相关论文: Correlation lengths in the language of computable …

The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to…

This article proposes a novel iterative algorithm based on Low Density Parity Check (LDPC) codes for compression of correlated sources at rates approaching the Slepian-Wolf bound. The setup considered in the article looks at the problem of…

Information and correlations in a quantum system are closely related through the process of measurement. We explore such relation in a many-body quantum setting, effectively bridging between quantum metrology and condensed matter physics.…

Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. Here,…

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…

While mutual information effectively quantifies dependence between two variables, it does not by itself reveal the complex, fine-grained interactions among variables, i.e., how multiple sources contribute redundantly, uniquely, or…

The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of…

We show that in the case of unknown {\em harmonic oscillator coherent states} it is possible to achieve what we call {\it perfect information cloning}. By this we mean that it is still possible to make arbitrary number of copies of a state…

We quantify the amount of correlation generated between two different output modes in the process of im- perfect cloning and deletion processes. We use three different measures of correlations and study their role in determining the…

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…

The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to…

This article proposes a new method to estimate an existing mutual information based dependence measure using histogram density estimates. Finding a suitable bin length for histogram is an open problem. We propose a new way of computing the…

Canonical Correlation Analysis, CCA, is a widely used multivariate method in omics research for integrating high dimensional datasets. CCA identifies hidden links by deriving linear projections of features maximally correlating datasets.…

Understanding the relationship between data compression and the capabilities of Large Language Models (LLMs) is crucial, especially in specialized domains like code intelligence. Prior work posited a linear relationship between compression…

One of the most fundamental problems in science is to define {\it quantitatively} the complexity of organized matters, i.e., {\it organized complexity}. Although many measures have been proposed toward this aim in previous decades, there is…

ABCDE is a sophisticated technique for evaluating differences between very large clusterings. Its main metric that characterizes the magnitude of the difference between two clusterings is the JaccardDistance, which is a true distance metric…

During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…

Dense non-Brownian suspension flows of hard particles display mystifying properties: as the jamming threshold is approached, the viscosity diverges, as well as a length scale that can be identified from velocity correlations. To unravel the…

A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…

A new approach to data compression is developed and applied to multimedia content. This method separates messages into components suitable for both lossless coding and 'lossy' or statistical coding techniques, compressing complex objects by…