We extend the notions of finite free convolution and finite free cumulants to the setting of formal power series by introducing their natural analogues, namely $t$-deformed convolution and $t$-deformed cumulants. In this framework, we establish $t$-deformed analogues of the law of large numbers and the central limit theorem, revealing structural parallels with classical, free, and finite free probability theories. We show that the case $t=-1$ recovers classical convolution at the level of moment generating functions, thereby connecting the theory directly to classical probability. We further investigate the infinitesimal generators associated with $\boxplus^t$-continuous semigroups, deriving explicit representation formulas that clarify how these generators describe the infinitesimal evolution of the semigroup. In the case $t = d$, our results yield explicit formulas for finite free infinitesimal generators. In the case $t = -1$, we relate these generators to those of one-dimensional Lévy processes by identifying the corresponding terms in their representations. This establishes a direct connection between $\boxplus^t$-convolution semigroups and classical Lévy-Khintchine-type generators.

Over the past few decades, the hypothetically dark photon has been extensively studied from both phenomenological and experimental perspectives. It should be noted that the local symmetry for dark photon does not gauge the standard model Higgs scalar and chiral fermions. In this paper, we show that an artificially introduced $U(1)_X$ gauge group for dark photon and the standard model $U(1)_Y$ gauge group for hypercharge can be simultaneously born from two $U(1)_1\times U(1)_2$ gauge groups under which the standard model scalar and fermions carry the same $U(1)_1$ and $U(1)_2$ charges without causing any gauge anomalies. We further introduce a spontaneously broken mirror symmetry between the $U(1)_1$ and $U(1)_2$ gauge groups so that the $U(1)_1$ and $U(1)_2$ gauge couplings can acquire a small difference at one-loop level and hence the $U_X \times U_Y$ kinetic mixing can be highly suppressed in a natural way.

Merging is a core operation in version control systems such as Git, but traditional line-based algorithms often yield spurious conflicts, particularly in the presence of refactorings or parallel edits. While syntax- and semantics-aware merging approaches can reduce conflicts, they introduce drawbacks such as loss of formatting, dependence on language-specific parsers, and limited flexibility across heterogeneous artifacts. To address this gap, we present Summer, a novel textual token-based merge algorithm independent of document formats. Dividing text into tokens, our approach formulates token-level changes in one branch into string-rewriting rules and move rules, and applies these rules to the text of the other branch to construct a merge. Despite being independent on programming languages, our move rules model extracting and inlining functions. We evaluated Summer on ConflictBench, a large benchmark of real-world merge scenarios, comparing it with five pioneering merge tools across Java and non-Java files. Experimental results show that Summer achieved the highest 36% accuracy in reproducing merges verbatim identical to developers', and ranked second in semantic accuracy.

We show that electron drag by nonequilibrium phonons describes the actual waveform and spectrum of terahertz pulses generated during femtosecond laser irradiation of metals. In contrast to previous models, there is a picosecond delay in the drag force development due to the relatively slow lattice heating and finite phonon lifetime. We also predict that, at high pump fluences, a macroscopic deformation wave enhances nonlinearly the drag force and terahertz response. Our results establish the terahertz pulse waveform as a direct probe of ultrafast lattice dynamics in metals.

We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(ϕ^3)$ amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that occurs in Feynman diagrams when summing over shuffle permutations. The loop-level hidden zeros and $2$-split identified in this work differ from those in the literature. In our result, the kinematic conditions for loop-level hidden zeros and $2$-split are remarkably simple. Their connection is as tight as at tree-level, with the same procedure for obtaining the $2$-split condition from the zero condition. The resulting $2$-split formula at loop-level represents a generalization of that at tree-level: the $L$-loop integrand is expressed as a sum over $L+1$ terms, each of which exhibits a $2$-split structure.

We present CubicJordanMatrixAlg, a GAP package for symbolic computation in cubic Jordan matrix algebras and in related Lie-theoretic structures. As an application, we use it to compute certain (commutator) relations in $F_4$-graded groups that were constructed by De Medts and the author from cubic Jordan matrix algebras.

When charged particles are subjected to strong magnetic fields, they form discrete energy levels known as Landau levels. The Landau levels consist of a series of degenerate states of Landau modes, making them a promising platform for large-capacity information processing. However, to date, exploiting the high-order Landau modes and control their spatial distributions has remained elusive. Here, we propose to construct magnetic fields, electric fields, and imaginary momentum simultaneously to reshape high-order Landau modes in non-Hermitian systems. By building a non-Hermitian electric circuit platform, we experimentally realize pseudomagnetic fields via inhomogeneous coupling and pseudoelectric fields via a gradient on-site potential, while simultaneously introducing an imaginary momentum via non-reciprocal coupling. We directly observe multi-frequency single-peak localization of high-order Landau modes. Our work provides a universal method for manipulating high-order Landau modes and exploring applications in nonHermitian systems, such as frequency multiplexing and wave packet reshaping.

This paper investigates the uplink capacity of single-input single-output (SISO) systems assisted by a swarm of network-controlled repeaters (NCRs). We develop a rigorous wideband formulation based on OFDM signaling. Starting from the continuous-time passband model, we derive the capacity expression for the repeater-assisted OFDM channel, accounting for amplified noise contributions from multiple repeaters. Numerical results demonstrate that NCRs can substantially enhance system capacity even with simple activation strategies, and that activating only the closest repeater yields nearly the same performance as activating all repeaters, thereby offering significant energy-saving opportunities. These findings highlight the potential of NCR swarms as a cost-effective and scalable solution for coverage extension and capacity enhancement in wideband wireless networks.

We study the Rokhlin lemma in the context of infinite measure-preserving bijections, and completely classify such bijections up to $λ$-approximate conjugacy, where $λ$ is the infinite measure which is preserved. This sharpens the classical version of the Rokhlin lemma, which only provides such a classification up to $μ$-approximate conjugacy where $μ$ is a probability measure equivalent to $λ$.

Traditional recommendation systems represent users and items as dense vectors and learn to align them in a shared latent space for relevance estimation. Recent LLM-based recommenders instead leverage natural-language representations that are easier to interpret and integrate with downstream reasoning modules. This paper studies how to construct effective textual profiles for users and items, and how to align them for recommendation. A central difficulty is that the best profile format is not known a priori: manually designed templates can be brittle and misaligned with task objectives. Moreover, generating user and item profiles independently may produce descriptions that are individually plausible yet semantically inconsistent for a specific user--item pair. We propose Duet, an interaction-aware profile generator that jointly produces user and item profiles conditioned on both user history and item evidence. Duet follows a three-stage procedure: it first turns raw histories and metadata into compact cues, then expands these cues into paired profile prompts and then generate profiles, and finally optimizes the generation policy with reinforcement learning using downstream recommendation performance as feedback. Experiments on three real-world datasets show that Duet consistently outperforms strong baselines, demonstrating the benefits of template-free profile exploration and joint user-item textual alignment.

We take a close look at a classical magic trick performed with a string, where a trivial knot is seemingly isotoped into a trefoil, and generalize it to a family of magic tricks for transforming the unknot into other knots. We encode such a trick by depicting the target knot as a special type of knot diagram, which we call a "knotholder diagram". By proving that all knots admit knotholder diagrams, we obtain variants of the trick for producing every knot.

Using only the characteristic function, we derive short-time at-the-money (ATM) call-price asymptotics for the exponential CGMY model with activity parameter $Y\in(1,2)$. The Lipton--Lewis formula expresses the normalized ATM call price, denoted $c(t,0)$, in terms of the characteristic exponent, which, upon rescaling at the rate $t^{-1/Y}$ from the $Y$-stable domain of attraction, yields $c(t,0) = d_{1} t^{1/Y} + d_{2} t + o(t)$ as $t\downarrow 0$. The first-order coefficient $d_{1}$ is the known stable limit from the domain of attraction of a symmetric $Y$-stable law, and $d_{2}$ is given by an explicit integral involving the characteristic exponent and the limiting stable exponent. We then extract closed-form higher-order coefficients by keeping the full Lipton--Lewis integrand intact and introducing a dynamic cutoff that partitions the domain into inner, core, and tail regions, establishing the expansion with controlled remainder. All coefficients are verified numerically against existing closed-form expressions where available.

For networks with externalities, where each component's worth may depend on the full network structure, balanced contributions and fairness lead to distinct component-efficient allocation rules. We characterize the unique component-efficient allocation rule satisfying balanced contributions -- the BCE rule. Existence is the main challenge: balanced contributions must hold on every edge, but the construction uses only spanning-tree edges. A cycle-sum identity bridges this gap by reducing balanced contributions on non-tree edges to relations in proper subnetworks. The BCE rule coincides with the Myerson value for TU games and with its generalization by Jackson--Wolinsky for network games without externalities, it recovers the externality-free value on the complete network, and -- unlike the fairness-based FCE rule -- it does not reduce to a graph-free formula applied to the graph-restricted game.

Data-driven reachability analysis using matrix zonotopes faces a fundamental challenge: the number of generators in the reachable set grows exponentially during propagation, while current order reduction yields overly conservative approximations in data-driven settings. This paper introduces an orthogonal matrix-based framework that appropriately transfers the coordinate system before reducing the generators of the reachable set, dramatically reducing reachable set volumes. By exploiting the factorized structure of data-driven matrix zonotope generators, we develop several efficient algorithms to solve the problem. Numerical experiments demonstrate order-of-magnitude volume reductions compared to traditional methods, while maintaining comparable generator numbers. Our method provides a practical solution to improve precision in data-driven safety verification.

Ferromagnetic elastic slender structures offer the potential for large actuation displacements under modest external magnetic fields, due to the magneto-mechanical coupling. This paper investigates the phase portraits of the Hamiltonian governing the three-dimensional deformation of inextensible ferromagnetic elastic rods subjected to combined terminal tension and twisting moment in the presence of a longitudinal magnetic field. The total energy functional is formulated by combining the Kirchhoff elastic strain energy with micromagnetic energy contributions appropriate to soft and hard ferromagnetic materials: magnetostatic (demagnetization) energy for the former, and exchange and Zeeman energies for the latter. Exploiting the circular cross-sectional symmetry and the integrable structure of the governing equations, conserved Casimir invariants are identified and the Hamiltonian is reduced to a single-degree-of-freedom system in the Euler polar angle. Analysis of the resulting phase portraits reveals that purely elastic and hard ferromagnetic rods undergo a supercritical Hamiltonian Hopf pitchfork bifurcation, whereas soft ferromagnetic rods exhibit this bifurcation only within a restricted range of the magnetoelastic parameter, $0<\tilde{K}_{dM}<1/8$. Both helical and localized post-buckling configurations are analyzed, and the corresponding load-deformation relationships are systematically characterized across a range of loading scenarios. Localized buckling modes, corresponding to homoclinic orbits in the Hamiltonian phase space, are constructed numerically. In contrast to the purely elastic case, the localized configurations of soft ferromagnetic rods exhibit non-collinear extended straight segments, a geometrically distinctive feature arising directly from the magnetoelastic coupling.

Four coframes of invariant 1-forms are explicitly constructed using the Inductive Cartan equivalence method with rank zero corresponding to four distinct branches. These coframes are employed to characterize non-linearizable fourth-order ODEs under point transformation with a five-point symmetry Lie subalgebra. Moreover, we propose a procedure for obtaining the point transformation by using the derived invariant coframes, demonstrated through examples.

Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary conditions on the spinor components which were proposed in [Berry and Mondragon 1987, {\it Proc. R. Soc.} A {\bf 412} 53) . We review their general features and the properties of neutrino billiards with shapes of billiards with integrable dynamics. Furthermore, we review the features of two neutrino billiards with the shapes of billiards generating a chaotic dynamics, whose nonrelativistic counterpart exhibits particular properties. Finally we briefly discuss possible experimental realizations of relativistic quantium billiards based on graphene billiards, that is, finite size sheets of graphene.

Large Language Models (LLMs) have surged as a transformative technology for science and society, prompting governments worldwide to pursue sovereign AI capabilities that ensure data compliance and cultural representation. However, the associated capital costs and engineering complexity required to train these models have largely restricted such capabilities to the private sector, leaving a significant gap for public institutions. This paper details the engineering journey behind training Apertus, a fully open multilingual foundation model, on the Alps supercomputer. Representing a first-of-its-kind achievement for academia at the 70B parameter scale, we successfully deployed a massive pre-training campaign on one of Europe's largest systems for open science, powered by NVIDIA GH200 Grace Hopper Superchips. We detail the challenges encountered in readying HPC infrastructure for training AI models, from overcoming storage bottlenecks to stabilizing large-scale interconnects, and the lessons learned in transforming a supercomputer into a resilient software-defined Machine Learning Platform. Finally, we discuss the post-training requirements and evolution of our Machine Learning platform, outlining how this initial release lays the groundwork for a sustained, iterative operational capability, in particular for fine tuning foundation models, that extends well beyond a single model training run.

One of the fundamental manifestations of classical chaos is exponential sensitivity to initial conditions that is, two trajectories starting from nearly identical initial states diverge exponentially over time. This behavior is quantified by the Lyapunov exponents. Due to the unitary nature of quantum mechanics, such exponential divergence is elusive in quantum systems. As a result, several alternative quantities have been proposed and studied in recent years to capture analogous behavior. In this article, we present a pedagogical overview of three such quantities that have been the focus of intense research in recent years: the Loschmidt echo, out-of-time-order correlators (OTOCs), and Krylov complexity.

Chromium-based materials with complex lattice geometries provide an important platform for investigating correlated electronic and magnetic states. However, Cr-based compounds with unusual crystal geometries are still rarely reported. Here, we report a new Cr-based compound, Cs$_4$Cr$_7$Te$_{10}$, featuring interwoven Cr and Te sublattices that can be viewed as reconstructed networks derived from Archimedean (3.4.6.4) tiling and the kagome lattice, respectively. Transport measurements reveal the semiconducting nature in Cs$_4$Cr$_7$Te$_{10}$. Magnetization measurements show a weak anisotropy between H//b and H//ac planes, and uncover an anomaly near 130 K that is insensitive to the applied magnetic fields. Specific-heat measurements further confirm this transition, indicating its bulk thermodynamic nature. The associated entropy change is as small as 0.41 J mol^-1 K^-1, ruling out a structural phase transition and pointing to a possible electronic and/or magnetic phase transition. These results provide a new route for designing complex crystal geometries and exploring their associated emergent phenomena.

By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is to capture the interplay of microscopic scales that include a confinement length in the emergence of the surface plasmon, a collective low-energy charge excitation in the vicinity of the plane. We start with a time-dependent Hartree-type equation in 3D. This model accounts for particle binding to the plane and the repulsive Coulomb interaction associated with the induced charge density relative to the ground state. By linearizing the equation of motion, we formulate a homogeneous integral equation for the scattering amplitude of the particle wave function in the (z-) coordinate vertical to the plane. For a binding potential proportional to a negative delta function and symmetric-in-z wave function, we apply the Laplace transform with respect to positive z and convert the integral equation into a functional equation that involves several values of the transformed solution. The scattering amplitude and dispersion relation are derived exactly in terms of rapidly convergent series via the Mittag-Leffler theorem. In the semiclassical regime, our result furnishes an asymptotic expansion for the energy excitation spectrum. The leading-order term is found in agreement with the prediction of a classical hydrodynamic model based on a projected-Euler-Poisson system.

We present the first formulation of linearised gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e. treats the two frames related by electric-magnetic duality on equal footing. It is well-known that four-dimensional linearised gravity belongs to a class of singleton representations of the four-dimensional conformal algebra $\mathfrak{so}(2,4)$. Our key insight is viewing this algebra as the isometry of $\text{AdS}_5$ and realising the massless spin-2 field as an edge mode of a five-dimensional topological field taking values in a specific finite-dimensional representation of $\mathfrak{so}(2,4)$. The desired four-dimensional action is then found by a covariant boundary reduction procedure.

Berry curvature is ubiquitous in condensed matter physics and materials science. Its main consequence is the intrinsic anomalous Hall effect (AHE) in magnetic materials and plays a pivotal role in spintronic applications and quantum technologies. Here, we present a theoretical study of the intrinsic AHE in tetragonal FeTe, a semimetallic van der Waals antiferromagnet with compensated magnetic ordering at low temperatures. Using a realistic spin-fermion model, we demonstrate that FeTe exhibits a large Berry-curvature-driven AHE under an applied magnetic field. Our calculations reveal that the Hall conductivity of this compound is extremely sensitive to temperature and field strength and even exhibits sign reversal, highlighting FeTe as a prototypical platform where magnetism and topology combine to produce robust intrinsic Hall responses. This work establishes FeTe as a promising candidate for exploring quantum transport in low-dimensional correlated systems. We also discuss the implications for recent experimental results of the AHE and ordinary Hall effect reported for FeTe.

Ecological Momentary Assessment (EMA) is widely used to study adolescents' experiences; yet, how the design of EMA platforms shapes engagement, research practices, and power dynamics in youth studies remains under-examined. We developed a youth-centered EMA platform prioritizing youth engagement and researcher support, and evaluated it through a case study on a longitudinal investigation with adolescent twins focused on mental health and sleep behavior. Interviews with the research team examined how the platform design choices shaped participant onboarding, sustained engagement, risk monitoring, and data interpretation. The app's teen-centered design and gamified features sustained teen engagement, while the web portal streamlined administrative oversight through a centralized dashboard. However, technical instability and rigid data structures created significant hurdles, leading to privacy concerns among parents and complicating the researchers' ability to analyze raw usage metadata. We provide actionable interaction design guidelines for developing EMA platforms that prioritize youth agency, ethical practice, and research goals.

The pore-surface and surface-surface correlation functions are structural characteristics that play an important role in theoretical materials science and in small-angle scattering theory. Exact analytical expressions for the surface correlation functions are available only for very few models, and we here derive such expressions for the general class of dead-leaves models. Within these models, a two-phase pore/solid structure is created by sequentially and randomly filling space with pore-like or solid-like grains that overlap any pre-existing structure, in the same way as dead leaves fall on the ground. The obtained mathematical expressions are valid for any grain shape, in arbitrary dimension. The results are illustrated with monodispersed spherical grains,as well as with a dead-leaves realization of a Debye random medium. In the latter case, the size distribution of the grains is designed to produce a structure having exponential two-point correlation function. Compared to Debye random media obtained by numerical reconstruction, the dead-leaves structure has almost identical surface-surface correlation function, but distinctly different pore-surface correlation function. As a byproduct of our analysis, we also submit a general expression for the pore-surface and surface-surface correlation functions of the Boolean model, valid for arbitrary grains.

We consider a nonlinear constrained heat flow evolving on the manifold $\mathcal{M}=\{v\in L^{2}:\|v\|_{L^{2}}=1\}$ over bounded smooth domains. It is known that the solution corresponding to any nonnegative initial datum remains on $\mathcal{M}$ and converges to the unique positive ground state of the associated stationary problem. In this work, we first establish certain time-regularity estimates and then use these to derive explicit exponential rates of convergence for the energy, the solution in the $L^2, H^1$ and $H^2-$norms, and the associated nonlinear eigenvalue, thereby proving a sharp exponential stability of the ground state. Moreover, using the Łojasiewicz-Simon inequality, we obtain decay rates for locally stabilized solutions toward a stationary state in the $L^2$ and $H^1-$norms, where the rate depends on the corresponding Łojasiewicz-Simon exponent. Our results are new, and the approach relies on spectral analysis of the linearized operator, uniform higher-order estimates, and the compactness of solution trajectories.

Using nonequilibrium and equilibrium molecular dynamics simulations, we investigate heat conduction in a momentum-conserving mesoscopic fluid modeled by multiparticle collision dynamics. Across quasi-two-dimensional (q-2D) to three-dimensional (3D) systems, we identify three distinct transport regimes: (i) a \emph{ballistic regime}, where thermal conductivity scales linearly with system size ($κ\sim L$) and the total heat current autocorrelation function $C(t)$ remains constant; (ii)~a \emph{kinetic regime}, characterized by size-independent $κ$ and exponentially decaying $C(t)$, demonstrating that normal heat conduction dominated by kinetic effects is far more ubiquitous than previously observed in 1D systems; and (iii)~a \emph{hydrodynamic regime}, where the q-2D system exhibits logarithmically divergent conductivity ($ κ\sim \ln L $ ) with $ C(t) \sim t^{-1} $ , while the 3D system displays finite $ κ$ and $ C(t) \sim t^{-3/2} $. Our results, observed in the hydrodynamic regime, quantitatively validate the scaling predictions for heat transport and reveal a clear dimensional crossover -- from 2D-like anomalous transport to 3D Fourier behavior. These results lay a foundation for understanding thermal transport in q-2D to 3D systems and have practical implications for the design of micro- and nanoscale thermal devices.

The recently commissioned Subaru `Ōnohi`ula Prime Focus Spectrograph (PFS) will obtain spectra from nearly 2,400 fibers that cover 1.24 square degrees. The 360 night Subaru Strategic Program for PFS is dedicating approximately one-third of its allocation (130 nights) to study the structure and evolution of galaxies in the Local Group. This Galactic Archaeological survey has three pillars. (1) We will determine whether the mass density profiles of dwarf galaxies are consistent with cusps, as expected for cold dark matter, or cores, as expected from alternative dark matter theories or baryonic feedback. We will deduce the density profiles as a function of radius from modeling of the full line-of-sight velocity and abundance distributions for six dwarf galaxies. Our total sample will consist of 18,000 member stars to beyond the nominal tidal radius of each system. (2) From measurements of the [alpha/Fe] abundance ratio, we will learn the difference in assembly history of the two most massive galaxies in the Local Group: M31 and the Milky Way. We will observe 30,000 member stars over 45 square degrees of M31's halo and outer disk. (3) We will uncover how the most fragile (outer) part of the Milky Way responded to accretion events both in the distant past (such as Gaia-Sausage Enceladus) and in more recent history (such as the Sagittarius dwarf spheroidal galaxy). To support this study, PFS will provide velocities and metallicities--from which, in combination with photometry, we will deduce ages--for tens of thousands of main-sequence stars out to a Galactocentric distance of ~30 kpc.

Hamiltonian Monte Carlo (HMC) and its dynamic extensions, such as the No-U-Turn Sampler (NUTS), are powerful Markov chain Monte Carlo methods for sampling from complex, high-dimensional probability distributions. Riemannian manifold Hamiltonian Monte Carlo (RMHMC) extends HMC by allowing the mass matrix to depend on position, which can substantially improve mixing but also makes implementation considerably more challenging. In this paper, we study an adaptive hierarchical version of RMHMC that is well suited to many hierarchical sampling problems. A key feature of hierarchical RMHMC is that, unlike general RMHMC, it admits a closed-form explicit leapfrog integrator, enabling efficient implementation and direct use within dynamic HMC methods such as NUTS. We introduce an adaptive scheme that automatically tunes the parameters of the hierarchical mass matrix during simulation. Importantly, the target density need not exhibit any hierarchical or block structure; the hierarchy is instead imposed on the mass matrix as a modeling device to capture the local geometry of the target distribution. Numerical experiments demonstrate appealing empirical performance in high-dimensional Bayesian inference problems.

We prove that every ordinal $α<ω_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive answer to a problem posed by Nicolas Luzin in 1935.