Papers

A staged physics-informed neural network (PINN) is proposed for identifying the inductance, capacitance and parasitic resistances of a DC buck converter from time-domain data. Gradients are released in the order of L to C to rL to rC, a sequence derived from sensitivity analysis. The five-stage schedule recovers L and C to within 5% and the series ESR to 10%, while a three-stage variant attains the same accuracy 11% faster. An 84 factorial sweep confirms that the trained PINN remains accurate for simultaneous 8% perturbations of all four components, achieving a waveform RMSE of 2.6 x 10-2 over 5 ms-an order-of-magnitude better than a simultaneous-training baseline.

Cavity optomechanics represents a frontier research direction in quantum science and technology, centered on the control and exploration of interactions between electromagnetic fields and mechanical motion. Rooted in quantum mechanics, this field realizes efficient coupling and precise manipulation of optical fields and mechanical vibrations through the structural design and precise regulation of optical microcavities and mechanical oscillators, thereby revealing and harnessing novel quantum phenomena. In recent years, cavity optomechanics has evolved into an interdisciplinary frontier integrating quantum optics, condensed matter physics, and quantum precision measurement, exhibiting profound application in both fundamental physics research and quantum information science. With advancements in technologies such as nanomanufacturing and laser cooling, optomechanical interactions have been successfully demonstrated in various experimental systems. Among these platforms, cavity cold-atom systems stand out as one of the ideal platforms for implementing quantum optomechanics. Featuring exceptional environmental isolation, long quantum coherence times, and strong light-matter interaction, these systems provide a crucial testbed for exploring strong and even ultrastrong optomechanical coupling effects as well as rich nonlinear quantum phenomena. This paper reviews the recent progress in optomechanical control and manipulation based on cavity cold-atom systems. We first outline the fundamental principles of standard cavity optomechanical systems. Then, we describe the experimental realization of linear and nonlinear optomechanical couplings in cold-atom systems. After that, we focus on the representative applications of this platform in high-precision quantum sensing, quantum memory, and the preparation of macroscopic nonclassical states. Finally, we give an outlook and challenges in this field.

Optoelectronic Chromatic Dispersion (OED) is a source of significant wavelength-dependent current in photodiodes, offering a pathway to computational spectroscopy in a photodiode-only platform without the need for additional optical or mechanical components. Previous studies have activated OED through light modulation. Here, we present a theoretical and experimental investigation of bias-modulated OED in the C- and L-bands in a Ge PN photodiode, where the applied bias voltage is modulated sinusoidally, and the optical illumination is held constant. The spectral response is due to wavelength-dependent optical absorption together with bias-dependent competition between carrier drift, displacement current, and mobile-charge screening. With the RF phase-shift technique, the maximum measured OED sensitivity is +4.13 deg/nm in the L-band, significantly larger than that of light-modulated OED in Ge. The 15 mdeg phase-noise floor yields a spectral resolution of 3.6 pm. These results establish bm-OED as an electronically reconfigurable dispersive mechanism for applications in chip-scale computational spectrometers, photonic integrated circuits (PICs), on-chip RF photonics, and wavelength-division multiplexing.

Historical code changes provide convenient task boundaries, but do not identify which production functions selected tests exercise or support composing validated behaviors beyond a single change. We present SWE-Nexus, a fully automated pipeline that constructs repository-level implementation tasks from test execution. Four construction agents select tests, adapt tracing and evaluation protocols to each repository, and generate behavioral specifications. For each selected test file, tracing records an observed execution footprint of production function bodies. A scope is retained only if all expected scoring points pass in the original repository and masking the traced bodies causes at least one failure or error. Compatible scopes are composed deterministically, with shared functions counted once and every constituent test file revalidated under the complete combined mask. The benchmark contains 600 tasks from 105 repositories across six programming languages, including 116 atomic and 484 composite tasks. We evaluate 12 models under three agent scaffolds. The best configuration resolves 37.8% of tasks in one attempt, and scope-weighted scoring measures partial recovery. SWE-Nexus enables task construction from validated behavior beyond individual historical changes.

We develop a data-driven approach to dynamic portfolio selection that combines vine-copula simulation with reinforcement learning. The investor has constant relative risk aversion and maximises expected terminal utility with a running penalty on the conditional value-at-risk (CVaR) of one-period losses. We estimate a conditional vine model from historical returns and use it to generate joint scenarios for CVaR evaluation and conditional paths for training a recurrent portfolio policy. Under uniform local derivative bounds, we propagate edgewise pair-copula parameter errors through the conditional transforms to obtain power-law stability bounds in Hellinger distance and total variation. In a finite-horizon investment model, we combine these estimates with a marginal and structural approximation budget to bound policy values, optimal values and the true-market loss of policies selected under a fitted model, with separate simulation and numerical optimisation terms. On a seven-asset panel comprising US and Chinese equities and gold, the selected ensemble of ten trained policies achieves a compound annual growth rate of 34.13% and a Sharpe ratio of 2.31 over 22 complete monthly holding periods, exceeding the corresponding values of six classical and vine-based benchmarks. Combining simulated and historical training data reduces monthly target-to-target turnover by 41.5% relative to training on historical data alone, while maintaining comparable growth.

High penetration of single-phase distributed power production and frequent topology changes can significantly increase voltage unbalance in distribution networks. Reliable probabilistic power flow (PPF) assessment for the network, therefore, must account for topology-dependent power-flow equations, numerical error in the voltage unbalance factor (VUF), and finite-sample uncertainty in power measurements. In this paper, we propose Topology-Adaptive Certified Quantile Estimation (TACQE) to estimate the maximum VUF across monitored electric buses. Following a local network change, TACQE updates the cross-couplings among power-flow sequences, and certifies candidate PPF solutions against the updated nonlinear equations. The resulted power-flow state enclosures provide rigorous bounds on the maximum VUF. Furthermore, we derive independent reference-solver evaluations to calibrate discrepancies from the reference PPF solution. This leads to a uniform sampling bound that yields simultaneous upper-tail probabilities and quantiles, which provides a finite-sample guarantee for the estimated maximum-VUF distribution over an entire range of VUF thresholds. From our numerical simulations across 101 fixed-topology quantiles, it demonstrates that the designed TACQE can provide a fast candidate post-change power flow solution where it reuses most of the previous network model and modifies only the affected bus blocks.

We introduce Weighted Adjoint Matching, a method to finetune a pretrained diffusion or flow matching model given a differentiable reward. We derive it from Adjoint Matching, which reformulates finetuning as a stochastic optimal control problem with a quadratic control cost. Building on the observation that these models generate coarse features before fine details, we place a time-dependent weight on the control cost. A high cost early in the generative process preserves balance and diversity in the coarse features, which carry most of the semantics, while a low cost at the end lets the model increase the reward by refining details. We prove that our method is equivalent to maximizing the reward under time-varying Kullback–Leibler regularization on the generative paths. Experiments on Gaussian mixtures and on MNIST show a better tradeoff between reward and mode balance than Adjoint Matching.

Define $\nabla(n)$ as the least possible number of cells that must be removed from the $n\times n$ square board in order to leave no cycles. Put $L_n=\left\lceil\left((n-1)^2+1\right)/3\right\rceil$. The results of Luccio, Madelaine-Stewart, and Lien-Fu-Shih imply that $\nabla(n)=L_n$ in case $n\equiv 1\pmod 6$ and $n\equiv 4\pmod 6$, while for the remaining $4$ residue classes $\nabla(n)=L_n$ or $\nabla(n)=L_n+1$. In this paper, we provide optimal constructions in the odd residue classes $n\equiv3,5\pmod6$, (proving $\nabla(n)=L_n$) and a geometric obstruction showing that equality in lower bound is impossible when $n\equiv0,2\pmod6$ (yielding $\nabla(n)=L_n+1$). Starting with $n=3$, the resulting sequence is thus given by \[ \nabla(n)=\bigg{\lceil}\frac{n^2}{3}-\frac{n}{6}+\frac{4}{3}\bigg{\rceil}-\bigg{\lceil}\frac{n}{2}\bigg{\rceil}. \]

The Fomin-Kirillov algebras $\mathcal{FK}_n$ are shown to be infinite-dimensional for $n\geq 6$. By computer calculations, we find an explicit nonzero primitive element of degree 14 in the identity component of $\mathcal{FK}_6$. For every $n\geq 6$, the existence of such an element implies that $\mathcal{FK}_n$ contains a polynomial subalgebra and is therefore infinite-dimensional, and that the canonical homomorphism from $\mathcal{FK}_n$ onto its associated Nichols algebra is not an isomorphism.

Contact-rich robotic insertion is challenging because uncertainty in alignment, friction, and contact conditions can lead to unsuccessful assembly, excessive contact forces, and jamming. Designing a reliable controller therefore requires balancing insertion performance, robustness, and recovery from unexpected contact. In this paper, we propose PSO+TR, a derivative-free optimization (DFO) method that combines the exploratory search of particle swarm optimization (PSO) with a trust-region (TR) procedure for local refinement to improve the search process when progress stagnates. We apply the method to derivative-free policy optimization of an interpretable robotic insertion controller, jointly tuning its motion, feedback, and recovery parameters while preserving its predefined control structure. The proposed approach is evaluated on 93 eligible benchmark problems from the bound-constrained programs (BCP) collection and a synthetic contact-rich planar insertion task under uncertain operating conditions. Three random seeds per benchmark problem yield 279 matched problem–seed instances per method. PSO+TR reaches the prescribed target on 228 of these instances (81.72%), the highest observed target-attainment rate among the five compared methods, which also include PSO, randomized black-box optimization (VRBBO), matrix adaptation evolution strategy (MAES), and differential evolution (DE). Across eight robotic optimizer seeds, the deployed controller-selection pipeline achieves 97.78% completion under development conditions and 58.00% under withheld stress conditions, compared with 91.22% and 31.12%, respectively, for the fixed staged controller. The stress violation rate is reduced from 20.69% to 2.19%. These findings support combining global and local search for DFO and structured contact-rich controller tuning. The synthetic planar results require validation on physical robots.

In this paper, we study the background stability problem for three-dimensional compressible adiabatic flows through porous media. For two given equilibrium states $(\bar{P}^k,\vec{0},\bar{S}^k)$ ($k=0,1$), under the assumption of small initial perturbations around each equilibrium state, pointwise estimates of solutions for individual perturbation problems are obtained. Based on these pointwise structures, a comparison between two individual solutions could be applied and it is proved that the difference between two solutions depends continuously on the equilibrium distance $|\bar{P}^0-\bar{P}^1|+|\bar{S}^0-\bar{S}^1|$ as well as the initial perturbation difference, with additional decay rates, thereby establishing a nonlinear comparison principle for this system. Compared with previous works on background stability problems, it is the first time to obtain stabilities in the pointwise sense. Our main tools are Green's functions, a priori energy estimates, and refined decay estimates for higher-order derivatives.

Epithelial dynamics are often studied using two-dimensional models that omit cell height. Here, we investigate how this third dimension influences tissue fluidization driven by cell self-propulsion. We identify three effects absent from conventional 2D models. First, cell height controls fluidization through a reentrant transition: squamous and columnar tissues are more resistant to fluidization than cuboidal ones. Second, neighbor exchanges through transient scutoid states substantially enhance cell motility, compared to classic T1 transitions. Third, self-propelling cells develop pronounced apicobasal shape asymmetry, with the experimentally less accessible basal surface providing a more accurate indicator of cells' target shape index and motility.

Equivariant interatomic potentials enable accurate and efficient simulations of molecules and materials. Among them, models based on SO(2) convolutions reduce the cost of tensor products and achieve state-of-the-art accuracy, but their training remains time-consuming and memory-intensive. Existing training implementations materialize large edge tensors for representation transformations surrounding dense matrix multiplications, increasing memory usage and data movement. We observe that these transformations can be integrated into the model's existing dataflow, avoiding separate intermediate materialization. We introduce TrimSO(2), a fast and memory-efficient algorithm for SO(2)-based equivariant models. It realizes this principle through rotation on gather, recombination with activation, and inverse rotation on reduction, with support for the higher-order differentiation required for training. By avoiding intermediate materialization, TrimSO(2) delivers 2.71-16.73$\times$ operator speedups across forward, backward, and double backward and reduces model-level high-bandwidth memory traffic by 3.81-9.88$\times$. Finally, TrimSO(2) achieves 2.07-2.94$\times$ training speedups and 1.53-3.16$\times$ reductions in peak training memory over PyTorch implementations for official eSEN, UMA, and EquiformerV3 workloads on A100 and H100 GPUs.

A finite Gödel chain generates not one integer sequence but a large family of them. The combinatorial mechanism is developed in a companion paper; here the sequences themselves are the primary objects. For $V_m=\{v_0<\cdots<v_{m-1}\}$, let $g_{j,n}^{(m)}$ count outputs equal to $v_j$, aggregated over all full bracketings on $n$ variables and all $m^n$ valuations. The root-pair refinement produces $N_{i,j}^{(m)}(n)=\sum_{r=1}^{n-1}g_{i,r}^{(m)}g_{j,n-r}^{(m)}$, with generating functions $N_{i,j}^{(m)}(x)=G_i^{(m)}(x)G_j^{(m)}(x)$. We prove that the initial coefficients of these products uniquely identify the unordered root-value pair. Consequently, for each fixed $m$, there are exactly $\binom{m+1}{2}$ distinct root-pair generating functions. We catalogue the factories for $m=4,5,\ldots,10$, giving the first ten terms of every base sequence and every symmetric root-pair sequence. This range contains 49 base sequences and 210 symmetric pair classes, yielding 259 indexed sequence families before additional aggregates. The catalogue provides reproducible data for integer-sequence analysis and comparison with the On-Line Encyclopedia of Integer Sequences (OEIS).

Linters are widely used in code maintenance and real-time IDE editing to surface lint alerts related to performance, style, error-prone, and other patterns in source files. However, existing code benchmarks do not explicitly evaluate linter-guided file refactoring, where models must reduce lint alerts in source files with correct initial functionality while satisfying functionality preservation. We introduce LintEval, a multilingual benchmark for linter-guided file refactoring across C++, Python, and Java, comprising 13,061 programs with correct initial functionality and 171,662 lint alerts extracted using language-specific linters. LintEval jointly evaluates functionality preservation, lint alert reduction, new alert avoidance, and edit minimality. Experiments reveal a persistent trade-off: closed-source commercial models reach up to 90.4% Reduction@P but achieve only 67.1%-68.3% Pass@1, while several open-source small models show low or negative Reduction@P. A controlled fine-tuning study further shows that supervision format matters: refactoring-oriented SFT raises Qwen2.5-Coder-7B Reduction@P from 24.7% to 76.0%. LintEval enables controlled evaluation of models that improve source files under functionality preservation.

Context. Solar energetic particles (SEPs) in the heliosphere are produced by flaring processes on the Sun or shocks driven by coronal mass ejections (CMEs). Electrons, in particular, are regularly detected remotely as electromagnetic radiation (X-rays or radio emission), which they generate through various processes, as well as in situ by spacecraft monitoring the Sun and the heliosphere. Aims. We aim to combine remote-sensing and in situ observations of an energetic solar eruption to link energetic processes in the solar corona to energetic particles observed in situ in the heliosphere. This will be done using the tools developed in the Horizon Europe SOLER project. Methods. Here, we investigate a solar energetic eruption at the Sun together with its associated signatures of accelerated electrons observed at radio and X-ray wavelengths and combine these remote observations to in situ particles observed by spacecraft on 10 March 2024. These observations are combined with a magneto-hydrodynamic (MHD) model of the solar corona in order to make the remote to in situ connections. Results. We observe a high-energy SEP event at multiple spacecraft (>25 MeV protons and 1 MeV electrons), despite the event being associated with a slow white-light CME. Remote observations of the Sun show that the event was associated with a fast large scale coronal wave (1400 km/s) and also multiple regions where electrons are accelerated around this large scale wave observed as type II radio bursts. In addition, we observe a strong coronal dimming away from the main flaring region, providing evidence of field lines getting opened to interplanetary space, dislocated from the flare site.

In 1988 Broughton proved that if a complex polynomial function on ${\mathbb C}^n$ is tame at infinity its fibers are homotopy equivalent to bouquets of some spheres. Since then several basic properties of polynomial functions were studied by many mathematicians in various situations. In this paper, we show some evidence for the possibility of extending Broughton's result to rational functions satisfying some tameness condition at infinity and the one at their points of indeterminacy. Specifically, assuming some conditions on a rational function on ${\mathbb C}^n$ we prove that the cohomology groups of a generic fiber of it are isomorphic to those of a bouquet of $S^1$ and some spheres. In the course of the proof, the theory of the nearby and vanishing cycle sheaves for meromorphic functions will play an essential role.

We study maximal subgroups of topological full groups of irreducible one-sided shifts of finite type whose associated groupoids have Cantor unit space. For each wide open subgroupoid of such a groupoid, we construct a subgroupoid graph and identify the subgroupoid with a full compact open reduction of the corresponding countable graph groupoid. Every minimal wide open subgroupoid is either AF or purely infinite. A proper wide open subgroupoid is prime if it admits no proper intermediate wide open subgroupoid. We prove a trichotomy for prime subgroupoids: they are minimal, arise from a clopen bipartition, or have a unique nonempty proper closed invariant set, which is nowhere dense. For a prime subgroupoid, the normalizer of its topological full group is maximal in the ambient topological full group precisely when it maps onto the ambient abelianization. An analogous criterion holds in every subgroup containing the ambient commutator subgroup. For a minimal prime subgroupoid, its topological full group is maximal precisely when it equals its normalizer and the inclusion induces a surjection on first groupoid homology. We also describe all fully amplified maximal subgroups, namely those closed under local agreement. For Thompson's group $V$, the stabilizer of every simple type system is maximal, extending results of Belk, Bleak, Quick and Skipper for finite type systems and certain classes of infinite ones. Finally, every subgroup containing the ambient commutator subgroup has continuum many pairwise nonisomorphic maximal subgroups acting minimally on the unit space.

Metric spaces of negative type (NT) and strong negative type (SNT) are fundamental in wide applications across computer science and statistics. It is well-known that spheres equipped with geodesic distance are of NT, and subsets of a sphere that contain at most one pair of antipodal points (e.g. an open hemisphere) are of SNT. In this paper, we extend these results to a class of star-shaped manifolds. By constructing a metric $d$ based on layer-wise radial projections, we prove that every star-shaped manifold, equipped with $d$, is of NT. Moreover, we prove that a subset of a star-shaped manifold is of SNT under certain injectivity and directional asymmetry conditions. In particular, for a subset of a single layer, it is of SNT if it contains exactly one point from each preimage of an open hemisphere (a fully directional asymmetry); moreover, it is of SNT if and only if it contains at most one opposite-directional pair.

Memory systems for persistent personal agents must move beyond isolated memories, maintaining both personal memory about whom they serve and procedural memory about how to act. Crucially, in harness-based personal assistance, procedures or skills are inherently user-conditioned: personal context determines which procedures apply, how they are instantiated, and when they should change. Existing benchmarks typically emphasize either personal or procedural memory, leaving their interaction underexplored. We introduce PraxisMemBench, a harness-based benchmark for persistent personal assistance across daily-life and work trajectories, where personal and procedural memory evolve together and later tasks depend on both. Experiments show that maintaining two memory types separately is insufficient, with completion dropping from single-type to interdependent dependencies (84.6% to 77.9%). More broadly, across existing methods, relation-related failures increase from early to late sessions as interaction history grows (59.8% to 72.9%), revealing a continual-maintenance challenge: writing correct memories is not enough if their evolving content and organization cannot be preserved for later retrieval. To address this, we propose PraxisMem, which uses privileged joint-state supervision to internalize the ability to maintain memory content and organization into the memory manager, with location-aware GRPO and dynamic residual-routed OPSD. PraxisMem reaches 40.78% overall Session Success Rate, compared with 20.60% for Claude Code's native memory.

This paper studies popularity dynamics in social networks, where users' engagement with competing channels is driven by intrinsic content quality, social influence, and popularity feedback. We introduce a stochastic model in which users interact through a directed influence network and channel exposure depends jointly on these three mechanisms. We first characterize the resulting dynamics in the absence of intrinsic quality, showing that popularity concentrates asymptotically on a single channel, leading to a winner-takes-all regime. When all channels have positive intrinsic quality, we establish ergodicity of the popularity process and characterize its long-run behavior. We further show that, when intrinsic quality is small, the system exhibits metastable behavior: it can remain for long periods near configurations dominated by a single channel before transitioning to another. These results highlight how weak quality differences can coexist with strong path dependence induced by popularity feedback. We then investigate platform-level interventions and propose controls that compensate for network-induced exposure biases and mitigate excessive concentration. Analytical results are illustrated through numerical simulations and an empirical analysis of YouTube data, whose observed popularity dynamics are consistent with the proposed stochastic framework. The results provide a mathematical framework for understanding the interplay between quality, social influence, and reinforcement in online popularity dynamics.

It is folklore that passing "convergence" diagnostics does not guarantee that a Markov chain has converged. We prove this as an impossibility for any finite checklist of diagnostics. Running more chains, longer chains, and smarter diagnostics does not avoid this impossibility in certifying convergence. Under regularity assumptions, we determine how the worst-case undetected non-convergence decays as more diagnostics are added, and how to choose diagnostics optimally. Folklore suggests that the sampler's slowest mixing modes are the "dangerous" ones that must be monitored; we prove that the slow modes yield nearly optimal diagnostics as sampling proceeds. Given a source class, we also give an anytime-valid bound on the remaining discrepancy and show how undetected bias caps the effective sample size that a finite checklist can certify.

Progress toward general intelligence in the physical world requires scaling robot learning across diverse environments and interactions. However, existing robot policies use shared parameters that remain fixed across interaction contexts. When different operations favor competing parameter adjustments, fitting their mixture can leave individual operations insufficiently adapted. Our atomic-task diagnostics reveal competing update directions in both vision-language and action parameters, with source-improving updates increasing loss on other tasks. This motivates MorphAct, a contextual parameterization framework that dynamically adjusts robot policy parameters as interaction contexts change. Two coupled generators produce context-dependent low-rank updates for the vision-language and action modules. Their coupling follows the policy's computational dependency: vision-language updates shape the representations that condition action-side parameter generation. Both generators are trained jointly through the native action objective, without operation labels or expert-adapter targets. MorphAct improves performance across three VLA backbones on LIBERO and Meta-World, with gains of up to 16.30%. In real-world evaluation, it achieves gains of up to 14% over $\pi_{0.5}$. Ablations support the benefits of contextual parameter generation and representation coupling.

Training hardware by gradient descent requires a gradient to be computed using a separate backwards pass. If a circuit is reciprocal, meaning every connection is symmetric, the backward pass is the same network run a second time with the error as its input. The reciprocal tau-cell, a weak-inversion log-domain circuit, makes this practical in standard CMOS. Each cell is a current-mode leaky integrator with a built-in ReLU; each connection is two transistors whose signed strength is a ratio of bias currents. The equilibrium of the network is the solution to a convex program, and latching the cells that are off will hardware linearise the circuit, making its second run exactly linear. Transistor-level SKY130 simulations show that the second run gives the gradient within 1.9%; that hardware linearisation permits large, noise-robust error signals; that a 13-cell network learns the Iris data set; and that learning in situ restores mismatched circuits on which software-trained weights fail, from 53-63% to 88-96% test accuracy.

We investigate weak gravitational lensing by a charged black hole surrounded by anisotropic matter, described by the two-component Kiselev metric, and immersed in a homogeneous plasma. We first examine the black hole geometry and horizon structure and then derive the weak-deflection angle from the Hamiltonian description of light propagation in plasma, using an expansion with a fixed turning point that we verify against direct numerical integration. Using the gravitational lens equation, we obtain the Einstein-ring angle, the image positions, the total magnification and the fractional magnifications of the primary and secondary images. We then confront the model with the Einstein radii of two galaxy-scale lenses of the Sloan Lens ACS Survey, J0008$-$0004 and J0029$-$0055. Because the Einstein angle cannot be smaller than the reduced deficit deflection, the observed radii give the mass-independent bounds $K<6.5\times10^{-6}$ and $K<4.2\times10^{-6}$, respectively. The charge correction to the Einstein radius is suppressed by $r_s/R_E\approx 5\times10^{-6}$ and is unobservable, while the plasma parameter at the optical wavelengths of the SLACS imaging is of order $10^{-22}$ and cannot be constrained. Our results show that galaxy-scale strong lensing data place stringent limits on anisotropic matter surrounding the lens, whereas plasma effects can be probed only at low radio frequencies.

In quasi-Hermitian mixed-state quenches, the initial and final Hamiltonians generally possess different positive-definite metrics, so post-quench evolution is not quasi-unitary in the initial physical space. Choosing the preparation/measurement space as reference, we derive from first principles a normalized mixed-state Loschmidt amplitude using metric-compatible purifications. The resulting biorthogonal trace representation contains a normalization factor given by the norm of the evolved purification in the initial metric; this factor is essential for comparing states from different physical Hilbert spaces and directly encodes the metric mismatch. We prove that this normalization function is strictly positive on the real-time axis, so real-time criticality arises solely from destructive interference in the dynamical overlap. In complex time, zeros of the normalization factor generate branch singularities distinct from Fisher zeros. For a general two-level system, we derive analytic expressions for the Fisher and normalization zeros and analyze exceptional-point scaling together with the temperature- and quasi-Hermiticity-dependent DQPT critical times in two solvable quench protocols. In contrast to metric-stationary quenches, where non-Hermitian effects may be absorbed into an equivalent Hermitian description, the metric mismatch here produces genuine non-Hermitian dynamics: a time-dependent normalization factor and complex-time branch structure that cannot be removed by any global similarity transformation.

Magnetic null points define the magnetic field topology in stellar coronae, planetary magnetospheres, and astrospheres, and are commonly associated with magnetic reconnection. We investigate the local structure of stationary three-dimensional (3D) resistive, incompressible magnetohydrodynamic (MHD) flows in the vicinity of an isolated magnetic null and an isolated velocity stagnation point, assuming that the two nulls are colocated. The governing MHD equations are solved self-consistently using a first-order local expansion of the magnetic and velocity fields about the null. For any given magnetic-null configuration, the equations admit a two-parameter family of stationary solutions, comprising multiple solution branches with distinct velocity topologies. Along these families, the velocity-null polarity can change at bifurcation points where the flow becomes effectively 2.5D. A single magnetic null can therefore support positive-radial, negative-radial, and spiral stagnation flows, with qualitatively different inflow, outflow, and rotational properties. The associated pressure and resistivity distributions are likewise determined self-consistently and vary across the solution family, demonstrating that they are coupled to the flow topology rather than prescribed independently. The generic solutions do not require the velocity and magnetic separatrices to coincide, allowing plasma to cross the magnetic fan separatrix and providing a local reconnective flow. These results demonstrate that, in the presence of nonuniform resistivity, the magnetic topology alone does not uniquely determine the associated stationary flow, pressure, or resistivity structure around a 3D magnetic null, revealing the nonlinear feedback between all macroscopic variables and resistivity. The constant-resistivity field-aligned and spiral field-crossing solutions identified previously are recovered as special cases.

Semi-gradient temporal-difference learning is a core algorithmic component of reinforcement learning, but bootstrapping with function approximation generally induces a non-conservative vector field and can lead to instability. We analyze this effect for two-layer neural networks in the mean-field regime and identify a simple stability mechanism in which entropy-induced relaxation dominates the sensitivity of the moving bootstrap target. Under this condition, we prove exponential convergence to a unique fixed point and quantify its bias relative to the unregularized Bellman solution. We also show that the same mechanism extends to entropy-regularized off-policy control through soft Q-learning.

We study radially nonincreasing, positive blow-up solutions of a class of superlinear heat equations in the non-scale-invariant setting. This class contains nonlinearities with arbitrarily fast, super-exponential growth. Under suitable structural assumptions on the nonlinearity, we derive the sharp global blow-up profile in the original space-time variables. More precisely, for positive nonlinearities $f$ satisfying $$ \lim_{X\to \infty}f'(X)G(X)= q\ge1\quad \quad \hbox{ where }\quad\quad G(X)=\int_{X}^{\infty}\frac{ ds}{f(s)}<\infty\quad\forall\ X>0, $$ and assuming either the time monotonicity $u_t\ge0$ holds or $q>\frac{p_S}{p_S-1}$, we have $$ u(x,t)=(1+o(1))\,G^{-1}\bigg(T-t+\frac{|x|^2}{4q|\log |x|^2|}\bigg), \quad \hbox{as $(x,t)\to (0,T)$.} $$ This estimate in particular provides the sharp final space profile and the corresponding refined space-time profile. Moreover, our result recovers the universal structure of the global blow-up profile, given by the resolvent $G^{-1}$ of the associated ODE evaluated at a time-space building block, which only depends on the limit $q$.

Chemistry evaluation has moved past multiple-choice probes toward open-ended expert problems, yet the benchmarks that define the current frontier still score answer endpoints alone. Such scoring conflates memorized facts with stepwise derivation, treats visual and textual inputs as interchangeable, and confounds long-horizon planning with stepwise execution. These blind spots prevent any diagnosis of where the reasoning chain breaks in a model. We present ChemArgus, a competition-level chemistry benchmark drawn from chemistry competition material, textbooks, and research papers, whose scoring replaces the answer endpoint with three measurement properties. Fine-grained scoring grades every subquestion point by point with partial credit, so a score lands at the level of the step rather than the outcome. Multimodal capability is priced on every problem containing a real image, paired with a controlled text description, so visual understanding is measured against text on identical tasks. Diagnostic attribution reads paired metrics that share one scoring unit and differ only in context construction, so a gap between two scores isolates a single cause, namely integration, propagation, or local reasoning. GPT-5.6-Sol scores 23.2% on unassisted whole-problem solving against 28.8% and 30.4% under the two sequential metrics, a gap measuring the integration burden. Through rubric partial credit and these cause-isolating score gaps, ChemArgus shows not only whether a model answers chemistry correctly but where its reasoning chain fails, so that every score it reports doubles as a diagnosis, a readout of the chain rather than a verdict, aiming to guide language models step by step on their path toward chemistry expertise, one corrected step at a time, each step priced by the rubric, point by point.