The RELICS (REactor neutrino LIquid xenon Coherent elastic Scattering) experiment aims to detect coherent elastic neutrino-nucleus scattering from reactor antineutrinos using a dual-phase xenon time projection chamber. To validate the detector concept and ensure technical reliability for the full-scale experiment, a dedicated prototype was designed, constructed, and operated. This work presents an overview of the design, construction, and operational performance of the prototype, with emphasis on its major subsystems, including the TPC, cryogenic and xenon purification systems, slow control, and data acquisition. During operation, the detector demonstrated the capability to achieve a sub-keV energy threshold required for the RELICS physics program, as reflected by a measured single electron gain of 34.30~$\pm$~0.01~(stat.)~PE/e$^-$ and the successful detection of 0.27~keV L-shell decay events from $^{37}$Ar. In addition, essential data analysis techniques and simulation frameworks were developed and validated, establishing the methodological foundation for future RELICS operations. The successful construction and operation of this prototype confirm the feasibility of the core technologies and provide a crucial experimental basis for the final RELICS detector.

Natural and idiomatic expressions are essential for fluent, everyday communication, yet many second-language learners struggle to acquire and spontaneously use casual slang despite strong formal proficiency. To address this gap, we designed and evaluated an LLM-powered, task-based role-playing game in which a GPT-4o-based Game Master guides learners through an immersive, three-phase spoken narrative. After selecting five unfamiliar slang phrases to practice, participants engage in open-ended dialogue with non-player characters; the Game Master naturally incorporates the target phrases in rich semantic contexts (implicit input enhancement) while a dedicated Practice Box provides real-time explicit tracking and encouragement. Post-session, learners receive multi-level formative feedback analyzing the entire interaction. We evaluated the system in a between-subjects study with 14 international graduate students, randomly assigned to either the RPG condition or a control condition consisting of a traditional AI-led virtual classroom. Results from an immediate post-test show that the RPG group achieved greater gains in both comprehension of the target phrases and their accurate, contextual use in sentences. A one-week delayed post-test further demonstrates that these gains are retained over time, with the RPG group showing a 21-27% improvement, indicating the effectiveness of our approach in supporting longer-term learning. Qualitative survey responses assessing engagement and perceived effectiveness further indicate that the game-based approach provided more practice opportunities and a more natural learning experience. These findings highlight the potential of narrative-driven LLM interactions in vocabulary acquisition.

We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically relevant model is a nonlinear Schrödinger (NLS) equation with a periodic potential. We consider the evolution of piecewise smooth initial data composed of two distinct nonlinear periodic eigenmodes. To begin interpreting the resulting wave dynamics, we employ the tight-binding approximation, reducing the continuous system to a discrete NLS (DNLS) model with piecewise constant initial data (i.e., a Riemann problem), where each constant state represents a discrete Floquet-Bloch mode at the continuum model level. The resulting tight-binding approximation is shown to display higher-fidelity for {deeper} periodic potentials. This reduced DNLS model effectively models the dynamics at the minima of the periodic potential of the original continuum NLS. Within such a single-band DNLS framework, we apply tools from Whitham modulation theory and long-wave quasi-continuum reductions to uncover and analyze a rich spectrum of non-convex, discrete dispersive hydrodynamic phenomena, comparing the resulting phenomenology with that of the periodic-potential-bearing continuum model.

Quantitative morphology provides a key probe of galaxy evolution across cosmic time and environments. However, these metrics can be biased by changes in imaging quality - resolution and depth - either across the survey area or the sample. To prepare for the upcoming Rubin LSST data, we investigate this bias for all metrics measured by statmorph and single-component Sérsic fitting with Galfit. We find that geometrical measurements (ellipticity, axis ratio, Petrosian radius, and effective radius) are robust within 10% at most depths and resolutions. Light concentration measurements ($C$, Gini, $M_{20}$) systematically decrease with resolution, leading low-mass or high-redshift bulge-dominated sources to appear indistinguishable from disks. Sérsic index $n$, while unbiased, suffers from a 20-40% uncertainty due to degeneracies in the Sérsic fit. Disturbance measurements ($A$, $A_S$, $D$) depend on signal-to-noise and are thus affected by noise and surface-brightness dimming. We quantify this dependence for each parameter, offer empirical correction functions, and show that the evolution in $C$ observed in JWST galaxies can be explained purely by observational biases. We propose two new measurements - isophotal asymmetry $A_X$ and substructure $St$ - that aim to resolve some of these biases. Finally, we provide a Python package statmorph-lsst implementing these changes and a full dataset that enables tests of custom functions (see text for links).

On 27 December 2024, near-Earth object (NEO) 2024 YR$_4$ was discovered by the ATLAS survey and identified as a virtual impactor. A few weeks later, it eventually reached level 3 on the Torino Scale and was the first and only asteroid to be ever classified at that level. Here we report an intensive observational campaign combining time-series photometry in the visible, broadband visible and near-infrared colors, and low-resolution visible reflectance spectroscopy to assess its physical properties. Fourier analysis of the lightcurves yields a synodic rotation period of $P = 19.46341 \pm 0.00008$ min, placing 2024 YR$_4$ among the fast rotators, even if such rotation is common for objects of similar $H$ magnitude. Its visible and near-infrared colors and spectra are most consistent with an Sq or K taxonomic classification, though some ambiguity remains. Finally, its phase curve exhibits a notably shallow slope ($G = 0.51 \pm 0.11$), from which we derive an absolute magnitude of $H_\mathrm{R} = 23.82\pm0.09$ mag. After color correction and taking into account other models for the phase function, we report an absolute magnitude of $H_\mathrm{V} = 24.14\pm0.25$ mag. These characterizations, rotation period, taxonomy, and surface properties, would have been crucial for risk assessment and mitigation planning had the initially high impact probability scenario been confirmed, underscoring the importance for planetary defense of a rapid, coordinated international response.

We explore the cosmological signatures of neutrino and Hot Dark Matter (HDM) wakes, which refers to the preferential accumulation of neutrinos (or, more broadly, HDM particles) downstream of moving cold dark matter structures. We improve on existing theoretical models, and provide forecasts for the detectability of the effect in future surveys under more realistic conditions than previously considered in the literature. We show that neutrino and HDM wakes are unlikely to be ever observed with the most natural tracer of a hot subcomponent of the total dark matter on cosmological scales, i.e. 2D weak lensing surveys. However, the effect can be detected at a high significance with idealistic 3D maps of a tracer of HDM, for sufficiently small values of the effective free-streaming length (e.g. present-day values of $k_{\textrm{fs},0} \gtrsim 0.1\textrm{Mpc}^{-1}$ to reach $\textrm{SNR} \gtrsim 1$, for a HDM species accounting for a percent of the total dark matter). HDM wakes are a smoking gun of the effects of free-streaming, which cannot be mimicked by changes to the background expansion history (such as allowing for the dark energy to be dynamical), and hence offer another avenue to search for massive neutrinos, and hot subcomponents of the total dark matter more broadly, in a way that complements traditional observables.

Data-driven control methods based on subspace representations are powerful but are often limited to linear time-invariant systems where the model order is known. A key challenge is developing online data-driven control algorithms for time-varying systems, especially when the system's complexity is unknown or changes over time. To address this, we propose a novel online subspace learning framework that operates on flag manifolds. Our algorithm leverages streaming data to recursively track an ensemble of nested subspaces, allowing it to adapt to varying system dimensions without prior knowledge of the true model order. We show that our algorithm is a generalization of the Grassmannian Recursive Algorithm for Tracking. The learned subspace models are then integrated into a data-driven simulation framework to perform prediction for unknown dynamical systems. The effectiveness of this approach is demonstrated through a case study where the proposed adaptive predictor successfully handles abrupt changes in system dynamics and outperforms several baselines.

Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.

Efficacy testing is a cornerstone of clinical trials, ensuring that medical interventions achieve their intended therapeutic effects. Over the decades, a wide range of statistical methodologies have been developed to address the complexities of clinical trial data, including parametric, nonparametric, Bayesian, and machine learning approaches. Parametric methods, such as t-tests, ANOVA, and LMMs, have traditionally been the foundation of efficacy testing due to their efficiency under well-defined assumptions. Nonparametric techniques, including the Friedman test, Brunner-Munzel test, and modern extensions like nparLD, have emerged as robust alternatives, particularly for skewed, ordinal, or non-normal data. Bayesian methodologies have enabled the incorporation of prior information and uncertainty quantification, while machine learning techniques, such as deep learning and reinforcement learning, are revolutionizing trial designs and outcome predictions. Despite these advancements, significant gaps remain, including challenges in handling high-dimensional data, missingness, and ensuring equitable efficacy testing across diverse populations. This review provides a comprehensive overview of these statistical methods, highlighting their applications, strengths, limitations, and future directions. By bridging traditional statistical frameworks with modern computational techniques, the field can continue to advance toward more reliable and personalized clinical trial methodologies.

This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The method adapts the linear combination of unitaries algorithm to block encode the diffusive dynamics, while arbitrary boundary conditions are enforced by the method of images only at the cost of one additional qubit per spatial dimension. As an alternative to the non-periodic reflection, the direct encoding of Neumann conditions by the unitary decomposition of the discrete time-marching operator is proposed. All presented algorithms indicate optimal success probabilities while maintaining linear time complexity, thereby securing the practical applicability of the quantum algorithm on fault-tolerant quantum computers. The proposed time-marching method is demonstrated through state-vector simulations of the heat equation in combination with Neumann, Dirichlet, and mixed boundary conditions.

Loschmidt's paradox asks why macroscopic irreversibility is universal despite the time-reversal symmetry of microscopic dynamics. We argue that irreversibility is not a property of the dynamics but of accessibility: chaotic evolution drives phase-space structure below the quantum resolution scale $\ell_\hbar$, at a critical time $t_c = λ^{-1}\ln(δ_0/\ell_\hbar)$, after which the time-reversed microstate exists as a valid solution of Hamilton's equations but cannot be selected by any physically admissible operation. The mechanism operates entirely within the semiclassical regime $t_c \leq t_E$, where classical geometry is exact. This provides a dynamical resolution of the Loschmidt paradox. The quantum foundation is established using a Krylov-complexity framework: we prove that for any $H(t)=H(-t)$, the quantum Lyapunov exponent satisfies $λ_L^{\rm forward} = λ_L^{\rm backward}$. The arrow of time is not in the dynamics. The mechanism predicts sigmoid fidelity decay, logarithmic scaling of $t_c$ with $λ^{-1}$, and ensemble-size independence of the inaccessibility threshold -- all consistent with three decades of Loschmidt echo experiments and confirmed in a stadium-billiard simulation reported here. Underlying everything: quantum mechanics conserves information exactly. Entropy, defined as the logarithm of the multiplicity $Ω$ -- the number of possibilities consistent with the available information -- can only increase when information becomes operationally inaccessible. The second law reflects not a breakdown of microscopic reversibility, but the dynamical inaccessibility of the information required to reverse it.

Road grade can impact the energy efficiency, safety, and comfort associated with automated vehicle control systems. Currently, control systems that attempt to compensate for road grade are designed with one of two assumptions. Either the grade is only known once the vehicle is driving over the road segment through proprioception, or complete knowledge of the oncoming road grade is known from a pre-made map. Both assumptions limit the performance of a control system, as not having a preview signal prevents proactive grade compensation, whereas relying only on map data potentially subjects the control system to missing or outdated information. These limits can be avoided by measuring the oncoming grade in real-time using on-board lidar sensors. In this work, we use point returns accumulated during travel to estimate the grade at each waypoint along a path. The estimated grade is defined as the difference in height between the front and rear wheelbase at a given waypoint. Kalman filtering techniques are used to mitigate the effects of odometry and motion uncertainty on the grade estimates. This estimator's performance is compared to the measurements of a map created with a GNSS/INS system via a field experiment. When compared to the map-based system, the lidar-based estimator produces an unbiased error with a standard deviation of 0.6 degrees at an average range of 52.7 meters. By having similar precision to map-based systems, automotive lidar-based grade estimation systems are shown to be a valid approach for measuring road grade when a map is unavailable or inaccurate. In using lidar as an input signal for grade-based control system tasks, autonomous vehicles achieve higher redundancy and independence in contrast to existing methods.

We continue the development of a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations that we started in Akerson, Rajan and Bhattacharya (2024). We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive behavior that minimizes the difference between the experimental observation and the corresponding quantities computed with the model, while enforcing the balance laws. We formulate the forward problem as a boundary value problem corresponding to the experiment, and compute the sensitivity of the objective with respect to the model using the adjoint method. In this paper, we extend the approach to include contact and study dynamic indentation. Contact is a nonholonomic constraint, and we introduce a Lagrange multiplier and a slack variable to address it. We demonstrate the method on synthetic data before applying it to experimental observations on rolled homogeneous armor steel and a polycrystalline aluminum alloy.

The integration of distributed energy resources (DERs) into wholesale electricity markets, as mandated by FERC Order 2222, imposes new challenges on system operations. To remain consistent with existing market structures, regional transmission organizations (RTOs) have advanced the aggregation of transmission-node-level DERs (T-DERs), where a nodal virtual power plant (VPP) represents the mapping of all distribution-level DERs to their respective transmission nodes. This paper develops a real-time economic dispatch (RTED) framework that enables multi-transmission-node DER aggregation while addressing computational efficiency. To this end, we introduce a spatio-temporal graph convolutional network (ST-GCN) for adaptive prediction of distribution factors (DFs), thereby capturing the dynamic influence of individual T-DERs across the transmission system. Furthermore, an iterative constraint identification strategy is incorporated to alleviate transmission security constraints without compromising system reliability. Together, these innovations accelerate the market clearing process and support the effective participation of T-DER aggregators under current market paradigms. The proposed approach is validated on large-scale test systems, including modified 118-, 2383-, and 3012-bus networks under a rolling RTED setting with real demand data. Numerical results demonstrate significant improvements in reducing operational costs and maintaining transmission network feasibility, underscoring the scalability and practicality of the proposed framework.

Based on the convex hull construction algorithm, a new geometrical model of ice crystals is proposed to investigate the scattering properties of cirrus clouds particles. Light scattering matrices involving complete polarization information are calculated in geometric optics approximation for randomly oriented large crystals with random and given convex polyhedron shape. The proposed model construction method and computational scheme of light scattering matrix works for any convex polyhedron within the scope of geometrical optics. To illustrate the broad applicability of the proposed ice crystal model, scattering matrices for three ice crystal examples with different geometrical shapes are calculated under a unified computational framework. Diffraction and absorption are not considered in this work. The calculated results for the classical hexagonal column model show overall agreement with those reported by other authors. The crystal model and scattering matrix computational framework developed in this study are applicable to radiative transfer simulations and remote sensing data interpretation in terrestrial and planetary atmospheres.

We investigate the dynamics of elastic capsules suspended in two-dimensional active nematic fluids using lattice Boltzmann simulations. The capsules, modeled as flexible membranes enclosing active internal regions, exhibit a rich variety of behaviors shaped by their geometry and the interplay between internal and external activity. Circular capsules with active interiors undergo persistent rotation driven by internally confined +1/2 topological defects. Axisymmetric capsules, such as boomerangs, develop directed motion along their axis of symmetry due to unbalanced active forces generated by defect distributions near their boundaries. We further show that capsule flexibility suppresses motility and rotation, as active stresses are dissipated into shape deformations. These findings reveal how shape, deformability, and defect dynamics cooperate to produce emergent motility in soft active matter, with potential applications in the design of microswimmers and drug delivery vehicles.

We prove that any two $\mathbb{Z}$-odometers are sub-$L^1$-orbit equivalent, greatly strengthening previous results and giving a definitive picture of quantitative orbit equivalence for these systems.

Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively expensive under these conditions. Quantum computing and quantum-inspired methods have been investigated as promising alternatives. This review surveys advances at the intersection of quantum computing, quantum algorithms, machine learning, and tensor network techniques for CFD. We discuss the use of Variational Quantum Algorithms as hybrid quantum-classical solvers for PDEs, emphasizing their ability to incorporate nonlinearities through Quantum Nonlinear Processing Units. We further review Quantum Neural Networks and Quantum Physics-Informed Neural Networks, which extend classical machine learning frameworks to quantum hardware and have shown advantages in parameter efficiency and solution accuracy for certain CFD benchmarks. Beyond quantum computing, we examine tensor network methods, originally developed for quantum many-body systems and now adapted to CFD as efficient high-dimensional compression and solver tools. Reported studies include several orders of magnitude reductions in memory and runtime while preserving accuracy. Together, these approaches highlight quantum and quantum-inspired strategies that may enable more efficient CFD solvers. This review closes with perspectives: quantum CFD remains out of reach in the NISQ era, but quantum-inspired tensor networks already show practical benefits, with hybrid approaches offering the most promising near-term strategy.

The synthesis and characterization, along with the resulting properties, of fully dense \((\mathrm{Cr, Mo, Ta, V, W})\mathrm{C}\) high-entropy carbide ceramics were studied. The ceramics were synthesized from metal oxide and carbon powders by carbothermal reduction, followed by spark plasma sintering at various temperatures for densification. Increasing the densification temperature resulted in grain growth and an increase in the lattice parameter. Thermal diffusivity increased linearly with testing temperature, resulting in thermal conductivity values ranging from approximately \(7~\mathrm{W\,m^{-1}\,K^{-1}}\) at room temperature to \(12~\mathrm{W\,m^{-1}\,K^{-1}}\) at \(200~^\circ\mathrm{C}\). Measured heat capacity values matched theoretical estimates made using the Neumann--Kopp rule. Room-temperature electrical resistivity decreased from \(137\) to \(120~μΩ\cdot\mathrm{cm}\) as the excess carbon decreased from \(5.4\) to \(0.1~\mathrm{vol\%}\), suggesting an enhanced electronic contribution to thermal conductivity as excess carbon decreased. All specimens exhibited a Vickers hardness of approximately \(29~\mathrm{GPa}\) under a \(0.49~\mathrm{N}\) load. These results underscore the tunability of this high-entropy carbide system.

A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.

What-if analysis is widely used to explore hypothetical scenarios and evaluate alternative pathways to desired results. However, current approaches are fragmented: systems implement what-if capabilities under diverse terminologies with different analytic techniques. Such fragmentation limits expressiveness, impedes flexible composition and reuse of workflows, and hinders tighter integration with AI. We present PRAXA, a compositional grammar of what-if analysis derived from recurring patterns across 141 publications in visual analytics and HCI venues. PRAXA formulates three primitives: (1) data, defining variables under analysis, (2) model, specifying predictive mechanisms, and (3) interaction operations-pairs of user actions and system responses that execute analyses. We encode PRAXA into a declarative specification language, PSL. To evaluate PRAXA, we first show expressiveness by reconstructing representative workflows from prior work as structured compositions, exposing the predominant focus on single-step rather than multi-step reasoning. Second, we demonstrate composability by revealing that capabilities described under distinct terminologies share the same grammatical structure with different parameterizations, and that new multi-step workflows emerge through composition. Third, we illustrate PSL as an intermediate representation for translating natural-language what-if queries into executable interactive interfaces, enabling inspection, validation, and more transparent AI integration. By unifying diverse what-if approaches as a grammar, PRAXA provides a foundation for analyzing, composing, and supporting workflows in next-generation what-if systems.

We investigate how coupling to fluid flow influences defect-mediated transitions in two-dimensional passive nematic fluids using fluctuating nematohydrodynamic simulations. The system is driven by tuning the fluctuation strength, with increasing (decreasing) fluctuations defining the forward (backward) protocol. In the absence of flow coupling, the transition follows the Berezinskii--Kosterlitz--Thouless (BKT) scenario, governed by reversible binding and unbinding of $\pm 1/2$ defect pairs. When hydrodynamics is included, the outcome is controlled by the flow--alignment parameter. For non-aligning nematics ($λ=0$), the transition remains consistent with BKT. By contrast, for strain-rate--aligning nematics ($λ\neq 0$), bend--splay walls emerge, lowering the defect nucleation threshold and preventing sustained recombination: once created, defects remain unbound across the full range of fluctuation strengths in both forward and backward protocols. These results identify flow alignment as a fundamental control parameter for topological phase behavior and suggest that the canonical BKT transition emerges only in the absence of flow alignment.

Aging is a universal consequence of life, yet researchers have identified no universal theme. This manuscript considers aging from the perspective of entropy, wherein things fall apart. We first examine biological information change as a mutational distance, analogous to physical distance. In this model, informational change over time is fitted to an advection-diffusion equation, a normal distribution with a time component. The solution of the advection-diffusion equation provides a means of measuring the entropy of diverse biological systems. The binomial distribution is also sufficient to demonstrate that entropy increases as mutations or epimutations accumulate. As modeled, entropy scales with lifespans across the tree of life. This perspective provides potential mechanistic insights and testable hypotheses as to how evolution has attained enhanced longevity: entropy management. We find entropy is an inclusive rather than exclusive aging theory.

Purpose To investigate synthesis of nuclei in pycnonuclear reactions in dense medium of neutron stars on the basis of understanding, how the compound nucleus is formed during collision of two nuclei. To implement microscopic formulation of nuclear interactions and fusion in pycnonuclear reactions in dense medium. Methods (1) Nuclei synthesis in pycnonuclear reaction in dense medium of neutron star is investigated in the folding approximation of the cluster model. (2) Formation of compound nucleus in dense medium is studied with the method of Multiple Internal Reflections. Results (1) Wave functions of resonance states of $^{24}$Mg are determined by interaction of two $^{12}$C nuclei. (2) Clear maxima of probability of formation of compound nucleus in dense stellar medium are established at first time. (3) Difference between quasibound energies for potential of Woods-Saxon type and folding potentials with the shell-model approximation for wave functions is essential. (4) Formation of the compound nucleus is much more probable in the quasibound states than in states of zero-point vibrations. (5) Only the first quasibound energies for $^{12}$C + $^{12}$Care smaller than the barrier maximums. At these energies compound nuclear system has barrier which prevents its decay going through tunneling phenomenon. This is the new excited nucleus $^{24}$Mg synthesised in the neutron star. \item[Conclusions] Cluster approach with folding potential provides significant modification of picture of formation of compound nucleus, previously obtained concerning the potential of Woods-Saxon type. The highest precision is provided by the folding potential, created by semi-realistic nucleon-nucleon potential and shell-model description of the internal structure of interacting $p$-shell nuclei.

Under the natural action of the pure mapping class group of a surface of genus at least three, we show that any global fixed point in the low-dimensional deformation space of the surface group corresponds to the trivial representation. A key observation is that such a global fixed point gives rise to a linear representation of the pure mapping class group of the corresponding surface with a marked point. Our argument works directly on the deformation space, without assuming the semisimplicity of representations, and yields a short alternative proof of a special case of a theorem of Landesman and Litt with a slight improvement. We also discuss a possible extension of this approach from global fixed points to finite orbits of the mapping class group action.

We have used the auxiliary-field quantum Monte Carlo (AFQMC) many-body approach on the lattice to study the equation of state for a fermionic impurity interacting with a background sea of spin-polarized fermions. The impurity, or polaron, is an interesting system in both cold atomic and nuclear physics. Our approach is general, and we are able to straightforwardly study the polaron across these regimes. We first study the Fermi polaron at unitarity and for a wide range of scattering lengths, comparing against previous theoretical and experimental studies. We then explore the neutron polaron which has been shown to be an important constraint for nuclear physics. We have also employed the recently developed parametric matrix model to emulate AFQMC solutions to the two-body problem on the lattice, to accelerate the tuning of our lattice Hamiltonian parameters directly to two-body energies in a periodic box, following Luscher's formula. Our lattice quantum Monte Carlo results for the polaron in both a cold atomic and nuclear physics context can serve as stringent benchmarks for future theoretical and experimental research.

The defence of hacking (sometimes referred to as the "Trojan Horse Defence" or the "SODDI Defence", Some Other Dude Did It Defence) is prevalent in computer cases and a challenge for those working in the criminal justice system. Historical reviews of cases have demonstrated the defence operating to varying levels of success. However, there remains an absence in academic literature of case studies of how digital forensics investigators can address this defence, to assist courts in acquitting the innocent and convicting the guilty. This case study follows the case of R v F where a defendant asserted this defence and the author worked alongside a police investigator to investigate the merits of the defence and bring empirical evidence before the jury. As the first case study of its kind, it presents practical lessons and techniques for digital forensic investigators.

Continuum dislocation dynamics (CDD) has become the state-of-the-art theoretical approach for mesoscale dislocation plasticity of metals. Within this approach, there are multiple CDD theories that can all be derived from the principles of statistical mechanics. In these theories density-based measures are used to represent dislocation lines. Establishing these density measures requires some level of coarse graining with the result of losing track of some parts of the dislocation population due to cancellation in the tangent vectors of unaligned dislocations. The leading CDD theories either treat dislocations as nearly parallel or distributed locally over orientation space. The difference between these theories is a matter of the spatial resolution at which the definition of the relevant dislocation density field holds: for fine resolutions, single dislocations are resolved and there is no cancellation; for coarse resolutions, whole dislocation loops could contribute at a single point and there is complete cancellation. In the current work, a formulation of the resolution-dependent transition between these limits is presented in terms of the statistics of dislocation line orientation fluctuations about a local average line direction. From this formulation, a study of the orientation fluctuation behavior in intermediate resolution regimes is conducted. Two possible closure equations for truncating the moment sequence of the fluctuation distributions relating the two theories mentioned above are evaluated from data, the newly introduced line bundle closure and the previous standard maximum entropy closure relations. The line bundle closure relation is shown to be accurate for coarse-graining lengths up to half the dislocation spacing and the maximum entropy closure is found to poorly agree with the data at all coarse-graining lengths.

In this paper, we develop a variational foundation for stochastic thermodynamics of finite-dimensional, continuous-time systems. Requiring the second law (non-negative average total entropy production) systematically yields a consistent thermodynamic structure, from which novel generalized fluctuation-dissipation relations emerge naturally, ensuring local detailed balance. This principle extends key results of stochastic thermodynamics including an individual trajectory level description of both configurational and thermal variables and fluctuation theorems in an extended thermodynamic phase space. It applies to both closed and open systems, while accommodating state-dependent parameters, nonlinear couplings between configurational and thermal degrees of freedom, and cross-correlated noise consistent with Onsager symmetry. This is achieved by establishing a unified geometric framework in which stochastic thermodynamics emerges from a generalized Lagrange-d'Alembert principle, building on the variational structure introduced by Gay-Balmaz and Yoshimura [Phil. Trans. R. Soc. A 381, 2256 (2023)]. Irreversible and stochastic forces are incorporated through nonlinear nonholonomic constraints, with entropy treated as an independent dynamical variable. This work provides a novel approach for thermodynamically consistent modeling of stochastic systems, and paves the way to applications in continuum systems such as active and complex fluids.

We present a Myhill-Nerode theorem for hypergraphs. The theorem involves an operation which takes two input structures and produces a hypergraph as output. Using this operation, we define a Myhill-Nerode-type equivalence relation and show that if a class of hypergraphs is definable in the counting monadic second-order logic of hypergraphs, then the equivalence relation has finite index. We apply this tool to classes of gain-graphic matroids, and show that if the group $Γ$ is not uniformly locally finite, then the class of $Γ$\dash gain-graphic matroids is not monadically definable. (A group is uniformly locally finite if, for every $k$, there is a maximum size amongst subgroups generated by at most $k$ elements.) In addition, we define the conviviality graph of a group, and show that if the group $Γ$ has an infinite conviviality graph, then the class of $Γ$\dash gain-graphic matroids is not monadically definable. This will be useful in future constructions.