Papers

We introduce the concept of spin migration, i.e. time-dependent spin density, and the absolute smallest example of molecular spintronics. We illustrate the concept by ab initio calculations of the coupled vibronic motion of the electrons and the nuclei in the argon dimer cation, in which the vibrational level spacing is similar to the spin–orbit splitting of the atomic argon cations. We find that the spin density varies on multiple time scales, given by the natural time scales of the electronic and nuclear wavepackets.

We give an exposition of a proof, discovered by Astra, of an Aleksandrov estimate for kinetic equations with rough coefficients. We explain this method in the simpler elliptic and parabolic settings as well.

Emission-line galaxies provide key diagnostics of star formation, chemical enrichment, and AGN activity across cosmic time. We present a systematic census of emission-line sources using JWST/NIRCam wide-field slitless spectroscopy (WFSS) from the COSMOS-3D program, which covers a large contiguous area of 0.33 deg$^2$ and provides F444W grism spectroscopy over $3.9$–$5.1\ \mu$m. By combining slitless spectroscopy with deep multi-band imaging data, we construct a homogeneous spectroscopic sample of 12,275 objects at redshift 0–9. The typical $3\sigma$ line-flux limit reaches $3.2\times10^{-18}\ {\rm erg\ s^{-1}\ cm^{-2}}$. To address source confusion inherent to slitless spectroscopy, we develop a multi-step identification framework that combines information from spectra, images, spectral energy distributions, and spatial distributions. We introduce convolutional neural network and large language model to emulate the human identification process and improve efficiency. The resulting catalog provides spectroscopic redshifts, emission-line measurements, and derived physical properties for all sources. The F444W WFSS enables the detection of multiple emission lines, including primarily [O III], H$\alpha$, He I $\lambda10830$, [S III] $\lambda\lambda9531,9069$, Pa$\beta$, Pa$\alpha$, Br$\beta$, PAH, Br$\alpha$, allowing a continuous census of galaxies across cosmic time. We construct composite spectra in several redshift bins and detect a variety of faint spectral features that are difficult to identify in individual spectra, including higher-order hydrogen recombination lines, CO absorption bands, and [Fe II] lines. This catalog provides a key reference dataset for studies of galaxy evolution and AGN activity, and demonstrates the power of WFSS for constructing large, unbiased spectroscopic samples over wide areas. The full catalog will be publicly available online upon publication.

Euler's constant $\gamma$, also known as the Euler-Mascheroni constant, remains one of the most elusive constants in mathematics. Despite extensive study, its irrationality is still unproven, and Apéry-like approximations of it are remarkably scarce. We present a novel identity that expresses $\gamma$ in terms of a Meijer G-function and its first few derivatives. This identity is then generalized and used to systematically generate infinitely many Apéry-like approximations of $\gamma$ using a Conservative Matrix Field construction based on the Meijer G-function.

Clinical sleep medicine repeatedly documents profound divergences between objective sleep duration and subjective daytime impairment, notably exemplified by sleep state misperception in paradoxical insomnia and boundary instability in narcolepsy type 1. Here, we present DyssomniaNN: a multi-scale biophysical computational framework coupling Borbély's two-process regulation of sleep homeostasis and circadian drive with Saper's hypothalamic reciprocal flip-flop circuit and a recurrent corticothalamic leaky integrate-and-fire spiking neural network. We formalize five clinical cohorts across an identical 72-hour photoperiod: healthy control, circadian rhythm sleep-wake disorder (delayed-phase), chronic insomnia, paradoxical insomnia, and narcolepsy type 1. The synthetic local field potential converges closely with empirical human electroencephalography spectra from the PhysioNet Sleep-EDF database across all canonical frequency bands (spectral mean absolute error of 0.33–0.35). Furthermore, we introduce the Well-Rested Index to quantify restorative efficacy. Simulations reveal that sleep duration fails to predict restorative recovery: paradoxical insomnia achieves normal total sleep time (21.15 h) yet yields low restoration (37.6%) from unsuppressed cortical beta-band intrusion, whereas hypocretin deficiency in narcolepsy produces severe nocturnal fragmentation (781 min of wake after sleep onset) and 35 sleep-onset rapid eye movement periods. DyssomniaNN provides an in silico platform for mechanistic sleep research and virtual neuropharmacology.

A central challenge in de novo protein design is generating proteins with desired structural and functional properties. Existing design models typically require a dedicated input representation for each property, limiting the design objectives they support. We develop Prompteina, the first all-atom structure generation model that supports new and broader design objectives specified in natural language, analogous to text-to-image generation. To train Prompteina, we construct Prompteina-Data, a paired text–protein structure dataset of 1.8M structures and 50M+ captions describing global and residue-specific structural and functional properties. We adapt Proteina-Complexa, a pretrained structure generation model, through text-conditioned pretraining and finetuning that aligns residues with their corresponding text. Prompteina outperforms baselines on 15 of 18 structural properties and generates proteins that more closely match descriptions of their intended functions. In binder design, it leads baselines on at least 13 of 20 targets and improves interface confidence by 14% over the strongest baseline. With iterative in silico feedback, Prompteina's gain over non-iterative generation is 57% larger than the next-best baseline on the hardest targets. Finally, we experimentally validate Prompteina designs against GM2A, a target with no reported de novo binders. We identify nine binders, with the strongest at an apparent $K_{\mathrm{D}}$ of 107 nM. These results establish natural language as an effective and powerful conditioning interface for protein structure generation.

We study the convergence of Markov chains in the geometry induced by Hilbertian embeddings associated with positive definite kernels, also called Maximum Mean Discrepancy (MMD). Under a contraction assumption in the kernel-induced geometry, and a standard spectral gap assumption, we establish non-asymptotic, high-probability bounds for the convergence of the empirical occupation measure to the invariant measure. The obtained bounds separate the roles of the two conditions: the spectral gap determines the effective sample size in the leading term, while the kernel contraction enters only through a linear correction. As an application, we study one-step prediction of dynamical systems from a single trajectory, deriving fast learning rates for a nonlinear least-squares estimator. The rates highlight the interplay between mixing properties in the kernel-induced geometry and the classical source and capacity conditions used in the analysis of least-squares.

Self-supervised learning on 3D medical images commonly relies on random sub-volume sampling during pretraining. However, random cropping implicitly treats all spatial regions as equally worth observing, despite anatomical priors and spatial redundancy that make regions inherently unequal in their value for representation learning. To this end, we first show through controlled crop-quality manipulations that better sub-volumes lead to better downstream transfer, revealing the observation policy as an overlooked bottleneck in 3D medical SSL. Motivated by this finding, we revisit sub-volume sampling as a where-to-look problem. We propose VolumeProbe, a plug-and-play framework that replaces random cropping with an offline coarse-to-fine probe bank guided by anatomy-awareness, informativeness, and diversity. We instantiate VolumeProbe as a lightweight Lite variant using geometric and image-statistical cues, and a diagnostic Feat variant using frozen visual features, to examine whether lightweight volume-intrinsic priors suffice or richer semantic cues reliably provide additional value. Extensive experiments across multiple 3D medical SSL backbones and downstream tasks demonstrate that VolumeProbe-Lite consistently improves transfer performance over random sampling. Mechanistic analyses further link these gains to more anatomically plausible and informative observations, reduced spatial redundancy, more efficient learning dynamics, and more structured representations.

We consider the demand-private coded caching problem with heterogeneous file sizes and cache capacities, where each user must recover its requested file without learning any information about the demands of the other users. We first extend the virtual-user reduction technique to accommodate heterogeneous cache sizes, thereby enabling the construction of demand-private coded caching schemes from non-private schemes. Our main contribution is an exact characterization of the memory-rate trade-off for the fundamental setting of two users and two files with arbitrary file sizes and cache capacities. Specifically, we characterize the optimal trade-off through eight linear inequalities and establish achievability by constructing explicit coded caching schemes for the non-trivial corner points, followed by memory sharing. These constructions include novel asymmetric cache placement strategies tailored to heterogeneous file sizes and cache capacities. For the converse, we exploit the distributional equivalences induced by demand privacy to derive information-theoretic lower bounds that explicitly account for the underlying heterogeneity. Our results generalize the exact memory-rate trade-off characterization for the homogeneous demand-private coded caching setting with two users and two files, while quantifying the additional transmission cost imposed by demand privacy compared with the non-private heterogeneous setting.

In every sub-Riemannian Heisenberg group $\mathbb H^n$, with $n\geq 2$, we prove the existence of a global perimeter minimizer whose boundary is a smooth, non-characteristic, entire intrinsic graph but it is not a vertical hyperplane.

Recursive self-improvement (RSI) aims to transform interaction experience into persistent improvements, yet external feedback is costly and world-model predictions may become unreliable as policies evolve. We introduce RSI-Anything, a domain-general framework built on JEPA-Anything that uses predictive world models to guide action and learning-data selection. Observed feedback drives policy or workflow improvement and conditional world-model adaptation, while component and compatibility checks govern the retention of updated policy-model pairs. Across diverse computational and scientific domains, RSI-Anything demonstrates substantial gains. In code repair, with the coder fixed, success increases from 26.3% with a static verifier to 29.2% through predictive selection and 31.2% after world-model adaptation, at comparable test usage. Graphical user interface (GUI) evaluations showed higher task completion, while average actions decrease by 39.4%. Across five successive policy versions, laboratory-planning scores more than double from 21.80% to 46.01%. In reaction optimization, RSI-Anything achieves 96.15% mean best observed yield versus 82.16% for Bayesian optimization under the same 40-experiment budget. An end-to-end immune-science application further connects workflow evolution and predictive modeling with therapeutic hypothesis generation. These results demonstrate how predictive world models and retained system updates enable recursive improvement across diverse environments.

Consider a queueing system operated by Bob, which is intended to serve only jobs generated by a legitimate user, Willie. Willie's jobs arrive according to a Poisson process, and the service times are exponentially distributed. Bob seeks to covertly serve additional jobs arriving according to an independent Poisson process, without Willie detecting their presence. As the legitimate user, Willie is provided with certain statistics of each busy period by Bob. In particular, we consider two statistics: (i) the number of jobs served during each busy period and (ii) the duration of each busy period. We establish that, under either statistic, the maximum expected number of additional jobs that Bob can covertly serve obeys a square-root law. Specifically, over n busy periods, Bob can covertly serve additional jobs in the order of square root of n, whereas any scaling which is above square root of n enables Willie to asymptotically detect the presence of these additional jobs with vanishing error probability. Furthermore, we characterize the scaling constant associated with the square-root law, which we refer to as the covert queueing constant, for each of the two statistics. We compare the scaling constants corresponding to the two statistics and argue that the scaling constant under statistic (i) is no greater than that under statistic (ii).

Vision-Language Models (VLMs) increasingly analyze and reason about images, yet it remains unclear whether their internal representations faithfully encode the structured relations required for such reasoning. We introduce EICS (Evaluation-Invariant Concept Stability), a metric for testing whether representations consistently encode concepts under controlled one-concept interventions, and CASP-VL (Causally controlled Spatial Perturbations for Vision-Language models), a benchmark of causally controlled spatial perturbations derived from Visual Genome scene graphs. Across multiple VLM architectures, we find that spatial relations are represented substantially less faithfully than lexical information, even when the same models score well above chance on compositional benchmarks. Further analysis shows that the relation is identifiable at the predicate's own tokens but is lost when the sentence is aggregated into a global representation, whether through the (EOS) token or by mean pooling. These findings reveal a systematic failure invisible to output-based evaluation: VLMs do not preserve, in the representation used downstream, relational information that is present in their own input.

While deep learning models for tabular data have recently received significant research attention, the choice of objective functions for regression tasks remains an understudied degree of freedom. Several lines of research offer alternatives to the standard Mean Squared Error (MSE), but differences in datasets, backbones, and evaluation protocols make their practical benefits difficult to compare. In this work, we address this gap by performing a systematic re-evaluation of regression objectives across a broad collection of established tabular datasets and multiple neural backbones. Our comparison reveals that many proposed objectives provide limited or inconsistent gains over a properly tuned MSE baseline, while quantile loss yields consistent aggregate improvements over MSE across the tested backbones. We then identify a limitation that remains even with this strong objective: regions with different levels of target noise can reach their best predictive performance at different training epochs. Consequently, a single global early-stopping checkpoint can impose a compromise between uncertainty regions, even when the objective can represent heteroskedastic target distributions. Motivated by this limitation, we introduce a heteroskedasticity-aware extension of quantile loss that uses input-dependent label smoothing as a potential remedy and improves over quantile loss on several backbones. Overall, our results provide a modern empirical picture of regression objectives for tabular deep learning and highlight how differences in optimal stopping times across uncertainty regions can limit the effectiveness of global early stopping. The code is available at https://github.com/yandex-research/tabular-regression.

The $(0,x,1,2)$-hiccup sequence starts at $x$ and increases by 1 when the current index has already appeared as a value, and by 2 otherwise. We prove directly that for $x\geq3$ the gaps between its missing values are $1,2,3,\ldots$, each repeated $x-2$ times, and we derive closed formulas, an explicit error bound, and a generating function in terms of Ramanujan's theta functions. The counting functions of the complements satisfy nested recurrences. The sequences of missing values are the partial complements of polygonal numbers. In particular, the $(x-2)$-fold composition of the enumeration of the positive integers that are not $x$-gonal is the hiccup sequence minus 1. We extend the nested recurrence and a tree interpretation to every miss increment $z\geq2$ and every initial value $x\geq2$. Further interpretations involve polyomino vertices, monochromatic pairs, and, by a theorem of Bickle, Ramsey core numbers.

A scalable ground-state solver to be used in sample-based quantum diagonalization (SQD) is presented. The solver is built on JAX API, and is intended to be run on GPU platforms and possibly many-GPU high-performance computing facilities. It is capable of subspace diagonalization in up to $2^{30}$-dimensional subspace, with possible upgrades to enable even larger-scale operations. The two main components, a general-purpose eigensolver and an SQD-specific matrix-vector operation function, are described in detail. Efficiency of the eigensolver with respect to the GPU memory is demonstrated using a simple physics model. Furthermore, good strong scaling of the eigensolver in many-GPU environment is observed.

We study the quantum query complexity of several basic graph problems. 1) We prove a tight $\Theta(n^{3/2})$ bound for finding a maximum-out-degree vertex in an $n$-vertex tournament, resolving a conjecture of Mande, Paraashar, and Saurabh [FSTTCS'23]. 2) Using the same proof idea, we give a direct proof that finding a maximum-degree vertex in an $n$-vertex undirected graph requires $\Theta(n^{3/2})$ quantum queries, a bound implicit in the work of Apers and Lee [CCC'21]. Both lower bounds above hold even for computing only the maximum degree or maximum out-degree. 3) We also study Maximum $(k,n-k)$-Cut, which asks for the largest cut with one side of size $k$. For every constant $k\geq 1$, we give an $O(n^{2-1/(k+1)})$-query quantum algorithm. 4) We establish a reduction to Maximum $(k,n-k)$-Cut involving $k$-Graph Collision, which asks whether the marked vertices of a known graph contain a $k$-clique. For $k\geq 3$, this yields unconditional lower bounds with exponents strictly larger than $3/2$, showing that this problem is strictly harder than computing maximum degree. Additionally, under a conjecture we propose for $k$-Graph Collision, the reduction yields a lower bound matching our upper bound above.

We present several new and surprising results on the theory and practice of Arbitrary Precision Approximate (APA) matrix multiplication, which refers to algorithms that output merely approximations to matrix multiplication even in exact arithmetic. While APA algorithms have been around for nearly half a century, and despite the fact that they have potentially lower (asymptotic) cost than many fast exact matrix multiplication schemes, they have not been studied as closely, to the extent that relatively little is known about their numerical properties. In this paper, we shine a spotlight on these algorithms by presenting three important results. First, we provide a new search algorithm for APA routines that is easy to use, automatically generates encoding matrices with functional entries, and can match or beat the best known APA algorithms for several sizes. In particular, we improve the upper bound on the border rank of $\langle 2,4,5 \rangle$ matrix multiplication. Second, we combine this insight with alternative bases to minimize the number of additions in an APA algorithm, thereby improving its leading coefficient. Finally, we prove the same kind of stability that characterizes fast exact matrix multiplication for an algorithm of Bini [Calcolo 1980] that computes an exact product of two matrices using a modified APA scheme (with or without alternative bases).

We prove that every length-preserving automorphism of a nonspherical Artin or Coxeter group has infinite Reidemeister number. As a consequence, we establish property $R_\infty$ for large-type free-of-infinity Artin groups, infinite strongly rigid Coxeter groups, and infinite virtually abelian Coxeter groups, including all affine Coxeter groups. We also prove that the automorphism group of every infinite irreducible non-affine strongly rigid Coxeter group is acylindrically hyperbolic.

Fermionic Gaussian states are completely characterized by their two-point correlations, making the covariance matrix a natural reference for quantifying non-Gaussian structure. Motivated by fermionic antiflatness, we study its extremal form for pure number-conserving states and ask which states can be maximally antiflat and how they can be constructed. We show that, at fixed particle number, maximal first antiflatness is equivalent to a completely flat one-body reduced density matrix, and we obtain a complete existence classification together with explicit block and cyclic-orbit constructions of all allowed sectors. We then investigate the structure that appears beyond the covariance level. Maximally antiflat states with identical one-body data can exhibit distinct connected four-point correlations, which we characterize through the four-point Majorana Wick error and, equivalently, the connected two-body reduced density matrix cumulant. We show that this quartic structure is necessarily nonzero and formulate its extremization as a two-body reduced density matrix (2RDM) purity problem. Combining this framework with a Hilbert–Schmidt estimate of Christiansen for truncated two-body correlations, we obtain an upper bound on the connected quartic structure in terms of first antiflatness. Our results establish both a complete characterization of maximal fermionic antiflatness at fixed particle number and a constrained hierarchy linking covariance-level flatness to higher-order non-Gaussian correlations.

Machine-learning force fields (MLFFs) enable the calculation of transformation pathways in molecular crystals at a fraction of the computational cost of density functional theory (DFT). However, a good agreement in energies and structures does not necessarily imply an accurate description of vibrational properties, which are essential for characterizing transition states and determining free energies at finite temperatures. Herein, we assess the accuracy of system-specific SO3krates MLFFs trained on PBE+MBD reference data for describing vibrational properties of molecular crystal transformations. As examples, we consider a polymorph transition of 1,4-diiodobenzene and a single-crystal-to-single-crystal Diels-Alder reaction. The transition state structures obtained from solid-state nudged-elastic-band (NEB) calculations with the MLFFs exhibit a single imaginary $\Gamma$-point frequency associated with the respective transformation. Compared with PBE+MBD, the mean absolute errors of $\Gamma$-point vibrational frequencies and relative harmonic free energies at 300 K are about 3 cm$^{-1}$ and 1 kJ/mol, respectively. Furthermore, we compare for the Diels-Alder reaction a collective transformation pathway with a sequential one, in which individual diene-dienophile pairs react successively, and demonstrate that PBE0+MBD single-point corrections can significantly affect the predicted reaction energetics. These results demonstrate that system-specific MLFFs can reproduce not only the energies and forces but also the local curvature of the potential-energy surface with high accuracy, enabling reliable calculations of harmonic vibrational free energies, providing a basis for extending the studies of molecular crystal transformations to larger supercells.

We study the last iterate of standard asynchronous Q-learning from a single trajectory of a finite Markov decision process. The trajectory follows a fixed behavior policy whose state–action chain is irreducible and may be periodic. For discount factor $\gamma$, write $H=(1-\gamma)^{-1}$, and let $\mu_{\min}$ be the minimum stationary state–action probability and $\mathfrak h_\star$ the largest expected hitting time of the reverse state–action chain. We prove that zero-initialized Q-learning with a constant step size achieves sup-norm error at most $\varepsilon$ with high probability using $\widetilde{O}(H^4/(\mu_{\min}\varepsilon^2)+\mathfrak h_\star)$ transitions, for $0<\varepsilon\le1$. The statistical term retains the quartic effective-horizon dependence of standard Q-learning, while initialization cost is additive in $\mathfrak h_\star$. For aperiodic behavior chains, a comparison with mixing time yields a transient term $\widetilde{O}(t_{\mathrm{mix}}/\mu_{\min})$. An empirical state–action count rule selects a constant step size for a subsequent training run and attains the same rate without prior knowledge of model parameters, target accuracy, or confidence level. The output is the last training iterate, with both stages included in the sample count. The proof uses two deterministic Bellman envelopes to separate statistical error from fixed-policy initialization error and adapts reverse-time hitting-cost compensation from TD learning to state–action propagation. An exploration lower bound holds for arbitrary predictable step sizes. Together with the existing statistical lower bound and its extension to pilot-selected constant steps, it yields matching mean-square rates up to logarithmic factors on the stated large-sample parameter classes.

We study how mixed-state correlations reorganize across island transitions in Jackiw-Teitelboim gravity coupled to a non-gravitating bath. Using the partial-dimensional-reduction realization of double holography, we compute reflected entropy for adjacent and disjoint radiation regions in the vacuum and in the thermofield-double state of an eternal black hole. Reflected entropy probes the internal partition of the entanglement wedge and therefore resolves structure that is invisible to the ordinary Page curve: its dominant saddle can change even when the entropy saddle of the union remains fixed, and it vanishes at leading order when the entanglement wedge disconnects. We show that the lower-dimensional reflected-island description agrees, to leading order in the dynamical brane fluctuation, with the higher-dimensional defect-extremal-surface picture. The finite-angle comparison further suggests a projection-covariant identification of island and brane endpoints at linear order. The resulting Page-like curves and Markov gaps provide a geometric probe of the reorganization of the purification and of non-Markovian, multipartite correlation structure during island transitions.

The $q$-deformed Weil-Petersson volumes of Do and Norbury are the top-degree parts of Okuyama's discrete volumes, which are defined by topological recursion on the spectral curve of the double-scaled SYK (DSSYK) model. We show that the same q-deformed volumes can be obtained from a double-scaled matrix model whose disk density is found by zooming in on the soft edges of the DSSYK density. Applying the same procedure to the hard edge of $\mathcal{N}=1$ DSSYK, we obtain candidate $q$-deformed $\mathcal{N}=1$ super Weil-Petersson volumes. They are polynomials of fixed degree, and they reduce to the $\mathcal{N}=1$ super Weil-Petersson volumes in a scaled $q\to1$ limit. These candidate volumes differ from the $\mathcal{N}=1$ volumes of Do and Norbury in (arXiv:2510.12431) up to what we call "irrelevant" contributions which exactly vanish in the scaled $q\to 1$ limit. Together, these results demonstrate how q-deformed volumes can be naturally associated to the spectral edges of various DSSYK models and provides an intuitive way to construct them in supersymmetric contexts.

We consider solutions to the two-dimensional Navier-Stokes and Euler equations with the velocity in $L^{\infty}(\mathbb{R}^2)$ and the vorticity in the uniformly local Yudovich space $Y^{\theta}_{ul}(\mathbb{R}^2)$. We show that if $\theta$ grows sufficiently slowly, then for every $T>0$, solutions of the Navier-Stokes equation converge to solutions of the Euler equation in $L^{\infty}([0,T];L^2_{ul}(\mathbb{R}^2))$ as $\nu \to 0^+$, provided they are generated from the same initial data.

We formalize the Hamilton–Perelman Ricci-flow proof of Thurston's geometrization conjecture. The public Lean declaration is reproduced in this paper. Its geometric interpretation follows, and verification is recorded in 4.

Neural semantic parsers generate meaning representations token by token, yet well-formedness depends on references, scope, and graph relations that unfold during generation. Constrained decoding prevents locally invalid tokens but does not guarantee that a valid prefix can be completed within a fixed output-length limit. We investigate structural automata at three stages of DRS parsing (decoding, post hoc processing, and training) and additionally evaluate decoding on AMR. For decoding, we introduce accepting-path decoding (APD), which maintains a verified completion within the remaining length limit and follows the model's preferred token whenever that token can also be completed. APD guarantees an accepted output without retracting tokens. Under tight length limits, it improves Smatch++ over local masking by 5.1 and 2.4 points on DRS and by 6.4 and 3.2 points on AMR, comparable to rollback under the same limit, which retracts tokens. For post hoc processing, invalid outputs concentrate on the same inputs: eight unconstrained samples yield no valid output for 10.2% of inputs with limited training data, compared with 0.4% with full data, where filtering comes within 0.2 Smatch++ points of APD. For training, penalizing automaton-rejected tokens improves development Smatch++ by 3.6-11.0 points after 10% of training, but this advantage diminishes as cross-entropy alone reduces the probability assigned to rejected tokens from 14% to below 2% within the first sixth of training with limited data.

Large language models reuse the same attention heads across tasks, but identifying these shared heads does not explain what they do differently in each task. A natural source of inspiration is task-dependent interactions among shared brain regions, which motivate a network view of language-model computation. Here, we compare fixed model components across tasks using identical graph facts, statements specifying which directed connections are present. We measure how interventions affect attention heads and the activation state in later layers (influence), as well as the answer (importance). Task changes redistribute the influence in five open-weight models spanning four families and 1.5-14 billion parameters. In Gemma-2-9B and Qwen3-14B, an activation edit changes an early internal activation vector and switches which fact the model reads while the written instruction stays fixed. The same heads then respond to different graph facts and influence later components differently. For each prompt, we construct two linear response maps, one before the edit and one after it. Each map predicts a later head's response from a measured change in an earlier head. For a separate factual intervention, the map for the corresponding condition reduces mean squared prediction error by 53.6% in Gemma and 5.0% in Qwen compared with the average of the two maps. These findings show that task context changes both which graph facts the shared components respond to and how their outputs affect later computation. A network account may help explain how models use shared parameters to perform different computations. Measurements of task-dependent influence could also guide interventions intended to alter one behavior while preserving others.

Nimbus Studio is a visual pipeline platform for brain-computer interface (BCI) experiments: researchers assemble preprocessing, feature extraction, decoding, and evaluation over public benchmark datasets or their own recordings, with cross-validated evaluation protocols (including leave-one-subject-out), BIDS export, and bring-your-own Python model classes. Whether its numbers can be trusted is a fair question for any such platform. We answer it with a parity study: six standard BCI decoding pipelines (CSP+LDA, Riemannian MDM, tangent-space logistic regression through the platform's bring-your-own-code node, P300 xDAWN+LDA, and the deep ShallowConvNet and EEGNet) were evaluated on three public datasets (motor-imagery BNCI-2014-001/004; P300 BNCI-2014-009) under two protocols (per-subject session holdout and pooled leave-one-subject-out cross-validation via the platform's planned-CV driver), once through Nimbus Studio's execution engine and once through independent, hand-written reference implementations built directly on MNE-Python, scikit-learn, pyriemann, and braindecode. Every deterministic pipeline matched the reference exactly (0.00 points maximum difference across all 54 session-holdout subject-runs and all CSP/MDM grouped-CV folds), including pipelines through the bring-your-own-code node and the CV orchestration; the remaining grouped-CV cells agree to floating-point precision (worst case 0.06 points, about one trial per fold). The stochastic deep models agreed within seed-to-seed training variability, estimated with multi-seed reruns on each side. The platform's execution engine therefore computes the same science as the reference stack across protocols, paradigms, and extensibility surfaces. The platform is available at https://studio.nimbusbci.com/, and the complete harness and per-subject results accompany this paper for independent verification.

Target tracking over wide areas using a network of sensor agents is a challenging problem when agents have limited sensing coverage and communication topologies vary over time. Existing distributed filtering approaches commonly assume that each agent, or at least one of its neighbors, can directly observe the target, and further rely on fixed network topologies, global network parameters, or multiple consensus rounds per time step. These requirements limit their applicability in wide-area network deployments. In this paper, we propose an Information-Weighted Distributed Kalman Filter (IWDKF) that relaxes these assumptions through a weighted-consensus mechanism applicable to arbitrary switching topologies satisfying joint connectivity. The proposed approach requires no prior knowledge of global network properties and limits communication overhead to a single consensus exchange per time step, while enabling information fusion even when some agents lack direct target measurements. The weighted-consensus covariance matrix is shown to remain positive definite, and the resulting consensus update is proven to maintain estimate consistency. It is also established that the proposed weighting strategy preserves the asymptotic agreement property of the underlying consensus protocol under joint connectivity. Numerical simulations of a multi-target tracking scenario involving a network of sensor agents demonstrate the improved estimation accuracy of the proposed IWDKF under both fixed and switching network topologies. The performance of the proposed filter is close to that of the centralized Kalman filter, and is compared with three existing distributed filters.