We consider a coded caching problem with multiple demands under a privacy constraint. In this problem, a server with access to \(N\) files serves \(K\) users over a shared link, and each user requests \(L\) distinct files. The privacy constraint requires that each user obtain no information about the demands of the other users. We propose a new achievable scheme for arbitrary numbers of files and users. The scheme is obtained via a transformation from a non-private coded caching scheme under uncoded placement for \(N\) files and \(K \cdot \min\{N,KL\}\) users, where each user requests one file and the demands are restricted to a subset of all possible demands. We then derive a converse bound, and the proposed scheme is shown to be order optimal within a factor of 6 of this bound.

Binary size reduction is an increasingly important optimization objective for compilers. One emerging technique is function merging, where multiple similar functions are merged into one, thereby eliminating redundancy. The SOTA approach to perform the merging is based on sequence alignment, where functions are viewed as linear sequences of instructions that are then matched in a way maximizing their alignment. In this paper, we consider a significantly generalized formulation of the problem by allowing reordering of branches within each function, subsequently allowing for more flexible matching and better merging. We show that this makes the problem NP-hard, and thus we study it through the lens of parameterized algorithms and complexity, where we identify certain parameters of the input that govern its complexity. We look at two natural parameters: the branching factor and nesting depth of input functions. Concretely, our input consists of two functions $F_1, F_2,$ where each $F_i$ has size $n_i,$ branching factor $b_i,$ and nesting depth $d_i.$ Our task is to reorder the branches of $F_1$ and $F_2$ in a way that yields linearizations achieving the maximum sequence alignment. Let $n=\max(n_1, n_2),$ and define $b, d$ similarly. Our results are as follows: - A simple algorithm running in time $2^{O(bd)} n^2,$ establishing that the problem is fixed-parameter tractable (FPT) with respect to all four parameters $b_1,d_1, b_2, d_2.$ - An algorithm running in time $2^{O(bd_2)} n^7,$ showing that even when one of the functions has an unbounded nesting depth, the problem remains in FPT. - A hardness result showing that the problem is NP-hard even when constrained to constant $d_1, b_2, d_2.$ To the best of our knowledge, this is the first systematic study of function merging with branch reordering from an algorithmic or complexity-theoretic perspective.

We searched for proton decay via $p \to e^{+}π^{0}π^{0}$ and $p \to μ^{+}π^{0}π^{0}$ in 0.401 megaton-years of data collected in all pure water detector phases of Super-Kamiokande (SK) I-V. A theoretical study predicts proton decay rates without assuming a particular grand unified theory and suggests that three-body proton decays involving two pions can have decay rates comparable to those of $p \to e^{+}π^{0}$ and $p \to μ^{+}π^{0}$. This is the first search for proton decay into a charged anti-lepton and two neutral pions in SK. One data candidate event was found for each of the two decay modes, which is consistent with the expected atmospheric neutrino background. We set lower limits on the lifetime of $τ/B(p \to e^{+}π^{0}π^{0}) > 7.2 \times 10^{33}$ years and $τ/B(p \to μ^{+}π^{0}π^{0}) > 4.5 \times 10^{33}$ years at 90 $\%$ confidence level. These limits are more than one order of magnitude higher than those of the previous experiment.

The topology of cosmic reionization, the sizes, shapes, and connectivity of ionized bubbles is a primary observable of next-generation 21\,cm experiments. We show that this topology is sensitive to the microphysics of dark matter. Self-interacting dark matter (SIDM), with cross-sections $σ/m\sim 1$--$10\;\mathrm{cm^2/g}$ motivated by small-scale structure anomalies, reduces halo gas binding energies and increases the duty cycle of ionizing-photon escape. At fixed global neutral fraction $\bar{x}_{\rm HI}$, this reshapes the source population from rare, very bright emitters to more numerous, moderate emitters, producing qualitatively different ionization morphology. We decompose the effect into two scale-dependent levers: a $2$--$3\%$ emissivity-weighted bias shift at $k\lesssim 0.1\;h/\mathrm{Mpc}$, and a factor $2$--$4$ shot-noise suppression at $k\sim 0.1$--$1\;h/\mathrm{Mpc}$. A halo-by-halo semi-numerical simulation at $128^3$ resolution confirms a $\sim 60$--$70\%$ increase in the Euler characteristic of the ionization field for $σ/m \gtrsim 2\;\mathrm{cm^2/g}$, detected at $3.8σ$ across ten independent realizations. A blowout model connecting the binding-energy reduction to the duty cycle through the ISM column density distribution yields a detection threshold at $σ/m \sim 1$--$2\;\mathrm{cm^2/g}$. The signal exceeds the CDM baryonic uncertainty band and is robust to the functional form of the emissivity parametrization. The signal persists even if gravitational heating offsets $50$--$75\%$ of the blowout enhancement, and is not diluted by unresolved low-mass sources. Velocity-dependent SIDM produces a qualitatively distinct opposite-sign bias shift. These predictions are testable with SKA1-Low, establishing reionization as a new arena for probing dark matter models complementary to dwarf galaxies and galaxy clusters.

Low-ionization metal absorption lines provide a primary probe of cool gas in and around galaxies. We confront observations of metal-line absorption in quasar spectra with predictions from the IllustrisTNG cosmological simulation in order to benchmark how well current galaxy formation models reproduce the observed circumgalactic medium (CGM) and intergalactic medium (IGM) absorption signatures. We implement two ionization prescriptions: a purely collisional model and a model including photo-ionization by a uniform ultraviolet background (UVB). Using a grid-based framework, we compute MgI, MgII and FeII column densities and construct column density probability distribution functions (PDFs) and equivalent width (EW) statistics for comparison with observations. The observational samples considered here are based on the High Resolution Echelle Spectrometer (HIRES), the Ultraviolet and Visual Echelle Spectrograph (UVES), the Sloan Digital Sky Survey (SDSS) and the Dark Energy Spectroscopic Instrument (DESI). The computed PDFs broadly reproduce the observed ones across the sampled column density range of $10^{11.4}\lesssim \text{N}\lesssim 10^{16}\ \rm{cm^{-2}}$, indicating that the simulation captures the dominant physical drivers of low-ionization absorption. We then compute the cosmic incidence of MgII systems, namely the evolution of their number with redshift $d\mathcal{N}/{dz}$. The model that includes UVB accurately produces $d\mathcal{N}/{dz}$ up to equivalent widths (EW) of $\rm W_0^{2796} < 0.6\ \mathring{A}$, consistent with low-density photo-ionized gas in the outer CGM. At high EWs of $\rm W_0^{2796} > 1\ \mathring{A}$ TNG underestimates $d\mathcal{N}/{dz}$ and fails to capture its rise toward $z\sim2$.

Volatility forecasting becomes challenging when market conditions shift and model performance varies across market states. Motivated by this instability, we develop a risk-sensitive specialist routing framework for ETF volatility forecasting. The framework uses online risk-sensitive evaluation and state-dependent gating to combine different forecasting specialists across calm and stressed market states. Using a daily panel of six ETFs under a rolling walk-forward design, we find that the strongest forecaster is regime-dependent rather than stable across all states. Relative to the rolling-best baseline, the proposed routing framework reduces high-volatility forecast loss by about 24% and underprediction loss by about 22%. These results suggest that specialist routing provides a practical forecasting architecture that adapts to changing market conditions.

We construct a gravitationally decoupled anisotropic strange star model using the minimal geometric deformation approach with a MIT bag equation of state and an additional source sector controlled by a deformation parameter $β$ and a radial perturbation scale $Ψ$ through $g(r)=\sin(Ψr^{2})$. The resulting Einstein system is consistently split into seed and $θ$-sectors and matched to an exterior Schwarzschild geometry. The model is constrained by high-mass pulsars: PSR J0740+6620 $(2.08\pm0.07\,M_\odot)$, PSR J1810+1744 $(2.13\pm0.04\,M_\odot)$, PSR J1959+2048 $(2.18\pm0.09\,M_\odot)$, and PSR J2215+5135 $(2.28^{+0.10}_{-0.09}\,M_\odot)$. It reproduces these objects with predicted radii $R \approx 11.3$--$12.9$ km. The maximum mass reaches $M_{\max} \approx 2.28\,M_\odot$ for $β= 3\times 10^{-3}$ and $Ψ\approx 0.03\,\text{km}^{-2}$, while for $β= 10^{-3}$ the configuration yields $M_{\max} \approx 2.12\,M_\odot$ with $R \approx 12.2$ km. The central density lies in $ρ_c \approx (2.4$--$3.1)\times 10^{-4}\,\text{km}^{-2}$, decreasing smoothly to $ρ_s \approx 2.0\times 10^{-4}\,\text{km}^{-2}$. The anisotropy increases from zero at the center to $Δ\approx (0.25$--$0.45)\times 10^{-4}\,\text{km}^{-2}$ near the surface, generating additional outward support that enhances compactness by $\sim 15\%$. The compactness parameter spans $C \approx 0.17$--$0.22$, safely below the Buchdahl limit, while the surface redshift reaches $z_s \approx 0.25$--$0.38$. The condition $dM/dρ_c > 0$ is satisfied throughout, confirming dynamical stability. Overall, $β$ enhances the maximum mass by up to $\sim 15\%$, while $Ψ$ introduces controlled oscillatory structure without violating observational constraints, producing stable ultra-compact stars consistent with current pulsar data.

We develop the foundations of effective ultraproducts of fields and their Galois groups using the methods of computability theory. These computability-theoretic analogs of ultraproducts are called cohesive products, since the role of an ultrafilter is played by a cohesive set. A set of natural numbers is cohesive if it is infinite and cannot be partitioned into two infinite subsets by any computably enumerable set. In particular, we investigate the way cohesive products interact with field extensions with emphasis on both finite and infinite Galois extensions, and the associated Galois groups. We study the first-order theories and definability of cohesive powers of number fields, and characterize the infinite Galois groups of cohesive powers for a large class of infinite Galois extensions. Finally, we introduce hyper-automorphisms, which are automorphisms of a cohesive power that respect non-standard field operations, and give a complete description of the hyper-automorphism groups of cohesive powers of a large class of computable Galois extensions, and use them to describe the classical infinite Galois groups of such fields.

Autoregressive generative models -- including Transformers, recurrent neural networks, classical Kalman filters, state space models, and Mamba -- all generate sequences by sampling each output from a deterministic summary of the past, producing genuinely non-Markovian observed processes. We develop a general theoretical framework based on stochastic thermodynamics for this class of architectures and introduce the entropy production, which can be efficiently estimated from sampled trajectories without exponential sampling cost, despite the non-Markovian nature of the observed dynamics. As a proof-of-concept experiment with a large language model (LLM), we evaluate the entropy production for a pre-trained Transformer-based model, GPT-2. We find that the token-level entropy production is dominated by a syntactic artifact, while the sentence-level entropy production may yield a more interpretable signal in comparisons between causally ordered and non-causal text sets. We also demonstrate the framework in the linear Gaussian case, where the model reduces to the Kalman innovation representation and the entropy production admits an analytical expression. We further show that the entropy production decomposes exactly into non-negative per-step contributions in terms of retrospective inference, and each of those terms further splits into information-theoretically meaningful terms: a compression loss and a model mismatch. Our results establish a bridge between stochastic thermodynamics and modern generative models, and provide a starting point for quantifying irreversibility in a broad class of highly non-Markovian processes such as LLMs.

We identify the Bourgain-Brezis-Mironescu pointwise limit of the nonlocal potential operator $(1-α)\, I_α(\mathcal D^αf)$, $0<α<1$, where $I_α$ denotes the Riesz potential and $\mathcal D^α$ a nonlinear fractional differential operator. Specifically, for every $f\in C_c^\infty(\mathbb R^n)$ and every $x\in \mathbb R^n$, we show that \begin{equation*} \lim_{α\to 1^-} (1-α)\, I_α(\mathcal D^αf)(x) = K_n\, I_1(|\nabla f|)(x), \end{equation*} where $K_n$ is the geometric constant appearing in the well-known Bourgain-Brezis-Mironescu formula [BBM02]. By a density argument, we further extend this result to every $f\in W^{1,1}(\mathbb R^n)$, obtaining almost everywhere convergence along subsequences.

The following hypothesis was formulated by Goreinov, Tyrtyshnikov, and Zamarashkin in \cite{goreinov1997theory}. If $U$ is $n\times k$ real matrix with the orthonormal columns $(n>k)$, then there exists a submatrix $Q$ of $U$ of size $k\times k$ such that its smallest singular value is at least $\frac{1}{\sqrt{n}}.$ Although this statement is supported by numerical experiments, the problem remains open for all $1<k<n-1,$ except for the case of $n = 4,\ k=2.$ In this work, we provide a proof for the case $k=2$ and arbitrary $n.$

Gravitational wave (GW) and short Gamma Ray Burst (sGRB) observations provide us with complementary views of compact object mergers. The paucity of binary neutron star merger (BNS) detections in the latest LIGO/Virgo/KAGRA (LVK) observing run raises the question of whether the GW merger rates are sufficient to explain the observed sGRB rate with compact object mergers alone. We investigate this connection using the latest merger rate constraints from the fourth LVK observing run (O4) and published estimates of the local sGRB rate density. For an observed sGRB rate density of $ \sim 1-7~\mathrm{Gpc^{-3}\,yr^{-1}}$, if $>55\%$ of BNS mergers can successfully launch a jet, we find that the current LVK BNS merger rate can be reconciled with a sGRB merger population containing a significant fraction of relatively wide jets with core half-opening angles $θ_j \geq 10^\circ$. Meanwhile, a narrow jet population ($θ_j \sim 6^\circ$) can only be matched with the O4 neutron star merger rate estimates for an observed sGRB rate density of $\lesssim 1~\mathrm{Gpc^{-3}\,yr^{-1}}$, which is broadly consistent with several of the latest available estimates. We also find that neutron star-black hole mergers (NSBH) are expected to be a subdominant component of the sGRB population compared to BNS mergers, and they cannot help reconcile some of the highest available sGRB rate ($ >7~\mathrm{Gpc^{-3}\,yr^{-1}}$) with the GW rate estimates. However, they can still substantially contribute to the sGRB population, comprising $\sim 6-16\%$ of it for an observed sGRB rate density of $\sim 1-3~\mathrm{Gpc^{-3}\,yr^{-1}}$. Overall, our results indicate that present GW and sGRB observations remain broadly consistent with BNS mergers as the main progenitors of sGRBs.

Blockchain assets are increasingly controlled by organizations rather than individuals. DAO treasuries, consortium wallets, and custodial exchanges rely on threshold authorization and multi-party key management, yet existing payment mechanisms still target single-user wallets, leaving no unified solution for organizational transfers. We formalize the problem of \emph{DAO-to-(anonymous)-DAO} transactions and present \textsc{Dao$^2$}, a framework that enables one threshold-controlled organization to pay another, optionally with recipient anonymity, while keeping received funds under distributed control. \textsc{Dao$^2$} combines three components: \emph{distributed key derivation} (DKD) for non-stealth child addresses, \emph{distributed stealth-address generation} (DSAG) for unlinkable one-time destinations, and \emph{threshold signatures} for authorization. For ordinary transfers, the receiver derives a non-stealth address via DKD; for anonymous transfers, it derives a stealth address via DSAG. The sender then threshold-signs the payment, and the receiver redeems the funds without reconstructing any master secret. We formally prove its security and evaluate a prototype. A complete anonymous DAO-to-DAO transaction for a typical-sized (e.g., 7-member) DAO finishes in under 27\,ms with less than 1.2\,KB of communication, and scales linearly with DAO size.

A modified set of Mosseri-Sadoc (MS) tiles tessellating 3D Euclidean space with icosahedral symmetry is introduced. The new set of tiles are embedded in dodecahedron with a threefold symmetric order. The modified Mosseri-Sadoc (MMS) tiles can be inflated by a new inflation matrix with positive eigenvalues $τ^3$ and $τ$ with the corresponding eigenvectors representing the volumes and the Dehn invariants of the tiles, respectively, where $τ=\frac{1+\sqrt5}{2}$ is the golden ratio. The MMS tiles are obtained by projection of the 4D and 5D facets of the Delone cells tiling the $D_6$ root lattice in an alternating order. It is also proved that a subset of the lattice $D_6$ projects into the dodecahedron inflated by $τ^n$ with an arbitrary integer $n$ and tiled by the MMS tiles.

In this Letter, we report a novel discovery of unique characteristics for the tidal dwarf galaxy (candidate) Holmberg IX via a multiwavelength investigation. New observations are taken for deeply mapping Hα emission and combined with archival/published data for comprehensively probing dust, gas, and stellar populations in this galaxy. We find in Holmberg IX a dearth of dust incompatible with its rich gas and metal; globally young stellar populations with prominent far-ultraviolet but deficient and marginal Hα emissions, distinct from other tidal dwarf galaxies ever known. By assuming a normal initial mass function (IMF), Holmberg IX is suggested to be born ~130 Myr ago from a bursty star formation event, which then rapidly ceased, with very few stars formed in the past ~80 Myr that demarcates a lower age limit for the galactic mainbody; current star formation occurs only in outskirts, bringing a conundrum about the reason for the recent quenching in such a gas-rich environment. Contradicting the general expectation for tidal dwarf galaxies hosting continuous star formation, the present quiescence implies Holmberg IX currently staying in a rarely-seen transient period. Without star formation continuing, Holmberg IX is likely transforming into a dwarf spheroidal galaxy, or oppositely into a(n) (ultra-)diffuse system which will probably dissolve in the end. Instead, if Holmberg IX possesses peculiar IMF and hosts low-mass, weak-Hα star formation, it is able to maintain long-term survival in its current status. On whichever evolutionary pathway in reality, Holmberg IX appears as a special case updating conventional understandings of tidal dwarf galaxies and hinting potential existence of similar analogs in the Universe.

We prove a sharp phase transition in the regularity of the extremal distribution $E^s \oplus E^u$ for $C^\infty$ volume-preserving partially hyperbolic diffeomorphisms on closed $3$-manifolds: if $E^s \oplus E^u$ is Lipschitz, then it is automatically $C^\infty$. This extends the rigidity phenomenon established by Foulon--Hasselblatt for conservative Anosov flows in dimension $3$ to the partially hyperbolic setting. This gain in regularity has several applications to rigidity problems. In particular, we study the relationship between the $\ell$-integrability condition introduced by Eskin--Potrie--Zhang and joint integrability in the conservative setting, yielding rigidity results for $u$-Gibbs measures. We also obtain several $C^\infty$ classification results for partially hyperbolic diffeomorphisms on $3$-manifolds under various assumptions.

Despite their key role in astrophysics, the binary properties of RR Lyrae stars (RRL) remain almost completely unknown since only a single RRL is confirmed as belonging to a binary system. Finding companions to RRL is difficult since most of them will be at wider orbits, given that close orbits will likely ensue mass transfer disrupting the conditions to develop stellar pulsations. These wide orbits open the possibility that RRL companions may be more easily found by high-resolution imaging. We observed 81 RRL with the speckle interferometers Zorro and 'Alopeke at the Gemini telescopes, reaching the diffraction limit of $\sim$20 mas of these 8m-class telescopes, and therefore exploring a new parameter space around RRL. We have detected 10 newly identified companions around these 81 RRL, with projected separations between 20 AU to 220 AU. An analysis of the field contamination shows that all of these detected companions are most likely gravitationally bound binaries. From these observations we can estimate an RRL binary fraction higher than 12%, ruling out a binary fraction higher than 25% at the 99% confidence level. These numbers are significantly more elevated than previous estimations which were close to a binary fraction of only 1%, albeit derived with methods exploring a different parameter space. For RRL with thin disc kinematics, we find that the binary fraction is significantly lower, at around 6%, with a single thin disc RRL having a companion out of the 16 observed. The nature of the companions, found to be stars in the lower red giant branch and upper main sequence, is also studied via the measurement of the minimum light colors of the RRL, which appears as a useful method for the search and analysis of RRL in binary systems.

In this work, we present a multi-fidelity, physics-informed framework for tritium fuel cycle modelling based on the open-source PathSim/PathView platform. Three complementary modelling approaches are demonstrated within a unified dynamic simulation environment. First, a zero-dimensional residence time model is used to reproduce the fuel cycle behaviour of an ARC-class fusion power plant, providing a baseline system-level description. Second, an intermediate-fidelity component model based on coupled one-dimensional ordinary differential equations is developed to describe tritium mass transfer in a liquid metal bubble column reactor and validated against published literature before integration into the full fuel cycle. Finally, high-fidelity multi-dimensional tritium transport models implemented using the finite element code FESTIM are coupled directly to the system model, enabling the inclusion of multi-dimensional effects, material interfaces, and complex transport phenomena. This work demonstrates how fuel cycle components of varying physical fidelity can be combined consistently within a single, open-source framework. The proposed approach enables more physically grounded fuel cycle analyses while retaining the flexibility required for system-level studies and provides a foundation for future integration with neutronics, fluid dynamics, and surrogate modelling tools.

We study a four-fold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of X$_9$ type at the Fermi energy. First, we analyze in detail its form, type and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature T$_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate Sr$_3$Ru$_2$O$_7$ which has been shown to exhibit this type of singularity.

The control and steering of light at nanometre length scales is crucial for the development of both fundamental science and nanophotonic technologies. Recent advancements have been achieved by exploiting various crystalline anisotropies, allowing for subdiffractional and diffraction-less canalisation of energy. These studies in particular benefit from stacking and twisting of 2D materials, whereas corresponding capabilities of anisotropic bulk crystals are rather unexplored. In this work, we show that ferroelastic twin walls - crystallographically perfect 2D-sheets that separate regions of differently oriented domains - in the distorted perovskite LaAlO3 provide a natural platform for broadband lateral confinement and superb canalisation of light at the nanoscale. Without fabrication processes, the electromagnetic fields localised at such walls exhibit lateral optical sizes up to 260 times smaller than the free-space wavelength. Depending on the adjacent domain orientation and frequency, the twin wall pattern preferentially concentrates or repels the electromagnetic energy, constituting a natural building block towards broadband MIR and THz nanophotonics for polaritonic circuitry.

Industrial 5G deployments using Time Division Duplex (TDD) networks face a critical challenge: existing schedulers rely on static configuration of Uplink (UL) to Downlink (DL) resource ratios, failing to adapt to dynamic asymmetric traffic demands. This limitation is particularly problematic in Industry 4.0 scenarios where traffic patterns exhibit significant asymmetry between directions and heterogeneous Quality of Service (QoS) requirements. We present FLEX, a novel QoS-aware scheduler that dynamically adjusts the UL/DL ratio in flexible TDD slots while respecting diverse QoS requirements. FLEX introduces DL buffer state estimation to prevent starvation of high-priority DL traffic, exploiting the deterministic nature of industrial traffic patterns for accurate predictions. Through extensive simulations of industrial scenarios using 5G LENA and ns-3, we demonstrate that FLEX achieves similar throughput compared to established scheduling while correctly enforcing QoS priorities in both traffic directions. For deterministic traffic patterns, FLEX maintains minimal latency overhead (less than 1 slot duration), making it particularly suitable for industrial automation applications.

Scientists have long been fascinated by magnetoreception, the innate capacity of many animals to sense and use the Earth's magnetic field for navigation. In eusocial insects like honey bees, magnetoreception has been linked to communication and foraging. However, little is known about magnetoreception's phylogenetic patterns and relationship to species traits and natural history. Here, we demonstrate that putative magnetoreception based on ferromagnetic particles is widespread across a diversity of bee species (72 out of 96 species tested), with no phylogenetic signal. We also detected such putative magnetoreception in non-bee outgroups, suggesting this magnetic capacity predates the evolution of the Anthophila. While magnetic signals were found across a diversity of life history traits, the strength of the magnetic signal varied within and between species, and increased with body size and social behavior.

We consider cross-diffusion systems describing evolution of two species $u$ and $v$ moving according to Darcy's law with the pressure law $p(s) = \frac{1}{α-1} s^{α-1}$ where $s=u+v$. One of the most challenging questions in the field is the construction of solutions to the problem in the presence of additional advection fields, without imposing any artificial structure on the fields or the initial conditions. Although advection arises naturally in these models, it breaks the symmetry of the system and prevents application of techniques developed in recent years. Here, we provide a new approach to construct solutions in one space dimension that works in a unified manner for all pressure exponents $α\in (0,\infty)$ and for arbitrary initial data. In~particular, in the regime $α> 1$, this yields the first existence result of its kind, obtained without any structural assumptions. We construct the solutions as a limit of a vanishing viscosity approximation $(u_{\varepsilon}, v_{\varepsilon})$. The main challenge is to identify the limit of $u_{\varepsilon} \, \partial_x p(s_{\varepsilon})$, where $s_{\varepsilon} = u_{\varepsilon} + v_{\varepsilon}$. The key new insight is that possible oscillations of $u_\varepsilon$ and $\partial_x p(s_\varepsilon)$ are correlated, simplifying the Young measure analysis in the compensated compactness argument and allowing identification of the limit. Somewhat surprisingly, in contrast to the theory of $2\times2$ hyperbolic systems, the argument relies on only three entropy-entropy flux pairs. This is particularly useful for $α>2$, where it is unclear whether additional entropies are available.

We establish annealed and quenched invariance principles for random walks in random conductances lifted to the p-variation rough path topology, allowing for degenerate environments and long-range jumps. Our proof is based on a unified structural strategy where pathwise convergence is viewed as a natural upgrade of the classical theory. This approach decouples the martingale lift from terms involving the integrals with respect to the corrector and the quadratic covariations. In the quenched regime, we show that the existence of a stationary potential for the corrector with $2+ε$ moments is sufficient to ensure the vanishing of the corrector in $p$-variation for any $p>2$. This input, combined with our structural framework, provides a direct and modular pathway to rough path convergence. We further provide a transfer lemma to construct this potential from spatial moment bounds. While presently verified in the literature primarily for nearest-neighbor settings, our formulation isolates the exact analytic input required for pathwise convergence in more general environments.

Dusty plasmas are ubiquitous throughout the universe, spanning laboratory and industrial plasmas, fusion devices, planetary environments, cometary comae, and interstellar media. Despite decades of research, many aspects of their behavior remain poorly understood within a unified framework. While numerous theoretical and numerical models describe specific phenomena, such as dust charging, transport, waves, and self-organization, fully predictive models across the wide range of spatial and temporal scales in both laboratory and natural systems remain elusive. Conventional plasma descriptions rely on coupled differential equations for particle densities, momenta, and energies, but their solutions are often limited by computational cost, numerical uncertainties, and incomplete knowledge of boundary conditions and transport processes. Recent advances in machine learning (ML), particularly deep neural networks, offer new opportunities to complement traditional physics-based modeling. Here we review ML and artificial intelligence (AI) approaches, termed bottom-up data-driven methods, for dusty plasma research. Central to this effort is Dust Neural nEtworks Technology (DustNET), a community-driven dataset initiative inspired by ImageNet, integrating experimental, simulation, and synthetic data to enable predictive modeling, uncertainty quantification, and multi-scale analysis. DustNET-trained models may also be deployed in real-time experimental settings under edge computing constraints. Combined with emerging multi-modal AI foundation models and autonomous agents, this framework provides a pathway toward a unified, physics-informed understanding of dusty plasmas across laboratory, industrial, space, and astrophysical environments.

We present a controllable quantum spin-chain model that reproduces the Page curve (the rise-and-fall of bipartite entanglement expected in black-hole evaporation), using only local interactions and a kinematic reduction of the subsystem size. Two transverse-field Ising chains are coupled to form a pure bipartite state; Hawking-like evaporation is implemented by dynamically shrinking the 'system' chain and enlarging the 'environment' chain, while unitary real-time evolution is simulated with matrix product state (MPS) tensor networks. The characteristic Page curve profile emerges robustly under this controlled subsystem resizing and notably persists even when the explicit Hamiltonian coupling across the boundary is set to zero, demonstrating that shrinking Hilbert-space dimension alone can generate Page curve behaviour. We show that the detailed shape of the curve depends on the internal information dynamics: operation at criticality yields a smooth profile, whereas moving away from criticality distorts entanglement growth and decay. These results position locally interacting spin chains as a realistic platform for probing black-hole-inspired information dynamics on current quantum hardware.

Motivated by the recent BESIII measurements of the $J/ψ\to Ξ^0 \barΛK_S^0 + c.c.$ process, we investigate this reaction by considering the contributions from the $Ξ(1690)$ and $Λ(1890)$ resonances. The $Ξ(1690)$ state is dynamically generated from the $S$-wave pseudoscalar meson-octet baryon interactions within the chiral unitary approach. Our theoretical model provides a good description of the $\barΛK^0$, $Ξ^0 K^0$, and $\barΛΞ^0$ invariant mass distributions. The results indicate that the $Ξ(1690)$ resonance, which was neglected in the experimental analysis by BESIII, plays a crucial role in this process. Furthermore, we evaluate the theoretical uncertainties of our model using the parametric bootstrap method. Future high-precision measurements of this process will further help to elucidate the properties of the $Ξ(1690)$ and $Λ(1890)$ states.

We extend the Fokker-Planck framework of Froseth (2026, arXiv:2603.05283) to populations of investors with heterogeneous, persistent return-generating ability. When the drift coefficient in the Langevin equation for log-wealth varies across investors, the proportional wealth tax remains a uniform drift shift but ceases to be neutral in the economic sense: its real incidence differs across ability types, and the stationary wealth distribution changes shape. We derive the extended Fokker-Planck equation on the joint space of log-wealth and ability, characterise the conditions under which the drift-shift symmetry breaks, and identify the consequences for asset prices and portfolio allocations. The analysis connects the neutrality results of Froseth (2026, arXiv:2603.05264) and the Fokker-Planck dynamics of Froseth (2026, arXiv:2603.05283) to the heterogeneous-returns literature, notably the "use-it-or-lose-it" mechanism of Guvenen, Kambourov, Kuruscu, Ocampo-Diaz and Chen (2023).

Realistic simulation of quantum materials is a central goal of quantum computation. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform quantitatively reliable material simulations. We demonstrate that a superconducting quantum processor operating on up to 50 qubits can already produce meaningful, quantitative comparisons with inelastic neutron-scattering measurements of KCuF$_3$, a canonical realization of a gapless Luttinger liquid system with a strongly correlated ground state and a spectrum of emergent spinons. The quantum simulation is enabled by a quantum-classical workflow for computing dynamical structure factors (DSFs). The resulting spectra are benchmarked against experimental measurements using multiple metrics, highlighting the impact of circuit depth and circuit fidelity on simulation accuracy. Finally, we extend our simulations to a 1D XXZ Heisenberg model with next-nearest-neighbor (NNN) interactions and a strong anisotropy, producing a gapped excitation spectrum, which could be used to describe the CsCoX$_3$ compounds above the Néel temperature. Our results establish a framework for computing DSFs for quantum materials in classically challenging regimes of strong entanglement and long-range interactions, enabling quantum simulations that are directly testable against laboratory measurements.

We investigate massive scalar perturbations and several characteristics of particle motion in the spacetime of regular black holes arising in four-dimensional quasi-topological gravity. Quasinormal modes are computed using high-order WKB approximations with Padé resummation and verified through time-domain integration. For moderate values of the scalar-field mass, the time-domain profiles confirm the WKB results with excellent accuracy. As the mass increases, the damping rate decreases substantially, indicating the approach to the quasi-resonant regime of long-lived modes. For sufficiently large masses, the late-time signal becomes dominated by oscillatory power-law tails, which mask the quasi-resonant mode in the time-domain profile. In addition, we analyze photon motion and circular geodesics, including the photon-sphere radius, shadow size, Lyapunov exponent, and ISCO characteristics. These quantities exhibit only moderate deviations from their Schwarzschild values, unlike the Hawking temperature of the black hole.