Papers

We investigate the geometry of the Fermion mixing matrix in the Standard Model. The principal structure studied is the CKM matrix, $V$, viewed as an element of the double coset space $M$, where $M=T\backslash SU(3)/T$, and $T=U(1)\times U(1)$. The space $M$ is given a Riemannian metric, and has both point singularities, which it is shown correspond to the known renormalization group fixed points, and line singularities connecting the fixed points. A key discrete object inducing many of these properties is the Weyl group, $W$, of $SU(3)$, $W$ being the symmetric group $S_3$, which appears in the guise of the vertices of a hexagon in $V$.

Helicon waves are widely used for efficient plasma production in low-temperature devices and have recently attracted attention as a candidate for current drive in fusion plasmas. Yet experimental investigations of helicon waves in toroidal geometries, and of their interaction with plasma dynamics, remain extremely limited. In this work, we present, to our knowledge, the first detailed experimental characterization of helicon waves in a toroidal configuration. A birdcage resonant antenna operating at 13.56 MHz is used to launch helicon waves in the toroidal basic plasma physics device TORPEX, either into a pre-existing magnetron-generated plasma, or as the plasma source. Measurements are performed in pure toroidal and simple magnetized torus magnetic configurations, for both argon and hydrogen plasmas. Three-axis magnetic probe measurements enable clear identification of a dominant m=+1 helicon mode over our parameter space. The helicon amplitude is found to scale linearly with the antenna power, and decreases with the confining magnetic field amplitude. As the antenna power is increased the helicon amplitude exhibits a saturation, correlated with enhanced low-frequency fluctuations and turbulent transport. In addition, a strong interaction between helicon waves and low-frequency density fluctuations is observed, revealing a non-linear coupling between RF waves and plasma turbulence. These results provide the first detailed experimental characterization of helicon waves in a toroidal low-temperature plasma device and establish TORPEX as a unique testbed for studying toroidal helicon wave physics under controlled and well-diagnosed conditions.

We revisit the hierarchy of relaxation time scales in stochastic kinetically constrained models (KCMs) obeying detailed balance, using an expansion method developed recently for their quantum counterparts. In the classical setting, we expand the stochastic generator in the low-temperature equilibrium concentration of excitations. As in quantum KCMs, successive truncations of the expansion reveal a nested hierarchy of metastable configurations that remain frozen on progressively longer time scales. Applying the method to the high-to-low temperature quench in the classical one-dimensional East and Fredrickson-Andersen models, we recover the known hierarchy of metastable plateaus and the associated perturbative time scales. We find that the hierarchical time scales are related to the smallest domain lengths. Our results show that the method developed for quantum kinetically constrained models can be used to provide a systematic description of slow relaxation in their classical counterparts as well.

First-person-view (FPV) teleoperation of aerial swarms requires an operator to coordinate collective translation, viewing direction, and formation spacing. We present an upper-body interface that maps torso inclination, hand position, and head rotation to five continuous command dimensions. Neutral postures and motion ranges are calibrated for each participant. In a within-subject study, 14 participants navigated a simulated 15-agent swarm through three-dimensional obstacle courses using this interface and a conventional transmitter. Body-motion control reduced completion time by 19.4% and centroid path length by 7.0%, and increased path directness. Delivered-command variation was 88.8% lower, and concurrent command changes were more frequent. These command measures characterize the complete interfaces, which differed in calibration and filtering. No differences were detected in gate-centering error, collection yield, crash or disconnection counts, overall workload, or usability. All participants reported higher physical demand with body-motion control. The implemented interface therefore improved FPV navigation efficiency at the cost of greater physical demand.

We consider the boundary trace process of a new class of sticky Brownian motions and study the telegraph signals of the boundary local time. For the fractional telegraph equation \begin{align*} (\sigma/\eta) D^\alpha_t v(t,x) + D^{2\alpha}_t v(t,x) = \frac{\partial^2 v}{\partial x^2}(t,x), \quad t>0,\, x \in \mathbb{R}, \quad \alpha \in (0,1] \end{align*} we provide a probabilistic representation of the solution in anisotropic Sobolev spaces and compare it with well-known representations in the literature. We subsequently discuss the associated processes and provide their pathwise representations. Based on these representations, we introduce a characterization of the local times for a wide class of sticky Brownian motions on $\Omega$ governed by the non-local dynamic boundary condition \begin{align*} \eta D^\alpha_t \varpi(t,x) = - \sigma \partial_n \varpi(t,x), \qquad t>0, \; x \in \partial \Omega \end{align*} where $D^\alpha_t$ denotes the fractional derivative in the Caputo-Džrbašjan sense. We focus mainly on the interval $[a,b]$ to construct a prototype model, and then lay the foundation for the analysis on balls in $\mathbb{R}^d$. The smooth interpolation between wave propagation and diffusion under anomalous dynamics captures the behaviour of the underlying sticky Brownian motion experiencing significantly prolonged trapping times on the boundary. The solution $v$ retains its continuity up to $t=0$ in $H^1(\mathbb{R})$, which corresponds to the mean-square continuity of the telegrapher's process at the initial instant. However, for $t>0$, the severe sticky effect causes the stochastic trajectories to undergo prolonged trapping periods, leading to highly irregular and rough paths for the local time of the sticky Brownian motion. In our construction the Brownian structure appears immediately, rather than only as a hydrodynamic limit.

Browning and Sawin conjectured that random hypersurfaces with sign coefficients are smooth with probability tending to one as the degree grows. We prove this conjecture and obtain a quantitative bound. For each $n\geq1$, a degree $d$ form in $n+1$ variables, with independent uniform coefficients in $\{-1,1\}$, defines a singular complex hypersurface with probability $O_n(d^{-1/2})$. The positive-dimensional singular loci occur with exponentially small probability. For $n\geq3$, the same exponential bound holds for failure of absolute irreducibility. These results have been formalized in Lean by AxiomProver assuming existing literature.

Large Language Models (LLMs) are now routinely trained using synthetic data, since high-quality human data has been exhausted by the ever increasing needs of larger and larger models. However, recursive training on synthetic data frequently induces model collapse, a degenerative feedback loop where models progressively forget the true underlying data distribution. Training on a mixture of synthetic and fresh human data is a logical countermeasure and can prevent model collapse. However, it is an open question as to what is the exact minimum required ratio of human-to-synthetic data to maintain training stability. In this paper, we establish rigorous theoretical guarantees on the minimum rate of human data required to prevent model collapse. Although previous work established a formal lower bound for this ratio, such bound can be vacuous for very high dimensions, as the analysis relies on the usual Euclidean metric in R^n and is not adapted to the space of categorical probability distributions. Instead, in this paper we explicitly leverage the information-geometric structure of the probability simplex by analyzing the dynamics of the process under the Fisher-Rao metric. We derive quantitative contraction and invariance bounds that are stable and do not become trivial as the dimensions increase. Thus, we show that the effective required data ratio to prevent model collapse is different than previously implied.

A set $S$ of vertices of a graph $G$ is a connected mutual-visibility set if every two vertices of $S$ are joined by a shortest path whose internal vertices lie outside $S$, and the subgraph induced by $S$ is connected. We introduce the connected mutual-visibility number $\mu_c(G)$, defined as the maximum cardinality of such a set, and investigate its structural and algorithmic properties. We establish fundamental bounds, derive Nordhaus–Gaddum type inequalities, and characterise the graphs attaining the minimum and maximum possible values. For regular $(d,2,-\delta)$-graphs, we derive general bounds on $\mu_c(G)$ and determine its exact value for the two cubic graphs of defect $2$. We further show that $\mu_c(G)$ is determined locally by the block structure of $G$, namely, it is equal to the maximum of the corresponding values over the blocks of $G$. Finally, we present a polynomial-time algorithm for recognising connected mutual-visibility sets and prove that the associated decision problem is $\mathsf{NP}$-complete, even for connected bipartite graphs of diameter at most $4$.

We study the statistical privacy of outsourcing matrix multiplication over a finite field ${\mathbb F_q}$ to a single server using additive masks of rank at most $r$. For independent uniform $n\times n$ inputs, we show that uniform rank-ball masks and products of independent uniform factors give maximal-correlation secrecy of at most $q^{-r}$ against the complete server view, with $O(n^2r)$ field operations for encoding and decoding. This secrecy captures how effectively the server is prevented from estimating functions of the inputs. We prove an asymptotically matching lower bound of this secrecy measure for $r=o(n)$, showing that both sampling methods are asymptotically optimal among input-independent additive masks of rank at most $r$, even when secret invertible transformations are allowed. We also characterize the posterior distribution for uniform rank-ball masks under arbitrary joint input distributions and prove approximate individual security for rows and columns under independent uniform inputs. Finally, we show that every input-independent additive mask of rank at most $r=o(n)$ requires $\delta\to1$ in entry-level $(\varepsilon,\delta)$-differential privacy for fixed field size $q$ and bounded $\varepsilon$.

For every effectively nowhere dense class $\mathcal{C}$ of relational structures, we present an algorithm that runs an almost-linear-time preprocessing step on a given structure $\mathcal{A} \in \mathcal{C}$ and a first-order formula $\phi(x_1, \dots, x_k, y_1, \dots, y_\ell)$. After the preprocessing, whenever given a tuple $\bar{v} \in A^k$, the algorithm computes the number of tuples $\bar{w} \in A^\ell$ that satisfy $\mathcal{A} \models \phi(\bar{v}, \bar{w})$ in constant time. Building on this, we provide an algorithm for constant-time query answering and constant-delay enumeration after almost-linear-time preprocessing for the recently introduced logic clique-guarded first-order logic with counting (cgFOC) on effectively nowhere dense classes. This generalises the testing and enumeration results for first-order logic [Schweikardt, Segoufin, and Vigny, JACM 2022] and the evaluation result for the first-order logic with counting FOC1 [Grohe and Schweikardt, PODS 2018] on nowhere dense classes.

In this paper we address a basic question that has not been considered in the literature on the parabolic Regularity problem. Let $\Omega$ be the region above the graph of a $\mathrm{Lip}(1,\tfrac12)$ function $\phi$ on $\mathbb R^{n-1}\times\mathbb R$. The corresponding $\dot L^p_{1,1/2}$ Regularity boundary space on $\partial\Omega$ is defined by pulling the datum back to the flat space where we have the norm $\|\nabla f\|_{L^p}+\|D^{1/2}_t f\|_{L^p}$. As there is more than one graph parametrisation of such a domain, this could petentially lead to different notions of $\dot L^p_{1,1/2}(\partial\Omega)$. This issue arises only on time-varying domains, which is likely why the issue has not been noticed before. We show by example that the boundary spaces can indeed disagree. We then prove that an additional assumption $D^{1/2}_t\phi\in\mathrm{BMOpar}$ (called the Lewis–Murray condition), resolves the issue completely: the spaces defined through different graphs agree.\medskip This gives us a well-defined Regularity datum space on every Lewis–Murray graph domain. We then extend the duality between the parabolic Dirichlet and Regularity problems, proved on cylinders by the author and E.~Nyström, to such domains.

In this paper we prove a free-join decomposition theorem on Gorenstein polytopes significantly improving upon results in prior joint work of the second author with Batyrev, Borger, Haase, Kretschmer, and Payne. In particular, as a strong extension of the Batyrev-Juny lattice pyramid theorem it implies that any $d$-dimensional Gorenstein polytope $P$ of index larger than $\frac{d+2}{2}$ is a free join of Gorenstein polytopes. Here, the index (also called codegree) is the dilation factor $r$ such that $rP$ is reflexive. As our main application, we prove that the stringy $E$-polynomial of a Gorenstein polytope $P$ vanishes if and only if $P$ is thin (i.e., its local $h^*$-polynomial vanishes), and it has the expected degree otherwise. The latter was conjectured by Batyrev and the second author. The proofs of the general results were found via ChatGPT 5.6 Sol, while a proof of the extremal case of the Batyrev-Juny conjecture is contained in the master thesis of the first author.

This paper addresses the problem of designing time-optimal control profiles for point-to-point control of a gantry crane moving in a two dimensional plane. It is assumed that the hoisting motor completes the hoisting maneuver at a constant rate and completes its transition in the same time that it takes for the cart to reach its terminal position. This results in a linear time-varying model and a closed form solution to the time-optimal control problem is shown to be parameterized with Bessel functions. A comprehensive analysis of the structure of the time-optimal control profile is studied by examining the switching function which illustrates the mechanism of introduction and decimation of switches in the bang-off-bang control profile. The variation of the number of switches in the optimal control profile is presented and a non-intuitive control profile structure is noted, one which initiates with a stationary cart, while the hoisting cable length is changed prior to the initiation of motion of the cart. To address the issue of uncertainties in the initial cable length, a model with the sensitivity of the system states with respect to the initial cable length is used to augment the system model and is used for the design of robust time-optimal controllers. Experimental results validate the time-optimal and robust time-optimal control profiles.

Region-of-attraction (ROA) certificates for polynomial systems become expensive as state dimension and degree grow: direct sum-of-squares (SOS) formulations require combinatorially growing monomial bases. Quadratization represents a polynomial vector field exactly on an invariant manifold of a quadratic system, allowing a quadratic Lyapunov function to certify the ROA. For a fixed lift, stabilizer gains shape the off-manifold extension and transverse dynamics, while representation gauges change the matrix representation but not the vector field. Both affect the spectral-norm certificate, yet prior work fixes the gain by a feasibility heuristic before optimizing the gauge. We formulate optimal dissipative quadratization (ODQ), jointly designing gains and gauges for a fixed monomial lift, reference extension, stabilizer factorization, and Lyapunov weight $Q=I$. Gains lie in a prescribed compact Hurwitz box. At each gain, an exact semidefinite program globally minimizes the spectral-norm bound over the gauge. Residual-aware bounds yield a certified closed Lyapunov sublevel set, accounting for the floating-point Lyapunov residual. Under our stated assumptions, every accumulation point of the idealized outer search is box-Clarke stationary. A finite run returns the best independently verified candidate; global optimality of the gain search is not claimed. On a planar quintic, optimizing the gain increases the certified area by a factor of $2.238$ over a matched zero-gain gauge. Across 16 heterogeneous polynomial systems with stabilizer freedom, ODQ improves on both fixed-gain lifted baselines. All 36 ODQ runs on the relay benchmark complete, and all 27 repeat-level comparisons across nine fully paired cases favor ODQ over an SOS baseline with a fixed quadratic Lyapunov function in both the fixed-direction proxy and construction time. Broader comparisons with direct SOS methods remain mixed.

A family $F$ of subsets of $[n]$ is 3AP-intersecting if every two members have intersection containing a non-trivial three-term arithmetic progression. We prove that there is an absolute constant $c>0$ such that any such $F$ has size at most $(\tfrac12 - c)2^n$. This is the first non-trivial progress towards a conjecture of Simonovits and Sós that the maximum possible size is $2^{n-3}$. More generally, we show the same bound for $H$-intersecting families whenever $H$ is a $3$-graph on $[n]$ with bounded codegrees. A clique shows that this is sharp, in that the bounded codegree assumption cannot be removed.

Humanoid loco-manipulation requires robots to interpret task instructions and scene semantics while executing coordinated whole-body motions. We propose a hierarchical framework that uses motion keyframes as an intermediate representation between Vision-Language Model (VLM) planning and Reinforcement Learning (RL) control. Each keyframe specifies a target whole-body robot pose and, when applicable, an object pose. Given a language instruction, scene observations, and execution feedback, the VLM selects successive task-relevant keyframes from a predefined library. The selected keyframes are retargeted to the current scene to account for object poses and dimensions. A keyframe-conditioned whole-body policy then generates joint-level actions to reach these goals. We introduce a saliency-based keyframe sampling strategy for low-level policy training that improves end-to-end task success rate from 44% to 92% when using sparse VLM keyframes. We evaluate our framework on object pickup, transport, and placement tasks in simulation and on a Unitree G1 humanoid. The system successfully performs both one- and two-handed manipulation and generalises to placement locations beyond the training reference data.

Accurate and unbiased determination of stellar parameters is of importance in many astrophysical domains. We therefore present an improved method to estimate stellar parameters, based on interferometric observations and stellar atmosphere models, as well as spectroscopic and photometric data. The fundamental stellar parameters were estimated by fitting a model of intensity profiles to interferometric data over a large spectral window and combining them with spectroscopic and photometric observations as an additional constraint on the fitting. Based on stellar atmosphere models, we have developed an algorithm that trains artificial neural networks (ANNs) to estimate the spectrum and intensity profile of a star over three bands: R, H, and K. The ANNs cover effective temperatures (Teff) ranging from 4500-7000 K for dwarf stars and 2500-8000 K for giant stars, with surface gravities (log g) ranging from 3.0-5.0 dex and -0.5-3.5 dex, respectively, and 12 viewing angles. As a result, consistent and precise stellar parameters, such as Teff, log g, and angular diameter ($\theta$), can be estimated. We fitted $\iota$ Psc (F7V) and $\delta$ Ari (G9.5IIIb) observed with SPICA, MIRC-X, and MYSTIC at the CHARA Array, and archival data of $\alpha$ Cen A and B (G2V and K1V) from VLTI/PIONIER with PIMS. For angular diameter estimations, when fitting with a one-dimensional stellar atmosphere model, we reached a precision of 0.5%. For Teff and radius, we obtained a precision of approximately 1%, while we obtained a precision of 5% for log g. Through evolutionary models, we further show how these constraints can improve the mass and age determination, as they attain a precision of approximately 2% for mass and 5-10% for age.

The coupling between self-sustained oscillators, such as lasers or polariton condensates, leads to different steady-states in different regimes. Weak coupling allows the oscillators to behave independently, with different frequencies and uncorrelated phases, while stronger coupling can produce synchronization. In classical or semiclassical theories transitions between these steady-states correspond to changes in the topology of the phase space attractors and occur at generalized exceptional points. We investigate the corresponding changes in a quantum theory of coupled lasers or condensates. We show how the different steady-state regimes of the classical limit give rise to distinct forms for the spectra and eigenmatrices of the slow modes of the Liouvillian. By following the spectral flow between the different regimes we show that the synchronization transition is controlled by cascades of exceptional points in these slow modes, protected by a generalized PT symmetry. Our results show how singularities of the quantum Liouvillian control the different dynamical regimes, and give rise to experimental signatures of the synchronization transition which remain well-defined in the few-particle regime dominated by quantum effects.

We investigate an algebraic approach to the Syndrome Decoding Problem, based on a reformulation of the Hamming weight constraint and its integration with the Information Set Decoding paradigm. We begin with a systematic analysis of the Hamming variety, deriving its defining equations in terms of elementary symmetric functions. Since these equations may have high degree, we exploit convolution identities for elementary symmetric functions, together with factorizations based on Lucas' identity, to derive an equivalent formulation with auxiliary variables and equations of bounded degree. Building on this modeling, we generalize the ISD paradigm through an ISD-like decoding strategy, implemented by the GBDecode algorithm, in which only a subset of an information set is fixed. This approach reduces the size of the combinatorial search space at the cost of solving the associated multivariate nonlinear systems. To handle this algebraic component, we employ the MultiSolve algorithm, which replaces a single Grobner basis computation with a collection of computations on simpler systems, obtained by exhaustively assigning a varying number of indeterminates over the finite field. This provides a tunable balance between combinatorial search and algebraic solving. We evaluate the resulting approach experimentally on instances of the Syndrome Decoding Problem for random binary linear codes, using parameters corresponding to the NIST Security Category 1 parameter set of the Classic McEliece cryptosystem. The experiments assess the feasibility of this combinatorial-algebraic approach and provide insights into the practical behavior of Grobner basis techniques within an ISD-like decoding framework.

The conditional probabilities achievable by local measurements on a shared quantum state in a Bell scenario form the set of quantum behaviors, whose structure was studied by Tsirelson. In 1993, Tsirelson asked whether this set is semialgebraic, that is, describable by finite Boolean combinations of polynomial equations and inequalities. This question has remained open. We answer it in the negative: with four binary measurements per party, the set of finite-dimensional quantum behaviors, its closure, and the commuting-operator set are all nonsemialgebraic. More strongly, none admits a finite real-analytic description even locally near a particular classical behavior. These results rule out exact finite semidefinite representations and show that no finite level of the Navascués-Pironio-Acín hierarchy characterizes these sets exactly.

Privacy evaluations of tool-using LLM agents often inspect a designated action, final response, or attacker report. These local proxies can miss unauthorized exposure elsewhere in a multi-step session and lack common ground truth across outlets, reports, and tool paths. We introduce privacy exposure displacement, the mismatch between a local evaluation proxy and target-grounded session exposure, and ASLEval, an authorization-aware framework that pre-registers a hidden target set, measures all declared visible exits, and reserves internal traces for diagnosis. Across multiple enterprise-style environments and independently implemented runtimes, we observe three recurring patterns. An expected-outlet-only view misses 46.9% of exposure recovered by the visible-exit union; attacker self-reports combine omissions with high false discovery; and schema-aligned internal evidence usually precedes visible exposure at the request/probe level. Reducing model-visible returns changes this path but can eliminate normal-task success. Independent human review supports the adjudication pipeline while identifying harder console and candidate cases. These findings motivate benchmarks that declare the complete visible boundary, ground claims in pre-specified targets and authorization, and report privacy together with task utility.

Reliable prediction of crystallographic texture in laser powder bed fusion is critical for linking process conditions with anisotropic response and for qualification. However, black-box models may fail under shift and cannot distinguish weak data support from loss of physical validity. This study develops a two-stage physics-based model for <001> || BD (build direction) texture in Inconel 718. Stage 1 maps process variables to melting mode and melt pool geometry. Stage 2 predicts texture by combining an empirical physics model with a random-forest residual model. A k-nearest-neighbor weight attenuates residual corrections for poorly supported queries, while a study-specific areal beam-power-density criterion withholds predictions outside the adopted conduction envelope. Conformal intervals are evaluated on the retained physics-valid set, and SHAP and Sobol analyses assess residual sensitivity. Under a controlled leave-one-defocus-out evaluation, the physics anchor achieved R^2 = 0.778, against -0.001 for the black-box model and 0.750 for the gated hybrid. Under leave-one-group-out cross-validation, the gated hybrid reached R^2 = 0.592 against 0.538 for the black-box model. Retained-set coverage was 92.9% at a mean full width of 3.65 multiples of a uniform distribution (MUD) under grouped cross-validation and 100% at a width of 3.21 MUD under transfer to a withheld +80 mm defocus regime. An illustrative mapping produced a retained BD elastic-modulus span of 127-187 GPa. On nine conditions from a separately built sample set, the framework withheld three, attenuated three, and matched the measured ordering for the rest. Separating data applicability, physics validity, and predictive uncertainty into distinct decisions lets the framework transfer where an unconstrained model does not, and withhold predictions where no model class performs adequately.

Malicious npm package detection tools now leverage LLMs' semantic understanding of source code to detect malicious intent at scale. This capability has proven invaluable in identifying packages involved in recent supply-chain attacks such as Shai-Hulud. However, threat actors exploit the limited context windows of LLMs through JavaScript techniques such as code obfuscation that yields high token density and bundling malicious code with benign packages, causing detectors to skip large files or miss malicious behavior. This creates an attack surface for evading detection. In this paper, we present CASHEWS, a JavaScript preprocessor that reduces file size by rewriting source code to remove code that is irrelevant to analysis or likely to mislead the model. Given a package source file, CASHEWS deobfuscates it through iterative decoding, extracts bundled modules and dynamically executed code, identifies malicious sinks and computes backward slices that reach them, and abbreviates long literals and identifiers to produce a compact representation for the detector. Across 512 large package files, two scanner types, and three LLMs, CASHEWS increases analysis coverage from 69.1–85.7% to 98.8–100% and reduces the false-negative rate by up to 18.6 percentage points. CASHEWS also has a median preprocessing time of 30 seconds while reducing net analysis cost by 34.6%, making registry-wide LLM-based analysis more practical. By preprocessing source code before analysis, CASHEWS enables researchers and industry practitioners to use more powerful models for malicious package detection at the same or lower analysis cost as less powerful models.

Adaptive learning systems commonly formulate learning path planning as Exercise-Centric (EC) recommendation, where the next step is inferred from item-level interaction logs. Evaluating goal-oriented guidance additionally requires explicit learner goals and curriculum-scale prerequisites: learners with similar exercise records may need different paths toward their targets. We therefore study Knowledge-Centric (KC) personalized learning path planning, where a planner must reason over learner profiles, mastery states, and prerequisite knowledge structures to decide which textbook, unit, and concept should be studied next. To support this setting, we introduce PersonaPath, a benchmark that pairs 2,000 fine-grained learner personas with a hierarchical knowledge graph of 347 textbooks, 1,751 units, and 4,092 concepts across 77 subjects. We evaluate representative LLMs on PersonaPath. Results show that even the strongest LLM reaches only a 29.5% final pass rate in Basic Education, and that the main bottleneck lies in adaptivity, where no model exceeds 44.7% in tailoring paths to individual learners.

When large vision-language models misclassify harmful memes, the failure may reflect missing internal evidence or an inability to route represented evidence to their outputs. We distinguish these cases in Gemma-3 and Qwen3.5 using sparse autoencoders, role-conditioned probes, causal interventions, and recovery experiments across six harmful content benchmarks, with additional Spanish and Hindi-English code-mixed evaluations. Sparse readouts outperform native prediction on all six primary binary tasks: Qwen averages $0.740$ versus $0.432$ for native macro-F1, residual reconstruction reaches $0.486$, and Gemma improves from $0.532$ to $0.714$. These gains measure how accessible the label is to a supervised readout; they do not show that the model's native generation already applies such a decision rule. Under the evaluated scales, Qwen silent-feature ablation is $24-63$ times more probe-sensitive, whereas routed-feature patching on literal yes/no tasks is $16-140$ times more output-sensitive. Native-only threshold calibration explains much, but not all of the gap: on five tasks with matched probe scores, it recovers $69.8$% of the raw native-to-probe difference, while direct routing adds $0.094$ mean macro-F1 beyond calibrated native scoring. Joint gold-label, probe-KL, and pairwise LoRA supervision improves dedicated FHM prediction, but a gold-only adapter performs better on the shared seven-task mean. A case study of Gemma-3-12B on the Facebook Hateful Memes dataset finds a distributed rank-32 image-prompt interaction, reaching $0.756$ versus $0.685$ native macro-F1. Robustness controls show that the signal is not explained solely by accompanying OCR and depends on paired visual evidence, and that it extends beyond English. In many of the errors we study, the evidence is represented but does not reach the answer; therefore, routing is a common bottleneck in harmful meme classification.

Two-stage stochastic Mixed-Integer Linear Programs are a canonical modeling tool to optimize power system operations under uncertainty, yet their extensive-form counterparts scale linearly with the number of scenarios and quickly become computationally prohibitive under day-ahead time constraints. We propose an Input Convex Neural Network architecture to learn a convex surrogate of the second-stage value function, enabling fast first-stage optimization while preserving convexity by construction. We couple the surrogate with a Neural-Benders correction loop that refines the first-stage solution a posteriori, recovering the exact optimum whether the network overestimates or underestimates the recourse cost, and certifying solution quality independently of surrogate accuracy. We evaluate the method on IEEE Stochastic Unit Commitment benchmarks (case9-case118) under both continuous and integer recourse. The proposed approach achieves solutions with zero optimality gap on the $K$-scenario instance across all test cases and scenario dimensions $K \in \{10, 50, 100\}$, with speedups up to $214\times$ over the Extensive Form in the integer setting. Solve times are stable across scenario realizations and compatible with day-ahead time windows on the tested benchmark instances.

The Madden-Julian Oscillation (MJO) is the leading intraseasonal driver of tropical weather, comparable to the interannual ”El Niño/La Niña”, yet remains largely unfamiliar outside the scientific community. The MJO is atmospherically like a ”La Niña” going around the earth, and metaphorically as ”La Ola”, Spanish for ”The Wave”, evoking a stadium wave. Thus a pedagogical nickname such as ”La Ola-MJO” could enhance forecast uptake, especially among climate-vulnerable communities.

The O-RAN control plane is becoming agentic: autonomous AI agents, deployed as rApps by different vendors, independently close control loops over shared radio resources. We demonstrate on a live O-RAN system that this independence is unsafe. Two agents with individually correct objectives, one protecting a latency SLA and one maximizing utilization for energy efficiency, jointly drive recurring opposing excursions of the shared resource partition that neither produces alone. Existing conflict-mitigation mechanisms presume a statically known application population and cannot govern agents whose behavior emerges at run time. We present AURA, a lightweight arbitration layer that admits agent actions only when they satisfy feasibility invariants, per-variable dwell times, and a deadband, and we prove the arbitrated system converges to a feasible operating point. Implemented on an OpenAirInterface (OAI) testbed with measured one-way latency and throughput, AURA reduces recurring shared-state excursions by more than an order of magnitude (from 8.4 to 0.4 PRB amplitude) and virtually eliminates cross-slice throughput starvation (from 40-55% to 0.3%), while leaving the protected slice's own latency compliance unchanged, a trade-off the convergence guarantee makes explicit.

Compact acoustic models face a challenging quality-capacity trade-off. We investigate two factors in this regime: encoder context and Mel-spectrogram supervision. A receptive-field-scaling study shows that expanding self-attention beyond 15 phonemes provides no consistent gains in pitch, energy, or duration prediction. Guided by this finding, we introduce a fixed-receptive-field convolutional encoder that reduces the respective prediction errors by 36.0%, 17.3%, and 3.4%. We further show that directly transferring image-domain gradient-variance supervision restores fine-scale variation but degrades predicted quality, motivating a Mel-specific formulation with axis-specific gradients, overlapping local statistics, and log-domain variance matching. GrainSpeech contains only 264.8K parameters and achieves 17.9x real-time Mel generation on a microcontroller (MCU), while attaining UTMOS scores comparable to substantially larger models with less than 1.5% of their parameters. Source code and demos are available at https://github.com/lab-emi/GrainSpeech.

We introduce an intrinsic notion of p-roughness for continuous paths,for p>1, defined by the uniform convergence of discrete p-energies over all shifted sufficiently fine uniform grids. We prove that this self-averaging property is equivalent to mesoscopic cancellation of the coarse-graining error for discrete p-energy, yielding a characterization that can be verified on a single uniform multiresolution. $p$-roughness refines the finite p-th variation property and implies the invariance of p-th variation across a class of partition sequences. We prove that Brownian motion is almost surely 2-rough and that fractional Brownian motion with Hurst parameter $H$ is almost surely $1/H$-rough. We also derive criteria for p-roughness based on Faber-Schauder coefficients. These results yield partition-robust formulations of higher-order pathwise calculus and energy occupation measures. Finally, we interpret coarse-graining as a renormalization flow for the p-energy and show that the p-roughness class is stable under critical time-amplitude scaling, with linear p-energy profiles as fixed points.