Entropy最新文献

ROUGE is a common objective for extractive summarization because n-gram overlap aligns with sentence-level selection. However, models that focus only on ROUGE often choose sentences with similar content, and the resulting summaries contain redundant information. We propose DiCo-EXT, a training framework that integrates two new loss terms into a standard extractive model: a semantic consistency term and a diversity penalty. The consistency module encourages selected sentences to stay close to document-level meaning, and the diversity penalty reduces semantic overlap within the summary. Both components are fully differentiable and can be optimized together with the base loss, without extra heuristics or multi-stage post-processing. Experiments on CNN/DailyMail, XSum, and WikiHow show lower redundancy and higher lexical diversity, while ROUGE remains comparable to a strong baseline. These results indicate that simple training objectives can balance coverage and redundancy without increasing model size or architectural complexity.

Kaprekar's routine, i.e., sorting the digits of an integer in ascending and descending order and subtracting the two, defines a finite deterministic map on the state space of fixed-length digit strings. While its attractors (such as 495 for D=3 and 6174 for D=4) are classical, the global information-theoretic structure of the induced dynamics and its dependence on the digit length D have received little attention. Here an exhaustive analysis is carried out for D∈{3,4,5,6}. For each D, all states are enumerated and the transition structure is computed numerically; attractors and convergence distances are obtained, and the induced distribution over attractors across iterations is used to construct "entropy funnels". Despite the combinatorial growth of the state space, average distances remain small and entropy decays rapidly before entering a slow tail. Permutation symmetry is then exploited by grouping states into digit multisets and, in a further reduction, into low-dimensional digit-gap features. On this gap space, a first-order Markov approximation is empirically estimated by counting one-step transitions induced by the exhaustively enumerated deterministic map. From the resulting empirical transition matrix, drift fields and the stationary distribution are computed numerically. These quantities serve as descriptive summaries of the projected dynamics and are not derived in closed form.

The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a recovery operation with a high success rate. In this work, we implement a decoder that finds the recovery operation with the highest success probability by mapping the decoding problem to a spin system and using Population Annealing to estimate the free energy of the different error classes. We study the decoder performance on a 4.8.8 color code lattice under different noise models, including code capacity with bit-flip and depolarizing noise, and phenomenological noise, which considers noisy measurements, with performance reaching near-optimal thresholds for bit-flip and depolarizing noise, and the highest reported threshold for phenomenological noise. This decoding algorithm can be applied to a wide variety of stabilizer codes, including surface codes and quantum Low-Density Parity Check (qLDPC) codes.

Pan-Homophonic events denote fluctuations in stock prices that are triggered by phonetic similarities between event keywords and stock tickers. As a relatively novel and under-researched phenomenon, they mirror a subtle yet influential behavioral deviation within financial markets. Centering on the case of Chuandazhisheng, this study delves into how such events produce dynamic and time-varying impacts on stock prices. A linguistic amplitude segmentation method is devised to discriminate between high- and low-intensity events based on information entropy. To separate pan-homophonic-driven price movements from broader market trends, the Relational Stock Ranking (RSR) model is integrated with a Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) framework to establish an adjusted price benchmark. The empirical analysis reveals a sequential price response: initial moderate fluctuations in the low-amplitude phase often yield to more prominent volatility in the high-amplitude phase. While price surges typically occur within one or two days of the event, they generally revert within approximately three weeks. Moreover, repeated exposures to homo- phonic stimuli seem to attenuate the response, indicating a decaying spillover pattern. These findings contribute to a more profound understanding of the intersection between linguistic cues and market behavior and provide practical insights for investor education, information filtering, and regulatory supervision.

Semantic communication frameworks aim to convey the underlying significance of data rather than reproducing it exactly, a perspective that enables substantial efficiency gains in settings constrained by latency or bandwidth. Motivated by this shift, we study the rate-distortion-perception (RDP) trade-off for image compression, a setting in which reconstructions must be not only accurate but also perceptually faithful. Our analysis is carried out through the lens of randomized distributed function computation (RDFC) framework, which provides a principled means of synthesizing randomness and shaping output distributions. Leveraging this framework, we establish finite-blocklength characterizations of the RDP region, quantifying how communication rate, distortion, and perceptual fidelity interact in non-asymptotic regimes. We further broaden this characterization by incorporating two practically relevant extensions: (i) scenarios in which encoder and decoder share side information, and (ii) settings that require strong secrecy guarantees against adversaries, which might include those with quantum capabilities. Moreover, we identify the corresponding asymptotic region under a perfect realism constraint and examine how side information, finite blocklength effects, and secrecy demands influence achievable performance. The resulting insights provide actionable guidance for the development of low-latency, secure, and realism-aware image compression and generative modeling systems.

Structural balance in fully signed networks, integrating both individual attributes and relationships, represents a critical challenge in social computing; however, its dynamic transformation remains underexplored. This study extends structural balance theory by incorporating node attributes and formulating a mathematical framework for optimizing balance dynamics in fully signed networks. A memetic algorithm is designed to achieve structural balance with minimal cost. Evaluations on both synthetic and real-world networks demonstrate the proposed method's effectiveness, efficiency, and social interpretability.

Stock price prediction is a core challenge in quantitative finance. While machine learning has advanced the modeling of complex financial time series, existing methods often rely on single-target predictions, underutilize multidimensional market information, and are disconnected from practical trading systems. To address these gaps, this research develops a hybrid machine learning framework for flexible target forecasting and systematic trading of major American technology stocks. The framework integrates Ensemble Models (AdaBoost, Decision Tree, LightGBM, Random Forest, XGBoost) with Fusion Models (Voting, Stacking, Blending) and introduces a Transfer Learning method enhanced by Dynamic Time Warping to facilitate knowledge sharing across assets, improving robustness. Focusing on ten key stocks, we forecast three distinct momentum indicators: next-day Closing Price Difference, Moving Average Difference, and Exponential Moving Average Difference. Empirical results demonstrate that the proposed Transfer Learning approach achieves superior predictive performance and trading simulations confirm that strategies based on these predicted momentum signals generate substantial returns. This research demonstrates that the proposed hybrid machine learning framework can mitigate the high information entropy inherent in financial markets, offering a systematic and practical method for integrating machine learning with quantitative trading.

This paper is a first attempt to marry constructive nonlinear control theory techniques with active inference. Specifically, we are interested in the relationship between differential flatness and the design of generative models for use in control settings. We place specific emphasis on the pathwise properties of differentially flat systems that inherit from their definition in terms of successive temporal derivatives and relate this to the use of generalised coordinates of motion in formulating continuous-time generative models in active inference. To illustrate the basic concepts, we appeal to the example of oculomotor control.

We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and its scope, we show that KC correctly identifies that probabilities are classical within a fixed measurement context but does not by itself remove the conceptual tension that motivates nonlocal or conspiratorial explanations of Bell inequality violations. We argue that predictive incompleteness-the view that the quantum state is operationally incomplete until the measurement context is specified-provides a simple, minimal, and explanatory framework that preserves relativistic locality while matching experimental practice. Finally we clarify logical relations among these positions, highlight the assumptions behind them, and justify the move from Kolmogorov's to Gleason's framework for quantum probabilities.

We present several remarks on the spread of the COVID-19 epidemics in Bulgaria. The remarks are based on the hypothesis that the spread of the infection exhibits scaling properties similar to the scaling in urban dynamics. The corresponding mathematical theory leads us to a relationship for a power-law dependence of the number of infected in a certain region on the corresponding homochrony number. We prove the correctness of the mathematical theory on the basis of data for several Bulgarian regions for the first large COVID-19 wave in 2020. We observe a collapse of the real data along a single straight line.