Daily Papers

For a vertex v of a graph G, the triangle-degree td_G(v) is the number of triangles containing v. A graph is triangle-distinct, or K_3-irregular, if its vertex triangle-degrees are pairwise distinct. Chartrand, Erdős, and Oellermann asked whether a regular K_3-irregular graph exists. We prove that such graphs exist for every regularity rge 9. More precisely, for every integer kge 15 we construct a 2k-regular triangle-distinct graph on 4k+2 vertices; complementation gives a (2k+1)-regular example of the same order. The construction uses two antiregular threshold blocks joined by a zero-one matrix with prescribed margins, followed by matrix 2-switches that preserve those margins. After a uniform reference perturbation, exactly three triangle-degree collisions remain. Switches chosen according to parity remove two of them, and the last possible collision is controlled by a short quadratic discriminant argument. Odd kge 17 and even kge 62 are handled symbolically, while the remaining 24 values are settled by exact finite verification. Together with the known examples for 9le rle 29, this closes the positive existence problem for every rge 9.

Intermittent Androgen Suppression (IAS) is a treatment strategy for delaying or even preventing time to relapse of advanced prostate cancer. IAS consists of alternating cycles of therapy (in the form of androgen suppression) and off-treatment periods. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. In spite of extensive recent clinical experience with IAS, the design of an ideal protocol for any given patient remains one of the main challenges associated with effectively implementing this therapy. We use a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We apply Infinitesimal Perturbation Analysis (IPA) to a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and derive unbiased estimators of the cost metric gradient with respect to various model and therapy parameters. These estimators are subsequently used for system analysis. By evaluating sensitivity estimates with respect to several model parameters, we identify critical parameters and demonstrate that relaxing the optimality condition in favor of increased robustness to modeling errors provides an alternative objective to therapy design for at least some patients.

We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under intermittent androgen suppression (IAS) to study a threshold-based policy for therapy design. IAS is currently one of the most widely used treatments for advanced prostate cancer. Patients undergoing IAS are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. One of the main challenges in IAS is to optimally design a therapy scheme, i.e., to determine when to discontinue and recommence androgen suppression. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. The threshold-based policy we propose is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. Using Infinitesimal Perturbation Analysis (IPA), we derive unbiased gradient estimators of this cost metric with respect to the controllable PSA threshold values based on actual data and show how these estimators can be used to adaptively adjust controllable parameters so as to improve therapy outcomes based on the cost metric defined.

Non-invasive continuous blood pressure (BP) monitoring using photoplethysmography (PPG) is a promising alternative to cuff-based measurements. However, existing PPG-based BP estimation studies predominantly rely on aggregated performance metrics (e.g., mean absolute error) computed over entire evaluation intervals, which can obscure model failures during rapid BP fluctuations and limit clinical relevance. In this work, we propose a fluctuation-aware evaluation framework for PPG-based BP estimation based on time-series change point detection. Instead of heuristic BP thresholding (e.g., ΔBP > 10mmHg), we identify BP change points by capturing abrupt distributional shifts in BP trajectories and evaluate estimation performance specifically during these fluctuation periods. Our analysis shows that several state-of-the-art models exhibit substantial performance degradation around BP change points, and that periodic test-time calibration is insufficient to handle such dynamic BP variations. To address this limitation, we introduce a targeted re-calibration framework triggered by detected BP change points, improving robustness without modifying model architectures. To the best of our knowledge, this is the first systematic evaluation of PPG-based BP estimation from a BP change point perspective, highlighting the importance of fluctuation-aware evaluation and calibration for real-world continuous BP monitoring.

Mechanistic interpretability has emerged as the primary means to understand safety behavior of LLMs. However, existing tools primarily focus on the activating neurons or features of a model. The role of the remaining large set of inactive components is invisible to such methods. This work demonstrates that the inactive set contains safety-critical features that are causally relevant for refusal of harmful prompts. Suppressing such features could turn refusals into compliance, while passing undetected by prevalent interpretability tools. We introduce the Counterfactual Activation Potential (CAP), a metric that quantifies a suppressed feature's latent activation tendency as the product of its encoder alignment (how strongly the input drives it), suppression strength (how strongly active features inhibit it), and safety criticality (how much refusal depends on it). To find suppressed safety features at scale, we propose CAP-guided Safety Feature Discovery (CSFD), a two-stage filtering algorithm that identifies candidate safety features from hundreds of thousands of transcoder features without exhaustive ablation. A significant fraction of trials turn compliant with harmful prompts when a candidate feature is ablated. Under natural jailbreaks, the suppression acting on the highest-CAP features rises 2-4x, and their activation correspondingly falls by up to 80%. Amplifying a feature's suppressors pushes its activation down and raises harmful compliance with prompts related to the suppressed feature, with no such effect for random features. Our experiments span five Gemma, Qwen, and Llama models across various parameter sizes. Our findings indicate that jailbreaks could operate in part by suppressing safety-critical features rather than solely activating harmful ones, and that suppressed features are a necessary complement to activation-focused interpretability of safety behavior.

In mobile telecommunications, alarms act as early warning signals. They are triggered when a cell, the basic unit of radio coverage, shuts down or behaves abnormally. This signals a degradation in service quality, which directly affects the customer experience. To fix the issue, operators rely on preset thresholds to decide when an engineer should be sent out. In practice, these thresholds are set manually and remain fixed regardless of the time of day, traffic levels, or overall network conditions. This often leads to serious faults slipping through during busy hours, while minor issues can cause unnecessary callouts when the network is quiet. This paper presents a machine learning framework that automatically predicts four alarm thresholds, audit window duration, inactive time limit, total fluctuation count, and per hour fluctuation limit, from live network behavior. Since no ground truth labels exist for thresholds, we introduce a percentile guided label derivation strategy and evaluate four models on an anonymized dataset of 10,648 cells across three vendors and nine regions from a real 4G network, comprising a Gradient Boosted Trees baseline, a CNN-BiLSTM with attention, the proposed PCTN, and an iTransformer. PCTN performs the best overall with respect to three of the four targets, outperforming a state-of-the-art iTransformer while using 83 percent fewer parameters. Its mixed output heads and dynamic alpha mechanism produce thresholds that are both accurate and interpretable, allowing operators to inspect and adjust the learned policy without retraining. All comparisons are statistically significant at p < 0.001. The framework undergoes daily retraining using new data, which enables the thresholds to constantly adjust to changes in the network.

Context can change whether a request is harmful without changing its topic or surface form. We ask whether residual-stream probes distinguish harmful requests from surface-matched benign controls at a useful operating point. Across three 7-8B model families, an activation sensor blocks 95.5-97.7 percent of judge-classified compliant attacks in a taxonomy-selected set. It also blocks 59.6-68.4 percent of XSTest prompts. A fully disjoint audit reconstructs near-ceiling source-contrast AUROC (0.996-0.999), but fixed transfer to matched pairs is weaker: 0.656-0.819 on the guard-selected Twin-n70 subset and 0.590-0.690 on the full Twin-n163 cohort. We test ten axes on the reference family and seven across all families with leakage, hold-out, and permutation controls. On Twin-n163, no axis evaluated without direct pair-boundary fitting reaches the specified numerical threshold. Requiring persistence on that full cohort was added at analysis time. A separately specified 24B/32B extension gives the same result. Pair-trained classifiers weaken under category and generation-batch hold-out and false-block 79.6-100 percent of XSTest at 95 percent in-corpus TPR. At the tested read points, these activation scores behave as broad-risk detectors rather than standalone context adjudicators.