Related papers: Partial Information Decomposition of Boolean Funct…
The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behaviour, it is crucial to convene as much information as possible about…
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…
Fourier analysis on the Boolean hypercube is fundamentally defined as the orthogonal decomposition of the space of pseudo-Boolean functions with respect to the uniform probability measure. In this work, we propose an ANOVA-based…
We propose an effect called information constraint which is characterized by the existence of different decay rates of signal strengths propagating along opposite directions. It is an intrinsic property of a type of open quantum system,…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information.…
Variational inference (VI) has become the method of choice for fitting many modern probabilistic models. However, practitioners are faced with a fragmented literature that offers a bewildering array of algorithmic options. First, the…
This paper provides a description of a new method for information processing based on holistic approach wherein analysis is a direct product of synthesis. The core of the method is iterative averaging of all the elements of a system…
Bayesian inference provides a natural framework for updating knowledge as new information becomes available, often in a sequential manner by incorporating datasets in stages or reusing previous posteriors as priors. In practice, this is…
Biological and artificial neural systems are composed of many local processors, and their capabilities depend upon the transfer function that relates each local processor's outputs to its inputs. This paper uses a recent advance in the…
The fruits of science are relationships made comprehensible, often by way of approximation. While deep learning is an extremely powerful way to find relationships in data, its use in science has been hindered by the difficulty of…
Time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time-gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived and the locus of…
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is…
In analysis of multi-component complex systems, such as neural systems, identifying groups of units that share similar functionality will aid understanding of the underlying structures of the system. To find such a grouping, it is useful to…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
Collaborative perception systems leverage multiple edge devices, such surveillance cameras or autonomous cars, to enhance sensing quality and eliminate blind spots. Despite their advantages, challenges such as limited channel capacity and…
Time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time-gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived and the locus of…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
The applications of the partial fraction decomposition in control and systems engineering are several. In this letter, we propose a new interpretation of residues in the partial fraction decomposition, which is employed for the following…