We provide an inferential framework to assess variable importance for heterogeneous treatment effects. This assessment is especially useful in high-risk domains such as medicine, where decision makers hesitate to rely on black-box treatment recommendation algorithms. The variable importance measures we consider are local in that they may differ across individuals, while the inference is global in that it tests whether a given variable is important for any individual. Our approach builds on recent developments in semiparametric theory for function-valued parameters, and is valid even when statistical machine learning algorithms are employed to quantify treatment effect heterogeneity. We demonstrate the applicability of our method to infectious disease prevention strategies.

A MICRO 2024 best paper runner-up publication (the Mess paper) with all three artifact badges awarded (including ``Reproducible'') proposes a new benchmark to evaluate real and simulated memory system performance. The publication contends that Ramulator 2.0 and DAMOV (ZSim+Ramulator) (along with other existing memory system simulators) ``poorly resemble the actual system performance'' and asserts that their simulator is better. In this paper, we show that the Mess paper has 1) demonstrable technical misconfigurations, 2) methodological errors in interpreting simulation statistics, and 3) an incomplete artifact that makes its key results irreproducible. We demonstrate that the Ramulator 2.0 simulation results reported in the Mess paper are incorrect due to multiple configuration errors instead of inherent simulation inaccuracy claimed by the Mess paper. We show that by correctly configuring Ramulator 2.0, Ramulator 2.0's simulated memory system performance actually resembles real system characteristics well, and thus a key claimed contribution of the Mess paper is factually incorrect. We also identify that the DAMOV simulation results in the Mess paper use wrong simulation statistics that are unrelated to the simulated DRAM performance. We show that DAMOV's simulated DRAM latency is not constant, in contrast to the Mess paper's claim. Moreover, the Mess paper's artifact repository lacks the necessary sources to fully reproduce all the Mess paper's results. We find that the experiment scripts use simulator executables and other resources that are neither described in the Mess paper nor found in the artifact repository. We strongly encourage the computer architecture community to consider our corrections to the Ramulator 2.0 and DAMOV results of the Mess paper to prevent the propagation of inaccurate and misleading results and to maintain the reliability of the scientific record.

In this paper we study the short-maturity asymptotics of up-and-in barrier options under a broad class of stochastic volatility models. Our approach uses Malliavin calculus techniques, typically used for linear stochastic partial differential equations, to analyse the law of the supremum of the log-price process. We derive a concentration inequality and explicit bounds on the density of the supremum in terms of the time to maturity. These results yield an upper bound on the asymptotic decay rate of up-and-in barrier option prices as maturity vanishes. We further demonstrate the applicability of our framework to the rough Bergomi model and validate the theoretical results with numerical experiments.

We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets of values, and this allows us to define a complement operator on types that acts as a negation on typing formulas. We show that the complement allows us to derive a wide range of refutation principles within the system, including the type-theoretic analogue of co-implication, and we use them to certify that a number of Erlang-like programs go wrong. An expressive axiomatisation of the complement operator via subtyping is shown decidable, and the type system as a whole is shown to be not only sound, but also complete for normal forms.

Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly to those on large scales. Adaptive resolution, multi-physics, and hybrid numerical methods have enabled tremendous progress on the spatial, physics, and numerical challenges involved. But often the limiter for following the long timescales of global evolution is the extremely short numerical timestep required in some subdomains (which leads to their dominating simulation costs). Recently several approaches have been developed for tackling this in problems where the short timescale solution is sampled and then projected as an effective subgrid model over longer timescales (e.g. 'zooming in and out'). We generalize these to a family of models where time evolution is modulated by a variable but continuous in space-and-time dilation/stretch factor $a({\bf x},\,t)$. This extends previous well-studied approaches (including reduced-speed-of-light and binary orbital dynamics methods), and ensures that the system comes to correct local steady-state solutions, and derive criteria that the dilation factor/timesteps/resolution must obey to ensure good behavior. We present a variety of generalizations to different physics or coupling scales. Compared to previous approaches, this method makes it possible to avoid imprinting arbitrary scales where there is no clear scale-separation, and couples well to Lagrangian or Eulerian methods. It is flexible and easily-implemented and we demonstrate its validity (and limitations) in test problems. We discuss the relationship between these methods and physical time dilation in GRMHD. We demonstrate how this can be used to obtain effective speedup factors exceeding $\gtrsim 10^{4}$ in multiphysics simulations.

LaMg2H7 is a ternary wide band gap semiconductor that is a member of the hydride family. The bulk physical characteristics of the LaMg2H7 compound, including its structural, electronic band structure, elastic, thermal, and optical characteristics, have been examined in this work utilizing density functional theory (DFT). The elastic constants indicate that {\rm LaMg}_2H_7 is mechanically stable, brittle in nature, and anisotropic. This studied compound possesses a moderate level of hardness. The band structure and density of states have been examined to have a better understanding of its electronic behavior. The intrinsic carrier concentrations and effective masses have been determined using the band structure. The gravimetric hydrogen storage capacity (Cwt%) has been calculated, indicating that this compound is suitable for hydrogen storage applications. This compound is dynamically stable, as confirmed by its phonon dispersion. Here, the details of this wide-band-gap semiconductor's reflectivity, absorption coefficient, refractive index, dielectric function, optical conductivity, and loss function are investigated. The substance is a moderate reflector of ultraviolet (UV) light. The absorption and conductivity support the gap in the band structure. The thermodynamic properties, such as bulk modulus, internal energy, specific heat capacity, entropy, thermal expansion coefficient, and Debye temperature, have been explored at varying temperatures and pressures. {\rm LaMg}_2H_7 has a moderate level of melting temperature with higher lattice thermal conductivity. The value of the thermal expansion coefficient and minimum thermal conductivity is highly recommended for use as a thermal barrier coating (TBC).

We study the dissociative associated production of a $J/ψ$ meson and a dimuon via double parton scattering (DPS) in nucleus--proton ultraperipheral collisions. This new channel, characterized by a rapidity gap, is sensitive to the photon and gluon distributions of the proton. We derive a DPS pocket formula for this process, together with a corresponding expression for the effective cross section. Furthermore, we demonstrate the kinematic dependence of the effective cross section and present predictions for the differential DPS cross section at LHC and FCC energies.

The recent detection of refractory molecules in massive star-forming regions provides a means of probing the innermost regions of disks around massive stars. These detections also make it possible to explore the chemical composition of refractories through gas-phase observations. In this regard, identifying refractory compounds containing sulfur could reveal potential connections between sulfur and refractories, as well as help determine the sulfur budget in these extreme environments. We find convincing evidence of a reliable detection of CaS, and tentative detections of KS and KSH in the disk G351.77-mm1. These are the first ever identifications of these species in the interstellar medium. The CaS, KS, and KSH column densities are about 3 orders of magnitude lower than those of the abundant sulfur compounds SO$_2$, CH$_3$SH and SiS, proving that these species are not the major reservoir of sulfur at the spatial scales probed by our observations. Higher angular resolution observations at different wavelengths are required to confirm these detections, which are of paramount importance to gain insights into the formation of gas-phase refractory molecules.

The 4-metre Multi-Object Spectroscopic Telescope Cosmology Redshift Survey (4MOST CRS) will obtain 5.4 million spectroscopic redshifts over ~5700 deg^2 to map large-scale structure and enable measurements of baryon acoustic oscillations, growth rates via redshift-space distortions, and cross-correlations with weak-lensing surveys. We validate the target selections, photometry, masking, systematics, and redshift distributions of the bright galaxy (BG) and luminous red galaxy (LRG) target catalogues selected from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey DR10.1 (LS) imaging. We measure the angular two-point correlation function, $w(θ)$, test masking strategies, and recover redshift distributions via cross-correlation with DESI DR1 spectroscopy. For BGs, we adopt LS MASKBITS that veto bright stars and extended sources; for LRGs, we pair these with unblurred coadds of the WISE imaging (unWISE) W1 artefact masks. These choices suppress small-scale excess power without imprinting large-scale modes. A Limber-scaling test across BG $r$-band magnitude slices shows that, after applying the scaling, the $w(θ)$ curves collapse to a near-common power law, demonstrating photometric uniformity with depth and consistency between the North and South Galactic Caps. Cross-correlations with DESI spectroscopy recover the expected N(z), albeit with high shot noise at the brightest magnitudes. For LRGs, angular clustering in photo-$z$ slices ($0.4\le z<1.0$) is consistent between the Dark Energy Camera Legacy Survey (DECaLS) and Dark Energy Survey (DES) footprints and is well described by an approximate power law once photo-$z$ smearing is included; halo-occupation fits are consistent with recent LRG studies. Together, these tests indicate that the masks and target selections yield reliable clustering statistics, supporting precision large-scale structure analyses with 4MOST CRS.

Antimicrobial resistance (AMR) threatens global health. A promising and underexplored strategy to tackle this problem is sequential therapies exploiting collateral sensitivity (CS), whereby resistance to one drug increases sensitivity to another. Here, we develop a four-genotype stochastic birth-death model with two bacteriostatic antibiotics to identify switching periods that maximize bacterial extinction under subinhibitory concentrations. We show that extinction probability depends nonlinearly on switching period, with stepwise increases aligned to discrete switch events: fast sequential therapies are suboptimal as they do not allow for the evolution of resistance, a key ingredient in these therapies. A geometric distribution framework accurately predicts cumulative extinction probabilities, where the per-switch extinction probability rises with switching period. We further derive a heuristic approximation for the extinction probability based on times to fixation of single-resistant mutants. Sensitivity analyses reveal that strong reciprocal CS is required for this strategy to work, and we explore how increasing antibiotic doses and higher mutation rates modulate extinction in a nonmonotonic manner. Finally, we discuss how longer therapies maximize extinction but also cause higher resistance, leading to a Pareto front of optimal switching periods. Our results provide quantitative design principles for in vitro and clinical sequential antibiotic therapies, underscoring the potential of CS-guided regimens to suppress resistance evolution and eradicate infections.

This work tackles the problem of achieving consistent drying rates of a solution film deposited on a $20\,\rm{cm}$-wide substrate ($\approx $ silicon-wafer size) that is driven under a narrow air flow ejected by a slot nozzle (or "air knife"). The main prerequisite of the work is that the drying rate of the solution film is highly decisive for a certain performance indicator of the deposited film at a particular, critical concentration $c_{\rm crit.}$. Empirically, this concentration can be associated with the visual observation of "the drying front" as, for the example of hybrid perovskite thin films, caused by the onset of a crystallization process. As a main result, a set of equations for achieving consistent drying rates, $\dot{d}_{\rm crit.}$, at critical concentration is presented that is solved by a simple two-staged least-squares gradient decent. From the resulting velocity vector, an optimal trajectory of the air knife, $\hat{x}(t)$, depending on the initial wet film thickness distribution over the substrate is derived. It is demonstrated that scenarios where the wet film thickness increases along the movement direction of the air knife have a consistent set of equations. Wet thin films that do not obey this constraint, as in the demonstrated scenarios with convex and concave shapes of wet film thickness over the substrate area, cannot always be dried in a fully consistent way by optimizing the air-knife trajectory alone. However, with the presented methods, optimal trajectories can still be derived that enable more homogeneous drying results.

Several experiments searching for direct dark matter interactions aim to achieve unprecedented sensitivity to sub-GeV/c$^2$ dark matter masses through elastic scattering with nuclei in various target crystals at cryogenic temperatures. Hydrogen-rich materials, such as organic compounds, are promising candidates for the detection of sub-GeV/c$^2$ dark matter due to favourable kinematics. In this paper, we present for the first time results obtained with a sugar-based phonon detector employing sucrose crystals ($\mathbf{C_{12}H_{22}O_{11}}$), capable of particle detection with associated scintillation light.

In arXiv:2509.02905 [hep-th], we introduced an approximation that allows one to study Horowitz-Polchinski backgrounds beyond the weak coupling regime. In this paper we describe the resulting solutions, and discuss a few related issues.

String theory relies on spacetime supersymmetry to guarantee the existence of stable vacua. In this review, we survey two features of non-supersymmetric strings that challenge both aspects: the appearance of tachyons and worldsheet tadpoles. We describe how tachyons arise, how to characterise their presence in closed strings and in their orientifold projections, and how off-shell approaches can be used to tackle them. We then turn to tachyon-free, non-supersymmetric strings. After introducing the simplest ten-dimensional models, we address the additional issues raised by tadpoles and the spacetime consequences of their cancellation. Finally, we discuss recent attempts to explore the non-supersymmetric string landscape.

Superconducting radiation detectors typically exhibit detection and single photon sensitivity limited to the mid infrared wavelength range. Extending their detection capabilities into the far infrared range (>10 um) requires careful selection of substrate materials and detector geometries. The overall detection efficiency is linked to absorption and coupling efficiencies. In this study, the resonator geometry and absorption efficiency were estimated using electromagnetic simulations in CST Microwave Studio for a lumped-element meander structure. Simulations were performed for the 12 to 50 um wavelength range, corresponding to the Infrared Free Electron Laser (IR FEL) at RRCAT, Indore. Absorption in the meander inductor was influenced by the substrate material, thickness, and impedance matching between the detector and incident photon medium. The results indicate that SiO2 and diamond substrates are suitable for developing lumped-element kinetic inductance detectors (LEKID) in this range. Optimized meander geometries on diamond substrates demonstrated absorption efficiencies of up to 95% for narrow bandwidths and over 50% for wide bandwidths. A 30-pixel LEKID structure was fabricated using electron beam lithography on a 500 um SiO2 coated Si substrate, with a 20 nm thick Ti40V60 alloy resonator. Experimental absorption efficiency was determined through transmission and reflection measurements. Results show that in the 14 to 26 um IR-FEL range, the LEKID achieved up to 75% absorption efficiency. These studies demonstrate that the LEKID structure is ideal for detecting far infrared wavelengths above 10 um, with high absorption efficiency.

We present a systematic study of the evolution of the band structure in the Fe-based superconductor family BaFe$_{2-x}$M$_x$As$_2$ (M = Cr, Co, Cu, Ru and Mn) using polarization-dependent angle-resolved photoemission spectroscopy (ARPES). Low-substituted samples, with comparable spin-density wave transition temperatures ($T_\text{SDW}$), were chosen to facilitate controlled comparisons. The sizes of the central hole pockets ($α$, $β$, and $γ$) remain largely unchanged across different substitutions, showing no clear correlation with either $T_\text{SDW}$ or the As height relative to the Fe planes. However, subtle trends are observed: a modest increase in the size of the $η_\text{X}$ electron pocket correlates with the suppression of $T_\text{SDW}$. Furthermore, the contraction of the $η_\text{X}$ pocket appears to be linked to an increase in the As height relative to the Fe planes. Our results suggest that the suppression of $T_\text{SDW}$ is primarily driven by changes in the Fe-As bond length, with the effect being more pronounced in electronic states with planar character. These findings provide insight into the electronic structure of BaFe$_{2-x}$M$_x$As$_2$.

Let $k$ be an arbitrary field of characteristic $p$ and let $G$ be a finite group. We investigate the representation type, derived representation type, and singularity category of the $k$-linear (cohomological) Mackey algebra. We classify when the cohomological Mackey algebra is wild for $G$ a cyclic $p$-group. Furthermore, we show the cohomological Mackey algebra is derived wild whenever $G$ surjects onto a $p$-group of order more than two, and the Mackey algebra is derived wild whenever $G$ is a nontrivial $p$-group. Derived wildness has some immediate consequences in equivariant homotopy theory. In particular, for the constant Mackey functor $\underline{k}$, the classification of compact modules over the $G$-equivariant Eilenberg--MacLane spectrum $H\underline{k}$ is also wild whenever $G$ surjects onto a $p$-group of order more than two. Thus, in contrast to recent work at the prime $2$ by Dugger, Hazel, and the second author, no meaningful classification of compact $C_p$-equivariant $H\underline{\mathbb{F}}_p$-modules exists at odd primes. For the Burnside Mackey functor $\underline{A}_k$, there is no classification of compact $G$-equivariant $H\underline{A}_k$-modules whenever $G$ is a nontrivial $p$-group.

For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving problems that are otherwise quite intractable. Being surprising and unexpected, dualities have been taken to raise philosophical questions about the nature and formulation of scientific theories, scientific realism, emergence, symmetries, explanation, understanding, and theory construction. This book discusses what dualities are, gives a selection of examples, explores the themes and roles that make dualities interesting, and highlights their most salient types. It aims to be an entry point into discussions of dualities in both physics and philosophy. The philosophical discussion emphasises three main topics: whether duals are theoretically equivalent, the view of scientific theories that is suggested by dualities (namely, a geometric view of theories), and the compatibility between duality and emergence.

We first derive the exponential ergodicity of the stochastic theta method (STM) with $θ\in (1/2,1]$ for monotone jump-diffusion stochastic ordinary differential equations (SODEs) under a dissipative condition. Then we establish the weak error estimates of the backward Euler method (BEM), corresponding to the STM with $θ=1$. In particular, the time-independent estimate for the BEM in the jump-free case yields a one-order convergence rate between the exact and numerical invariant measures, answering a question left in {\it Z. Liu and Z. Liu, J. Sci. Comput. (2025) 103:87}.

Magnetic topological semimetals often exhibit unusual electronic and thermal transport due to nontrivial bulk band crossings, enabling simultaneous realization of large anomalous Hall and Nernst conductivities ($σ_{xy}$ and $α_{xy}$). Here, a comprehensive experimental and theoretical study of the anomalous transport properties of ferromagnetic Co$_2$MnSn is reported. First-principles calculations reveal topological Weyl points producing significant Berry curvature, driving dominant intrinsic anomalous Hall/Nernst effects. Electronic and thermal transport measurements demonstrate robust anomalous transport with substantial conductivity values that persist at room temperature ($σ_{xy}\sim$ 500 S/cm, $α_{xy}\sim$ 1.3 A/m/K). We also show how the chemical substitution (via tuning Fermi level) can boost these effects (up to $σ_{xy}\sim$ 1376 S/cm, $α_{xy}\sim$ 1.49 A/m/K at 150 K). These findings position Co$_2$MnSn as a compelling platform for exploring topological transport phenomena and advancing next-generation thermoelectric and spintronic technologies.

Arrays of neutral atoms present a promising system for quantum computing, quantum sensors, and other applications, several of which would profit from the ability to load, cool, and image the atoms in a finite magnetic field. In this work, we develop a technique to image and prepare $^{87}$Rb atom arrays in a finite magnetic field by combining EIT cooling with fluorescence imaging. We achieve an average readout fidelity of $99.7(1)\,\%$ at $98.2(3)\,\%$ survival probability and up to $68(2)\%$ single-atom stochastic loading probability in a 2.3 G magnetic field, with performance validated at fields up to 10 G. We further develop a model to predict the survival probability, which also agrees well with several other atom array experiments. Our technique cools both the axial and radial directions, and will enable future continuously-operated neutral atom quantum processors and quantum sensors.

Perturbation theory, as well as most thermal field resummation methods widely used to study finite-temperature quantum field theories, presents a non-negligible renormalization scale dependence. To address this limitation, we propose an alternative method that combines the renormalization group improvement prescription for the thermal effective potential with the optimized perturbation theory variational resummation technique. Here, we apply this new framework, termed variational renormalization group, to evaluate the effective potential of the scalar $λϕ^4$ theory at finite temperatures, which represents a benchmark model for phase transition studies. We show that the proposed approach significantly improves scale stability, compared to the use of optimized perturbation theory alone, across key thermodynamic quantities, including the effective potential, critical temperature, and pressure. These results establish the variational renormalization group as a robust alternative tool for precision studies of thermal phase transitions, with direct implications for cosmological applications (e.g., early-Universe thermodynamics) and condensed matter systems.

Recent years have seen many arguments for cosmic rays (CRs) as an important influence on galactic and circumgalactic (CGM) physics, star and galaxy formation. We present a pedagogical overview of state-of-the-art modeling of CR-magnetohydrodynamics (CR-MHD) on macro scales (~kpc), highlighting their fundamental dependence on the micro (< au) scales of CR gyro orbits and meso (~pc) scales of CR mean-free-paths, intended to connect the extragalactic, Galactic, and plasma CR transport modeling communities. We note the pitfalls and systematic errors that arise from older assumptions in CR modeling, including: use of a simple Fokker-Planck equation or ad-hoc two-moment formalisms for transport; assumption of leaky boxes or plane-parallel or shear-periodic boundaries for comparison to local interstellar medium (LISM) observations; ignoring detailed LISM constraints on CR spectra (e.g. focusing only on extragalactic observables or spectrally integrated models); assuming CR transport is mediated by classical models of advection, streaming from self-confinement (super-Alfvenic or Alfvenic), or extrinsic turbulence. We emphasize recent progress addressing these: development of rigorously-derived CR-MHD equations; use of global, 3D galaxy+halo models for LISM comparisons; new methods for full-spectrum dynamics; novel models for intermittent scattering and/or new drivers. We compile extragalactic+LISM observations to show how ~GeV CR transport is being rapidly constrained in the CGM, and present phenomenological models which can be used in future simulations. We conclude by highlighting critical open questions for micro, meso, and macro-scale CR-MHD simulations.

The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be realized in a local sign problem-free Hamiltonian due to the non-positivity of the wavefunction. We show that this is not the case. Despite failing to be stoquastic - the standard criteria for the existence of a sign problem - the double semion model as well as all twisted quantum double phases of matter for finite groups $\mathcal{G}$ can be realized in local Hamiltonians that are sign problem-free within a stochastic series expansion. The lack of a sign problem is not fine-tuned and does not require the Hamiltonian to be exactly solvable, with sign problem-free perturbations allowing access to a variety of topological phase transitions.

Motivated by the studies of twisted generalized Reed-Solomon (TGRS) codes, we initiate the study of twisted elliptic curve codes (TECCs) in this paper. In particular, we study a class of TECCs with one twist. The parity-check matrices of the TECCs are explicitly given by computing the Weil differentials. Then the sufficient and necessary conditions of self-duality are presented. The minimum distances of the TECCs are also determined. Moreover, examples of MDS, AMDS, self-dual and MDS self-dual TECCs are given. Finally, we calculate the dimensions of the Schur squares of TECCs and show the non-equivalence between TECCs and ECCs/GRS codes.

Anisotropic van der Waals (vdW) materials exhibit direction-dependent optical and electronic properties, making them valuable for tailoring directional light-matter interactions. Rhenium disulfide (ReS$_2$) stands out for its strong in-plane anisotropy and its thickness-independent direct-bandgap excitons, which can hybridize with light to form exciton-polaritons. In parallel, metasurfaces, engineered arrays of nanoscale subwavelength resonators, can support ultra-sharp photonic modes in the form of quasi-bound states in the continuum (qBICs). Topological transformations of photonic modes can give rise to flatbands, i.e., dispersionless states with quenched kinetic energy and vanishing group velocity. Intrinsic material anisotropy offers an unexplored route to robust far-field flatband formation and control. Here, we demonstrate how structuring an intrinsically anisotropic excitonic material into a resonant metasurface fundamentally transforms its photonic topological features and light-matter coupling behavior, allowing us to drive and topologically control extended far-field flatband formation. To this end, we fabricate C$_4$-symmetric metasurfaces directly from bulk ReS$_2$. The intrinsic anisotropy lifts the initial double degeneracy of the qBIC mode and yields two distinctly polarized resonances. It also reshapes the topological landscape: the integer topological charge of the qBIC mode splits into momentum-separated half-integer singularities, thereby flattening the far-field photonic dispersion. The resulting topologically-controlled photonic flatbands are then tuned in resonance with the linearly polarized excitonic transitions of ReS$_2$, resulting in two distinct, directionally hybridized exciton-polariton flatband regimes. These findings establish anisotropic vdW metasurfaces as a new platform for topologically engineered flatbands and flatband-driven light-matter coupling.

We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another, given the ability to push up to one block at a time? In particular, we remove the need for fixed (immovable) walls from a 2022 result. This fundamental model of block pushing, introduced in 1999, abstracts the mechanics of many video games. It was shown NP-hard in 2000, but its final complexity remained open for 25 years. Our result uses a new framework for checkable gadgets/gizmos, extending a prior framework for checkable gadgets to handle reconfiguration problems, at the cost of requiring a stronger auxiliary gadget. We also introduce a new connection between the motion-planning-through-gadgets framework (with an agent) and the Graph Orientation Reconfiguration Problem (with no agent), including Nondeterministic Constraint Logic.

Let $G=(V,E)$ be a matching-covered graph, denote by $P$ its perfect matching polytope, and by $L$ the integer lattice generated by the integral points in $P$. In this paper, we give short, polyhedral proofs for two difficult results established by Lovász (1987), and by Carvalho, Lucchesi, and Murty (2002) in a series of three papers totaling over 120 pages. More specifically, we prove that $L$ has a lattice basis consisting solely of incidence vectors of some perfect matchings of $G$, $2x\in L$ for all $x\in \mathrm{lin}(P)\cap \mathbb{Z}^E$, and if $G$ has no Petersen brick then $L = \mathrm{lin}(P)\cap \mathbb{Z}^E$. Our proof avoids major technical aspects of the previous proofs, the most important of these being a characterization of the dual lattice, and a `Petersen-brick-sensitive' ear decomposition result for matching-covered graphs. This is achieved by a novel study of the facial structure of the polytope $P$ and its relationship with the lattice $L$. It is also based on a first-of-its-kind polyhedral characterization of the Petersen graph.

Analyzing students' written solutions to physics questions is a major area in PER. However, gauging student understanding in college courses is bottlenecked by large class sizes, which limits assessments to a multiple-choice (MC) format for ease of grading. Although sufficient in quantifying scientifically correct conceptions, MC assessments do not uncover students' deeper ways of understanding physics. Large language models (LLMs) offer a promising approach for assessing students' written responses at scale. Our study used an LLM, validated by human graders, to classify students' written explanations to three questions on the Energy and Momentum Conceptual Survey as correct or incorrect, and organized students' incorrect explanations into emergent categories. We found that the LLM (GPT-4o) can fairly assess students' explanations, comparable to human graders (0-3% discrepancy). Furthermore, the categories of incorrect explanations were different from corresponding MC distractors, allowing for different and deeper conceptions to become accessible to educators.

Graphical LASSO (GLASSO) is a widely used method for estimating sparse precision matrices and learning undirected graphical models in high-dimensional settings. Because GLASSO penalizes entries of the precision matrix directly, however, it is not scale-invariant. Partial Correlation Graphical LASSO (PCGLASSO), introduced by Carter et al. (2024), addresses this limitation by penalizing partial correlations, which directly characterize conditional dependence. In this paper, we study both statistical and computational properties of the PCGLASSO estimator. Our main contribution is the introduction of a scale-invariant irrepresentability condition for PCGLASSO and the proof that this condition is sufficient for consistent model selection. We further show that this condition is weaker than the corresponding irrepresentability condition for GLASSO, helping to explain the improved empirical behavior of PCGLASSO in settings such as hub-structured graphs. In addition, we develop two efficient algorithms for computing the estimator and analyze the nonconvex optimization problem underlying PCGLASSO, deriving conditions for global uniqueness and showing consistency of all minimizers.