arXiv subjects

Krzysztof Domino

Publications and source records attributed to Krzysztof Domino.

27 records · Page 2Linked to original sources

arXiv2019

Investigating conformation changes and network formation of mucin in joints functioning in human locomotion

Many different processes take place to facilitate lubrication of the joints functioning in human locomotion system. The main purpose of this is to avoid destroying the articular cartilage. Viscoelastic properties of the joints system are very sensitive on both temperature and concentration changes because of the change in conformation presented in the system proteins and protein network formation. We are searching for an answer to the question on how changes in temperature and concentration influence the conformational entropy of mucin protein which is a part of one of the key components, lubricin, which is believed to be responsible for gel formation inside synovial fluid. We are using molecular dynamic technique to obtain the information about dihedral (phi, psi) angles of the mucin during protein self - assembly by means of the computer simulation with a time duration up to 50 ns, parameterized by six temperatures ranged between 300 - 315 K, and six concentrations 10.68 - 267.1 g/L. The results show that between c3 and c4 (160 g/L and 214 g/L) a transition exists where crowding begins affecting the dynamics of protein network formation. In such a concentration ranges mucin has a chance to change the frictional properties of the system. Simultaneously there were no significant changes in conformations of the mucins molecules even after they created networks. The temperature changes also did not affect much of mucins conformations but it introduced slightly modifications in dihedral angles and after some critical value T=306 K it changed conformational entropy trend from decreasing to raising.

physics.bio-ph↗

arXiv2019

The dynamics of the stomatognathic system from 4D multimodal data

The purpose of this chapter is to discuss methods of acquisition, visualization and analysis of the dynamics of a complex biomedical system, illustrated by the human stomatognathic system. The stomatognathic system consists of the teeth and the skull bones with the maxilla and the mandible. Its dynamics can be described by the change of mutual position of the lower/mandibular part versus the upper/maxillary one due to the physiological motion of opening, chewing and swallowing. In order to analyse the dynamics of the stomatognathic system its morphology and motion has to be digitized, which is done using static and dynamic multimodal imagery like CBCT and 3D scans data and temporal measurements of motion. The integration of multimodal data incorporates different direct and indirect methods of registration - aligning of all the data in the same coordinate system. The integrated sets of data form 4D multimodal data which can be further visualized, modeled, and subjected to multivariate time series analysis. Example results are shown. Although there is no direct method of imaging the TMJ motion, the integration of multimodal data forms an adequate tool. As medical imaging becomes ever more diverse and ever more accessible, organizing the imagery and measurements into unified, comprehensive records can deliver to the doctor the most information in the most accessible form, creating a new quality in data simulation, analysis and interpretation.

cs.CV↗

arXiv2019

Selected Methods for non-Gaussian Data Analysis

The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the case of univariate data analysis we discuss stochastic processes with auto-correlated increments and univariate distributions derived from specific stochastic processes, i.e. Levy and Tsallis distributions. Deep investigation of multivariate non-Gaussian distributions requires the copula approach. A copula is an component of multivariate distribution that models the mutual interdependence between marginals. There are many copula families characterised by various measures of the dependence between marginals. Importantly, one of those are `tail' dependencies that model the simultaneous appearance of extreme values in many marginals. Those extreme events may reflect a crisis given financial data, outliers in machine learning, or a traffic congestion. Next we discuss higher order multivariate cumulants that are non-zero if multivariate distribution is non-Gaussian. However, the relation between cumulants and copulas is not straight forward and rather complicated. We discuss the application of those cumulants to extract information about non-Gaussian multivariate distributions, such that information about non-Gaussian copulas. The use of higher order multivariate cumulants in computer science is inspired by financial data analysis, especially by the safe investment portfolio evaluation. There are many other applications of higher order multivariate cumulants in data engineering, especially in: signal processing, non-linear system identification, blind sources separation, and direction finding algorithms of multi-source signals.

stat.ME↗

arXiv2018

Algorithm for an arbitrary-order cumulant tensor calculation in a sliding window of data streams

High order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary order in a sliding window for data streams. We showed that this algorithms enables speedups of cumulants updates compared to current algorithms. This algorithm can be used for processing on-line high-frequency multivariate data and can find applications in, e.g., on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an estimator of non-Gaussianity of a data stream based on the norms of high-order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a~data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ the block structure to store and calculate only one hyper-pyramid part of such tensors.

cs.DS↗

arXiv2018

Introducing higher order correlations to marginals' subset of multivariate data by means of Archimedean copulas

In this paper, we present the algorithm that alters the subset of marginals of multivariate standard distributed data into such modelled by an Archimedean copula. Proposed algorithm leaves a correlation matrix almost unchanged, but introduces a higher order correlation into a subset of marginals. Our data transformation algorithm can be used to analyse whether particular machine learning algorithm, especially a dimensionality reduction one, utilises higher order correlations or not. We present an exemplary application on two features selection algorithms, mention that features selection is one of the approaches to dimensionality reduction. To measure higher order correlation, we use multivariate higher order cumulants, hence to utilises higher order correlations be to use the Joint Skewness Band Selection (JSBS) algorithm that uses third-order multivariate cumulant. We show the robust performance of the JSBS in contrary to the poor performance of the Maximum Ellipsoid Volume (MEV) algorithm that does not utilise such higher order correlations. With this result, we confirm the potential application of our data generation algorithm to analyse a performance of various dimensionality reduction algorithms.

cs.DS↗

arXiv2018

Band selection with Higher Order Multivariate Cumulants for small target detection in hyperspectral images

In the small target detection problem a pattern to be located is on the order of magnitude less numerous than other patterns present in the dataset. This applies both to the case of supervised detection, where the known template is expected to match in just a few areas and unsupervised anomaly detection, as anomalies are rare by definition. This problem is frequently related to the imaging applications, i.e. detection within the scene acquired by a camera. To maximize available data about the scene, hyperspectral cameras are used; at each pixel, they record spectral data in hundreds of narrow bands. The typical feature of hyperspectral imaging is that characteristic properties of target materials are visible in the small number of bands, where light of certain wavelength interacts with characteristic molecules. A target-independent band selection method based on statistical principles is a versatile tool for solving this problem in different practical applications. Combination of a regular background and a rare standing out anomaly will produce a distortion in the joint distribution of hyperspectral pixels. Higher Order Cumulants Tensors are a natural `window' into this distribution, allowing to measure properties and suggest candidate bands for removal. While there have been attempts at producing band selection algorithms based on the 3 rd cumulant's tensor i.e. the joint skewness, the literature lacks a systematic analysis of how the order of the cumulant tensor used affects effectiveness of band selection in detection applications. In this paper we present an analysis of a general algorithm for band selection based on higher order cumulants. We discuss its usability related to the observed breaking points in performance, depending both on method order and the desired number of bands. Finally we perform experiments and evaluate these methods in a hyperspectral detection scenario.

cs.CV↗

arXiv2018

Efficient computation of higher order cumulant tensors

In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of super-symmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of $d!$ compared to the naive algorithm.

math.NA↗

arXiv2017

Properties of quantum stochastic walks from the asymptotic scaling exponent

This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic scaling exponent of the second moment of the walk i. e. of the mean squared distance covered by a walk. As the quantum stochastic walk model encompasses both classical random walks and quantum walks, we are interested how the continuous change from one regime to the other influences the asymptotic scaling exponent. Moreover this model allows for behavior which is not found in any of the previously mentioned model -- the model with global dissipation. We derive the probability distribution for the walker, and determine the asymptotic scaling exponent analytically, showing that ballistic regime of the walk is maintained even at large dissipation strength.

quant-ph↗

arXiv2016

The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios

The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm of is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.

q-fin.PM↗