AI for Science

The tropical semiring is a semiring of extended real numbers, where the operations of `max' and `+' replace the usual addition and multiplication, respectively. Difference equations obtained from the ultradiscrete limit of discrete dynamical systems are described in terms of the tropical semiring. We propose a tropical linearization approach for the stability analysis of difference equations, including those describing ulradiscrete dynamical systems. We show that the fixed point at the tropical origin is asymptotically stable if the maximum eigenvalue of the tropical Jacobian matrix is negative. On the other hand, it is unstable if the maximum eigenvalue of the tropical Jacobian matrix is positive. Since $0$ is the tropical multiplicative identity, these results are analogous to those in the usual linearization process.

We report the observation of charge-exchange collisions between trapped calcium monohydride molecular ions ($^{40}$CaH$^+$) and ultracold potassium atoms ($^{39}$K) in a hybrid ion-atom trap. The measured charge-exchange rate coefficient is significantly suppressed relative to the Langevin rate constant for the system. We use $\mathit{ab\ initio}$ quantum-chemical calculations to model the (CaH-K)$^+$ complex in the ground and excited electronic states and to identify possible charge-exchange mechanisms. Our calculations rule out a direct non-radiative charge-exchange reaction and instead point to a radiative mechanism, but do not quantitatively reproduce the measured rate, highlighting the need for a full-dimensional quantum dynamics treatment that includes vibrational motion and intermediate complex formation. Our work demonstrates that cold hybrid ion-atom platforms with molecular ions enable access to richer chemical complexity and collisional dynamics inaccessible in purely atomic systems.

We consider image registration as an optimal control problem using an optical flow formulation, i.e., we discuss an optimization problem that is governed by a linear hyperbolic transport equation. Requiring Lipschitz continuity of the vector fields that parametrize the transformation leads to an optimization problem in a non-reflexive Banach space. We introduce relaxations of the optimization problem involving smoothed maximum and minimum functions and appropriate Orlicz spaces. To derive well-posedness results for the relaxed optimization problem, we revisit and establish new existence and uniqueness results for the linear hyperbolic transport equations. We further discuss limit considerations with respect to the relaxation parameter and discretizations.

We propose a Bayesian framework for feedback boundary control of hyperbolic balance laws. The method propagates a probability distribution over feedback parameters using Lyapunov decay estimates as a likelihood. For linear models, it recovers available analytical stability results and extends to nonlinear regimes where theory is limited. Using first-order local Lax-Friedrichs (LLF) discretizations, we validate the approach on the decoupled wave system and the linearized Saint-Venant equations, reproducing known stability intervals and mixed boundary couplings. We then treat nonlinear and stochastic problems, including the nonlinear Saint-Venant system, one- and two-dimensional Burgers equations, Burgers equation with random initial data, and nonconservative perturbations with source terms, and show that the inferred stability domains are robust with respect to the indicator and the prior. Finally, we demonstrate transfer to a second-order semi-discrete LLF scheme and to a two-parameter feedback model for laser powder bed fusion with power regulation.

We consider the optimal control of large-scale systems using distributed controllers whose network topology mirrors the coupling graph between subsystems. In this work, we introduce spatial regret, a graph-informed metric measuring the worst-case performance gap between a distributed controller and an oracle with access to additional sensor information. The oracle's graph is a user-specified augmentation of the information graph, yielding a benchmark policy that penalizes disturbances for which additional sensing would improve performance. Minimizing spatial regret yields distributed controllers - respecting the nominal information graph - that emulate the oracle's response to disturbances characteristic of large-scale networks, such as localized perturbations. We show that minimizing spatial regret admits a convex reformulation as an infinite program with a finite-dimensional approximation. To scale to large networks, we derive an upper bound on the spatial regret that can be efficiently minimized in a distributed way. Numerical experiments on power-system models show that the resulting controllers mitigate localized disturbances more effectively than those based on classical metrics.

To address the challenges of interoperability in computational science, we present the latest updates to the software package MaRDI Open Interfaces. This software package aims to decrease the time and coding/testing efforts spent by computational scientists on tasks such as writing bindings to numerical solvers and adapting experiment codes to the varying interfaces of solvers for the same problem type (e.g., for benchmarking, which solver is better). By streamlining these tasks, this software package helps researchers focus on the actual essence of their computational projects. Here, we demonstrate a recently developed interface for nonlinear optimization and illustrate how it can be applied for computational experiments with optimization problems. As an example of such problem, we consider training of physics-informed neural networks to predict the solutions of viscous Burgers' equation.

In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau type singular dimension descent method for positive scalar curvature obstructions in arbitrary dimensions. We prove obstructions to positive scalar curvature on enlargeable manifolds and establish the corresponding cubical width inequalities and two-systole estimates. The method also applies to enlargeable AM--PI spaces, giving a positive scalar curvature obstruction when the singular set has Assouad codimension greater than \(3-2/n\).

An elastic space curve is a critical point of the bending energy subject to appropriate constraints. An analytic representation, equivalent to the spherical pendulum equation, leads to an 11-parameter description of the space of 3D elastic curve segments. We give a numerically stable method for recovering the 11 parameters from a given elastic curve segment. Using this, we give a fast and stable method to approximate an arbitrary space curve segment by a 3D elastica. Applications include interactive design with exact elastic curves and CAD surface rationalization for robotic hot-blade cutting.

Machine learning models have scaled to unprecedented sizes, making training across distributed devices the de facto standard in the field. In this work, we explore how quantum communications can make distributed training both more communication-efficient and information-theoretically private, for both classical and quantum learning models. Ring all-reduce is the foundational communication primitive for large-scale distributed training. We present a quantum version that reduces per-link online communication by a provably optimal factor of two using pre-shared entanglement and superdense coding, without requiring the learning model or gradient computation to change. Beyond bandwidth, the primitive enables privacy guarantees that are information-theoretically impossible for any classical protocol, achieving composable ε-secure aggregation, via verified entanglement, at a 2x overhead in GHZ copies. Our hybrid quantum-classical communication architecture yields simultaneous communication and security advantages for large scale distributed training, regardless of whether the learning itself is quantum or classical. Finally, we characterise quantum advantages in gradient conflict detection for server-to-client communication under bandwidth constraints, a setting that arises after ring all-reduce is completed, when full gradient broadcast to external clients is infeasible. Two variants of the problem admit different separations. For margin-based alignment testing (\textsc{GapIP}_τ), the quantum advantage is quadratic in the margin parameter: \widetilde{O}(τ^{-1}\log P) qubits versus \widetilde{O}(\min(\τ^{-2},P)) bits. For sign-consistency auditing against a private parameter matching (\textsc{TieAudit}_ε), the advantage represents an exponential separation in communication complexity: Ω(\sqrt{P}) bits whereas O(ε^{-2}\log P) qubits suffice.

As silicon photonic integrated circuits (PICs) scale in complexity, testing and calibration increasingly depend on effective phase modulation mechanisms. This work compares thermally induced phase modulation and carrier-based electrical modulation in Mach-Zehnder and microring modulators. The devices are designed and evaluated for extinction ratio, tuning efficiency, power consumption, and modulation bandwidth. The study identifies key trade-offs among modulation speed, energy consumption, and tuning controllability that directly influence the suitability of these methods for test signal generation and calibration tasks. The results highlight the relative advantages and limitations of thermal and electrical approaches across different operating regimes. These findings provide practical design guidance for selecting phase modulation strategies in scalable silicon photonic systems with integrated test and calibration requirements.

In seismology and related fields, the measurement of rotation in all three spatial dimensions is essential to complement the observation of translations. Access to all six degrees of freedom allows for full reconstruction of seismic wavefields and improves the understanding of complex ground motion during seismic events. In this regard, Sagnac interferometers in the form of large active ring laser systems have demonstrated remarkable performance. So-called passive ring gyroscopes offer the potential to bypass some of the limitations of active ring lasers and could represent a promising complement to existing sensor technology. Here, we present a prototype of a transportable three dimensional free-space passive ring gyroscope, reaching a sensitivity in the micro rad/s/sqrt(Hz) regime in all spatial dimensions. We demonstrate the sensor performance by reconstructing the rotational components of a simulated seismic event.

Velocity slip at the solid--fluid (SF) interface plays a key role in fluid transport at the nanoscale, and the SF friction coefficient has been extensively studied because it indicates the degree of slippage. Owing to the scale of this phenomenon, molecular dynamics (MD) simulations are commonly employed using two major approaches: the Green-Kubo integral method in equilibrium MD (EMD), and the direct calculation of friction force and slip velocity in non-equilibrium MD (NEMD) systems under shear. Regarding the latter, a strict definition of the slip velocity is missing due to the nonzero thickness of the boundary at the microscale, and the average velocity of the first adsorption layer or the velocity at the boundary obtained by extrapolation or interpolation is often used. In this study, we propose an alternative description of the slip velocity based on a thermal perspective from the two different scales, i.e., at the macroscale, frictional heat is defined as the product of the friction force and slip velocity, whereas at the microscale, it can be expressed as the sum of the works exerted on the fluid and solid by each other. By combining the two different scales, we defined the slip velocity based on the dissipation induced at the SF interface under shear, which avoids the arbitrariness in the slip velocity at the microscale.

We present a forcing-informed (FI) resolvent analysis framework to identify input-output relations for statistically stationary self-sustained unsteady flows. The central idea of this method is to inform the resolvent operator about the spatiotemporal structures of the nonlinear terms that act as exogenous forcing with respect to the mean flow. To construct the FI resolvent operator, we estimate the basis vectors for the input subspace spanned by forcing snapshots and, similarly, for the output subspace, from simulation data. The extracted FI response and forcing modes are expressed through the estimated bases of the output and input subspaces, respectively, and the singular values of the FI resolvent operator correspond to the actual output amplitudes. These properties ensure that the extracted modes are consistent with the actual self-sustained flow fields. Additionally, the forcing snapshots can be used to construct the linear operator, enabling a fully data-driven FI resolvent analysis. The proposed framework is validated using the Stuart-Landau oscillator and demonstrated for a two-dimensional cylinder wake and a three-dimensional transitional boundary layer. We successfully identify the gains and the corresponding pairs of forcing and response modes, even at frequencies where the nonlinear amplification mechanism is crucial. Furthermore, leveraging the balance between the time-averaged energy amplification/attenuation by the linear operator and nonlinear forcing, we introduce a nonlinear energy transfer map that identifies the spatial domains where the extracted forcing mode injects or removes fluctuation energy, thereby providing key physical insight into the self-sustaining mechanisms.

Tree-like structures appear in many areas of science, and their shapes can help understand the underlying processes they drive or that give rise to them. By thinking of these structures as geometric graphs in $\mathbb{R}^3$, we gain access to tools from computational geometry and topology to study them. In this paper, we adopt the theory of quadratic forms to measure the directional spread of geometric graphs, and we introduce the hexplot model -- equipped with a metric derived from the Fisher metric on the standard triangle -- to visualize, measure, and collect statistics.

Tsetlin Machine (TM) is a logic-based machine learning approach that relies on simple bitwise operations and finite-state automata, which makes it attractive for edge AI deployments. Recent work has focused on co-processor and accelerator designs based on Tsetlin Machines (TMs). Although these designs achieve high performance, they typically depend on tightly coupled interfaces, microcode-style programming, and external host processors, limiting flexibility and ease of programming. In this work, we present a domain-specific RISC-V microprocessor architecture and design flow tailored for TM inference. Leveraging the modular structure of RISC-V, we design a reduced instruction subset processor that retains programmability while targeting improved performance and lower energy consumption for TM workloads. Instruction profiling is employed to guide instruction reduction, followed by datapath and control path simplifications tailored to TM inference. Both the baseline RV32IM core and the proposed reduced core are evaluated across multiple datasets and compared with Binarized Neural Networks (BNNs), which serve as a hardware-efficient baseline due to their reliance on bitwise operations during inference. Results show that TM achieves comparable or higher accuracy (e.g., up to 88.18% on CIFAR-2 compared to 60.0% for BNN) while reducing execution time by up to 98% across multiple datasets. Furthermore, the proposed design achieves an average $29.7\times$ reduction in energy consumption, demonstrating its effectiveness for programmable and efficient edge AI systems.

Graph neural networks (GNNs) provide a flexible framework for learning from scientific data linked through physical, biological, or functional relationships. One promising domain is plant physiology, where measured responses often arise from multiple interacting processes whose exact separation remains difficult even with manual intervention. In plant physiology, a key example is the A-Ci curve, which relates net CO2 assimilation rate (Anet) to leaf intercellular CO2 concentration (Ci) and is used to estimate photosynthetic parameters in leaf and crop-canopy models. However, reliable estimation requires identifying the active biochemical limitation state at each curve point, which remains a major source of uncertainty. Here, we formulate limitation-state identification along A-Ci curves as a graph-based node classification problem, with curve points as nodes. Domain-specific graph representations are created using distance-based k-nearest-neighbor (kNN) and auxiliary-signal-guided (ASG) connectivity, with edge attributes encoding pairwise relations. The framework was evaluated against conventional learning baselines, graph-based architectures, and an automated fitting-based benchmark. Results on a large synthetic dataset with known ground-truth limitation states show that graph-based models improve classification, particularly near biochemical transition regions. The best-performing configuration, SEAGAN (domain-Specific and Edge-Aware Graph Attention Network for Dynamic Plant Processes), integrates process-aware node features, edge attributes, kNN connectivity, and graph attention with weighted cross-entropy loss, achieving an F1-score of 0.857 and an accuracy of 0.882. The results show that representing A-Ci curves as graphs improves biochemical limitation-state analysis, with edge-aware attention over local kNN neighborhoods providing the most effective strategy.

Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a geometric screen that proposes a high-recall family of admissible arrows, identifies non-closing visible pairs as latent-obstruction candidates, and passes the reduced family to downstream score-based or differentiable discovery routines. The second algorithmic contribution, Spectral Kan-Do Flow Matching (SKFM), learns amortized intervention fields and factors latent curvature spectrally, exposing the direct Lie-space endpoint toward which BRIDGE points. A detailed set of experiments show that both algorithms are capable of discovering causal models with latent confounders while collapsing the super-exponential space of possible DAGs by many orders of magnitude. This paper introduces a new paradigm in causal discovery, where latent structure is inferred directly from the geometry of intervention-induced flows.

Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.

Dense Eisenstein--Jacobi (EJ) networks are degree-six algebraic interconnection networks whose finite quotient geometry is naturally represented by a hexagonal axial-coordinate ball. This paper studies non-redundant one-to-all broadcast repair in the dense EJ network generated by $α=(t+1)+tω$, where $t$ is the network diameter. We propose EJ-MOEM, a multi-orientation edge-minimum repair method that evaluates a constant-size family of hexagonal broadcast-tree orientations, selects a fault-aware candidate, contracts the fault-pruned tree into healthy components, and reconnects these components using external component-crossing repair edges. The resulting structure is a rooted spanning tree of the healthy subgraph: every healthy node receives the message exactly once, no faulty node is used, and the original healthy tree components are preserved. We prove that, for a chosen orientation whose fault-pruned component graph is connected, exactly $c-1$ external repair edges are necessary and sufficient, where $c$ is the number of healthy components. We also prove a depth-certificate theorem for EJ coordinate-reduction trees: every one-fault placement admits a repair of depth at most $t+1$, and every two-fault placement admits a repair of depth at most $t+2$. The proof uses the three-strip representation of EJ hexagons, a sector-suffix attachment lemma, a non-adjacent-sector separation lemma, and a six-direction shielding classification for paired cuts. Extended validation includes exhaustive one- and two-fault enumeration for $t=2,\ldots,12,14,16,18$ (up to $N=1027$ and 525,825 two-fault placements at $t=18$), structured theorem-critical tests through $t=30$, and large random tests through $t=200$, all with 100\% success and no violation of the theorem.

Circulant interconnection networks provide symmetric addressing, compact generator descriptions, and uniform local connectivity. This paper maps a degree--redundancy landscape for a fault-tolerant two-hop primitive in directed circulants: given $n$ nodes and degree budget $m$, how large can the worst-case shared-relay multiplicity $R(n,m)$ be? A node is a shared relay for an ordered terminal pair if it has outgoing links to both terminals; an $f$-relay-fault-tolerant circulant requires at least $f+1$ such relays for every pair. The underlying feasibility condition is a cyclic difference-multiplicity condition, which we use as a mathematical tool rather than claim as a new object. The contribution is the network-design framework around this tool: the parameters $R(n,m)$ and $D_f(n)$, a negative theorem for interval circulants, relay-table preprocessing and lookup algorithms, adversarial and random failure guarantees, load-balance scope, certified upper-bound interpretation of heuristic designs, exact small-$n$ calibration, a software lookup-versus-search microbenchmark, and a reproducible study of 526,539 generator sets. The results show that generator choice critically determines worst-case relay survivability: optimized threshold designs achieve $f$-relay-fault tolerance within about $1.16$--$1.63$ of the counting lower bound, while standard interval generators can fail structurally even at much larger degrees.

Eisenstein--Jacobi (EJ) networks are degree-six quotient-lattice interconnection networks. For a generator $α=a+bρ$, let $N=a^2+ab+b^2$ and $d=\gcd(a,b)$. If $d=1$, the three natural unit directions already give three edge-disjoint Hamiltonian cycles. If $d>1$, each unit direction splits into $d$ cycles and the EDHC problem becomes a cycle-splicing problem. Existing non-coprime EJ decompositions prove existence by using a rectangular representation and exchange schedules. This paper develops a different, local switch calculus in the natural Cayley geometry. The first two Hamiltonian cycles are built using the minimum possible $d-1$ intercomponent switches each, and the third factor is obtained as the unused edge complement. The contribution is deliberately not a new existence theorem for all non-coprime EJ networks; rather, it is a compact, formula-driven, minimal-switch decomposition for Euclidean-residue families whose complement incidence is proved symbolically. The proof separates four ingredients: component-label collapse, anchor cancellation, noncollision of lifted switch representatives, and connected complement incidence. No infinite-family theorem in this manuscript is proved by finite witnesses or by computational enumeration. The theorem scope is stated for the parameter ranges where an algebraic complement-incidence certificate is written down. Tables and CSV data are used only to verify and reproduce the formulas, never as proof of an infinite-family theorem.

We consider an intrusion detection task in which a defender must jointly optimize sensor placement locations and orientations to minimize the probability of missed detection of an intruder traversing a protected environment. We decompose this problem into a meta problem, termed SensorPlacement, and an embedded subproblem, termed OrientationScheduling. The OrientationScheduling subproblem, for a fixed sensor placement, is modeled as a 2-player zero-sum game between the defender and the intruder, where the defender seeks an orientation strategy for the deployed sensors to minimize the probability of missed detection, while the intruder seeks a path selection strategy to maximize it. Since the defender's strategy space grows combinatorially with the number of sensors and orientations, solving the game via standard linear programming becomes prohibitive. To this end, we develop an iterative and efficient equilibrium-seeking algorithm that exploits the structure of the game's payoff function and establishes theoretical guarantees for convergence to the Nash equilibrium (NE) of the game. This NE value is then used as a utility measure in the SensorPlacement meta problem. We show that this game-value-based utility function is weakly submodular over the set of sensor placements and propose a greedy placement algorithm with near-optimality guarantees. To our knowledge, this is the first unified framework to integrate game-theoretic utility design with (weak) submodular optimization, enabling principled joint optimization of sensor placement and orientation scheduling. Through extensive simulations, we demonstrate that the proposed approach achieves near-optimal detection performance while significantly reducing computation time compared to baselines.

Standard MCMC diagnostics ($\hat{R}$, effective sample size, divergence counts) detect whether a chain has mixed, but not why it has not. We ask whether the centring/non-centring obstruction in hierarchical models has a geometric cause beyond the metric. The joint parameter space is a fiber bundle (hyperparameters the base, group-level parameters the fibers), and the Fisher information metric induces an Ehresmann connection $A = -G_{FF}^{-1}G_{BF}$; the natural hypothesis is that the obstruction is its curvature, felt by the sampler as holonomy. We prove this false. The connection is flat for any smooth hierarchical posterior, not only the Gaussian case, because its horizontal leaves are the level sets of the fiber score $\partial_α\log p$: there is no geometric obstruction above the metric. What remains is statistical, not geometric, and the flat connection identifies it as a single quantity: the conditional dependence of fiber on base, governed per group by the prior fraction $π_j$, the classical pooling factor. From it the framework recovers the established picture, that prior-dominated groups mix slowly and that the optimal per-group non-centring weight follows in closed form, and a simulation study separates this base-fiber coupling from the funnel, a distinct base-space pathology, by their opposite dependence on the hierarchical variance. A direct attribution test confirms that NUTS does not transport the fiber: the chain-level footprint is excess conditional autocorrelation in prior-dominated groups, exactly as $π_j$ predicts. Genuine, even rotational, curvature does appear, but only for connections built from a sampler's working metric (a fixed mass matrix), where holonomy re-enters as an algorithmic rather than geometric phenomenon. The prior-fraction diagnostic is distributed as the R package fibr, with the geometric methods as accompanying reproduction code.

We introduce the CLUSTER algorithm (\textbf{c}oordinate-\textbf{l}evel \textbf{u}pdate \textbf{s}trategy for \textbf{t}rust-region step \textbf{e}valuation \textbf{r}efinement) for local derivative-free optimization problems where there is a cost to changing each parameter (or clusters of parameters). For example, this type of cost model is appropriate for optimizing robot-controlled laboratory experiments, in which a robot may incur a separate motion for each parameter cluster to be adjusted. We build off of a class of quadratic-interpolation optimization algorithms by Powell and Conn that are known to perform well for twice-differentiable objectives (e.g. low-noise experiments), and show that the CLUSTER variants improve performance on a variety of test problems (including an optics laboratory experiment) by around 50$\%$, and greatly outperform common competing algorithms for laboratory optimization (Bayesian optimization and Nelder--Mead). We also adapt the convergence proof of the Conn algorithm to obtain a similar convergence guarantee for CLUSTER-Conn.

In practical multispectral computed tomography (MSCT), the scanning geometric parameters under different X-ray energy spectra are often inconsistent, and the distributions of the energy spectra are even ray-dependent. However, existing algorithms cannot effectively and accurately solve the associated image reconstruction problem. To address this limitation, using the proposed aggregated energy spectra, we approximate the Jacobian matrix of the nonlinear forward operator at certain special points (e.g., the zero point) as a block product of a diagonal matrix composed of projection matrices and a very small-scale matrix, and then based on this matrix with a special structure, propose an efficient and accurate image reconstruction algorithm tailored for geometric-inconsistent MSCT with ray-dependent energy spectra. Under appropriate conditions, we establish the convergence theory for the proposed algorithm. Furthermore, numerical experiments using both noiseless and noisy projection data are conducted to verify the performance of the proposed algorithm, which demonstrate that the efficiency and accuracy of this algorithm are much higher than existing algorithms, offering the flexibility and scalability to accommodate various MSCT imaging configurations.

Cosmic-ray muon tomography records only a few detector-plane crossings per particle, while material information enters through stochastic scattering and energy loss along the path. Most pipelines first compress these hits to a per-muon scattering summary and assign a nominal momentum, moving the inverse problem away from the raw measurements. We introduce Raw-Hit Muon Tomography (RHMT), a measurement-domain formulation built directly on detector hits. RHMT-S projects out the unknown straight track and evaluates the remaining hit contrast with a Fermi--Eyges covariance; marginalizing the unknown scattering scale gives a blank-calibrated Student-$t$-type likelihood. RHMT-E fits the hits in a six-plane magnetic spectrometer to estimate each muon's log momentum loss and models it as a Bethe--Bloch line integral of the electron-density-related contrast $ρZ/A$. In a controlled Geant4 benchmark, RHMT-S improves the mean ROC-AUC over four-plane scattering baselines ($0.84$--$0.86$ versus $0.81$ for ASR), and RHMT-E provides a separate energy-loss contrast for aluminium, where scattering contrast is weak.

We include elliptical cross-sections to physically represent people, and irregular polygons to represent wheelchair users, in an anisotropic social force model whose velocity and angular dependence also captures the social tendency for people to avoid walking into one another. Physical interactions are included that depend on the area of overlap between people, or obstacles, to capture normal forces that resist compression and tangential forces that resist sliding motion. The model is further extended to include decision making capabilities, small social groups, the spread of panic, and herding behavior. A large box store is simulated during an evacuation where people move through the store, along the shortest path, to their desired exits. The effects of exit choice, or the perceived availability of exits, on exit times is elucidated. It is found that ignoring 'staff only' exits, and only exiting from the main entrances, can significantly increase average egress times.

The question of optimal experimental design has been addressed in a vast variety of contexts and answered using manifold approaches. Assuming additive white Gaussian noise, this work applies the Bayesian framework for design optimization to the posterior distribution after marginalization over linear parameters and discusses the implications. Examples of exponentially decaying signals with and without oscillations complement the discussion. Application of the examples considered include but are not limited to nuclear magnetic resonance and relaxometry experiments using solid-state spins sensors.

Extending earlier work in Physics-informed Meta-instrument for eXperiments (PiMiX) [1], PiMiX~2.0 is an artificial-intelligence (AI)-enhanced data-fusion and analysis framework that integrates multi-experiment multi-modal radiographic imaging and tomography (RadIT) with physics-informed reasoning and agentic AI workflows. The framework supports automated data ingestion, multimodal image processing from one or more experiments, three-dimensional (3D) and time-resolved three-dimensional (4D) reconstruction, and physics-aware interpretation of experimental observations. The PiMiX agents are designed for deployment on desktop and laptop systems commonly used in experimental workflows, while remaining scalable to high-performance computing environments for computationally intensive tasks. By coupling RadIT instrumentation and measurements with geometry, physics, computation, and statistical inference, PiMiX 2.0 aims to accelerate RadIT data processing, knowledge extraction, improve reproducibility, and enable more integrated analysis and workflows in high-temperature plasmas, nuclear fusion, advanced manufacturing, other static and dynamic experiments.

We report temperature-dependent charge transport measurements in p-type high-resistivity germanium crystals grown at the University of South Dakota. Hall-effect and four-probe resistivity measurements were performed on five planar samples over the temperature range of 2-300 K. The apparent Hall mobility exceeds 10$^6$ cm$^2$ V$^{-1}$ s${^-1}$ at cryogenic temperatures and decreases systematically with increasing temperature, while the effective Hall carrier concentration exhibits strong carrier freeze-out behavior at low temperatures. The combined evolution of Hall mobility, effective Hall carrier concentration, and resistivity reveals distinct transport regimes associated with carrier freeze-out, extrinsic conduction, and phonon-limited scattering. The transport behavior is interpreted using a Matthiessens-rule-inspired phenomenological mobility model motivated by the combined influence of ionized impurity, neutral impurity, and acoustic phonon scattering. Variations among samples are correlated with differences in effective Hall carrier concentration and transport behavior. These measurements establish a transport baseline for USD-grown high-resistivity germanium crystals and provide guidance for future material optimization toward detector-grade high-purity germanium for low-background rare-event detector applications.