable devices, made from Grover multiports in combination with other standard optical components, that can implement multiple different one-, two-, and three-qubit gates, including the Fredkin and Toffoli gates.

Electromagnetic transient (EMT) models are index-2 differential-algebraic equations when they include certain topologies and are formulated with modified nodal analysis. Such systems are difficult to numerically integrate, a challenge that is currently addressed by applying model approximations or reformulating with index-reduction algorithms. These algorithms exist in general-purpose software tools, but their reliance on symbolic representation makes them computationally prohibitive for large network-wide EMT models. This paper derives and presents two modular index-reduced subsystem models that allow EMT models to be integrated with standard solvers, without approximations or symbolic algorithms. Both subsystems include a transformer, one isolated and one machine-coupled. We measure the computational performance of constructing EMT models with up to 1152 buses using the custom subsystem models and the symbolic algorithms. The custom approach reduces memory usage and runtime of model construction by several orders of magnitude compared to the general approach, shifting the bottleneck from construction to integration.

Partially miscible ganglia trapped in a porous medium evolve through Ostwald ripening, driven by differences in interfacial curvature. In practice, ganglia can span multiple pores and undergo discrete capillary events - invasion, snap-off, retraction, fragmentation, coalescence, and dislocation - that alter their topology and induce local flow. Existing pore-network models (PNMs) for ripening are limited to single-pore ganglia, assume idealized pore shapes, and operate under quasi-static conditions that preclude flow. We present an image-based pore-network model (iPNM) that removes these limitations. Unlike existing PNMs, iPNM requires no idealization of pore shapes, as the effect on capillarity is encoded locally in curvature-saturation curves computed via the pore-morphology method. iPNM couples two-phase flow, solute transport, and Ostwald ripening within a unified framework. We first verify iPNM against a prior quasi-static PNM, then validate it against recent high-resolution microfluidic experiments of hydrogen ripening in a sandstone-patterned micromodel over 15-24 days at 40C and 80C. Good agreement is obtained without adjustable parameters. Comparison with a continuum model shows that while macroscopic saturation is captured by both approaches, iPNM uniquely resolves population statistics, individual ganglion curvatures, and pre-equilibrium ripening dynamics within a representative elementary volume. Its computational efficiency over direct numerical simulation makes it suitable for guiding the development of improved theories of ripening in confined geometries.

Context: Corporate education is a strategic investment in the software industry, but little is known about how different professional profiles perceive these initiatives. Objective: To investigate whether sociodemographic and professional variables influence the perception of quality and effectiveness of corporate training in Software Engineering (SE). Method: Non-parametric significance tests were applied to data from a survey with 282 Brazilian professionals, crossing 27 perception items with 9 sociodemographic variables (gender, age, education level, state, experience, professional level, company size, area of work, and nature of participation), totaling 243 combinations. Results: Of the 243 combinations tested, only 35 showed statistical significance. Training mandatoriness was the dominant factor, affecting 24 of 27 items. Length of experience revealed a non-linear descriptive pattern with a low-engagement zone between 3 and 6 years. Differences by area of work indicated an expressive gap in soft skills training for advanced technical roles. Personal profile variables and company size produced no relevant significant differences. Conclusion: Personal profile variables do not determine the perception of quality and effectiveness, while professional trajectory variables (experience, level, area of work) produce localized differences. The voluntariness of participation remains a determining factor, in line with the literature. The absence of gender differences in a sample with 23\% women suggests that barriers operate before training, in access and representation, not during the learning experience.

Grover's algorithm searches for data satisfying a desired condition in an unstructured database. This algorithm can search a space of size $N$ in $\sqrt{N}$ queries, thereby achieving a quadratic speedup. However, within the Grover oracle circuit that is repeatedly applied, the quantum state preparation circuit -- which embeds database information into quantum states -- suffers from a large gate count and circuit depth. To address this problem, we propose reducing the quantum state preparation circuit by reordering the database. Specifically, we consider a Quantum Read-Only Memory (QROM), where data are assigned to addresses, and assume that the address assignment of data can be freely permuted. By applying Exclusive Sum-of-Products (ESOP) minimization to the resulting truth table, we reduce the quantum circuit. Although the resulting circuit logic differs from the original, the state preparation remains correct in the sense that every desired datum is encoded at some address. Furthermore, we propose a proxy metric that estimates circuit size without compilation, and combine it with simulated annealing to efficiently find a near-optimal data ordering. In our experiments, an exhaustive search over all orderings for databases of size $N=8$ reveals that circuit size varies by up to approximately a factor of two depending on the ordering, demonstrating the utility of reordering. Compared with applying ESOP minimization without reordering, simulated annealing reduces the circuit size by approximately 30\% and yields circuits close to optimal. For $N=64$ and $128$, simulated annealing is shown to discover smaller circuits compared with random search.

The purpose of this paper is to investigate the coherent feedback $H^\infty$ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.

We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions. Applied to the two-vertex model, this framework yields analytical bounds on the evolution of the total area, proving the existence of a non-vanishing lower bound at finite times. These findings, previously observed only numerically, suggest a bounce-like behavior and highlight the usefulness of these variables for the study of more general configurations. As a second result, the canonical variables are shown to simplify the gauge-fixing procedure, generalizing previous results restricted to two-vertex models with four links.

For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter bifurcation diagrams. From any such point there issues a curve of grazing bifurcations, where the limit cycle born in the Hopf bifurcation hits the switching surface. For Filippov systems, these are usually grazing-sliding bifurcations whose local dynamics are dictated by piecewise-linear maps. In general, these maps have many independent parameters and extraordinarily rich dynamical behaviour. We show that for three-dimensional Filippov systems only a two-parameter family of piecewise-linear maps is relevant, because sliding motion induces a loss of dimension, and the stability of the limit cycle is degenerate at the Hopf bifurcation. We derive explicit formulas for the two parameters in terms of quantities associated with the boundary Hopf bifurcation, and perform a comprehensive numerical analysis to characterise the attractor of the family, which may be chaotic. The results are illustrated with a pedagogical example, a pest control model, and a model of a food chain with threshold-based harvesting. To evaluate the parameters, we use a formula for the linear term of the discontinuity map associated with grazing-sliding bifurcations. In this paper we present a new, simpler derivation of this formula for $n$-dimensional systems based on displacements from a virtual counterpart.

Extrachromosomal DNA (ecDNA) represents one of the most pressing challenges in cancer biology: circular DNA structures that amplify oncogenes, evade targeted therapies, and drive tumor evolution in ~30% of aggressive cancers. Despite its clinical importance, computational ecDNA research has been built on broken foundations. We discover that existing benchmarks suffer from circular reasoning -- models trained on features that already require knowing ecDNA status -- artificially inflating performance from AUROC 0.724 to 0.967. We introduce ECLIPSE, the first methodologically sound framework for ecDNA analysis, comprising three modules that transform how we predict, model, and target these structures. ecDNA-Former achieves AUROC 0.812 using only standard genomic features, demonstrating for the first time that ecDNA status is predictable without specialized sequencing, and that careful feature curation matters more than complex architectures. CircularODE captures ecDNA's unique stochastic dynamics through physics-constrained neural SDEs, achieving r > 0.997 on experimental data via zero-shot transfer. VulnCausal applies causal inference to identify therapeutic vulnerabilities, achieving 80x enrichment over chance and 3.7x higher validation than standard approaches by filtering spurious correlations. Together, these modules establish rigorous baselines for an emerging application area and reveal a broader lesson: in high-stakes biomedical ML, methodological rigor -- eliminating leakage, encoding domain physics, addressing confounding -- outweighs architectural innovation. ECLIPSE provides both the tools and the template for principled computational oncology.

Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.

In this paper we analyze Nitsche's method for the stationary Boussinesq system with Navier's slip and a nonlinear boundary condition. Our analysis of the formulation establishes the robustness of a finite elements scheme in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using fixed-point theorems under a standard smallness assumption on the data. We also provide optimal convergence rates for the approximation error. Furthermore, the efficiency and reliability of residual-based a posteriori error estimators are established. We validate our theory through several numerical tests.

Chalcogenide perovskites are an emerging class of photovoltaic absorbers offering stable, lead-free structures and promising optoelectronic properties. To date, the literature on chalcogenide perovskites has focused primarily on fully inorganic systems such as \ce{BaZrS3}. This contrasts with the halide perovskites, for which hybrid organic-inorganic systems exhibit record performance. In this work, we assess the viability of hybrid chalcogenide perovskite absorbers using first-principles calculations. We screen a wide range of monovalent and divalent organic cations within the A-site to evaluate their electronic, optical, and thermodynamic properties. Our analysis reveals that the majority of candidates are structurally unstable; however, we identify the hydrazinium cation (\ce{N2H6^{2+}}) as a unique candidate that maintains a stable perovskite structure. Specifically, we identify \ce{N2H6ZrSe3} as the most promising candidate, exhibiting a quasi-direct band gap of \SI{1.31}{eV} and a theoretical maximum efficiency of \SI{24.5}{\percent} for a \SI{200}{\nm} thin film. This study represents the first comprehensive computational report on hybrid chalcogenide perovskites, opening new avenues for the development of Earth-abundant photovoltaic materials.

Decentralized Gaussian process (GP) methods offer a scalable framework for multi-agent scalar-field estimation by replacing a centralized global model with multiple local models maintained by individual agents. A team of agents operates through overlapping domains; neighboring agents generally produce inconsistent distributions over shared regions. This paper investigates whether these inter-agent posterior discrepancies can be systematically exploited to improve team-level predictive performance and answers this question positively through a novel decentralized intersection data-sharing and assimilation protocol. Specifically, each agent constructs neighbor-specific packets from its local GP together with the geometry of the overlap between subdomains and selectively assimilates information received from neighboring agents to improve consistency of its posterior over the shared regions. The proposed architecture preserves locality in both computation and communication, supports decentralized neighbor-to-neighbor data assimilation, and allows local GP models to evolve cooperatively across the network without requiring the exchange full packet exchange or centralized inference.

Let $K$ be a convex body in the 3-dimensional Euclidian space $\mathbb{E}^3$ and let $N,S$ in the boubdary bd$K$ of $K$, $N\not=S$. Suppose that the support plane $Π_S$ of $K$ at $S$ is unique. For every point $x$ in bd$ K$, different than $N$, we define the stereographic projection $Ψ:\textrm{bd}K\backslash \{N\} \rightarrow Π_S$ of $x$ onto $Π_S$ as the point $y:=L(N,x)\cap Π_S$. It is a well known property of the sphere $\mathbb{S}^2$ in $\mathbb{E}^3$ that the stereographic projection maps circles onto circles (see \cite{Hilbert} pag. 248). In this work we investigate what geometric elements determines that this property is fulfilled. Here we demonstrate that the following two properties of a convex body $K\subset \mathbb{E}^3$ in terms of the stereographic projection characterize the sphere in $\mathbb{E}^3$: (1) The cones defined by the sections of $K$ and the point $N$ are axially symmetric (that is, they are invariant under a rotation by an angle of $π$). (2) given a section $K_Γ$ of $K$, the rotation that leaves the cone defined by $K_Γ$ and $N$ invariant is such that it maps $K_Γ$ into a homothetic figure to $Ψ(K_Γ)$ by a homothety with center of homothety at $N$. An important element in the proof of the main theorem of this work is a cha\-racterization of the circle based on a geometric property, which will be called the stereographic property. It is worth highlighting that the stereographic projection defined on the sphere maps circles onto circles is intimately linked to the conditions (1) and (2) and the stereographic property of the circle.

Genomic language models (gLMs) have transformed computational biology, achieving state-of-the-art performance across genomic tasks. Yet a fundamental question threatens the foundation of this success: do these models learn the mechanistic principles governing gene regulation, or do they merely exploit statistical shortcuts? We introduce the Mechanistic Invariance Test (MIT), a rigorous 650-sequence benchmark across 8 classes with scrambled controls that enables clean discrimination between compositional sensitivity and genuine positional understanding. We evaluate five gLMs spanning all major architectural paradigms (autoregressive, masked, and bidirectional state-space models) and uncover a universal failure mode. Through systematic mechanistic probing via AT titration, positional ablation, spacing perturbation, and strand orientation tests, we demonstrate that apparent compensation sensitivity is driven entirely by AT content correlation (r=0.78-0.96 across architectures), not positional regulatory logic. The failures are striking: Evo2-1B and Caduceus score regulatory elements at incorrect positions higher than correct positions, inverting biological reality. All models are strand-blind. Compositional effects dominate positional effects by 46-fold. Perhaps most revealing, a simple 100-parameter position-aware PWM achieves perfect performance (CSS=1.00, SCR=0.98), exposing that billion-parameter gLMs fail not from insufficient capacity but from fundamentally misaligned inductive biases. Larger models show stronger compositional bias, demonstrating that scale amplifies rather than corrects this limitation. These findings reveal that current gLMs capture surface statistics while missing the positional grammar essential for gene regulation, demanding architectural innovation before deployment in synthetic biology, gene therapy, and clinical variant interpretation.

NBA franchise management is not a sequence of independent tasks, but a single dynamic control problem in which roster construction, cash-flow discipline, media strategy, external market shocks, and player-health uncertainty interact over time. Using the New York Knicks as a case study, this paper develops a unified decision architecture for franchise management under competitive, financial, and regulatory constraints. The core layer is formulated as a rolling-horizon stochastic mixed-integer program augmented with distributionally robust optimization and conditional value-at-risk constraints, so that long-run franchise value can be optimized while downside exposure remains explicitly controlled. On top of this core layer, we construct coordinated modules for transaction execution, league-expansion shock transmission, media-rights regime transition, and injury-triggered re-optimization. This integrated design reframes multiple managerial mechanisms inside one research problem: how should an NBA franchise allocate resources and update decisions when performance objectives and commercial objectives are jointly determined under uncertainty? The manuscript is organized around problem formulation, model architecture, empirical validation, robustness analysis, and managerial interpretation.

We study complete non-compact manifolds of positive scalar curvature, with a focus on how curvature decay is constrained by topology at infinity. Our first main result shows that topological linking at infinity forces polynomial decay of scalar curvature on manifolds of weakly bounded geometry. This result provides a conceptual generalization of recently discovered examples of metrics with quadratic scalar curvature decay. Building on this decay mechanism, we develop an obstruction theory localized at the ends of non-compact manifolds. Using $μ$--bubble exhaustions together with the analysis of stable minimal hypersurfaces and index theory, we obtain qualitative obstructions to uniformly positive scalar curvature on individual ends.

Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs--Runge oscillations that result from traditional numerics. These approaches face a delicate balance in achieving sufficiently regular solutions without dissipating fine-scale features, such as turbulence or acoustics. Recent work by Cao and Schäfer introduces information geometric regularization (IGR), the first inviscid regularization method for fluid dynamics. IGR replaces shock singularities with smooth profiles of adjustable width, without dissipating fine-scale features. This work provides a strategy for the practical use of IGR in finite-volume-based numerical methods. We illustrate its performance on canonical test problems and compare it against established approaches based on limiters and Riemann solvers. Results show that the finite volume IGR approach recovers the expected solutions in all cases. Across canonical benchmarks, IGR achieves accuracy competitive with WENO and LAD shock-capturing schemes in both smooth and discontinuous flow regimes. The IGR approach is computationally light, with meaningfully fewer memory accesses and arithmetic operations per time step.

In this paper, we study Vekua-type operators associated with diagonal operators on compact Lie groups. Characterizations of global hypoellipticity and global solvability properties are presented on classes of Vekua-type operators with constant coefficients. We also present sufficient conditions in order to get global solvability for a class of Vekua-type operators with non-constant coefficients.

The local H theorem is shown to hold for the Enskog equation with a modified Enskog factor proposed by the authors [Phys. Rev. E 111, 065108 (2025)]. This is a stronger statement than the global one in the same paper and has been obtained along the lines of Mareschal et al. [Phys. Rev. Lett. 52, 1169-1172 (1984)] for the modified (or revised) Enskog equation. Furthermore, it is shown that the local H theorem also holds for the corresponding Enskog-Vlasov equation.

An association scheme is called amorphic if every possible fusion of relations gives rise to another association scheme. In earlier work, we showed that if an association scheme has at most one relation that is neither strongly regular of Latin square type nor strongly regular of negative Latin square type, then it must be amorphic. We now construct non-amorphic $d$-class association schemes in which precisely two relations are not strongly regular of Latin square type or strongly regular of negative Latin square type, for any $d \geq 4$. We also raise the question whether different types of strongly regular graphs can coexist in an association scheme. Among some other results, we show that if one of the relations is a lattice graph, then any other strongly regular relation in the scheme must be of Latin square type.

The increasing interconnection of power systems through AC and DC links enables energy storage units to access multiple electricity markets yet most existing arbitrage models remain limited to singlemarket participation This gap restricts understanding of the economic value and operational constraints associated with crossborder storage operation To address this an optimal multiregion energy storage arbitrage model is developed for a gridscale battery located at one end of an interconnector linking two distinct dayahead markets The formulation incorporates battery capacity and ramping limits converter and interconnector losses and marketspecific buying and selling prices Using disjunctive linearization of nonlinear terms this work exactly reformulates the multiregion energy arbitrage optimization as a mixedinteger linear programming problem The proposed formulation ensures that the battery either charges or discharges from all participating energy markets simultaneously at any given time Case studies using eight years of BelgianUK price data demonstrate that multiregion participation can increase arbitrage revenue by more than 40% compared to local energy arbitrage operation only while also highlighting the negative impact of interconnector congestion on achievable gains The results indicate that crossborder market access substantially enhances storage profitability while considering the cycle of battery and that the proposed formulation provides a computationally efficient framework for evaluating and operating storage assets in interconnected power systems Finally a pseudoefficiency term is introduced to improve battery utilization by discarding less profitable charging and discharging battery cycles

We have evaluated fluctuations in neutrino fluxes caused by solar gravity (g) modes based on the analysis of linear adiabatic oscillation of a spherically symmetric star. We find that the first-order fluctuation is zero due to geometrical cancellation. We still find that the second-order fluctuation is non-zero, which consists of time-varying and non-time-varying components. The amplitude of the time-varying component is small (${\sim} 10^{-9}$ in relative difference, in the case of $\mathrm{^{8}B}$ neutrino) and well below the detection limits of the current neutrino detectors, when we assume the g-mode amplitude parameter $A_{n \ell}$ to be $10^{-5}$, which corresponds to the assumed maximum relative temperature perturbation inside the Sun. Thus, it is at the moment fair to say that detecting individual solar g-modes via the solar neutrino flux measurement is almost impossible. However, the net increase in the mean neutrino flux that originates from the non-time-varying component could be non-negligible. In particular, since $A_{n \ell}$ may be related to convection amplitude, which could change in accordance with the solar magnetic activity, the total net increase in the neutrino flux, which is proportional to $A_{n \ell}^2$, should also change with the solar activity cycle. Such a long-period variation~(${\sim} 11$~years) in the neutrino flux could thus be interpreted as evidence for a bunch of solar g-modes. Comparison of the theoretical prediction with the solar neutrino measurements by, e.g., Super-Kamiokande, may have a potential to put constraints on the theory of the excitation mechanism of solar g-modes.