Daily Papers

We study community recovery in the sparse symmetric stochastic block model with q communities, average degree d and signal strength λ through statistical decision theory and Fisher information, and obtain three characterizations of the Kesten-Stigum threshold dλ^2=1 and of the information-computation gap below it. First, on each community-size profile the minimax risk of any class of rules closed under averaging and vertex relabeling equals its Bayes risk under the uniform prior; the posterior mean is the unique Bayes rule and is admissible, and the Bayes risk of degree-D polynomial rules is the trivial risk times 1-Corr_D^2. Combined with known low-degree and information-theoretic results, this gives the gap as a worst-case statement: for qge 5 there is a window below the threshold in which no low-degree rule beats the trivial risk asymptotically, while an exponential-time rule does on a set of labelings of probability 1-o(1). Second, the Fisher information about λ carried by cycle counts is a series with terms of order k(dλ^2)^k, convergent exactly when dλ^2<1; below the threshold the relative error of every unbiased cycle-based estimator of λ^k stays above an explicit constant, and every cycle-count test has success probability bounded below one. Third, the derivative of belief propagation at its uninformative fixed point multiplies a random perturbation by |λ|d per iteration, and one EM step taken there leaves λ unchanged. A signal-to-noise computation recovers the condition dλ^{1/χ}>1 of Chin et al. for q=n^χ communities and identifies personalized PageRank as a walk count with suboptimal weights. Experiments on networks with up to 3times 10^5 vertices confirm the threshold for q=2, the hard window for q=5, and the many-community scaling.

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105 585-593 (2003), Annu. Rev. Phys. Chem. 58 113-142 (2007)], emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models, and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential triangle G=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in phosphorylation-dephosphorylation cycle respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants", which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule which can not be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein which can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.

For a signing σ of a d-regular graph, the spectrum of A_σ depends only on the signs of cycles. We study the affine mathbb F_2 family of signings making every short even cycle unbalanced, and show that averaging over it converts the sign problem of the Bilu-Linial conjecture into a counting problem: a master identity expresses the family-averaged trace as a parity-weighted sum over wrap classes confined to the span W of the constraint cycles, and the family-averaged Ihara L-function diagonalizes so that every prime whose parity escapes W contributes the Ramanujan rate d-1 automatically. Uniform averaging over all signings, by contrast, provably cannot certify a spectral radius below the Kesten profile. We prove matched upper and lower bounds for the confined walk counts, a doubling injection from below, and from above an ear-decomposition encoding in which the number of fresh runs of a non-backtracking walk equals the cycle rank of its support, combined with a window lemma for bicycle-free graphs and a rank bound via the Moore bound for irregular graphs. Consequences include varepsilon-versions of the Bilu-Linial conjecture: every d-regular graph that is subcritical at scale log n, and every d-regular graph bicycle-free at radius Cloglog n/δ, admits a signing in the parity family with ρ(A_σ)le2d-1(1+Cδlog(1/δ))(1+o(1)). We further identify the necessary hypotheses exactly (K_d-trapping; tree-burst gadgets), give an exact certificate on the hypercube, and record a decisive obstruction to two-sided interlacing: mathbb E_σdet(xI-A_σ^2) is not real-rooted, already for the quadrilateral, where it equals (x^2-4x+2)^2+4.

Video understanding requires models to continuously track and update world state during playback. Although existing benchmarks have advanced video understanding evaluation across multiple dimensions, they provide limited visibility into how models maintain world state over time. We propose SVCBench, a Streaming Video Counting Benchmark that repositions counting as a minimal, controlled probe for diagnosing models' world-state maintenance capability. We decompose this capability into object counting and event counting, forming 8 fine-grained subcategories. Object counting covers tracking currently visible objects and cumulative unique identities, while event counting covers detecting instantaneous actions and tracking complete activity cycles. SVCBench contains 406 videos with frame-by-frame annotations of 10,071 event occurrences and object state changes, yielding 1,000 streaming QA pairs with 4,576 query points distributed along video timelines. By observing state maintenance trajectories through streaming multi-point queries, we design three complementary metrics to diagnose numerical precision, trajectory consistency, and temporal awareness. Evaluations of mainstream video-language models show that current models still exhibit significant deficiencies in spatial-temporal state maintenance, with especially poor performance on periodic event counting. SVCBench provides a diagnostic framework for measuring and improving state maintenance in video understanding systems. Our code and data are available at https://buaa-colalab.github.io/SVCBench.

Generalised object counting aims to estimate the number of instances of an arbitrary object category from a single image, but many recent methods can struggle on structurally complex objects due to limited spatial modelling. We present UpCount, a class-agnostic counter designed to better preserve spatial structure. UpCount strengthens the visual representation by extracting multi-layer features from a ViT-B/16 encoder and reassembling them into a refined multi-scale pyramid that is spatially refined using Dense Prediction Transformers and FeatUp, yielding features with improved structural and spatial sensitivity; a proposal--verification counting head then identifies repeated patterns and produces a density map for the final count. On FSC-147, UpCount achieves 12.39 MAE and 100.89 RMSE on the test set, and it transfers effectively to vehicle counting on CARPK (6.27 MAE, 8.79 RMSE). Code: https://github.com/r28112072-rgb/upcount

Complex numerical time series analysis often demands multi-step reasoning capabilities beyond current models' reach. Tasks like medical diagnosis and weather forecasting require sequential reasoning processes - including counterfactual analysis, logical deduction, knowledge application, and multi-modal contextual integration - that existing time series models cannot explicitly perform. While recent research has shown large language models (LLMs) can achieve sophisticated Chain-of-Thought (CoT) reasoning through reinforcement learning (RL), these advances have primarily focused on mathematical and coding domains, with LLMs still demonstrating poor performance on time series tasks. We introduce Chain Of thought for Understanding Numerical Time Series (COUNTS), the first framework that trains LLMs to perform CoT reasoning across diverse time series tasks using RL with verifiable rewards. Our approach employs a Residual Vector-Quantized VAE to create high-fidelity discrete tokens that seamlessly integrate into a pre-trained LLM's vocabulary. COUNTS undergoes a two-stage training process: first, supervised fine-tuning on time series analysis tasks to master our novel representations, followed by Group Relative Policy Optimization training on verifiable problems using prompting strategies that encourage explicit reasoning steps before producing final answers. Our experiments demonstrate that this RL-driven approach with intermediate CoT reasoning significantly enhances LLM performance across various time series analysis tasks, opening new possibilities for complex temporal data reasoning.

Active travel is an essential component in intelligent transportation systems. Cycling, as a form of active travel, shares the road space with motorised traffic which often affects the cyclists' safety and comfort and therefore peoples' propensity to uptake cycling instead of driving. This paper presents a unique dataset, collected by cyclists across London, that includes video footage, accelerometer, GPS, and gyroscope data. The dataset is then labelled by an independent group of London cyclists to rank the safety level of each frame and to identify objects in the cyclist's field of vision that might affect their experience. Furthermore, in this dataset, the quality of the road is measured by the international roughness index of the surface, which indicates the comfort of cycling on the road. The dataset will be made available for open access in the hope of motivating more research in this area to underpin the requirements for cyclists' safety and comfort and encourage more people to replace vehicle travel with cycling.

This study concentrates on evaluating the efficacy of Large Language Models (LLMs) in healthcare, with a specific focus on their application in personal anomalous health monitoring. Our research primarily investigates the capabilities of LLMs in interpreting and analyzing physiological data obtained from FDA-approved devices. We conducted an extensive analysis using anomalous physiological data gathered in a simulated low-air-pressure plateau environment. This allowed us to assess the precision and reliability of LLMs in understanding and evaluating users' health status with notable specificity. Our findings reveal that LLMs exhibit exceptional performance in determining medical indicators, including a Mean Absolute Error (MAE) of less than 1 beat per minute for heart rate and less than 1% for oxygen saturation (SpO2). Furthermore, the Mean Absolute Percentage Error (MAPE) for these evaluations remained below 1%, with the overall accuracy of health assessments surpassing 85%. In image analysis tasks, such as interpreting photoplethysmography (PPG) data, our specially adapted GPT models demonstrated remarkable proficiency, achieving less than 1 bpm error in cycle count and 7.28 MAE for heart rate estimation. This study highlights LLMs' dual role as health data analysis tools and pivotal elements in advanced AI health assistants, offering personalized health insights and recommendations within the future health assistant framework.

Counting repetitive actions are widely seen in human activities such as physical exercise. Existing methods focus on performing repetitive action counting in short videos, which is tough for dealing with longer videos in more realistic scenarios. In the data-driven era, the degradation of such generalization capability is mainly attributed to the lack of long video datasets. To complement this margin, we introduce a new large-scale repetitive action counting dataset covering a wide variety of video lengths, along with more realistic situations where action interruption or action inconsistencies occur in the video. Besides, we also provide a fine-grained annotation of the action cycles instead of just counting annotation along with a numerical value. Such a dataset contains 1,451 videos with about 20,000 annotations, which is more challenging. For repetitive action counting towards more realistic scenarios, we further propose encoding multi-scale temporal correlation with transformers that can take into account both performance and efficiency. Furthermore, with the help of fine-grained annotation of action cycles, we propose a density map regression-based method to predict the action period, which yields better performance with sufficient interpretability. Our proposed method outperforms state-of-the-art methods on all datasets and also achieves better performance on the unseen dataset without fine-tuning. The dataset and code are available.

We apply a complex network approach to analyse the time series of five solar parameters, and propose an strategy to predict the number of sunspots for the next solar maximum, and when will this maximum will occur. The approach is based on the Visibility Graph (VG) algorithm, and a slightly modified version of it, the Horizontal Visibility Graph (HVG), which map a time series into a complex network. Various network metrics exhibit either an exponential or a scale-free behavior, and we find that the evolution of the characteristic decay exponents is consistent with variations of the sunspots number along solar cycles. During solar minimum, the sunspots number and the solar index time series have characteristic decay exponents that correlate well with the next maximum sunspots number, suggesting that they may be good precursors of the intensity of the next solar maximum. Based on this observation, we find that, based on current data, the algorithm predicts a number of 179 sunspots for cycle 25. Combining this with the Hathaway function, adjusted to yield such maximum sunspots number, we find that the maximum for solar cycle 25 will occur in December 2024/January 2025.

Automated exercise repetition counting has applications across the physical fitness realm, from personal health to rehabilitation. Motivated by the ubiquity of mobile phones and the benefits of tracking physical activity, this study explored the feasibility of counting exercise repetitions in real-time, using only on-device inference, on smartphones. In this work, after providing an extensive overview of the state-of-the-art automatic exercise repetition counting methods, we introduce a deep learning based exercise repetition counting system for smartphones consisting of five components: (1) Pose estimation, (2) Thresholding, (3) Optical flow, (4) State machine, and (5) Counter. The system is then implemented via a cross-platform mobile application named P\=uioio that uses only the smartphone camera to track repetitions in real time for three standard exercises: Squats, Push-ups, and Pull-ups. The proposed system was evaluated via a dataset of pre-recorded videos of individuals exercising as well as testing by subjects exercising in real time. Evaluation results indicated the system was 98.89% accurate in real-world tests and up to 98.85% when evaluated via the pre-recorded dataset. This makes it an effective, low-cost, and convenient alternative to existing solutions since the proposed system has minimal hardware requirements without requiring any wearable or specific sensors or network connectivity.