Papers

Let $T$ be a bounded linear operator on a complex Banach space $X$. We prove that the algebraic decomposition \[ X=\K(T)\oplus \Hq(T) \] forces both summands to be closed and hence characterizes generalized Drazin invertibility. This improves the classical characterizations of Mbekhta~\resultcite{Theorem~1.6}{MbekhtaKato}, Schmoeger~\resultcite{Theorem~4}{Schmoeger}, and Dajić and Koliha~\resultcite{Theorem~6.7}{DajicKoliha}, by removing their closedness assumptions. We also show that $T$ is generalized Drazin invertible if and only if \[ \dim\bigl(\K(T)\cap \Hq(T)\bigr)<\infty \quad\text{and}\quad \codim\bigl(\K(T)+\Hq(T)\bigr)<\infty. \] For ordinary Drazin invertibility, we obtain analogous finite-defect characterizations involving the hyperkernel and the hyperrange. We also give a characterization using pointwise nilpotence on an invariant summand. Finally, we consider arbitrary invariant algebraic decompositions and give a counterexample when the inverse of the restriction to one summand is not assumed bounded.

We construct smooth functions on the flat torus $\mathbb{T}^{n\ge5}$ that change sign and have negative mean but cannot be realized as the scalar curvature of any metric in the given conformal class.

In this paper, we give a constructive proof that for any integer n>7 (resp. n>6), the numbers 1,2,...,n can be arranged in a circle (resp. in a line) such that the sum of the reciprocals of all adjacent sums equals 1. The above conjecture was originally posed by Zhi-Wei Sun. Partitioning the integers according to n mod 12 into nine residue classes, we prove a recursive proposition and inductively construct new examples. Main lemmas and propositions in introduction are proved in Section 2. The rest of the cases are handled by explicit constructions in appendix.

Federated fine-tuning of large language models (LLMs) allows multiple clients to collaboratively adapt models without sharing raw data, offering strong privacy benefits. However, this setting is highly vulnerable to backdoor attacks, in which malicious clients manipulate their updates to induce targeted behaviors while maintaining normal performance on benign inputs. In this work, we make a key observation specific to federated LLM fine-tuning: malicious clients tend to exhibit strong consistency in their model updates, whereas benign clients produce more diverse and dispersed updates. This structural difference is not well captured by existing defense methods, which typically rely on direct anomaly detection in high-dimensional parameter space and therefore struggle in the presence of entangled LLM updates. Motivated by this observation, we propose FedGraph, a graph-based aggregation framework that explicitly models relationships among client updates. By representing clients as nodes in a dynamically constructed graph and extracting structural features that characterize their relative positions and interactions, FedGraph derives compact client representations that effectively separate malicious and benign behaviors. These representations are then used to identify and suppress malicious contributions during aggregation. Extensive experiments demonstrate that FedGraph significantly improves backdoor defense. It consistently reduces attack success rates to below 10% while achieving high detection accuracy (95.5% on average) and a low false positive rate (2.33%), substantially outperforming existing federated learning defenses.

NGC 3783 exhibits a prominent Fe XXV absorption trough in the time-averaged XRISM/Resolve spectrum. To investigate its short-term variability, we present a time-resolved analysis of the Fe XXV absorption line during the continuous 10-day observation. We divided the resolved absorption profile into five fixed velocity intervals and measured their normalized equivalent widths in 19 time-resolved spectra. Three velocity intervals exhibit significant equivalent-width (EW) variability. Two velocity intervals respond differently to low- and high-flux states with less emission line contamination. The time-dependent photoionisation modelling is unable to reproduce the most significant observed EW variation ($3.5 \, \sigma$), possibly owing to uncertainties in the assumed initial equilibrium state, which prevent a precise density measurement. Instead, using photoionisation calculations and assuming the high-density limit, we derive approximate constraints on the ionisation parameters of the two relevant components. The low-velocity component (-320 to -680 km/s) shows a delayed inverse response, indicating a high ionisation parameter, while its relatively short lag timescale indicates a relatively high density and a distance upper limit of 0.05 pc. In contrast, the high-velocity component (-680 to -1040 km/s) manifests a positive response with a longer lag to the ionising continuum, implying a relatively low ionisation parameter. This component appears to be less dense, with an inferred distance upper limit of 0.25 pc. The low-velocity component is consistent with a failed wind, as its outflow velocity is below the local escape velocity, whereas the high-velocity component lies near the escape threshold. Together with the lower-ionisation failed wind detected in 2001, this supports a multiphase failed-wind scenario in the unobscured state of NGC~3783 over more than two decades.

In this paper, we propose an adaptive variance-reduced stochastic sequential (quadratic constrained) quadratic programming (AVR-SS(QC)QP) method for nonlinear constrained optimization. The framework integrates SPIDER-based variance reduction, stochastic quasi-Newton curvature information, merit-function globalization, and adaptive switching between stochastic SQP and SQCQP models. The switching mechanism is governed by a relative constraint model curvature indicator that measures the second-order constraint information neglected by the linearized SQP model. A smoothed hysteresis rule ac?tivates the SQCQP model only when the relative constraint curvature is significant. An exact L1 merit function with Armijo backtracking globalizes the resulting directions, while a coupled stochastic Lyapunov analysis controls the interaction between gradient-estimation error and optimization progress. Under standard smoothness, sampling, regularity, and second-order conditions, we establish almost-sure consistency of the variance-reduced gradient estimator and global convergence of the KKT residual. We further show that, near regular KKT points, the curvature indicator vanishes and the method eventually selects the computationally cheaper SQP model. Numerical experiments on a sparse principal component analysis problem illustrate the practical be?havior of the proposed framework.

Persistent textual memory lets language-model agents reuse lessons from past tasks to improve on future multi-step tasks without retraining. Systems such as ACE and Dynamic Cheatsheet keep it as a playbook: lessons the agent writes after each task and reads in its prompt. A key challenge is to decide which lessons improve later tasks. Current systems leave the decision to the agent itself, which makes performance unstable: the same procedure can write a playbook that helps or one that falls up to 69.6 points below no playbook. These findings motivate valuing lessons by their measured effect on task success rather than by the agent's judgment. We propose Randomized Block Curation (RBC), which measures this effect with a randomized experiment on practice tasks. It groups related lessons into blocks large enough to move success measurably and, on each practice task, includes or leaves out every block at random. Random inclusion makes tasks with and without a block comparable, so the gap in their success estimates the block's effect. RBC keeps the blocks that help and, since the same procedure can write a helpful or a harmful playbook, grows several and serves whichever curated, whole or no playbook scores best on fresh practice episodes. Across two memory systems, three models and three benchmarks, RBC raises average success to 66.9, against 55.5 with the whole playbook, 54.1 with no playbook and 53.8 when the agent's own judgment picks the lessons to keep.

Deploying a workload on a cyber-secure industrial operational-technology (OT) network requires many cross-layer prerequisites to hold at once, including persistent addressing, name resolution, time synchronization, certificate trust, proxy traversal, and reachable industrial-protocol endpoints. These are owned by different teams, yet current tools treat pre-deployment checking, fault attribution, remediation, and ongoing compliance as separate problems, so evidence is rarely reused across stages. As edge platforms come to host self-adapting agents on shared infrastructure, this fragmentation becomes a governance problem. All four stages ask one question: do a workload's requirements hold on a given network? We present an evidence-governed framework that answers it through a single reference, a versioned network-intent artifact specifying a workload's cross-layer requirements for a specific release. A coverage-driven test loop attaches tested evidence to each requirement before deployment. At a site, readiness is reported as ready, not ready, or undecidable, separating untested requirements from genuine failures; a repair step proposes fixes that preserve co-located workloads; and a drift-watch component re-evaluates the site on change, extending assurance across the workload's lifetime. A multi-workload OPC UA commissioning case illustrates all four stages. By detecting runtime deviations and suspending an agent's guarantees until a refreshed artifact is registered, the framework grounds auditable governance for adapting agent collectives on shared industrial infrastructure.

Cooperative aerial manipulation is difficult under wind, payload motion, and noisy goal broadcasts because multiple Unmanned Aerial Vehicles (UAVs) are coupled through a shared payload. We present CALM (Cooperative Aerial Learned Manipulation), a decentralized controller for aerial manipulators carrying a basket while tracking a moving ground robot. CALM combines a parameter-shared Multi-Agent Reinforcement Learning (MARL) policy, trained using Multi-Agent Proximal Policy Optimization (MAPPO), with goal estimation, per-UAV Extended State Observers (ESOs), basket-mass estimation, and anticipatory formation-yaw feedforward. The anticipatory formation-yaw feedforward uses estimated goal motion to rotate the formation before position error develops, reducing basket-yaw lag without adding net commanded force. A disturbance-conditioned critic supports centralized training while execution remains decentralized. Across held-out trajectories, CALM achieves lower mean position and orientation errors than all evaluated baselines, including the matched arm baseline (7.68 versus 10.95 cm and 3.3 versus 4.7$^\circ$), the cable-suspended realization, and two model-based controllers. Under unseen full-information-path degradation, CALM remains statistically comparable or superior to the arm baseline. Videos are available at https://petreric.github.io/CALM/.

When one language-model agent asks another for money, which of the two decides how much changes hands? We ran a round-robin tournament of 1,049 negotiations among fifteen agents. In each game a requester tries to raise money from a holder that has been told to keep a $100 endowment. Knowing which agent holds the money explains 47% of the variance in the amount transferred; knowing which agent asks explains 2%. Dropping the most extreme agents narrows the split to 22% against 4%. Changing the requester's appeal from one named person to a group changed what requesters wrote, but the amounts transferred under the two framings are statistically equivalent. The holders that lose least are the ones that turn down the opening request, and their turn-1 refusal rate ranks them by total losses (Spearman correlation = -0.73). Training moves this behaviour in both directions. Fine-tuning Qwen3-8B on a persuasion corpus with almost no refusals raised what it gave away as a holder from 12% to 84% of the endowment. Distilling two never-losing holders into a 4B student cut its losses from 95% to 1%. Evaluations of agents that hold resources should test them in the holder role, including after persuasion fine-tuning.

In this paper, we introduce a concept of modified curvature measures for h-convex domains in hyperbolic space and prove a shifted version of the generalized Alexandrov theorem, which characterizes geodesic balls in hyperbolic space via modified curvature measures. This result generalizes the classical work of Kohlmann (1998). We further investigate a volume-preserving shifted $\alpha$-Gauss curvature flow for strictly h-convex hypersurfaces in hyperbolic space and prove that for any $\alpha>0$ the solution exists for all time and converges smoothly to a geodesic sphere. The theory of modified curvature measures developed in the first part serves as a key ingredient in characterizing the Hausdorff limit shape of the flow.

We present a real-time, hybrid framework for occlusion handling and depth-aware tracking in minimally invasive surgeries (MIS). Occlusions caused by surgical instruments often obscure the region of interest (ROI), affecting surgical precision. To address this, our approach integrates enhanced You Only Look Once (YOLO) based detection, Particle Filtering (PF), and monocular depth estimation using Multiple Depth Estimation Accuracy with Single Network (MiDaS). Occlusion is detected using a distance-based threshold between instruments and ROI. Experimental results demonstrate robust instrument detection with a confidence score of 0.85, effective occlusion event handling, and accurate depth prediction with an MAE of 0.34 cm and RMSE of 0.53 cm. Independent phantom-based validation against stereo depth measurements yielded an MAE of 0.65 cm and RMSE of 0.66 cm. The framework further achieved an occlusion detection accuracy of 81.95% while maintaining real-time performance at 38.7 FPS. Preliminary surgeon feedback indicates that the proposed visualization framework is clinically relevant and holds promise for future intraoperative image-guided navigation and decision support in MIS.

We study a one-dimensional single-excitation model of a scalar photon field coupled to a continuum of two-level atoms with quadratic density. The resulting matrix Hamiltonian has an unbounded spatially varying coupling and is not semibounded. We prove that it is essentially self-adjoint and determine its spectrum explicitly. The continuous spectrum is the half-line $(-\infty,\Omega]$, where $\Omega$ is the atomic resonance frequency, while the spectrum above $\Omega$ consists of a strictly increasing sequence of simple eigenvalues. These eigenvalues are characterized by the interlaced zeros of the Airy function and its derivative and satisfy \begin{align*} \omega_n = \left(\frac{3\pi g n}{4}\right)^{1/2} + \frac{\Omega}{4} + O(n^{-1/2}). \end{align*} The analysis is based on a nonlinear spectral reduction that yields a confining massless relativistic oscillator above $\Omega$ and an inverted oscillator below $\Omega$.

We trained Agaram 2.5B, a 2.5-billion-parameter Tamil-English language model, from scratch on about 50 billion tokens (58% Tamil, the rest English, math, code and parallel text) on one node of eight H100 GPUs in about six days, with a new tokenizer that, unlike our first model's, keeps line breaks. Supervised fine-tuning on 134,428 conversations, whose replies an open-weight teacher model wrote, and three short targeted rounds turned it into a chat model that answers in Tamil script, romanized Tamil (Tanglish) and English and can call tools: on 25 tool prompts whose schemas appear in training it picks the right tool 23 times and gives exactly the expected arguments 13 times. The released model translates better than Sarvam-1, a 2B Indic base model, in all six FLORES and IN22 directions (FLORES chrF 54.3 into Tamil and 55.2 into English, against 49.2 and 44.2), and nearly doubles its base model on native-Tamil IndicIFEval (19.3% from 10.0%). It is weak on knowledge: reading-comprehension and knowledge benchmarks sit near chance, and on 50 held-out everyday questions written by one native speaker, one LLM judge rated 46% of its replies usable (22-24 of 50 over three passes; 95% interval for 23 of 50, 33-60%), with nearly every failure a wrong fact. Our two further SFT experiments changed answer format but not the knowledge measures. We also describe our first model, Agaram 1.5B, whose failures shaped the choices here; how the judge's scores varied between passes on identical replies; and, item by item, what the targeted rounds trained against and where frontier-model text entered the data. The project ran on compute credits and our own funds, about USD 13,300 across both models; the weights are released (licence to be announced after legal review), with GGUF files for llama.cpp, at https://huggingface.co/murai-labs/agaram-2.5b-instruct; code at https://github.com/Murai-Labs/Agaram2.5b

In this work, we develop low-cost non-iterative Sylvester solvers for dynamical low-rank approximation of reaction-diffusion equations and incorporate them into a basis-update & Galerkin mass-lumped finite element method (\mbox{BUG-MLFEM}). By incorporating mass lumping via Gauss-Lobatto quadrature, the spatial discretization yields a matrix differential equation equipped with diagonal positive-definite mass matrices. We establish the weighted dynamical low-rank approximation (WDLRA) within the Galerkin framework of the MLFEM system, proving the theoretical equivalence between the BUG integrator and MLFEM on low-rank subspaces, which guarantees the discrete well-posedness of the implicit BUG steps. To overcome the severe computational bottleneck of standard $O(m^3+n^3)$ Sylvester solvers, we develop tailored, low-cost non-iterative solvers that exploit the inherent sparse-by-small algebraic structure. Under Dirichlet and Neumann boundary conditions (BCs), the large coefficient matrices are banded, enabling efficient diagonalization of the small $r \times r$ factor matrix and reducing the per-step computational complexity to $O((m+n)r^2)$ and storage to $O((m+n)r)$. For periodic BCs, we combine this diagonalization strategy with a rank-2 Sherman-Morrison-Woodbury update to handle wrap-around corner entries at negligible additional cost. Numerical experiments demonstrate first-order temporal and $(k+1)$th-order spatial convergence of the proposed BUG-MLFEM in the discrete $L^2$ norm, where $k$ denotes the polynomial degree of the finite element space, together with significant computational speedups over existing low-rank integrators.

Interdependent networks can be highly fragile because dependency links amplify local failures into cascades that trigger global collapse. Much of the theoretical understanding comes from geometric network models, where dependency range is imposed externally and coupling strength is distance independent, and it is unclear how these insights apply to real materials, where interdependence arises from physical transport. Here we study thermally coupled amorphous superconducting networks, in which dependencies emerge from current redistribution and heat-mediated interactions governed by thermal diffusivity. Using an experimentally calibrated model of resistively shunted Josephson junctions, we show the system reproduces the three canonical transition regimes: continuous, nucleation-dominated, and mixed-order. However, because heat-driven dependency simultaneously broadens and weakens with distance, long-range thermal coupling can stabilize the superconducting phase upon heating, in contrast with its destabilizing role in geometric models. Cascades are anisotropic, with one-dimensional front propagation. These results offer an experimentally testable perspective complementing the geometric framework.

End-to-end deep learning pipelines for camera-radar 3D object detection are well established in driver assistance systems and autonomous vehicles; however, adapting them to roadside-mounted infrastructure presents significant challenges. On vehicles, sensor heights, pitch angles, and relative geometries remain largely uniform, allowing end-to-end models to generalize effectively. On the contrary, roadside sensor installations vary drastically in height, tilt, and field of view across locations, rendering end-to-end models prone to failure and difficult to adapt without massive location-specific datasets. Hence, instead of designing a complex end-to-end pipeline for direct 3D bounding box estimation, a low-cost, resource-efficient two-stage approach is proposed for real-time 3D shape and orientation estimation. The first stage utilizes any off-the-shelf, state-of-the-art method to extract 2D camera bounding boxes and associated 3D radar points for each road user. The proposed second stage then processes these inputs to construct 3D oriented bounding boxes where radar data determines 3D position, predefined templates define size for each road user, and a tiny neural network predicts a site-specific and optimized yaw angle. The algorithm is successfully validated at a curved road with a junction for pedestrians, bicycles, and cars, where it achieves 25 frames per second on an NVIDIA Jetson ORIN for real-time applications.

The stability zone of Novikov's problem of planar sections of triply periodic surfaces are labeled by indivisible triples of integers, which we call the soul of the zone. Which triples may occur is not known. We show that, if a Morse function $f$ on $\mathbb T^3$ admits a translation $\tau(x)=x+v$ with $f\circ\tau=-f$, so that the sets $\{f<0\}$ and $\{f>0\}$ are congruent, then in the generic genus-$3$ situation every topological number $L$ satisfies $\langle L,2v\rangle\equiv1\pmod2$. The mechanism is that the electron/hole type of a null-homologous closed trajectory is invariant under the period lattice and is reversed by $\tau$. For $f=\cos2\pi x+\cos2\pi y+\cos2\pi z$ and the $\mu$-cube, this means that the sum of the components of each soul is odd.

Large Language Models (LLMs) are aligned to human preferences, after pre-training and supervised fine-tuning steps. However, standard RL alignment steps such as RLHF do not focus on factuality of LLMs, hence they may generate non-factual information, which could result in unintended consequences. In response, a number of factuality alignment approaches have been proposed in the literature which claim to improve factuality of LLMs on their own benchmarks. However, these methods have not been reproduced independently and are also not comparable since each uses a different base model, training data, evaluation set, judge, and metric. In this paper, we present the first independent reproduction of five factuality alignment methods, which span on-policy RL (PPO, GRPO, and Dr.~GRPO) and offline preference optimization (DPO and KTO), and compare them on a common benchmark with common evaluation metrics. We found that none of these methods reproduces in full, and on the common benchmark none of the methods significantly outperforms the base model. On closer inspection, the rewards optimize for format, length, or brevity rather than factuality and relevance, whereas the choice between on-policy and offline training matters little. Furthermore, the evaluation metrics and benchmarks are also part of the problem since they do not measure relevance of text to the prompt. Since there is no ground truth associated with the prompts, the reliance on LLM judges and retrieval for verification also makes the evaluation fragile. We release our code, data, and checkpoints.

Contextual and unigram surprisal are standard predictors of reading time in computational psycholinguistics. While contextual surprisal is typically derived from neural language models, unigram surprisal is usually obtained from independent corpus counts. Although both quantities are deterministic functionals of a single underlying distribution—capturing conditional and marginal structure respectively—this practice breaks their probabilistic link and may introduce estimation error from the mismatch. We propose three principles for estimating unigram surprisal in psycholinguistic research, including the requirement that both quantities be derived from the same language model. We operationalize this principle by introducing a Monte Carlo estimator of unigram surprisal from a language model, along with a marginalized variant that has lower variance empirically. When unigram surprisal is re-estimated under this unified framework, we find evidence that predictors change in their predictive contribution to reading time. We also confirm prior findings that frequency can be a stronger predictor of processing effort than contextual surprisal under this unified framework.

We prove an analogue of Min-Oo's conjecture for sufficiently small spherical caps in the unit round sphere. For every dimension $n\ge3$, there exists $r_*(n)>0$ such that the following holds for every round cap of radius $0<r\le r_*(n)$: any smooth compact connected oriented Riemannian fill-in with the same intrinsic boundary metric and with scalar curvature and outward boundary mean curvature at least those of the cap is isometric to the cap.

Prompt-based adaptation offers several ways to specialize a frozen language model, ranging from natural-language prompt optimization to learned continuous prompts. These methods are usually compared through downstream performance, although similar outputs need not arise from similar internal computations. We study how discrete prompt optimization, prompt tuning, and prefix tuning alter the processing of dense and mixture-of-experts language models. Our analysis shows that the location of the adaptation predicts how task information is carried to the output: optimized text primarily changes response construction, input-level prompts write their influence into content representations, and layer-wise prefixes maintain direct control through attention. In MoE models, these differences further induce distinct expert-routing patterns. At the same time, common representation-level measurements respond strongly to generic context changes and do not reliably distinguish useful adaptations from matched placebos. We argue that understanding prompt adaptation requires separating representation drift from the part of that drift that is aligned with, and causally used by, the model's task computation. This perspective provides practical guidance for selecting, evaluating, and interpreting prompt adaptation methods.

We examine how the Curie–Weiss cell fluid model can be quantitatively related to real fluids by determining its microscopic parameters from experimental critical-point data for water, carbon dioxide, and three polyol ester lubricants (POE5, POE7, and POE9). The microscopic parameters of the model are determined from the experimental values of the critical temperature and critical density: the global attraction coupling constant is fixed by the critical temperature, and the cell volume by the critical density. The critical pressure then follows as an independent model prediction, deviating from experimental values by 10–41$\%$ across the studied substances. Varying the ratio of local repulsion to global attraction $f=J_2/J_1$ over a wide range has only a weak effect on this deviation. For $f\geq1$, the model's critical compressibility factor lays within a narrow range $Z_c\approx0.382-0.386$, remaining close to the mean-field van der Waals value $Z_c=3/8=0.375$ and consistently overestimating experimental values. The best agreement with experiment is obtained for the polyol ester lubricants and improves along the POE5–POE7–POE9 series with increasing molar mass, suggesting that multiple-occupancy cell fluid models are well suited to systems of large molecules, particularly soft-matter systems with bounded interaction potentials. We further show that generalizing the model by introducing a temperature- and phase-dependent effective attraction allows it to describe a triple point and to reproduce the broad range of critical-to-triple temperature ratios $T_c/T_{\mathrm{tr}}$ characteristic of real fluids.

Dense vector retrieval can miss evidence connected through intermediate entities, while direct graph retrieval requires access to the graph at query time. We compare five offline graph-based embedding transformations and strategies for using the resulting graph-modified embeddings alongside the originals, without query-time graph access. On a synthetic professional-network benchmark with complete supporting-evidence sets, direct replacement of the original embeddings reduces evidence recovery. Multi-stage strategies improve recovery by using graph-modified embeddings to guide the search while retaining the originals for semantic relevance. On questions requiring linked facts or comparisons among candidates, the strongest configuration improves recovery by up to 25.9% relative to plain vector retrieval. It also matches baseline recovery with 40% fewer returned nodes. Controls confirm that graph information contributes beyond multi-stage retrieval alone. Across the tested methods, retrieval performance depends more on how graph-modified embeddings are used than on how they are produced.

The $\mathbb{Z}_{p^s}$-additive codes are subgroups of $\mathbb{Z}_{p^s}^n$. A $\mathbb{Z}_{p^s}$-linear generalized Hadamard (GH) code is a GH code over $\mathbb{Z}_p$ which is the Gray map image of a $\mathbb{Z}_{p^s}$-additive code. A recursive construction gives such codes $H_p^{t_1,\dots,t_s}$, of type $(n;t_1,\dots,t_s)$ and length $p^t$, and a partial classification of them is known. In this paper, we complete the classification of these codes for every prime $p$. The main tool is the derived code, obtained by puncturing the code outside a block of coordinates determined by its kernel. For a nonlinear code $H_p^{t_1,\dots,t_s}$ with $t_1\geq2$, the derived code is a $\mathbb{Z}_{p^{s-1}}$-linear GH code of the same family, although the mechanism for odd $p$ differs from the binary one. As a consequence, for $t\geq3$, there are $\mathcal P(t+1)-\mathcal P(t)$ nonequivalent such codes of length $p^t$ if $p$ is odd, and $\mathcal P(t+1)-\mathcal P(t)-1$ if $p=2$, where $\mathcal P(n)$ is the number of partitions of $n$. In particular, this completes the classification of the $\mathbb{Z}_{2^s}$-linear Hadamard codes. We also prove a conjecture on the codes with $t_1\geq2$ and $t_s=0$.

Linear probes on a model's hidden states are used as cheap monitors for indirect prompt injection: they screen the tool outputs an agent reads and send suspicious ones to a slower second check, so every false alarm has a cost. But a probe learns whatever separates its training examples. The standard evaluation of injection probes can be passed without the model: conversation position and text lengths alone reach 0.91-0.98 AUROC. When each attack is compared with the same conversation without the injection, or with harmless text formatted like an injection, standard probes flag most of these harmless cases. We add such cases to the training data as matched negatives. Across six open models, in applications seen during training and at the default threshold, changing only the training data cuts false alarms on injection-free conversations from 41-80% to 4-27%, and on harmless look-alikes from 92-98% to 3-16%. With a threshold set on normal traffic, our probe still catches a median 95% of the attacks that fooled the agent (91% without our data). In new applications, false alarms stay low, but detection depends on the model and on how the threshold is set. The same data also helps a text-only filter.

Diffusion language models reconstruct masked tokens in parallel, offering an alternative to autoregressive generation. Yet their Transformer backbones typically carry visible evidence and evolving masked predictions through a single residual stream. We equip masked diffusion models with multiple residual streams that persist through depth and adaptive routing between them, then investigate how they support these complementary roles. On the pretraining task, two streams reduce reconstruction perplexity by 5.71% on validation data and 5.13% on average across external corpora compared with standard residual connections. We observe that, without predefined roles, visible and masked positions learn distinct routing patterns. Causal interventions show that this distinction organizes read and write routing, while token-specific write strength remains important within each role. Guided by these findings, a model trained with role-conditioned routing recovers half the validation gain from adding a second stream. State interventions explain the benefit of the additional stream: it preserves early token representations for later reuse while evidence accumulates at masked positions. This mechanism recurs at a larger model scale, showing how persistent streams support context preservation alongside prediction refinement.

HTTP(S) DDoS attacks have surged in frequency and scale, posing a significant threat to network security. Flow-based detection is a promising solution for large-scale HTTP(S) DDoS detection due to its decryption-free operation and scalability. However, the coarse-grained numerical statistics in flow data limit accurate attack detection and lack robustness when benign and attack traffic patterns drift over time. In this paper, we present Tanchun, a drift-aware flow-based HTTP(S) DDoS detection system that relies solely on decryption-free flow data. Specifically, Tanchun groups flows by IP-pair and aggregates them over consecutive time slots into behavior sequences, capturing temporal access patterns to compensate for the limited information in individual flows. It further abstracts these sequences into human-understandable behavioral attributes that capture stable behavioral semantics. Tanchun then aligns behavior sequences with their corresponding behavioral attributes to guide representation learning, enabling robust detection under traffic drift. We evaluate Tanchun across diverse HTTP(S) DDoS scenarios. Tanchun achieves the best overall performance, with an average F1-score of 0.988, and outperforms the second-best method by 5.3% and 9.6% under benign-traffic and attack-traffic drift, respectively. Experiments on real-world traffic traces further demonstrate its practical effectiveness.

This paper assesses hyperscale data center hosting capacity in transmission grids. Hosting capacity (HC) analysis quantifies the maximum additional load a bus can accommodate without violating operational constraints. This paper defines data center HC as the maximum time-invariant active power demand at a single target bus over a 24-hour peak-day horizon, and evaluates it under four models of increasing fidelity (i.e., the extent to which the model enforces real-world operational security requirements) on the modified IEEE 24-bus system: (i) DC optimal power flow (DC-OPF) without unit commitment (UC), (ii) basic SCUC (security-constrained unit commitment) without reliability constraints, (iii) SCUC with spinning reserve, and (iv) N-SCUC with both reserve and branch-contingency security. Comparing these models quantifies the impact of unit commitment, reserve requirements, and N-1 security on bus-level HC estimates. The N-SCUC yields an average HC of 444 MW; omitting N-1 security raises this to 532 MW, a 19.8% overestimation. The DC-OPF and basic SCUC models further overestimate HC, indicating a trade-off between model complexity and estimation accuracy.

Automated radar waveform recognition classifies the waveform and modulation type of a received signal. As new waveform variants appear over time, a deployed classifier must learn them without retraining from scratch. Catastrophic Forgetting occurs when learning new waveforms overwrites prior knowledge. Continual Learning (CL) methods tackle this challenge, but prior radar studies only evaluate a few methods on narrow benchmarks. Practitioners lack evidence on which method to deploy or which mechanisms are effective. This work presents the first large-scale benchmark of continual learning for radar waveform recognition. Eighteen CL methods are evaluated on a sequential ten-task problem, drawn from four public datasets spanning 54 waveforms, under task- and class-incremental (TIL, CIL) settings and single- and multi-epoch regimes. Methods that retain data from old tasks lead both TIL and CIL settings. Plain replay alone closes 77-88% of the gap between the lower and upper practical limits under TIL, but only 46-55% under CIL. The internal mechanisms of the leading methods are ablated and statistically tested to identify effective mechanisms. Each ablation is paired against its full method over n=6 training seeds, topped up to n=12 when inconclusive, and p-values are Holm-Bonferroni corrected within each method's family. Ablation results show that several mechanisms confer smaller but statistically significant gains. Combining these mechanisms improves the leading F1 score by 3.4-5.5% and 2.7-4.9% under TIL and CIL, respectively, and the combined models exceed every benchmarked method in both settings for all SNRs. These results give researchers of radar waveform classification systems a mechanism-level basis for design.