Jarek Duda
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View article: Improving KAN with CDF normalization to quantiles
Improving KAN with CDF normalization to quantiles Open
Data normalization is crucial in machine learning, usually performed by subtracting the mean and dividing by standard deviation, or by rescaling to a fixed range. In copula theory, popular in finance, there is used normalization to approxi…
View article: Adaptive stable distribution and Hurst exponent by method of moments moving estimator for nonstationary time series
Adaptive stable distribution and Hurst exponent by method of moments moving estimator for nonstationary time series Open
Nonstationarity of real-life time series requires model adaptation. In classical approaches like ARMA-ARCH there is assumed some arbitrarily chosen dependence type. To avoid their bias, we will focus on novel more agnostic approach: moving…
View article: Pseudorandom bit generation with asymmetric numeral systems
Pseudorandom bit generation with asymmetric numeral systems Open
The generation of pseudorandom binary sequences is of great importance in numerous applications, ranging from simulation and gambling to cryptography. Pseudorandom bit generators (PRBGs) can be divided into two categories based on their cl…
View article: Time crystal $ϕ^4$ kinks by curvature coupling as toy model for mechanism of oscillations propelled by mass, like observed for electron and neutrinos
Time crystal $ϕ^4$ kinks by curvature coupling as toy model for mechanism of oscillations propelled by mass, like observed for electron and neutrinos Open
Dirac equation requires $E=mc^2$ energy of resting particle, leading to some $\exp(-iEt/\hbar)$ its evolution - periodic process of $ω=mc^2/\hbar$ frequency, literally propelled by mass of particle, confirmed experimentally e.g. for quantu…
View article: Shared file protection against unauthorised encryption using a Buffer-Based Signature Verification Method
Shared file protection against unauthorised encryption using a Buffer-Based Signature Verification Method Open
View article: 3-SAT solver for two-way quantum computers
3-SAT solver for two-way quantum computers Open
While quantum computers assume existence of state preparation process $|0\rangle$, CPT symmetry of physics says that performing such process in CPT symmetry perspective, e.g. reversing used EM impulses ($V(t)\to V(-t)$), we should get its …
View article: No-cloning theorem for 2WQC and postselection
No-cloning theorem for 2WQC and postselection Open
Two-way quantum computers (2WQC) are proposed extension of standard 1WQC: adding conjugated state preparation operation $\langle 0|$ similar to postselection $|0\ra \langle 0|$, by performing a process which from perspective of CPT symmetr…
View article: Biology-inspired joint distribution neurons based on Hierarchical Correlation Reconstruction allowing for multidirectional neural networks
Biology-inspired joint distribution neurons based on Hierarchical Correlation Reconstruction allowing for multidirectional neural networks Open
Biological neural networks seem qualitatively superior (e.g. in learning, flexibility, robustness) to current artificial like Multi-Layer Perceptron (MLP) or Kolmogorov-Arnold Network (KAN). Simultaneously, in contrast to them: biological …
View article: Simple inexpensive vertex and edge invariants distinguishing dataset strongly regular graphs
Simple inexpensive vertex and edge invariants distinguishing dataset strongly regular graphs Open
While standard Weisfeiler-Leman vertex labels are not able to distinguish even vertices of regular graphs, there is proposed and tested family of inexpensive polynomial time vertex and edge invariants, distinguishing much more difficult SR…
View article: Phase space maximal entropy random walk: Langevin-like ensembles of physical trajectories
Phase space maximal entropy random walk: Langevin-like ensembles of physical trajectories Open
As written by statistician George Box "All models are wrong, but some are useful", standard diffusion derivation or Feynman path ensembles use nonphysical infinite velocity/kinetic energy nowhere differentiable trajectories - what seems wr…
View article: Extracting individual variable information for their decoupling, direct mutual information and multi-feature Granger causality
Extracting individual variable information for their decoupling, direct mutual information and multi-feature Granger causality Open
Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. $\overline{X|Y}$ as random variable containing information from $X$, but…
View article: Two-way quantum computers adding CPT analog of state preparation
Two-way quantum computers adding CPT analog of state preparation Open
Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce a chosen initial state, however, for the final state measurement chooses a ran…
View article: Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals
Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals Open
Electroencephalography (EEG) signals are resultants of extremely complex brain activity. Some details of this hidden dynamics might be accessible through e.g. joint distributions $ρ_{Δt}$ of signals of pairs of electrodes shifted by variou…
View article: The Compression Optimality of Asymmetric Numeral Systems
The Compression Optimality of Asymmetric Numeral Systems Open
Source coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming, for instance) renews interest in fast compression that also squeezes out as much redu…
View article: Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series
Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series Open
The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnost…
View article: Predicting probability distributions for cancer therapy drug selection optimization
Predicting probability distributions for cancer therapy drug selection optimization Open
Large variability between cell lines brings a difficult optimization problem of drug selection for cancer therapy. Standard approaches use prediction of value for this purpose, corresponding e.g. to expected value of their distribution. Th…
View article: Compression Optimality of Asymmetric Numeral Systems
Compression Optimality of Asymmetric Numeral Systems Open
Compression also known as entropy coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming for instance) renews an interest in fast compression that a…
View article: Low cost prediction of probability distributions of molecular properties for early virtual screening
Low cost prediction of probability distributions of molecular properties for early virtual screening Open
While there is a general focus on predictions of values, mathematically more appropriate is prediction of probability distributions: with additional possibilities like prediction of uncertainty, higher moments and quantiles. For the purpos…
View article: ANS-based compression and encryption with 128-bit security
ANS-based compression and encryption with 128-bit security Open
The bulk of Internet interactions is highly redundant and also security sensitive. To reduce communication bandwidth and provide a desired level of security, a data stream is first compressed to squeeze out redundant bits and then encrypte…
View article: Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction
Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction Open
While there is a general focus on prediction of values, real data often only allows to predict conditional probability distributions, with capabilities bounded by conditional entropy $H(Y|X)$. If additionally estimating uncertainty, we can…
View article: Fast optimization of common basis for matrix set through Common Singular Value Decomposition
Fast optimization of common basis for matrix set through Common Singular Value Decomposition Open
SVD (singular value decomposition) is one of the basic tools of machine learning, allowing to optimize basis for a given matrix. However, sometimes we have a set of matrices $\{A_k\}_k$ instead, and would like to optimize a single common b…
View article: Context binning, model clustering and adaptivity for data compression of genetic data
Context binning, model clustering and adaptivity for data compression of genetic data Open
Rapid growth of genetic databases means huge savings from improvements in their data compression, what requires better inexpensive statistical models. This article proposes automatized optimizations e.g. of Markov-like models, especially c…
View article: Digital Immunity Module: Preventing Unwanted Encryption using Source Coding
Digital Immunity Module: Preventing Unwanted Encryption using Source Coding Open
Unwanted data encryption, such as ransomware attacks, continues to be a significant cybersecurity threat. Ransomware is a preferred weapon of cybercriminals who target small to large organizations' computer systems and data centres. It is …
View article: Digital Immunity Module: Preventing Unwanted Encryption using Source Coding
Digital Immunity Module: Preventing Unwanted Encryption using Source Coding Open
Unwanted data encryption, such as ransomware attacks, continues to be a significant cybersecurity threat. Ransomware is a preferred weapon of cybercriminals who target small to large organizations' computer systems and data centres. It is …
View article: Diffusion models for atomic scale electron currents in semiconductor, p-n junction
Diffusion models for atomic scale electron currents in semiconductor, p-n junction Open
While semiconductor electronics is at heart of modern world, and now uses 5nm or smaller processes of single atoms, it seems there are missing models of actual electron currents in these scales - which could help with more conscious design…
View article: Framework for liquid crystal based particle models
Framework for liquid crystal based particle models Open
Long-range e.g. Coulomb-like interactions for (quantized) topological charges are observed experimentally in liquid crystals, bringing open question this article is exploring: how far can we take this resemblance with particle physics? Uni…
View article: Encoding of probability distributions for Asymmetric Numeral Systems
Encoding of probability distributions for Asymmetric Numeral Systems Open
Many data compressors regularly encode probability distributions for entropy coding - requiring minimal description length type of optimizations. Canonical prefix/Huffman coding usually just writes lengths of bit sequences, this way approx…
View article: Compcrypt–Lightweight ANS-Based Compression and Encryption
Compcrypt–Lightweight ANS-Based Compression and Encryption Open
Compression is widely used in Internet applications to save communication time, bandwidth and storage. Recently invented by Jarek Duda asymmetric numeral system (ANS) offers an improved efficiency and a close to optimal compression. The AN…
View article: Improving distribution and flexible quantization for DCT coefficients
Improving distribution and flexible quantization for DCT coefficients Open
While it is a common knowledge that AC coefficients of Fourier-related transforms, like DCT-II of JPEG image compression, are from Laplace distribution, there was tested more general EPD (exponential power distribution) $ρ\sim \exp(-(|x-μ|…
View article: Exploiting context dependence for image compression with upsampling
Exploiting context dependence for image compression with upsampling Open
Image compression with upsampling encodes information to succeedingly increase image resolution, for example by encoding differences in FUIF and JPEG XL. It is useful for progressive decoding, also often can improve compression ratio - bot…