Papers

We study algebraic relations among functions in star-invariant subspaces. Let $\theta$ be an inner function and suppose that $f,g,h\in K_{\theta}^p$ satisfy $P(f,g,h)=0$, in which $P$ is a homogeneous polynomial and the associated projective plane curve is smooth. Then $\dim\operatorname{span}\{f,g,h\}\leq1$ if either $\operatorname{deg} P\geq 4$ and the boundary spectrum of $\theta$ has logarithmic capacity zero, or $\operatorname{deg} P = 3$ and the boundary spectrum contains at most one point. This settles new cases of a problem of Dyakonov, subsumes the previously known results, and recovers the classical fact that polynomial parametrizations of a smooth projective plane curve of degree at least three are projectively constant.

Tidal Love numbers characterize the conservative response of compact objects to external perturbations and provide a powerful probe of their nature. While the static Love numbers of Schwarzschild, Kerr, and Reissner–Nordström black holes remarkably vanish, the tidal response of a generic Kerr–Newman black hole has remained unexplored due to the intrinsic coupling between gravitational and electromagnetic perturbations. Exploiting a recent breakthrough in the separability of these perturbations, we analytically determine the static tidal response of the most general stationary black hole in four-dimensional Einstein–Maxwell theory. For arbitrary multipole order, charge, and spin, we show that the entire matrix of conservative Love numbers vanishes, including the mixed gravito-electromagnetic couplings. We also compute the nonvanishing static dissipative response induced by frame dragging.

Floor plan datasets underpin computational analysis of building layouts, spatial connectivity and graph machine learning. However, publicly available datasets often require substantial preprocessing before they can be used reliably. We present ModRes, a cleaned and enriched version of the ResPlan dataset, containing 8,431 valid and unique residential floor plans. Invalid and duplicate floor plans are removed through a dedicated cleaning workflow, producing a ready-to-use dataset. For each floor plan, ModRes provides two-dimensional geometry, images, three-dimensional building representations and three complementary dual graphs in CSV and JSON formats with graph-, node- and edge-level features. Continuous and categorical graph attributes support machine learning workflows. We characterise the dataset using graph-based statistics and demonstrate its utility through a range of case studies. ModRes provides structured geometric, topological and semantic representations needed to automate spatial analysis and support machine learning-based workflows for building design and performance evaluation.

We extend neural multi-channel importance sampling in MadNIS to full proton-proton processes in a production-ready event-generation setup. We benchmark a wide range of LHC processes, including multi-jet, vector-boson, top-quark, and Higgs production, and obtain event-generation speed-ups of up to a factor of 250 without process-specific hyperparameter tuning. We quantify how the speed-up scales with training time and final-state multiplicity, and when the training cost amortizes. MadNIS will become the default for phase-space integration and event generation at leading order in MadGraph.

We investigate whether controlled motion of a quantum sensor offers a metrological advantage in a field-detection task. We consider a localized field of known strength $B$ occupying an unknown contiguous region making up a fraction $1/N$ of the total search space, with a qubit sensor controlled for a total time $T$ to maximize the probability of detecting the field. We study the regime in which the characteristic timescale of the field is slow compared to the time to move the sensor between any two regions, and we distinguish classical motion, where the sensor follows a definite trajectory, from quantum motion, where the sensor can be in a coherent superposition of locations. For a single classically moving sensor, we derive an optimal multi-stop protocol and obtain the exact maximum detection probability. Allowing coherent spatial superposition maps the single-sensor problem onto Hamiltonian search and reduces the interrogation time for successfully detecting the field from $\Theta(N/B)$ to $\Theta(\sqrt{N}/B)$. We then extend the problem to $M$ sensors and identify a hierarchy of optimal time scalings for constant success probability determined by the available spatial and inter-sensor quantum resources. Unentangled coherently moving sensors achieve $T=\Theta(\sqrt{N/M}/B)$ by searching disjoint regions in parallel, while entanglement among the sensors can further enhance the effective field coupling and achieve $T=\Theta(\sqrt{N}/(MB))$. Matching lower bounds establish the optimality of these scalings in the presence of arbitrary controls and ancilla systems. Our results separate the roles of classical motion, spatial coherence, and entanglement in spatial field detection.

Decision models such as Jev score candidate answers or actions. A small decision head trained label-free can recover about 99% of a frozen language model's multiple-choice accuracy while using only two-thirds of its transformer layers. It learns the full model's answer probabilities with KL divergence, without correct-answer labels for training. One backbone pass reads the question and all options together; the head returns probabilities for every option. We call this model FunDM (Fun Decision Model). Using 24 of Qwen3-8B's 36 layers and skipping the LM head, its +1T variant reaches 75.0% mean accuracy over eight benchmarks, versus 75.7% for the full model. On MMLU-Pro, both heads achieve 1.56 to 1.57 times batched vLLM throughput with about one-third lower peak GPU allocator memory. Both heads score higher than released Contrastive Language Models (CLM), fine-tuned CLM, and CLM-shaped heads trained from scratch on the eight multiple-choice benchmarks and coding-agent selection. Separately trained agent heads learn judge probabilities without pass/fail labels and select passing runs for 74.4 to 74.6 of 100 held-out tasks on average, versus 74 for the full-model judge and 52.0 for a CLM-shaped action-trained head. Code is available at: https://github.com/Ujjawal-K-Panchal/FunDM

Achieving complex, long-horizon robot behavior remains challenging because successful execution depends on skills grounded in a robot's physical affordances. Existing training-task distributions are often handcrafted or sampled from large language models (LLMs), relying on semantic plausibility rather than embodiment-specific feasibility. This mismatch can produce curricula that are too difficult, redundant, or blind to non-obvious but learnable behaviors. We propose Generative Flow on Symbolic Abstractions (FOSA), a framework for discovering embodiment-specific capabilities by learning a grounded task generator. FOSA parameterizes an abstract policy as a Generative Flow Network that constructs symbolic task skeletons. Each skeleton is compiled into a simulation environment, where low-level policy-learning performance provides the reward signal for the abstract policy. Across heterogeneous robot platforms, FOSA discovers diverse and executable tasks near the robot's empirical capability frontier. After distilling the discovered task policies into a single language-conditioned policy, FOSA improves performance on unseen complex and long-horizon tasks. The code and demonstration videos are available at https://www.youwei-yu.com/fosa.

Let $X$ be a smooth projective variety over the complex numbers, and let $\mathbb{V}$ be an irreducible privileged $\mathrm{SL}_3$-local system on $X$ in the sense of Esnault and Groechenig. We show that $\mathbb{V}$ is of geometric origin. We also give an example of a privileged but non-rigid $\mathrm{SL}_3$-local system.

We consider the $k$-median problem on general metric spaces, subject to the condition that the instances are $\beta$-stable (i.e., the optimal solution using $k-1$ centers has a cost at least $(1+\beta)$ times that of the optimal solution with $k$ centers). We give a $(1.89+\epsilon)$-approximation algorithm for such instances running in time $\exp(1/(\beta \times \mathrm{poly}(\epsilon)))\cdot \mathrm{poly}_{\epsilon}(n)$. In particular, for $\beta =\mathrm{poly}(\epsilon)/\log n$ and $\epsilon$ a tiny constant, this is a polynomial-time algorithm. This improves on previous work showing a $(2 + \epsilon)$-approximation algorithm with similar running time [CGL+25]. Combined with the pseudo-approximation algorithm in our companion work, this results in a better-than-$2$ approximation algorithm for general $k$-median instances. Our main technical contribution is a novel nuanced analysis of local search that allows us to isolate a subset of clients on which we lose essentially nothing compared to the optimal solution, while losing an approximation factor of $3$ on the rest of the clients. We complement this with an algorithm based on sampling and partial enumeration, achieving a better-than-$2$ approximation on the rest of the clients. Trading off these two algorithms yields our final approximation.

Designing synthesizable materials with targeted properties remains one of the central objectives in materials sciences. Ionic liquids (ILs) are well suited to this goal due to their "tunability", where physical and chemical properties can be precisely customized by modifying their molecular structure, specifically by varying the combination of cations and anions. At the same time, current data-driven property models for ionic liquids often degrade in scarce, noisy, and uneven data regimes, where measurements cover only a small fraction of chemical space and a limited range of thermodynamic conditions. This makes out-of-distribution screening brittle: even when point predictions look plausible, it is difficult to compare candidates consistently, quantify downstream implications, or trust rankings enough to guide molecular discovery. We present a property-prediction and optimal candidate selection workflow that treats data processing, deep learning modeling, and physics-based calculations as a coupled system, linking property prediction with uncertainty estimation and physics-based filtering. By tightening the link between predicted properties and the criteria used for down-selection, the workflow supports reliable out-of-distribution ranking and enables prioritization of previously untested ionic liquid candidates with favorable predicted trade-offs. We demonstrate the application of our workflow by designing novel ionic liquids for CO2 capture from flue gas, predicting their properties and selecting Pareto-optimal candidates based on CO2 solubility, IL viscosity and working capacity.

A Latin square can be extended by replacing its symbols with probabilities or quantum states. We relate these two extensions through explicit examples, from classical and fractional Latin squares to quantum Latin squares and a real solution of Euler's quantum 36 officers problem. A simultaneous cyclic-shift ansatz on a four-torus of tensor coefficients gives a real absolutely maximally entangled (AME) state of four six-level systems. A local orthogonal change of basis yields a representative with 96 nonzero amplitudes. Two single-party arrays obtained from the corresponding quantum orthogonal Latin square yield fractional Latin squares. Signs matter: comparison with the independent real construction of Bruzda and its sign variant distinguishes three local-unitary classes, two of which have identical probabilities. We extend this probability representation to existing seven- and nine-party AME states with six levels each. Their amplitude matrices reveal 48 complex Hadamard blocks of order $3^3$ and six of order $6^4$, respectively. These constructions separate what can be read from a probability picture from the coherent conditions responsible for maximal entanglement.

Let $K/\mathbb{Q}_p$ be a finite extension, and let $X/K$ be an algebraic variety. We present a new proof that the unipotent completion of the étale fundamental group of $X_{\bar{K}}$ is a pro-de Rham representation, and show that it is pro-semi-stable whenever $X$ has semi-stable étale cohomology. We also reprove, using syntomic methods, that it is pro-crystalline at integral base points whenever $X$ admits a smooth proper formal model. All three proofs use the bar construction and are inspired by Wojtkowiak's approach to unipotent fundamental groups.

Time-domain surveys often produce asynchronous image sequences across irregular observation times and photometric bands. In many applications, predictions are needed after each new observation, particularly when transient sources must be identified early to trigger follow-up. Strongly lensed supernovae (LSNe), for which follow-up is particularly time-critical, provide a useful example. We formulate this setting as On-the-fly ASynchronous Image Stream (OASIS) classification and explore reusable transformer architectures for causal, on-the-fly classification. We demonstrate these architectures on the lensed-transient classification problem studied by Bag et al. (2026a,b), distinguishing LSNe Ia from unlensed astrophysical transients. We compare them with the recurrent baseline adopted by Bag et al. (2026b), which combines a ConvLSTM branch for image processing with a separate LSTM branch for encoding observation times. The baseline maps asynchronous observations onto a fixed band-by-observation grid, filling unobserved bands with zeros. Using a common training setup, we compare two transformer-based approaches to modeling interactions among spatio-temporal tokens: factorized attention, which separates spatial and temporal interactions, and joint attention, which models them together. On the demonstration dataset, factorized architectures achieve mean losses of $0.095$–$0.100$, compared with $0.128$ for the recurrent baseline and $0.107$ or higher for joint architectures. A selective readout further reduces the best loss to $0.089$ for a factorized model. These results suggest that factorized attention suits this dataset better, without implying universal architectural superiority. We release the architectures as reusable foundations for time-domain astronomy and other applications involving evolving spatial features that require on-the-fly predictions.

Compute-in-Memory (CiM) is an alternative computing paradigm that circumvents the memory bandwidth bottleneck. Variants utilizing non-volatile memory cells (NVCiM) to perform Boolean operations directly within memory arrays offer significant density and energy-efficiency advantages. Fully realizing this potential, however, requires NVCiM-specific compiler optimizations. In conventional digital NVCiM systems, an output cell must be written – or preset – to an operation-specific value before any Boolean operation can occur. Preset-induced extra writes can degrade energy efficiency and cell endurance, often to the point of negating CiM's efficiency gains. In this paper, we introduce PRIM (Preset Reduction In Memory), a compiler optimization framework tailored for digital NVCiM that effectively minimizes preset overhead without compromising computational accuracy or architectural complexity. Unlike existing optimization approaches, PRIM is not restricted to specific types of Boolean operations. Experimental results show that PRIM can reduce execution time and energy consumption by up to 50/% and 44/%, respectively, while boosting cell endurance by up to 50/%.

Independent control of line spacing and offset underpins programmable frequency-comb spectroscopy, yet it has not been established for hard-X-ray sources based on inverse Compton scattering after electron transport and angular collection. Self-consistent multi-particle tracking and Li'enard-Wiechert radiation calculations model a transported 10 pC beam and its angle-integrated spectrum near 11 keV. Laser pulse separation programs the comb spacing, while pulse-to-pulse phase translates the entire line grid at fixed spacing. The spacing model agrees within 0.52%, while transport and optics change the phase-transfer slope by less than 0.2%. At fixed electron spot size, the largest resolvable separation scales as the inverse square of normalized emittance; subnanometer bunches also produce a mode-locked train with 13.9 as spacing. This two-coordinate programmability enables phase-stepped multicolor measurements and offers routes to hard-X-ray Ramsey interferometry, coherent control of core and nuclear excitations, and attosecond nonlinear spectroscopy.

Timelike entanglement entropy provides a useful probe of holographic theoris, yet an explicit bulk realization of the modular flow underlying its timelike extremal curve construction has so far been lacking. We construct modular flows associated with spacelike and timelike intervals in AdS$_{3}$/CFT$_{2}$ and extend this framework to flat$_{3}$/CCFT$_{2}$. Beginning with the boundary symmetry generators, we explicitly derive the boundary modular flows and extend them into the bulk, providing a systematic procedure that relates bulk modular flows to the extremal curves and holographic (timelike) entanglement entropy. For spacelike intervals, the resulting bulk modular flows determine the extremal curves, whose integrated line elements reproduce the standard holographic entanglement entropy. We then generalize this approach to timelike intervals, explicitly constructing the modular flows whose fixed points reproduce the extremal spacelike and timelike curves which gives the holographic timelike entanglement entropy. To the best of our knowledge, this is the first explicit construction of the modular flow associated with a timelike extremal curve for a timelike interval. The same procedure is then carried over to flat$_{3}$/CCFT$_{2}$, which give rise to the holographic (timelike) entanglement entropy. Finally, we show that the flat space results obtained in this work can be recovered from their AdS$_3$ counterparts in the flat space limit.

The relationship between odor chemistry and perception remains incompletely understood. Many existing studies focus on the perception of single molecules, whereas natural odors contain tens to hundreds of components, adding extra layer of complexity to percept formation. Here, we explore the relationship between molecular composition and perceived similarity in natural odor objects. We study this using a database of more than 1,200 volatile-compound-in-food mixtures containing more than 8,000 molecular components, and use large language models (LLMs) as a scalable surrogate for deriving mixture-level perceptual descriptions. We find that language-derived representations provide useful supervision for predicting held-out mixture similarities from molecular composition. The prediction was consistently strongest when perceptual targets were derived from chemosensory prompts than from other sensory prompts. Further, during the mixture-level training, we learned low-rank molecular embeddings that enabled better prediction of held-out mixture similarities than component-overlap metrics, even for mixture pairs with no shared molecules. Although no single-molecule labels were used during training, the learned molecular geometry showed significant alignment with the independent human odor-descriptor space. Finally, we explored the use of external molecular features in our mixture-similarity prediction task. These features showed modest zero-shot alignment with mixture-level perceptual similarity. They improved prediction under limited supervision but offered little additional predictive benefit with the full training set. Together, these results show that language-derived descriptions can provide scalable supervision for predicting the perceptual organization of complex natural mixtures, contributing to a quantitative understanding of how molecular composition gives rise to odor perception.

We consider unstructured search using multimode bosonic quantum systems under energy constraints. The task is to locate an unknown marked mode among $N$ possibilities using arbitrary control, subject to a time-averaged mean-boson-number budget $n_{{\text{b}}}\gg 1$. We analyze a continuous-time phase-shift oracle of strength $B_{0}$, with cost given by the total oracle time, and a discrete oracle with fixed phase $\phi_{0}$, with cost given by the number of queries. We give algorithms that identify the target with query complexity $O(\sqrt{N}/{n_{{\text{b}}}}B_{0})$ for continuous-time oracles or $O(\sqrt{N}/n_{{\text{b}}} |{\sin(\phi_{0}/{2})}|)$ for discrete oracles with $n_{{\text{b}}} |{\sin(\phi_{0}/{2})}|=O(1)$. In contrast, for discrete oracles with $n_{{\text{b}}} |{\sin(\phi_{0}/{2})}|=\Omega(1)$, we provide an algorithm using $O(\max\{1,\sqrt{N/n_{{\text{b}}}|{\sin(\phi_{0}/{2})}|}\})$ queries. We also prove matching lower bounds on the query complexity, showing that these algorithms are asymptotically optimal. Furthermore, we show that, in the absence of loss, non-Gaussianity is necessary to achieve the optimal joint query scaling in $N$ and $n_{{\text{b}}}$, but entanglement is not. Under uniform boson loss at rate $\gamma$, we prove a query lower bound of $\Omega ( \gamma N / n _{{\text{b}}} B_{0}^{2} )$, attained for $\gamma = \Omega(B_{0} \sqrt{n _{{\text{b}}}/N})$ using coherent-state probes. Finally, we propose experimental implementations using multipass optical microscopy or superconducting circuits as potential routes to speeding up imaging or device calibration with a low boson-number budget.

We show that finite-order exponential mixing does not imply the central limit theorem for smooth diffeomorphisms. For every integer $R\geq2$, we construct a $\mathcal{C}^{\infty}$ diffeomorphism $T:M\to M$ of a compact smooth manifold $M$ and a $T$-invariant probability measure $\mu$ such that $(T,\mu)$ is exponentially mixing of order $R$ for $\mathcal{C}^1(M)$ observables, but not of order $2R+2$. For some centred observable $f_0\in\mathcal{C}^{\infty}(M)$, no subsequence of the normalised sums $\frac{1}{\sqrt n}\sum_{i=0}^{n-1}f_0\circ T^i$ converges in distribution to a Gaussian law. In particular, exponential decay of two-point correlations implies neither exponential mixing of all orders nor the central limit theorem. We realise $(T,\mu)$ in two ways. In the first, $T$ is a fixed linear Anosov diffeomorphism of $\mathbb T^2$ and $\mu$ is singular with respect to Lebesgue measure. In the second, $M$ can be any compact smooth surface without boundary and $\mu$ is a physical measure whose statistical basin contains a nonempty open set. The main theorems have been formalised in Lean 4.

Teleoperation is widely used to collect high-quality demonstrations for robot learning. Dexterous manipulation, however, requires coordinated control of motion and contact forces. Operators can specify motion, but struggle to reproduce the subtle force adjustments of human manipulation without feeling the robot's contacts. We introduce Force-Modulated Dexterity (FOMO-Dex), a unified compliance formulation for contact-rich manipulation. FOMO-Dex expresses nominal actions in coordinates defined by task geometry and contact structure. It applies force-driven motion corrections along selected directions while leaving the remaining command components unchanged. Across card picking, paper cutting, screwdriving, and nut-and-bolt assembly, FOMO-Dex reduces excessive contact forces compared with stiff control. A user study shows that operators collect more successful demonstration data per hour after brief practice. For policy learning, imitating the corrected actions improves card-picking success over imitating raw operator commands. Policies trained on FOMO-Dex demonstrations also achieve more rotation in nut-and-bolt manipulation and screwdriving than those trained on demonstrations collected with the stiff controller. Videos are shown on https://yingyuan0414.github.io/fomo-dex/ .

Let lambda(n) denote the infimum of -min_x sum_{a in A} cos(ax) over all sets A of n positive integers. While the classical Sidon-difference construction yields lambda(n) <= (1 + o(1))sqrt(n)/2, we construct sets achieving a leading constant of 1/2: lambda(n) <= (1/2)sqrt(n) + O(n^(1/4)sqrt(log n)), establishing limsup_{n->infinity} lambda(n)/sqrt(n) <= 1/2. This construction combines a two-sided Sidon square identity, a Singer difference set, a Fejer-kernel majorant, a parity-biased deletion, and an exact-cardinality probabilistic selection. We also provide an L^4 criterion and a multiplicity bound constraining any construction with a smaller leading constant. In the opposite direction, we incorporate the L^1 norm into Bedert's boundary estimate with an explicit constant, yielding two lower bounds for f_A(x) = sum_{a in A} cos(ax): (1) -min f_A >= cn^(1/4) for every n-element set A subset of [1, Cn]; and (2) (-min f_A)^3 ||f_A||_1^2 >= cn for every n-element set A subset of N. The second bound recovers the 1/5 exponent of Bedert and Shankar and improves it whenever ||f_A||_1 is small relative to -min f_A. Numerical values of the construction are reported up to |A| = 25,440.

We develop a novel generalization of McDiarmid's concentration inequality and use it to obtain a uniform law of large numbers result and error bounds on stochastic optimization problems which simultaneously incorporate two key features: 1) They capture the benefit of training sample reuse in algorithms that also employ easily-sampled auxiliary random variables. 2) They allow for one-component mean-difference bounding functions which are both unbounded in the component of interest and have non-uniform dependence on another component. We demonstrate the utility of our method by deriving concentration inequalities for score-based generative modeling. This application naturally leverages both key features of our new tools: 1) It utilizes auxiliary Gaussian random variables in conjunction with the training samples; accounting for training sample reuse results in tighter error bounds by effectively integrating out the dependence on the auxiliary random variables. 2) The ability to handle non-uniform mean-difference bounding functions allows us to treat unbounded score models and data distributions with unbounded support.

When an LLM judge filters instruction-tuning data, its scoring format (binary verdict, 1–5 rating, 0–100 score, or comparison) is rarely justified or ablated. Holding the candidate pool, judge prompt, decoding and selection budget fixed, we score 15,406 UltraFeedback candidates under five formats with three judges, curate, fine-tune 66 models, and evaluate them with four judges. A 0–100 scale is worth only 7–12 equally used levels, two to three times a 1–5 scale rather than twenty, and a binary verdict leaves the top score tied in 77–78% of prompts, so most selections are made at random. These properties are set by the format almost independently of the judge. Kendall's $\tau_b$ hides them: it ranks binary best while $\tau_a$ and top-1 agreement rank it last, because it discounts the ties a selector must break at random. Both comparative formats inherit a slot bias whose sign differs across judges. Downstream, curated data beat random selection under every evaluation judge, robust to length and markdown adjustment, but no ordering among formats is detectable. We propose four quantities that judge-based curation pipelines should report.

A classical theorem of Kaiser and Rabinovich implies that if every subfamily of size at most $\lfloor\log_2(d+1)\rfloor+1$ of a finite family of compact connected sets in $\mathbb{R}^d$ has a common axis-parallel hyperplane transversal, then the entire family has an orthogonal star transversal, i.e., a union of $d$ hyperplanes, one perpendicular to each coordinate axis. We study colorful variants of this result. First, we use standard KKM machinery to establish a colorful analogue with $d+1$ color classes and a $\lfloor\log_2(d+1)\rfloor+1$ transversal hypothesis for rainbow subfamiles. Then we focus on reducing the required number of colors. To this end, we introduce the rainbow pushability $\pi_r(P)$ of a polytope and we use it to state and prove few-color variants of the colorful Carathéodory theorem and the colorful polytopal KKMS theorem. Applying the latter to the $d$-dimensional cube, we show that $\lfloor\log_2 d\rfloor+2$ color classes suffice for our transversal problem, provided that every rainbow choice has a common axis-parallel hyperplane transversal. We also extend both colorful results to the setting of convex $(n,D)$-bodies and we show that three colors are needed for $d\geq 2$.

Quantum sensing is typically based on phase accumulation and is therefore fundamentally tied to the coherence time of the sensing system. Here we introduce an alternative sensing paradigm based on programmable Floquet locking in periodically driven two-level systems. We show that periodic control generates an effective Floquet locking field whose orientation and amplitude depend on global offset, allowing information to be encoded in the driven population relaxation dynamics, not in the integrated phase. By controlling transfer between distinct Floquet locking manifolds, external perturbations can be mapped onto engineered relaxation responses whose characteristics are programmable through the driving sequence. We numerically demonstrate this approach for both DC and frequency-selective AC sensing, and show that temporal encoding of the response can provide enhanced precision in the presence of slow instrumental fluctuations. These results illustrate the potential of programmable Floquet responses and open the way to exploring new sensing strategies in driven quantum systems.

Subcellular signaling pathways regulating, e.g., cell division or synaptic plasticity, are often modeled as dynamical networks of reactions satisfying the law of mass action. To remain physically grounded, these models must satisfy different physical conservation laws, such as conservation of energy. This gives rise to thermodynamic constraints formalized by the Wegscheider conditions, which ensure that the system is in detailed balance at thermodynamic equilibrium. Explicitly imposing Wegscheider conditions requires identifying cycles in the reaction network. This can become computationally cumbersome, especially in large, complex systems. Furthermore, even when these constraints are explicitly available, enforcing them requires choosing a reparameterization of the network, which may introduce asymmetries among the parameters and affect numerical conditioning. Moreover, this approach often causes inverse uncertainty quantification methods like Markov chain Monte Carlo (MCMC) to struggle. Instead of imposing Wegscheider conditions directly in the parameter space, we propose an approach for promoting physical consistency by penalizing parameters that violate detailed balance. We first illustrate the approach on a simple reaction network containing a single cycle. We show that parameter values inferred without thermodynamic constraints can reproduce the experimental data seemingly accurately, while substantially violating the Wegscheider condition. In contrast, the proposed approach preserves the agreement with the observed dynamics while yielding posterior samples that approximately satisfy the thermodynamic constraint. We further apply the approach to a model of PKA-calcineurin signaling in synaptic long-term depression, demonstrating its applicability to a more complex biochemical reaction network.

Decoding visual stimuli from the spiking activity of retinal ganglion cells (RGCs) informs both our understanding of the retinal code and the design of visual prostheses. Natural vision is dynamic, yet state-of-the-art decoders mostly reconstruct single frames with artificial neural networks that process dense, continuous-valued signals rather than the retina's sparse, asynchronous spikes. We asked whether dynamic scenes can be reconstructed and tracked entirely within the spike domain, and at what computational cost. We built an end-to-end spiking neural network (SNN) whose neurons integrate the recorded RGC spikes over time. Populations of up to 1836 RGCs were recorded ex vivo from mouse retina on high-density microelectrode arrays while flashed images, moving bars, drifting gratings and randomly moving handwritten digits were presented. For moving digits, one shared spiking encoder fed two readouts, one reconstructing the image and one decoding the digit's position. Compute energy was estimated from counted synaptic operations. The SNN decoded what and where at once. It reconstructed the stimuli with a structural similarity (SSIM) of up to 0.93, refining the reconstruction as spikes accumulated, and tracked a randomly moving target with a mean error of 1.33 pixels on a $32\times32$ grid. Its fidelity nearly matched that of the best of 17 larger spiking and artificial decoders (5.9 million to 1.7 billion parameters, versus 5.4 million), and at a mean firing rate of 14.2% it needed an estimated $\sim$70-fold less compute energy than a dense artificial network of the same architecture. Dynamic visual scenes can thus be decoded from retinal population activity in the spike domain, with a compact network and at a compute cost compatible with implantable and wearable neural interfaces, supporting spike-native decoders for visual prostheses.

We investigate the regularity of Lyapunov exponents for products of random invertible matrices of arbitrary dimension $d\ge 2$. We prove that the top Lyapunov exponent is pointwise Hölder continuous with respect to the Wasserstein-Hausdorff distance in the space of probability measures with compact support, in the case where this exponent is simple and the equator has dimension equal to or less than one.

A graph is called a threshold graph if there is an assignment of real valued weights to its vertices such that two vertices have an edge between them if and only if the sum of the weights of the two vertices is above a certain `threshold value'. We will denote the class of all threshold graphs as $TH$. For a graph $G=(V,E)$, if for some integer $t\geq 0$, there are $t$ many threshold graphs $\{G_i=(V,E_i)\}_{i\in [t]}$ such that we have $E=E_1\cap E_2\cap \cdots \cap E_t$, then we say that the collection of threshold graphs $\{G_i=(V,E_i)\}_{i\in [t]}$ forms a $TH$-representation of $G$ of size $t$. \emph{The intersection dimension of $G$ with respect to threshold graphs} (denoted as $dim_{TH}(G)$) is the smallest non-negative integer $t$ such that there is a $TH$-representation of $G$ of size $t$. It is known that for a graph $G$ and integer $t>0$, the problem of deciding whether $dim_{TH}(G)\leq t$ is NP-complete even for $t=3$. In this paper, we study this problem in the framework of parameterized algorithms. We consider the vertex cover number and the cluster vertex deletion number as our parameters. We give a FPT algorithm for determining an optimal $TH$-representation of a graph when parameterized by its vertex cover number. Our main result is an efficient parameterized approximation scheme for this problem when parameterized by the cluster vertex deletion number of $G$.

Variational inference is a flexible tool for modeling experimental data and has proven useful in crystallography. Pathwise gradient estimators provide low-variance gradients for reparameterized variational inference, but are not readily available for some distributions central to crystallography. This work derives and implements implicit and explicit reparameterized gradient estimators for the folded Normal and Rice distributions in \prog{PyTorch}, and compares their variance analytically and empirically. In each case the implicit estimator achieves lower variance for the location derivative, particularly at small location-to-scale ratios, while the scale-derivative variances are nearly equal. For both distributions, implicit estimator is proved to be the conditional expectation of the explicit estimator given the sampled magnitude, so its variance is never larger. As a practical application, French-Wilson scaling is formulated as a variational inference problem, using the folded Normal and Rice distributions as variational families for centric and acentric reflections, respectively. Both estimators recover the exact posterior to better than $1\%$ on the amplitude, and converge at the same rate. The implementations are available in the open-source package \prog{rs-distributions}.