Papers

We study the Yamabe–Escobar equation prescribing positive constant scalar curvature and minimal boundary. The compactness conjecture asks whether being conformally equivalent to the round hemisphere is the only obstruction for its set of positive solutions to be compact. In this paper we show that this is true for dimensions $3\leq n\leq 14$. We show that this dimensional threshold $n_*=14$ is sharp by constructing in $n\geq 15$ nonumbilic and non-locally-conformally-flat examples of metrics in the hemisphere for which a noncompact sequence of solutions exists. We do the same for the special classes of locally conformally flat metrics, $n_*^{LCF}=18$, and the metrics with umbilic boundary, $n_*^{umb} =20$. In all three settings we also prove that the Weyl–umbilicity vanishing conjecture holds for $4\leq n\leq n_*$ and construct counterexamples in $n>n_*$ by perturbing the noncompactness examples. To the best of the author's knowledge, these are the first locally conformally flat noncompactness constructions for the positive-scalar-curvature, minimal-boundary case of the Yamabe–Escobar equation, outside the conformal class of the round hemisphere.

At $\sim$3.9~Ga (stellar age $\sim$0.6~Gyr), the young Sun was far more magnetically active than today. It launched $\sim$$10^2$ large, fast coronal mass ejections (CMEs) per year into a denser, more magnetized wind. We follow these eruptions to Earth's atmosphere with a semi-analytic model chain. We find that a CME launched at $v_0\sim3\text{--}4\e{3}\unit{km\,s^{-1}}$ dissipates $\Delta E_k\sim6\e{25}\unit{J}$ as it decelerates, an amount set only by its launch and final speeds. Diffusive shock acceleration converts $\sim$10% of this energy into solar energetic particles (SEPs), whose deposition depth depends mainly on a spectral break energy $E_b$. We show that the stronger field moves the Alfvén surface, inside which the magnetic field controls the wind, from $\sim$10–25$\,\Rsun$ to $\sim$40–60$\,\Rsun$, so CME shocks deliver over ten times the particle fluence of flares. Because the forcing is powered by deceleration, it follows the measured wind history ($\dot M\propto t^{-2.3}$) and declines as $\sim t^{-3}$. It was $\sim$50–100 times stronger at 3.9~Ga than at 2~Ga and several hundred times today's level. This decline, strongest when the Sun was faintest, is what greenhouse solutions of the faint young Sun (FYS) problem usually impose by hand. The magnitude is small: SEP-driven $\mathrm{N_2O}$ adds at most a few $\unit{W\,m^{-2}}$ to a 20–40$\unit{W\,m^{-2}}$ greenhouse requirement, and only if a fractal organic haze extends its lifetime. Counting energy deposited below a survival level near 1~hPa, we find the particles fix $\sim$$4\e{10}$–$4\e{11}\unit{mol\,N\,yr^{-1}}$, which could supply prebiotic feedstock to surface pools. The largest uncertainties are $E_b$, the event rate, the survival depth, and the $\mathrm{N_2O}$ lifetime.

In recent work Phys. Rev. X 16, 031057 (2026), we proposed a self-consistent approach to entanglement certification based on generalized noncontextuality. It requires no prior characterization of the measurement devices and, given access to all local measurements, can certify every entangled state in a Bell circuit. Here, we study the complexity of this protocol in a finite experiment. At fixed local dimension $d$, we show that the optimal number of distinct local effects needed to reach a trace-distance entanglement resolution $\gamma$ is $\Theta_d(\gamma^{-(d-1)})$. This scaling is necessary even when the measurements are tailored to the target state. Independent Haar-random projective measurements instead require $\Theta_d(\gamma^{-(d-1)}\log(1/\gamma))$ effects. Finally, we show that, once the exact operational identities are known, $\Theta_d(\gamma^{-2}\log(1/\delta))$ copies of the target state are necessary and sufficient for certification with error probability at most $\delta$. Determining the optimal sample complexity when those identities must instead be inferred from the same finite target-state data remains open.

The same Gaussian of a 3D Gaussian Splatting model is seen from many views, and these views do not always agree on the class it belongs to. The Gaussian may be occluded in some of them, and the confidence of the detector is not the same from one view to another. The ground truth, on the other hand, is given as an annotated mesh, because two training runs do not produce the same Gaussians. In this work, we propose a post-training lifting method that works with one target class at a time and combines the information coming from all the views. Target and non-target evidence are accumulated simultaneously, weighted by the visibility of each Gaussian in each view. After that, the Gaussians are filtered with two thresholds: a main threshold $\beta$ selects the high-confidence seeds, and a lower one $\gamma\beta$ adds the connected components around them. For the evaluation, the labels are transferred from the Gaussians to the mesh vertices that are both visible and annotated. With this design, we can separate three sources of error: the 2D detector, the lifting and the transfer between representations. The thresholds and the transfer operator are chosen on seven Replica validation scenes, and the method is evaluated on ten held-out ScanNet++ scenes with the same values for every scene and class. The mean mIoU on the validation scenes was 0.93 with masks from the dataset annotations and 0.65 with YOLO masks, and on the ScanNet++ test scenes it was 0.80 and 0.54. Compared with thresholding the evidence per view, as a previous version of the method did, the fraction improves the test mIoU by 0.24 and makes it possible to use a single threshold for all the classes and scenes of both datasets. Finally, the error analysis shows that most of the remaining error comes from the detector.

We study metastability and long-time propagation-of-chaos for mean-field interacting diffusions on the circle with multiple local free-energy minima. Working modulo rotations, we identify sharp exponential time scales for metastability and the validity and breakdown of the McKean-Vlasov approximation. Assuming finitely many critical rotation orbits and distinct local-minimum energies, we show that, for initial data in the attraction basin of a nonglobal minimum, metastability and propagation-of-chaos hold uniformly over deterministic times up to $e^{N(D-\varepsilon)}$ and fail at every deterministic sequence growing faster than $e^{N(D+\varepsilon)}$. Here $N$ is the particle number and $D$ the depth of the maximal Freidlin-Wentzell energy cycle having that minimum as its bottom. The same threshold governs running averages of the squared approximation error in a stronger pathwise sense, with corresponding metastability and propagation-of-chaos bounds for suitably aligned time-averaged empirical measures. When the global-minimum orbit is unique, we establish uniform-in-time propagation-of-chaos in its attraction basin without assuming finitely many critical orbits. The proofs develop the Freidlin-Wentzell cycle analysis for the empirical measure process and exploit Dawson and Gärtner's fixed-horizon large deviation estimates to analyze long excursions between metastable wells. We give a checkable Fourier criterion for finiteness of the critical orbits. We also investigate connections with phase transitions in the free-energy landscape, and discuss applications to the noisy Kuramoto and noisy transformer models. We provide, to our knowledge, the first sharp exponential-time analysis of the Dawson-Gärtner `tunnelling phenomenon' for general smooth interactions, with two-sided probability bounds and matching propagation-of-chaos thresholds.

Methyl cyanide is one of the most abundant nitrogen-bearing complex organic molecules observed in the gas phase around low- and high-mass protostars. However, very few observations exist with a broad enough frequency coverage and sufficiently high sensitivity to systematically characterize its minor isotopologues toward such regions. We add to this number by analyzing data toward BHR71-IRS1 taken as part of the Complex Organic Molecules in Protostars with ALMA Spectral Surveys (COMPASS) Large Program over a ~33 GHz frequency range. We studied as many isotopologues of methyl cyanide as possible toward BHR71-IRS1. We found the column densities and excitation temperatures via spectral fitting and assuming local thermodynamic equilibrium. We then compared the derived column density ratios with those toward IRAS 16293-2422 A and B, V883 Ori, G31.41+0.31, and Sgr B2(N2b). We detect CH3CN, CH3CN $v_8$=1, 13-CH3CN, CH3-13-CN, CH3C-15-N, CH2DCN, and CHD2CN. The column density ratio of 13-CH3CN/CH3-13-CN is around unity, in agreement with previous observations. The CH2DCN/CH3CN ratios are similar for all the low-mass objects but are ~1 order of magnitude higher than those toward Sgr B2(N2b). This could be due to a warmer pre-stellar phase or a different formation timescale of Sgr B2(N2b). The D/H ratios found from methyl cyanide isotopologues agree well with those of methanol toward BHR71-IRS1, likely pointing to the formation and deuteration of methyl cyanide in a similar star-formation phase as methanol (i.e., the pre-stellar phase). We find an increase in the methyl cyanide D/H ratios with the number of deuterium atoms, which suggests that the deuterated isotopologues may form later in the pre-stellar phase. Future COMPASS studies will increase the sample size of low-mass systems with methyl cyanide analysis and potentially examine some of the trends observed here statistically.

For a smooth projective curve $C/\mathbb{Q}$ of genus $\geq 2$ and $L/\mathbb{Q}$ an extension, we write $C(L)_{\text{new}}=\{P\in C(L):\mathbb{Q}(P)=L\}$. Recent work of Khawaja and Siksek conjectures that this set is empty for $100\%$ of degree $n$ number fields $L$, when ordered by absolute discriminant. Moreover, they bring evidence towards this conjecture when $C$ is a degree $n$ cover of $\mathbb{P}^1$. We complement their work by proving analogous results for degree $n$ covers $\psi:C\to E$ of elliptic curves $E$. Our main result shows that, under suitable hypotheses, the number of distinct absolute discriminants at most $X$ of primitive degree $n$ fields $L$ with $C(L)_{\text{new}}\neq\varnothing$ is $O(X^{1/2})$ or $O(X/(\log X)^{\alpha})$, for some $\alpha>0$. In degrees $2,3,4$ and $5$ we show that these fields have density $0$ among all fields of the same degree (in degree $4$, also among the primitive ones). The novelty is for degrees $4$ and $5$, where we use work of Bhargava–Shankar–Wang and McGown–Thorne–Tucker to count fields with specified local constraints. Moreover, we give concrete examples of $8$ bielliptic modular curves $X_0(N)$, for which $X_0(N)(L)_{\text{new}}=\emptyset$ for $100 \%$ of quadratic fields $L$. Lastly, we point out modular covers of degrees $3$ and $5$ in the LMFDB for which similar conclusions hold.

High interpolation accuracy does not establish that physical parameters are identifiable. We study this distinction in a controlled Kiselev black hole benchmark with a validated timelike-emitter and three-dimensional null-geodesic shooting calculation. The exact $k=0$ boundary provides an analytically known null control because the spacetime becomes Schwarzschild and independent of $w_q$. Ringdown is informative for the deformation amplitude $k$, while photon geometry supplies an independent response direction that resolves much of the $w_q$ degeneracy. Relative to ringdown alone, ringdown plus photon geometry gives a median pointwise $4.54\times$ gain in minimum singular value and a $2.28\times$ improvement in Jacobian condition number. In grouped physical interpolation, identifiable-$w_q$ normalized mean absolute error decreases from 0.309 to 0.087. Random splitting is more optimistic, while directional extrapolation is substantially harder and split-conformal coverage degrades under distribution shift. A non-learned nearest-model inverse shows that the gain is not confined to the tested learned architectures. A uniform 161-phase audit gives a typical normalized prediction shift of $9.48\times10^{-4}$, while a targeted 321-phase audit resolves the remaining forward-feature comparisons. However, frozen HGB and random-forest tail shifts exceed prespecified robustness thresholds. Thus, physical observable complementarity is supported, but inverse-estimator robustness remains conditional. This is a theoretical identifiability benchmark, not an observational constraint.

We investigate prior-volume effects in Bayesian analyses of galaxy clustering based on state-of-the-art models, such as the EFT and the VDG$_\infty$ model. We show that these effects are largely driven by imposing priors on the model parameters defined in ${\rm Mpc}/h$ units, thereby introducing a spurious correlation with the Hubble parameter $h$, and that they can be strongly mitigated by adopting a more physically motivated formulation in ${\rm Mpc}$ units. We test this approach using a set of synthetic data vectors designed to reproduce the clustering signal expected in a Stage-IV survey across a range of cosmological models, including $\Lambda$CDM, $K$CDM, $w$CDM, and $w_0w_a$CDM. We find that the resulting constraints are largely free from shifts induced during the marginalisation process, even in the challenging $w_0w_a$CDM runs, reducing discrepancies with the fiducial values from several standard deviations to well within $1\sigma$. The performance of this approach is comparable to that of alternative mitigation strategies, such as the adoption of invariant priors or the reparametrisation of nuisance parameters in terms of growth and geometrical amplitudes. For the latter, we find that using $\sigma_{12}$ in place of the commonly adopted $\sigma_8$ to describe the amplitude of density fluctuations improves the performance of the reparametrisation technique, even at high redshifts, where constraints on the dark-energy equation of state are weaker. We further show that these conclusions hold with the inclusion of additional BAO constraints, and for data sets with reduced statistical power. These results add to the benefits of working with ${\rm Mpc}$ units, avoiding an explicit dependence on $h$, with direct relevance for the analyses of Stage-IV galaxy surveys.

Petri nets have been used to describe chemical processes such as reactions.They map well to chemistry: Places are the bonds between atoms and the free valence of each atom, a token is a unit of bond order, a transition forms or breaks a bond, the conserved quantities are the valence budgets of the atoms, and the enabling rule is the valence rule. These semantics are not guaranteed by learned models of reactions or neural networks that are built on Petri nets that use the net as a scaffold for message passing. Here, we ask what architecture remains a Petri net for every value of its weights. We find the answer in the theory, where all semantics of a net share the firing form $m^\prime=m+C\sigma$, locality, as enabling reads only the inputs of a transition, and the enabling rule, and we prove that conservation forces the firing form and that non-negativity forces the enabling rule on local rate laws. This leaves free the rate law, which is the propensity of each transition to fire. We introduce Neural Petri Flow, which learns this rate law, or a readout for classification, and hard-wires the rest as parameter-free layers. On what we denote a valence net, atom mapping, reaction classification, and forward prediction become three tasks on one firing vector. Without training, the minimum firing vector maps 88.8% of the curated Golden set against 85.6% for RXNMapper, and 88.7 against 77.9% of the enzymatic reactions of EnzymeMap. On USPTO-480K, NPF trained on these firing vectors predicts 87.7% of the products and 67.4% when trained on a 1% subset of the training reactions. EC numbers of ECREACT are predicted at the third level for 90.2% of reactions, 5.6 points ahead of the best published method. With electrons as tokens, the same token game predicts 90.5% of the elementary steps of FlowER first, ahead of the published baseline, and every top-1 prediction is a valid molecule without a filter.

Characterizing the set of quantum nonlocal correlations through information-theoretic constraints is a central problem in quantum foundations. We show that the convex hull of no-signalling behaviors in a bipartite Bell experiment satisfying a common-overlap no-disturbance-without-uncertainty condition is exactly the finite-dimensional quantum set whenever one party has two binary measurements and the other has an arbitrary finite number of settings, each with an arbitrary finite number of outcomes. In the simplest binary input-output Bell scenario, this characterizes the full eight-dimensional set of quantum behaviors, including the local marginals. The proof constructs a quantum realization directly from the conditional probabilities and no-signalling. The characterization also reduces optimization of any linear Bell expression in these scenarios to maximization over a one-parameter family of second-order cone programs. The results establish a connection between local uncertainty-disturbance constraints and quantum nonlocality, mediated by no-signalling and shared classical randomness.

Space-based neutrino detection employs celestial bodies, the Earth, moon, and the sun, as neutrino targets and particle cascade generators. These cascades, or showers, have an immense content of charged particles, mainly electrons and positrons, that can form signals that can be detected by orbiting or balloon-borne (for the Earth) experiments. Here the focus will be on the using the Earth as the neutrino target and using the atmosphere to generate optical and radio signals from extensive air showers (EAS). Cascades in the Earth itself can also generate Askaryan radiation in ice, where the radio transparency allows the signal from in ice neutrino-induced showers to eventually refract out of the Earth's surface. These different techniques also have different neutrino-flavor detection sensitivities and duty cycles, i.e. experimental live time fractions. For example, optical measurements need to be performed close to astronomical night and are also affected by the level of moonlight and distribution of clouds in the the viewing direction of the EAS. The radio technique can be operate with nearly 100% efficiency, as long as sources of anthropogenic and other backgrounds are minimal. Given the distances for viewing the neutrino-induced signals from sub-orbital or low Earth orbit (LEO) altitudes, the neutrino energy thresholds for detection are currently above $\sim$ 1 PeV for optical Cherenkov detection and 100 PeV for radio detection. In this chapter, the nature of the cosmic neutrino interactions, shower development, and optical and radio signal generation and detection will be detailed. This will be done by discussing experiments that have used such signals to set limits on the very-high and ultra-high energy cosmic neutrino flux. We will also discuss the design and simulated performance of the next generation of space-based cosmic neutrino detection experiments.

A common approach to measuring bias in Large Language Models is to compare the log-likelihoods of two contrastive stereotype sentences. We argue that such single-pair comparisons are often unreliable: simply rewriting the same stereotype with an alternative attribute can yield logically inconsistent preferences. To address this, we propose a dual minimal pair setup that introduces two axes of comparison for robust stereotype evaluation. First, we present a data-augmentation framework that fills critical gaps in existing stereotype datasets by generating paraphrases and alternate attributes. We apply our framework on a set of English, Russian, Spanish and Chinese stereotypes. Second, we introduce two evaluation metrics tailored to the dual minimal pair setup. One of these metrics provides a new perspective on bias by modeling the mutual information (MI) between social groups and stereotyped attributes. This MI-based metric is better suited for aggregation and enables more robust comparisons of stereotype strength across different languages and models. Our code is available at https://github.com/stepanat/missing-minimal-pair/.

We establish an Alexandrov–Fenchel type inequality in which one of the reference bodies is replaced by a function whose Hessian satisfies a balancing condition on its eigenvalues, without being required to be positive semidefinite. The proof hinges on a new extension of Alexandrov's inequality for mixed discriminants. As applications, we derive a log-concavity principle for linear functionals of area measures, answering a question of Colesanti, Hug, and Saorín-Gómez, as well as Brunn–Minkowski type inequalities for intrinsic volumes of mean section bodies, answering a question of Schuster.

We study linear bandits under exact sliding-window constraints, where every consecutive block of actions must belong to a prescribed feasible set. In the offline setting, where the reward function is known, we show that convexity and cyclic-shift invariance make a stationary solution optimal when $w\mid T$ and within an additive $O(w)$ gap otherwise. In the online setting, we show that geometric structure alone is insufficient for learning, and sublinear regret can be impossible. We introduce a transition diameter $\tau$ that quantifies feasible reachability and develop a rare-switching OFUL algorithm with regret $\widetilde{O}(d\sqrt{T}+\tau d+w)$ against the offline-optimal feasible trajectory. Finally, we remove cyclic invariance and consider general sliding-window constraints, where optimal behavior may be non-stationary. We represent recent action history as the state of a finite-memory control problem and introduce a history-state diameter $D$ that measures feasible communication between viable histories. Combining optimistic remaining-horizon planning with rare policy updates, we obtain a regret bound of $\widetilde{O}(d\sqrt{T}+dD+w)$. We evaluate our approach on real-world and synthetic benchmarks, showing that it maintains exact feasibility while achieving reward and regret comparable to baselines with substantially fewer policy updates.

In sixth-generation (6G) networks, supporting ultra-reliable low-latency communication (URLLC) services imposes stringent requirements on reliability, latency, and efficient resource utilization. The upper mid-band (FR3) spectrum has emerged as a promising candidate due to its favorable trade-off between coverage and bandwidth availability. However, achieving high reliability in dense deployments remains challenging due to interference and propagation impairments. To address these challenges, this paper investigates a reconfigurable intelligent surface (RIS)-assisted network operating in the FR3 band. We formulate a joint transmit power allocation and user equipment (UE)-RIS association problem to maximize network reliability under finite blocklength constraints. The resulting problem is nonconvex and combinatorial due to interference coupling and binary association variables. To solve this problem efficiently, we propose a multiphase resource allocation framework that integrates a successive convex approximation (SCA)-based power optimization scheme with a matching theory-based UE-RIS association algorithm. Simulation results show that the proposed scheme outperforms greedy and random baselines and achieves near-optimal performance close to the exhaustive search scheme.

Sequential recommenders typically use a fixed slate size even though the number of useful alternatives changes within a session. We propose Reinforcement Learning with Calibrated Pruning (RLCP), which adapts the retained action set using critic scores and an online threshold. The threshold is updated from binary feedback indicating whether the set contains an action in a proxy target. We prove a deterministic bound on the observed proxy miss rate along adaptive trajectories. To quantify the effect of pruning on reward, we derive an exact decomposition of value loss into filtering and selection losses. Under explicit proxy and critic approximation conditions, this decomposition yields a finite session reward bound that also accounts for imperfect selection and set truncation, without requiring the learning parameters to converge. Experiments on KuaiRand-Pure and MovieLens 1M compare two RLCP implementations with four RL baselines. In each of the 19 configurations, at least one RLCP variant achieves the highest catalog diversity, reaching $1.11\times$ to $5.21\times$ that of the strongest baseline, with competitive session depth and no larger retained sets.

We classify all open substacks admitting a proper good moduli space inside the stack $\mathcal{G}_{1,n}$ of log-canonically polarized Gorenstein curves of genus one with $n$ distinct marked points: they are exactly the stacks $\overline{\mathcal{M}}_{1,n}(c)$ defined by Bozlee–Kuo–Neff. Restricting to the case where $c$ is pure of level $m$, we then give a numerical criterion for the projectivity of the good moduli spaces: these turn out to be asymptotically almost never projective as $n$ tends to infinity.

In this paper, we study analytic multiplier ideal sheaves of toric plurisubharmonic functions on normal affine toric complex analytic spaces equipped with torus-invariant rational divisors, assuming that a positive integer multiple of the log canonical divisor is Cartier. We describe these sheaves in terms of Newton convex bodies and show that they are globally generated by finitely many meromorphic monomials. Our results generalize the description of An and the formulas of Howald and Blickle for monomial ideals, and recover the descriptions of Rashkovskii and Guenancia on affine space. We also extend this description to weights obtained by subtracting positive rational multiples of monomial ideal weights.

Learning when the environment does not belong to the learner's hypothesis class is typically handled using agnostic learning guarantees. However, for anything beyond supervised learning, agnostic guarantees are difficult to come by. Recently, imprecise bandits (Kosoy, 2025) (later renamed to robust bandits in Appel and Kosoy, 2025) were introduced as another approach to unrealizable learning in the bandits setting and a $\Theta(\sqrt{T})$ regret learner was shown for a large class. However, no computational guarantees were provided. In this paper we identify a special case that admits a polynomial-time learner with $\tilde{O}(\sqrt{T})$ regret. We also show that several small generalizations of this special case are NP-hard thus indicating that the special case is at the boundary of what is tractable. It has been recently suggested (Kosoy, 2018) that computationally efficient learners for unrealizable learning problems are crucial for solving the AI alignment problem. This work is a small step in that direction.

Deep Neural Networks (DNNs) are integral to many safety critical systems, yet they remain highly vulnerable to bit-flip attacks (BFAs), where a few memory level perturbations can drastically degrade accuracy. Existing defenses incur significant hardware overhead, depend on retraining, or fail against targeted flips. We propose BARE-AI, a runtime framework that detects, localizes, and mitigates BFAs during inference. BARE-AI introduces AI Performance Counters (APCs), lightweight hardware monitors in the accelerator datapath that capture per-layer activation statistics such as sparsity, entropy, kurtosis, and spectral shift. These are analyzed by the Predictive Unit for Layer Security Evaluation (PULSE), a compact detector trained offline as an ensemble of classifiers and realized on-chip as a small neural engine. For explainability and recovery, BARE-AI introduces an Activation Shift Index (ASI) for layer level fault localization and a z-score based repair that resets anomalous weights toward clean layer statistics. Across CNNs, Vision Transformers, and Large Language Models under random, targeted, adaptive, and magnitude based BFAs, BARE-AI achieves up to 98% detection accuracy on vision models and 74% to 95% on language models, restores near clean accuracy for CNNs and ViTs, and provides partial recovery for LLMs. Synthesized at 28nm, the monitoring infrastructure incurs under 3% energy, under 4% area, and about 10% latency overhead, with a configurable operating point that reduces latency overhead to about 6%. Unlike error correcting codes, whose redundancy grows with the number of tolerated flips, BARE-AI's overhead remains constant regardless of attack strength, making it attractive for resource constrained, safety critical edge applications such as autonomous systems, energy, and healthcare.

Diffusion Language Models (DLMs) hold the promise of order-agnostic, parallel text generation. Recently, continuous diffusion and flow matching models have seen substantial gains, driven by carefully crafted token representations and diffusion/flow spaces. In this work, we introduce Hierarchical Continuous Diffusion Language Models (H-CDLMs), a simple framework that further improves continuous DLMs with minimal compute and parameter overhead. Drawing on the discrete DLM and continuous image diffusion literature on joint diffusion, we diffuse multiple modalities in parallel. These modalities represent tokens at different semantic granularities: in our instantiation, the tokens themselves and coarser clusters obtained by clustering pretrained token embeddings. We propose a general setup that allows per-modality samplers and schedules to enhance the interplay between modalities. Applied to CoBit, this yields H-CoBit, which delivers large empirical gains across benchmarks. At dataset entropy, H-CoBit improves MAUVE and reaches a generative perplexity (GenPPL) of 49.4 on LM1B and 50.4 on OWT, improving on the baseline by 24.2 and 20.7 points and surpassing even discrete DLMs of comparable size. On GSM8K, it reaches 27.4% accuracy, outperforming prior continuous diffusion and flow-based models. We further apply H-CDLM to the flow matching model FLM, obtaining consistent gains with H-FLM and demonstrating that the framework generalizes across continuous generative paradigms. Our code will be made publicly available at https://github.com/matol-16/HCDLM.git .

The adoption of humanoid robots in education and research remains limited by high hardware costs, complex sensing systems, and substantial computational requirements. This paper presents PhoneBot, a low-cost, open-source humanoid robot platform that repurposes commodity smartphones as its primary sensing and computing unit. By using a smartphone's integrated inertial measurement unit (IMU), camera, wireless connectivity, and onboard processing capabilities, PhoneBot reduces hardware costs and simplifies the system architecture. The robot combines a modular lower-body structure driven by 13 low-cost actuators with a torso-mounted smartphone that supports perception, control computation, and user interaction. We describe the mechanical design, software architecture, and real-time communication framework that support stable locomotion and capabilities including vision-based human following, conversational interaction, filming, and mobile telepresence. Experimental evaluations demonstrate reliable walking, perception-driven interaction, and straightforward deployment using off-the-shelf consumer smartphones. With fully open-source hardware and software designs, PhoneBot provides an affordable, reproducible platform for education, research, and rapid prototyping. More details are available at https://phonebot.dev.

Identifying upstream regulators that connect several disease processes to therapeutic interventions is a central objective in Alzheimer's disease drug discovery. We propose an entropy-guided reverse-causal framework that makes candidate bottleneck genes the organizing link between disease mechanisms, pathways, molecular targets and drugs. The methodology integrates five stages: an Alzheimer's-specific knowledge graph with language-model assistance and expert review; reverse tracing from drugs to candidate genes; entropy-guided prioritization; forward propagation to drugs and complementary combinations; and staged validation with evidence feedback. The novelty lies in integrating upstream bottleneck identification, entropy-guided prioritization and iterative therapeutic selection within a dynamic, bidirectional discovery architecture. We demonstrate its molecular tracing and gene-prioritization components in a computational feasibility study using DeepDrug2 and MSigDB pathway annotations. Tracing amlodipine, indapamide and atorvastatin through a network of 11,300 molecular and drug nodes identifies 46 routes to nine genes. EGFR is the leading candidate, supported by 26 routes from all three drugs; MME and MAF rank next. These results show how pharmacological starting points can identify shared candidate genes with defined molecular connections. The framework's scientific significance lies in connecting convergent disease mechanisms to systematic intervention selection, with preservation of cognition and independence as the translational objective.

In online inverse linear optimization, a learner recommends an action and then observes the choice of an expert who maximizes a fixed, unknown linear objective on $\mathbb{R}^{d}$; the goal is to learn to optimize this objective without observing it. Sakaue recently obtained the optimal regret $O(\sqrt d)$ with a randomized algorithm making $(dT)^{O(d)}$ linear optimizations per round, and asked whether it can be attained in polynomial time. We answer positively: our deterministic algorithm has regret $O(\sqrt d)$ for every horizon $T$ and runs in time polynomial in $d$ and $T$. It is a variant of the variable-metric algorithms of Sakaue et al.\ and Cai et al., in which a metric update is revoked once the query point moves far enough from where the update was made.

We study sliced Wasserstein barycenters from a variational perspective in Wasserstein space, with emphasis on the analysis problem in the barycentric coding model: given a query measure and a finite dictionary of probability measures, recover simplex-constrained barycentric coordinates. We derive an explicit first-variation formula for the sliced Wasserstein barycenter functional with respect to the classical 2-Wasserstein geometry. The resulting gradient is expressed as an average of 1D monotone transport displacements over the sphere. The stationarity equation yields a Gram-matrix criterion for estimating barycentric coordinates through a quadratic program, while its fixed-point form leads to a synthesis iteration to new barycentric measures. For Gaussian templates, we show that every global sliced Wasserstein barycenter is Gaussian; however, the functional may admit non-Gaussian critical points. We also provide a certificate for global optimality built from the 1D transport potentials. Numerical experiments demonstrate accurate coordinate recovery on synthesized queries and illustrate the use of these coordinates for data representation and stationarity residuals for reliability assessment.

Language models provide a plug-and-play interface between humans and robots, but important challenges remain when speech, dialogue, fast interaction, and collaboration are required. We propose a benchmark for the community to use as a way to explore common spoken dialogue artifacts between robots and humans, including requests for clarification, interruptions, embodied signals (e.g., head nods or facial cues), and time constraints. We also explain our vision to extend the benchmark for other aspects of human-robot interaction that are important to the larger research community. To facilitate the benchmark, we further propose using Retico, a real-time communication framework that fulfills important technical requirements to enable robots to have spoken dialogue capabilities.

Generative Information Retrieval (GIR) has emerged as a transformative paradigm, shifting document retrieval from a traditional "retrieve-and-rank" workflow to sequence-to-sequence generation, where a model directly predicts document identifiers (DocIDs). While the semantic design of these DocIDs is known to be critical for performance, a fundamental question remains under-explored: what makes a good DocID? Current approaches rely heavily on computationally expensive downstream evaluations, hindering systematic analysis and rapid iteration. In this work, we address this challenge by presenting a comprehensive study on the properties, metrics, and trade-offs that define effective numerical DocIDs. Specifically, our contributions are threefold: First, we propose a unified framework that unifies Product Quantization (PQ) and Residual Quantization (RQ), and their hybrid variants within a single design space. This enables us to systematically study key DocID properties, such as hierarchy versus parallelism, as well as the impact of hyperparameters like DocID length and codebook size. Second, we define a suite of training-free, intrinsic metrics, to quantify DocID quality and evaluate structural fidelity without the overhead of full model training. Through extensive experiments on MS MARCO 300K and NQ320K, we analyze how these structural properties influence retrieval effectiveness.

The discovery by the James Webb Space Telescope (JWST) of massive galaxies and luminous active galactic nuclei (AGN) at high redshift provides an increasingly sensitive test of the connection between cosmological structure formation and the astrophysical processes that make dark matter halos observable. We develop a framework connecting the linear matter power spectrum to the mass variance, peak height, halo mass function (HMF), cumulative halo abundance, and observable galaxy and AGN populations. We use the Sheth-Tormen (ST) HMF as the baseline and compare it with an illustrative Bolshoi-Klypin-calibrated modification (KST) to quantify the sensitivity of predictions to the calibration of the HMF against cosmological N-body simulations. We apply the framework to three complementary tests: the baryonic and stellar mass reservoir available to massive galaxies, the abundance of halos capable of hosting luminous AGN, and the rest frame ultraviolet luminosity function of high redshift galaxies. Because the most massive systems occupy the rare, high peak tail of the halo distribution, modest changes in inferred host mass, baryonic conversion efficiency, black-hole occupation or duty cycle, and HMF calibration can produce large changes in predicted abundances. The ST-KST comparison shows that uncertainty in the high redshift halo population can materially affect the inferred host supply, particularly toward large z (10). Comparison with representative JWST massive galaxy, AGN, and UV luminosity function measurements demonstrates that matching the properties of an individual source is not sufficient for population consistency; the corresponding host halos must also exist in adequate numbers. Current observations provide increasingly stringent quantitative stress tests of both cosmological halo abundances and the baryonic and black hole physics at cosmic dawn.

Sliding-scale insulin is the default hospital response to high blood glucose. Its correction factor was designed for patients who make no insulin, yet it is routinely ordered for patients whose pancreas still works, including those on high-dose steroids. We treat the sliding scale as what it is, a proportional controller sampled every four hours, acting on a patient who already contains a working glucose controller of her own. We test it in a non-diabetic adolescent on high-dose corticosteroids and parenteral nutrition, and in 4,995 virtual patients. It fails for three structural reasons, and no choice of correction factor fixes any of them. First, the patient's own loop settles in 11.5 minutes while injected insulin takes 64 minutes to peak, so most of each dose simply replaces insulin she would have secreted; in simulation the ordered scale moved her mean glucose by less than 1.5 mg/dL. Second, one unit lowers glucose twice as much at 110 mg/dL as at 190, so any correction factor strong enough to work when glucose is high overshoots when it is low; in 99.5% of virtual patients no constant factor does both. Third, four-hour sampling is far below the Nyquist rate, so successive readings are uncorrelated and each dose responds to a value that does not persist. Even the argument that correction doses rest the beta cells, taken on its own terms, favors continuous delivery. We propose replacing the scale with a continuous insulin infusion co-delivered with the dextrose and adjusted once a day on mean glucose, the one quantity four-hour monitoring can measure.