Papers

The purpose of this article is to explicitly describe how the integration technique known as the change of variables is used in graduate-level Probability and Statistics courses. Throughout the article, we employ this integration technique seven times across various examples and results. We demonstrate that four applications of this technique are required to derive the probability density function (PDF) of the Student's t-distribution.

Online experiments must often be evaluated before long-term outcomes mature. Under rolling enrollment, these outcomes are observed only for early enrollees, while short-term surrogates are available for everyone. We compare seven estimators across eleven data-generating processes, spanning partial mediation, drift, outcome sparsity, and enrollment-time labeling, with up to $R = 2,000$ replications over more than 500 method-by-scenario cells. We find a sharp robustness-efficiency tradeoff: the surrogate index delivers large efficiency gains when surrogacy holds but its coverage collapses under violations, while PPI-family methods stay asymptotically valid under random labeling at smaller gains. We give the finite-sample variance of PPI++ in the all-units parameterization for a fixed predictor, a joint asymptotic distribution for the two estimators under cross-fitting, and a Hausman-type estimator-disagreement diagnostic, then quantify the detection-damage gap: in the partial-mediation design, where we locate both edges, a band of violations destroys surrogate-index coverage yet is too small to detect on most datasets. On the 64,000-customer Hillstrom experiment the diagnostic rarely flags a violation that biases the surrogate index, and a Cauchy-kernel hybrid of the two estimators inherits 10.7% relative bias; on the 14-million-user Criteo experiment the violation is detected, and subsampling traces detection turning on with scale as damage persists. PPI++ has limits: at a rare-conversion $n = 30,000$ Criteo subsample its empirical coverage is 85.0%. We recommend prespecifying PPI++ with the exact variance as the primary analysis under random labeling and adequate labeled outcome counts, reading the diagnostic as a warning, not a certificate, and treating the surrogate index as a sensitivity analysis.

Given a Riemannian manifold $(M,g)$ equipped with a positive density function $f = e^{-\varphi}$, we study the weighted sectional curvature $\overline{\sec}_\varphi(U,V)$ and the $k$-th intermediate weighted Ricci curvature $\overline{\text{Ric}}_{k,\varphi}(U,V)$. We show that $\overline{\sec}_\varphi(U,V)$ and $\overline{\text{Ric}}_{k,\varphi}(U,V)$, together with the weighted second fundamental form $\widetilde{\mathrm{I\!I}}$, play central roles in controlling the topology of the manifold. Using the theory of $\widetilde{C}(k)$ functions, variational methods, and Morse theory, we prove that by imposing suitable restrictions on these quantities, an $n$-dimensional compact manifold with boundary or a proper open $n$-dimensional manifold is diffeomorphic to an $n$-ball or to a certain CW complex. This shows that such rigidity phenomena is not confined in the unweighted case, but persist in the weighted setting as well. Lastly, we prove a weighted analogue of Frankel's Theorem under positive intermediate weighted Ricci curvature. These results extend classical theorems from the unweighted setting to the weighted case, demonstrating that $\overline{\sec}_\varphi(U,V)$ and $\overline{\text{Ric}}_{k,\varphi}(U,V)$ provide effective tools in Riemannian geometry.

We analyze the overluminous, 91T/99aa-like Type~Ia SN 2019vrq, based on light curves(LCs) and spectropolarimetric time-series. We employ 3D-radiation-hydrodynamical, full non-LTE simulations of low-amplitude, radially-pulsating-off-center-delayed-detonations(PDD) of a possibly rotating near-M(Ch) mass white dwarf (WD) to reproduce the LCs and spectra. The progenitor originates from a 7 Mo main-sequence star of solar metallicity. The explosion yields 0.86Mo of 56Ni and 0.023Mo of 58Ni. The latter falls a factor of 10 below that of `classical' delayed-detonations for 91T/99aa-like SNe, a diagnostic that is directly testable with JWST. The slow deflagration leaves a bound, pulsating WD. The detonation is triggered at 0.8 Mo. LCs and spectra require an outer 0.11 Mo of unburned material with twice-solar Fe, plausibly the ashes of an earlier, unsuccessful explosion, and low-level mixing of nuclear-statistical-equilibrium(NSE) elements. The spectra reflect early high ionization followed by recombination, with the photosphere shifting from intermediate-mass-element- to NSE-dominated layers about a week before maximum. The early high-velocity (HV) CaII IR3 line (likely produced by an aspherical density shell at 24,000km/s of 0.01 Mo) arises from an ionization sandwich rather than a double structure in abundances. After Ca recombines, the CaII IR3 wing reaches 33,000km/s well beyond the HV component. The low polarization is due to low scattering in an iron-group-dominated photosphere, consistent with asphericities <20% and resulting in a directional luminosity dependence 10-15% from the outer layers, and a dispersion of 35% in total. The LC-shape provides a further probe of asphericity, consistent with the locally tested polarimetry limits and relevant for high-z cosmology.

We prove the Sudakov minoration principle, with a universal constant, for unconditional log-concave random vectors whose coordinate magnitudes are negatively associated. The main step is a deterministic selection theorem: pairwise witnesses in convex downwardclosed sets yield, on an exponentially large subfamily, one fixed witness per label separating it from every other retained label. The selection combines a prefix counting inequality with convex separation in the space of all label-coordinate arrays. Negative association then controls the expected number of active joint-tail witnesses, while a Bernoulli argument on complementary coordinate sets retains the random signs. The proof uses joint upper-orthant probabilities and applies negative association only under the original law. Consequences include minoration for products of Orlicz-based log-concave measures and a covering estimate in the moment metric, expressed geometrically through polar Lp centroid bodies.

Breast cancer risk assessment and prediction models are very important tools for the clinical management of healthy women carrying pathogenic variants in known cancer genes. We propose in this paper a comprehensive prediction model for the personalized clinical management of women with pathogenic variants in BRCA1. This model is able to estimate the risk of BC accounting for the full history of this cancer within the family, the personal and family history of risk-reducing salpingo-oophorectomy as well as the exact age of this intervention among family members. The effect of oophorectomy on the risk of developing breast cancer is evaluated by estimating and conducting inference about the regression coefficients in a Cox model with time-varying covariates. We model the within-family dependence in the ages at onset of cancer using a Gaussian copula whose correlation matrix accommodates the different pairwise family relationships. We develop an iterative algorithm to estimate the parameters of the considered model in the presence of a selection bias. We evaluated the performance of the proposed cancer risk estimation method from family data by simulations and illustrated its use through an application to the breast cancer family registry.

Large language model (LLM)-powered multi-robot systems are vulnerable to semantic manipulation: an accepted false world-state claim can trigger a fleet-wide behavioral cascade, causing unnecessary replanning, increased path costs, congestion, or apparent mission infeasibility. Conditioning on a successful manipulation, we propose an active verification framework that contains its downstream effects before they propagate across the fleet. A dedicated verification module generates a structured Verify-Adapt-Hold plan: selected robots inspect consequential regions, a limited subset provisionally adapts when necessary, and the remaining robots retain their trusted plans. We evaluate the framework in a multi-robot transportation environment using injected false obstacle claims across different impacts and team sizes. Evaluation measures cascade containment, Sum-of-Costs, makespan, and coverage ratio. Results show that treating post-compromise verification as a team-level planning problem, rather than a binary trust decision, effectively limits the cascading physical consequences of semantic manipulation.

We investigate how weak optical injection changes single-pulse operation in a laser in the dissipative-soliton-resonance regime. The energy scans show that a small injected field suppresses multipulsing and extends predominantly single-pulse operation to higher energies. Further increasing the seed power makes this extended range nonuniform: regions of enhanced multipulse formation alternate with regions of suppression. We analyze timing and optical-phase fluctuations of the injection field. At the lowest energies, these fluctuations cause continuous-wave and multipulse generation to dominate the laser output. At the highest energies, injection-field phase fluctuations promote multiple pulses, whereas time fluctuations suppress them. Deterministic calculations without noise or injection show that both single pulses and prepared pulse pairs can persist under the same settings. We show that the spectral entropy of a dissipative soliton reflects changes in individual pulse spectra and pulse interference. It characterizes the probabilistic transition between single- and multipulse regimes, but it does not, by itself, predict in detail which regime the laser will form. Together, the results connect the energy-selective action of optical injection to pulse formation and structure, while distinguishing persistence of a prepared pulse from its formation out of a background.

Aerial manipulation in outdoor environments remains challenging due to the simultaneous requirements of reliable state estimation, stable aerial motion, and precise manipulation under external disturbances. In this work, we present a real-world outdoor aerial manipulation framework that integrates imitation learning, onboard LiDAR-inertial state estimation, and whole-body model predictive control. A Diffusion Policy is trained from manipulation demonstrations to generate desired end-effector motions from onboard observations. These learned commands are executed by a whole-body MPC that jointly coordinates the aerial platform and manipulator to realize the desired end-effector trajectory. To eliminate reliance on external motion-capture infrastructure, the platform employs onboard LiDAR-inertial odometry for state estimation during outdoor operation. We validate the complete framework on a physical aerial manipulator and demonstrate successful execution of outdoor manipulation tasks. The experimental results show that demonstration-driven manipulation policies can be effectively integrated with onboard state estimation and model-based whole-body control to enable aerial manipulation beyond controlled indoor environments.

The mechanical properties of network-based materials have been extensively studied under qui- escent conditions, yet their self-assembly in nature occurs mainly in a mechanically stressed envi- ronment. Here, we show that the stiffness of collagen networks, one of the main building blocks of the mammalian extracellular matrix, can be tuned by applying shear stress during gelation, which first strains and aligns the material, then triggers a dramatic irreversible increase in the elastic modulus. This stiffening is anchored by maintaining the stress until the gel is fully matured. Using particle-based simulations, we show that the underlying microscopic mechanism is likely generic to a broad class of network-based systems and arises from two synergetic effects: changes in the network orientation and topology through the formation of permanent contacts that stabilize the system. Our findings are rationalized using a rigidity percolation framework and offer a general principle for encoding elasticity in biological and synthetic networks.

We study asymptotic multiplicity sequences of graded families of arbitrary ideals in Noetherian local rings. We characterize convergence of the zeroth component and prove that the first positive component not forced to vanish always converges under natural equidimensionality and catenarity assumptions. In contrast, higher components may exhibit arbitrary asymptotic behavior: even in $k[[x,y]]$, integrally closed filtrations with fixed radical, height, and analytic spread can realize any prescribed lower and upper limits. For Noetherian graded filtrations, however, all asymptotic components exist, are finite and rational, and satisfy Rees-type and valuative criteria for integral dependence. In the reduced pure-dimensional complex analytic setting, a common principalizing modification provides a second convergence mechanism without finite-generation assumptions. We also develop a diagonal mixed theory: for graded $\mathfrak m$-primary families, the top diagonal components are sums of Cutkosky's mixed multiplicities, while on a common analytic model all diagonal mixed components converge. The latter result extends the one-family common-model theorem.

We study the effects of zero-point spin fluctuations on the nuclear spin-lattice relaxation rate 1/$T_1$ around a two-dimensional antiferromagnetic quantum critical point in the self-consistent renormalization theory. For a weak mode-mode coupling constant $y_1 < $ 0.1, the finite temperature behavior of 1/$T_1$ across the quantum critical point resembles that for only the thermal spin fluctuations. For a strong mode-mode coupling constant $y_1 > $ 0.1, 1/$T_1$ takes its local maximum as a function of temperature in the nearly antiferromagnetic state. Experimental observation of the local maximum in the $^{63}$Cu nuclear spin-lattice relaxation rate 1/$T_1$ of lightly-doped superconductors La$_{2-x}$Sr$_x$CuO$_4$ with $x$ = 0.06-0.10 is associated with the effects of the zero-point spin fluctuations. The two-dimensional magnetic quantum critical point and the role of the zero-point spin fluctuations are discussed in the electron spin dynamics of underdoped superconductors La$_{2-x}$Sr$_x$CuO$_4$.

Recent progress in speech-driven 3D facial animation has improved vertex-level reconstruction quality, but speech-consistent visible articulation remains difficult. This is because speech production follows structured and constrained articulators' coordination and the mapping from acoustics to motion is inherently one-to-many. Motivated by the structured patterns of visible articulation, we propose a novel articulation-aware framework that models visible speech through directional articulatory motions and composes them into surface-consistent 3D facial motion. To represent visible articulation with three directional articulatory motions, spreading, opening, and protrusion, we propose a Speech–Articulatory Memory (SAM) that captures the correspondence between speech and these motions under phonetic context through retrieval and decoding based on a key-value memory structure. Then, a Topology-aware Articulatory Composition (TAC) integrates the predicted directional articulatory motions under mesh topology to produce surface-consistent 3D facial motion. Experiments on VOCASET and TFHP show that our method achieves state-of-the-art performance on standard reconstruction metrics and improves visible articulatory distance and velocity errors for lip articulation, while a user study confirms clear preference in lip sync and realism.

In this paper, we study the pseudo-relativistic Schrödinger equation with logarithmic nonlinearity \begin{equation*} \left(\sqrt{-c^{2}\Delta+m^{2}c^{4}}-mc^{2}\right)u+\mu u=u\log|u| \quad\text{in }\mathbb{R}^{N}. \end{equation*} The existence and qualitative properties of action ground states are established, by means of a power-law approximation. We then prove that these states converge to the Gausson in $H^{1}(\mathbb{R}^{N})$ as $c\to\infty$. For sufficiently large $c$, we further obtain uniqueness of action ground states up to translation and sign change, as well as their nondegeneracy. Finally, we prove an exact correspondence between action and energy ground states, thereby extending the preceding results to energy ground states at arbitrary prescribed mass.

Influenza A persists by continually changing the antigens that its host population recognizes. How fast it evolves and how many hosts it infects are not independent, because the immunity that selects new variants is produced by the infections the pathogen has already caused. We analyze a model of Andreasen et.\ al.\ that captures this eco-evolutionary feedback, and we extend it to the case where infection may kill the host. In the model infected and recovered hosts are distributions over a one-dimensional antigenic space coupled by cross-immunity. The endemic state is a traveling pulse: the infected distribution keeps a fixed shape and advances through antigenic space at constant speed. In the limit of weak antigenic mutation we construct the pulse asymptotically and find that: (i) the speed of antigenic evolution decreases as prevalence rises, (ii) less standing antigenic variation accompanies either faster or slower antigenic evolution, depending on whether pathogens differ in immune evasion or host lifespan (iii) the total number of infected hosts is largest at an intermediate virulence when the host birth rate is sufficiently low.

Voice agents are increasingly deployed in workflows where failed interactions can affect transactions, access, and other consequential outcomes, creating a need for reproducible and interpretable evaluation. We introduce Inquesto Score (IS), a protocol for measuring voice-agent reliability as the percentage of calls in a fixed, versioned evaluation population that achieve the caller's goal without a functional failure or worse. Rather than combining heterogeneous metrics, IS defines explicit failure events and severity levels and evaluates the deployed voice pipeline. Timing failures, including talk-over and delayed responses, are measured directly from audio, while semantic and state-dependent failures are evaluated using scenario predicates, tool traces, and a pinned open-model judge. Diagnostic views of behavior, acoustic robustness, identity handling, and speaker groups accompany the score without being combined into it. Inquesto Score v0.1 evaluates 30 scenarios, three acoustic conditions, four speaker groups, and 306 calls per agent across 13 configurations of a reference voice-agent system. Our evaluation shows that reliable measurement requires evidence beyond transcripts, explicit treatment of deployment conditions, and validation of the evaluators used to determine outcomes. We release the protocol, reference implementation, and evaluation records.

The packing-covering constant of a point set $X\subseteq\mathbb{R}^d$ is $\gamma(X)=\mu(X)/\rho(X)$, the covering radius divided by the packing radius. Among lattices, its minimum $\gamma_d$ is known for $d\leq 5$, attained by $\mathsf{A}_2^*$, $\mathsf{A}_3^*$, and Horváth's lattices $\mathsf{Ho}_4$, $\mathsf{Ho}_5$; Böröczky proved that $\gamma_3$ is optimal without the lattice restriction, but for $d=4,5$ the non-lattice problem was open. We exhibit a $2$-periodic non-lattice point set of $\mathbb{R}^5$ with $\gamma = 9/\sqrt{40} = 1.423024\ldots < \gamma_5 = \sqrt{3/2+\sqrt{13}/6} = 1.4494568\ldots$, so that in dimension five the packing-covering problem is not solved by lattices.

Generalizations of magnetic skyrmions to the context of other areas of physics, such as plasmonics, optics (including microcavity polaritons) and even water waves have become an important research topic. However, the generalization of the skyrmion number in such systems is still the subject of active research. While magnetic skyrmions textures are inherently formed by vectors (magnetic spin vectors), recent developments in other areas of physics have generalized the concept of skyrmions and skyrmionic patterns to the case in which scalar fields are used to define 3-component pseudo-spin vectors. This gives rise to a wide variety of skyrmion-like textures, depending on the detailed functional forms of the scalar fields. For example, steady-state outgoing waves in driven-dissipative polariton systems fail to have a well-defined global skyrmion number in real (configuration) space but can have one in momentum space. We classify the skyrmion integral for various scalar fields with different asymptotic behaviors in real space as well as momentum space, and in both cases give conditions for the skyrmion number not to exist, or be integer, half-integer or non-integer. Examples of physical systems to which our analysis can be applied include polariton condensates, water waves and gain-guided lasers.

Consider the one-dimensional Schrödinger evolution $$ i\partial_tw+\partial_x^2w=Vw,\hspace{5mm}(t,x)\in [0,T]\times\mathbb{R},$$ where $V$ is a real-valued time-dependent potential belonging to $L^1_tL^\infty_x+L^2_{t,x}$. We prove that an $L^2$ solution to the above equation is determined by its mass density $|w|^2$ modulo a global unimodular phase factor. This answers a question recently posed by Jaming for a large class of potentials, and recovers his earlier result for the free Schrödinger evolution. Our proof is simple and robust. It combines the basic local smoothing properties of the above Schrödinger evolutions, Strichartz estimates, and a stripwise version of a unique continuation theorem of Ionescu and Kenig to show that the interaction function $$ F(t,x,y)=u(t,x)v(t,y)-u(t,y)v(t,x) $$ vanishes identically on $[0,T]\times\mathbb{R}^2$ whenever $u$ and $v$ are $L^2$ solutions to a Schröinder euqation with potential $V$ with the same mass density. The method immediately extends to several important nonlinear models such as the cubic NLS equation, which is globally well-posed in $L^2(\mathbb{R})$ with $V=|u|^2$. Interestingly, we also show that the above phase recovery property fails in dimensions two and higher, even for the free equation with Schwartz initial data.

Wireless local area network (WLAN) performance is jointly shaped by medium contention, propagation, Wi-Fi configuration, and transport-layer behavior. This study evaluates IEEE 802.11g and IEEE 802.11ax in a single-access-point uplink topology, comparing UDP and TCP under Friis, LogDistance, and cascaded Friis-Nakagami propagation models. The factorial design spans 5 to 50 stations, six access-point distances from 5 m to 50 m, and three random seeds. Of 1,080 scheduled executions, 1,073 produced valid CSV outputs; seven runs terminated with internal ns-3 and cppyy segmentation errors and were excluded. Across the global scenario summaries, TCP FlowMonitor packet delivery ratios (PDRs) range from 0.994 to 0.997, whereas UDP PDRs range from 0.298 to 0.731. The highest mean aggregate throughput is 2.619 Mb/s for TCP under the configured IEEE 802.11ax mode with Friis propagation; UDP reaches 25.854 Mb/s in the same topology. These results show that packet delivery ratio, throughput, delay, and fairness must be considered together. FlowMonitor metrics are IP-flow observations, so the study does not establish application-level delivery or isolate optional IEEE 802.11ax multi-user mechanisms.

Slashing is commonly argued to secure proof-of-stake blockchains by confiscating the stake of misbehaving validators. The usual justification is that, without slashing, validators can solicit an equivocation attack by signing conflicting blocks: if enough others join, the attack succeeds; otherwise, the attempt incurs no loss. Slashing is intended to make such attempts costly and thereby guarantee the security of applications whose economic value is comparable to the bonded stake. This rationale, however, rests on heuristic arguments rather than a formal game-theoretic guarantee. We challenge this rationale by constructing a risk-free coordination protocol for rational validators under algorithmic slashing. We show that the prescribed strategy profile, in which rational validators solicit other validators to equivocate, constitutes an ex post Nash equilibrium, even when validators do not know in advance how many others will participate. The equilibrium holds for any gain $\epsilon>0$ from successful equivocation, however small relative to the bonded stake. Thus, slashing alone does not guarantee economic security proportional to the value of bonded stake. Our results expose a fundamental limitation of algorithmic slashing. Whereas conventional collateral arrangements in many real-world scenarios can rely on external enforcement, for example through courts, algorithmic slashing depends on the same consensus process that the attackers control. These findings call for a formal analysis of slashing's security, rather than overly simplistic arguments drawn from financial systems with independent enforcement.

The aim of this work is to examine the connectomes of Caenorhabditis elegans through a computational lens using the reservoir computing framework. Connectomes are mappings of biological neural networks; C. elegans is the first organism for which physical connectomes covering the whole nervous system have been published. The connectomes of C. elegans used in this paper have been derived at different ages of the organism and are based on three different ways of measuring inter-cellular connections. They have, with minimal preprocessing, been implemented as reservoirs in the form of echo state networks, which are recurrent neural networks. In reservoir computing, the reservoir itself is not trained, rather the output of the reservoir is passed to a comparatively small read-out module in which training takes place. Training and testing is conducted in different neuro-inspired tasks, with the aim of using these tasks as a benchmark for the connectomes. This process has been repeated with different configurations of the reservoir and equally sized but randomized null models have been used for comparison. The results show that the biological wiring and a bio-informed configuration of input and output nodes of the reservoirs do not necessarily lead to better performance. Contrarily, the randomized null models are often outperforming the original connectomes on the chosen benchmarks. At the same time it becomes clear that the results depend a lot on the configuration of the reservoir and the way the connectome has been derived from the organism. Connectomes from different ages may produce varying outcome, without a clear trend becoming visible.

We address an incipient type of data-based faults, driven by increasing amounts of data reuse in AI-enhanced computational science workflows. A dataset is created under specific conditions; its categories, measures, and labels depend on that context, but that context is usually unavailable to downstream users and is completely abandoned when datasets are used to train models. We propose the encoding and association of this context, called domain bounds, with the data to which it applies. By specifying the conditions for valid reuse, a domain bound flags apparently valid data from being reused in an incompatible context, even when every value falls within its expected range. We present cases from computational science and biomedicine where missing domain bounds allow silent reuse errors, and show why description and provenance approaches do not detect them. Our detector uses standard data container technologies, catches faults drawn from a taxonomy of published cases, irrespective of dataset size. Against injected faults it caught 17 of 18 domain-bound reuses that lineage and descriptive records accepted.

Humanoid hands require tactile feedback across the whole finger, not just the fingertip, to grasp and manipulate objects properly. Vision and proprioception alone cannot reliably provide this information, particularly when the hand's own fingers occlude the camera's view of the grasp. We present a low-cost tactile array for a humanoid finger, made from Velostat and conductive tape. The fingertip carries seven contact points including a 2x3 matrix wrapped across its front, left, and right faces, and a separate contact point at the tip. The proximal and middle phalanges each carry a single front-facing contact line. We measure the sensor's hysteresis and recovery time after release, through repeated loading and press-release tests. We also test a compliant, 3D-printed contact structure with a gap and a bump, inspired by similar designs in prior work, and show it cuts recovery time by 74% compared to a flush-contact baseline. We then show the sensor can produce distinct activation patterns for different contact geometries (flat, edge, corner) at the fingertip, and that it registers contact across all three phalanges during a grip. Finally, we discuss the limits of our fabrication changes and point to software-based compensation as a promising way to more directly fix the remaining hysteresis in the future.

Context. Ethanimine is a prebiotically relevant complex organic molecule that has been proposed as a key precursor of amino acids in the interstellar medium. To date, both its E and Z isomers have only been detected toward the Sgr B2(N) molecular cloud. The pronounced non-local thermodynamic equilibrium (non-LTE) effects predicted for this molecule require accurate collisional rate coefficients for reliable astrophysical modeling and future astronomical searches. Aims. We aim to provide the first collisional datasets for both ethanimine isomers with the main cold molecular clouds collision partners, He and para-H2, in order to support non-LTE radiative-transfer modeling. Methods. State-to-state rate coefficients for collisions with He were computed by integration over mixed close-coupling (CC) and coupled-states (CS) scattering cross sections at different energy ranges. In addition, comparisons with mixed quantum-classical theory (MQCT) calculations performed for both He and para-H2 collisions enabled the derivation of transition-specific scaling factors, which were applied to predict collisional rate coefficients for para-H2. Results. We present the first state-to-state collisional datasets for both E- and Z-ethanimine in collision with He and para-H2, including all rotational transitions involving levels below 50 cm-1 and over the 5-100 K temperature range. Conclusions. The datasets reported here provide the first collisional information suitable for non-LTE modeling of ethanimine in cold interstellar environments. They represent a key step toward more reliable abundance determinations and may facilitate future astronomical detections of both ethanimine isomers beyond Sgr B2(N).

We derive the limiting distributions of the $M$-test family of unit root statistics in the nearly integrated nearly white noise (NINW) framework introduced by Nabeya and Perron (1994) in the case of an unknown linear time trend. In the case of known long run variance (LRV), the limiting distributions of the $M^{GLS}$ tests are contaminated by additional noise terms as a result of quasi differencing whereas these terms are less present in the $M^{OLS}$ limiting distributions, both of which display conservative properties under conventional critical values. Furthermore, we prove the Gaussian power envelope in the NINW model is asymptotically equivalent to the standard envelope of Elliott, Rothenberg, and Stock (1996), and that the oracle $M$-tests have inefficient power relative to this benchmark. We then derive the limiting distributions of the feasible statistics and show that the autoregressive estimate of the LRV commonly used overestimates the LRV, creating altered limiting distributions. Finally, finite sample simulations illustrate that, of the procedures considered, no uniformly satisfactory solution exists for handling a series with a large negative moving average coefficient.

The evidence behind a scientific or operational decision is often held by hospitals, banks, or registries that cannot pool individual observations. Cross-silo federated learning moves computation to the data and exchanges agreed summaries. Targeted maximum likelihood estimation (TMLE) refines a flexible initial fit, yielding plug-in estimators that respect the model and support efficient inference. TMLE itself, however, has remained a fully centralized procedure. To fill this gap, our paper introduces the first federated TMLE algorithm. We federate targeting itself, for an arbitrary target, loss, and fluctuation family, through two complementary frameworks. FedTMLE-G aggregates local gradients and reproduces centralized targeting step for step. FedTMLE-L lets each institution complete its own fluctuation fit before a single exchange of fitted updates, trading synchronized fidelity for local autonomy. For gradient aggregation, we develop a finite-precision protocol that transmits changes rather than values and certifies targeting accuracy within explicit bounds on exchanges and bits. A description-length analysis of the accepted updates then shows that this finite communication leaves numerical targeting error negligible against sampling uncertainty. The cost of computing an estimator is thus distinct from the complexity of selecting it. Our analysis also indicates that keeping data local is not itself a privacy guarantee of TMLE, since instability of full-record reconstruction need not prevent recovery of a specified sensitive attribute. For a personalized version of local averaging, institutions retain their own estimates and leave once local targeting is complete. A nonconvex convergence bound charges the improvement forfeited through averaging to disagreement among local fits and exposes a tradeoff between equal institutional influence and the sampling variability of small silos.

We study the minimal dimension of a nonsingular anisotropic universal quadratic form over a field $F$ of $\operatorname{char}(F)=2$, which we call the “$m$-invariant" of $F$. We show that every even number is the $m$-invariant of some field of characteristic 2, and consider cases when $u(F)$ and $m(F)$ are equal and when they are not.

Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.e., the lower-level objective function is assumed to be, at least, convex). While the LLSC/LLGC assumptions render more tractable algorithmic design and theoretical analysis, they are too rigid to encompass many machine learning problems in practice. The limitations of LLSC/LLGC assumptions in BLO motivate us to investigate solving the BLO problem in the general lower-level nonconvex (LLNC) settings, which remains in its infancy. In the literature on LLNC-BLO, most of the existing works either require additional structures in the lower-level objective function for tractable theoretical analysis, or adopt the first-order stationarity reformulation as a lower-level surrogate problem, which is inherited from the LLSC/LLGC settings but could lose their effectiveness in the LLNC setting. To bridge this gap, we propose to reformulate the nonconvex lower-level problem using a second-order stationarity-based surrogate, the solution of which guarantees a local optimal solution at the lower level. Based on this reformulation, we propose the PROBE (Perturbed gradient algorithm for bilevel problem) and show that it overcomes the limitations of prior works by probing and escaping lower-level saddle points. We prove that PROBE achieves a finite-time convergence rate of $O(T^{-2/5})$, where T denotes iterations. To our knowledge, this work is the first to establish the finite-time convergence for achieving lower-level second-order stationary solutions in general LLNC-BLO. Our experiments on both a large language model-based data curation task and a meta-learning task also show that PROBE outperforms SOTA methods.

Can causal softmax attention implement policy mirror descent as a repeated controller rather than a one-step algebraic identity? Negative-entropy policy mirror descent (PMD) has the statewise update $\operatorname{PMD}_\eta(\pi,Q)=\operatorname{softmax}(\log\pi+\eta Q)$. Building on the known Q-TD-PMD recursion, we construct one fixed causal-softmax actor–environment–one-step-critic protocol with explicit actor, routing, sampling, and normalization residuals, and propagate them to the policy actually returned. The construction states the finite-logit/full-support domain, the external tokenization and sampling boundary, and the mean-zero LayerNorm carrier conditions required by the normalized compilation. Separately trained pre-LN Transformers recover the target computation empirically. A frozen one-step audit model is closest to PMD among the tested fixed rules; in a preregistered five-run $S=4$ repeated-control test, the learned actor with an exact one-step critic reaches median returned-policy loss $1.052\times$ the Exact PMD oracle and retains the criterion across four no-retraining shifts. The same checkpoints with their learned critic give descriptive median $1.050\times$ the oracle (no registered margin). At $S=8$, replacing the exact critic by the learned critic raises median $T=20$ loss to $0.0225$ yet leaves the Liang–Lai and Algorithm Distillation adaptations $20.2$–$24.2\times$ higher-loss; this is a one-sided sampled-critic bound because PolicyAttention consumes 144 generative transitions per round versus 20 on-policy transitions for the adaptations. The strict 20-transition comparison remains open. At $S=8,16$, the exact-critic common-harness comparison remains $17.7$–$28.2\times$ lower-loss than those adaptations, with the information asymmetry stated locally.