25 papers · ranked by Valyu relevance
Rainer Breitling, Patrick Armengaud, Anna Amtmann
Background Gene expression studies increasingly compare expression responses between different experimental backgrounds (genetic, physiological, or phylogenetic). By focusing on dynamic responses rather than a direct comparison of static expression levels, this type of study allows a finer dissection of primary and…
Aarush Mohit Mittal, Andrew C. Lin, Nitin Gupta
Scientific studies often require assessment of similarity between ordered sets of values. Each set, containing one value for every dimension or class of data, can be conveniently represented as a vector. The commonly used metrics for vector similarity include angle-based metrics, such as cosine similarity or Pearson…
Tairone Paiva Leão
Preface 9 1 Mathematical preliminaries 11 1.1 Variables, parameters and functions . . . . . . . . . . . . . . . . . . . . . 11 1.2 Differentiation and integration . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Vector…
Vladimir Bostanov
Background Event-related brain potentials (ERPs) are usually assessed with univariate statistical tests although they are essentially multivariate objects. Brain-computer interface applications are a notable exception to this practice, because they are based on multivariate classification of single-trial ERPs.…
А. В. Соколов
| . | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | . | | | | | | | | | | . | | | | | | | | | | 2-dimensional geometry 5 2.1 Projective foundations 5 2.1.1 Projective duality 5 2.1.2 Top-down view of geometry 7 2.1.3 Points at infinity 8 2.1.4 Extending lines with points at infinity 10 2.1.5…
Stefan Goessner
This is one famous example of several others, that lead to the guiding principle of modern physics – physics is geometry [1][2]. The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry [2]. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable…
Tagir Akhmetshin, Arkadii Lin, Timur Madzhidov, Alexandre Varnek
Autoencoders represent a promising technique for the inverse quantitative structure-activity relationship (QSAR) task. However, undesirable bias, such as atom ordering, affects the neighbourhood behaviour of autoencoders’ latent space and, consequently, usage of the latent vectors as variables in machine-learning…
Daniela Dolciami, Robert Ziolek, Daniel Davies, Michael Carter + 2 more
Chemical diversity is challenging to describe objectively. Despite this, various notions of chemical diversity are used throughout the medicinal chemistry optimization process in drug discovery. In this work, we show the usefulness of considering exploited vectors during different phases of the drug design process to…
Jixin Chen
I have been teaching physical chemistry to undergraduate students for several years now. I have observed that my interpretation of vector-matrix calculations and complex calculations has not been well received by the chemistry students. The traditional vector notation of adding an arrow on top of a variable and the…
William G. Faris
This paper is a modern exposition of old ideas. The setting is a Euclidian space E of dimension n with associated vector space V of dimension n. A (non-zero) sliding vector is a vector in V that is free to move, but only within a line L of E. The set of sliding vectors has dimension 2n−1. This set is naturally embedded…
Khaled Abuhmaidan, Monther Aldwairi, Benedek Nagy, Vitaly Kocharovsky + 1 more
'Vitaly Kocharovsky' 'José A. Tenreiro Machado'] Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is…
Stefan Bode, Elektra Schubert, Hinze Hogendoorn, Daniel Feuerriegel
Multivariate classification analysis for event-related potential (ERP) data is a powerful tool for predicting cognitive variables. However, classification is often restricted to categorical variables and under-utilises continuous data, such as response times, response force, or subjective ratings. An alternative…
A. Alexiadis, S. Ferson, E. A. Patterson
Advances in technology allow the acquisition of data with high spatial and temporal resolution. These datasets are usually accompanied by estimates of the measurement uncertainty, which may be spatially or temporally varying and should be taken into consideration when making decisions based on the data. At the same…
Lorin M. Towle-Miller, Jeffrey C. Miecznikowski
Background Advancements in genomic sequencing continually improve personalized medicine, and recent breakthroughs generate multimodal data on a cellular level. We introduce MOSCATO, a technique for selecting features across multimodal single-cell datasets that relate to clinical outcomes. We summarize the single-cell…
shriprakash sinha
It is widely known that the sensitivity analysis plays a major role in computing the strength of the influence of involved factors in any phenomena under investigation. When applied to expression profiles of various intra/extracellular factors that form an integral part of a signaling pathway, the variance and density…
shriprakash sinha
Ever since the accidental discovery of Wingless [Sharma R.P., Drosophila information service, 1973, 50, p 134], research in the field of Wnt signaling pathway has taken significant strides in wet lab experiments and various cancer clinical trials augmented by recent developments in advanced computational modeling of…
Aapo Hyvärinen
Independent component analysis is a probabilistic method for learning a linear transform of a random vector. The goal is to find components that are maximally independent and non-Gaussian (non-normal). Its fundamental difference to classical multi-variate statistical methods is in the assumption of non-Gaussianity…
Roxana Bujack, Gerik Scheuermann, Eckhard Hitzer
[1] In signal processing correlation is one of the elementary techniques to measure the similarity of two input signals. It can be imagined like sliding one signal across the other and multiplying both at every shifted location. The point of registration is the very position, where the normalized cross correlation…
Authors not listed
We establish a low-dimensional vector embedding of density functional approximations (DFAs) from a low-rank decomposition of the GMTKN55 database. The optimal embedding of DFAs simultaneously provides a dual embedding for chemical tasks, revealing a strong correlation between different tasks and signifying the…
Luciano Dyballa, Andra M. Rudzite, Mahmood S. Hoseini, Mishek Thapa + 3 more
The retina and primary visual cortex (V1) both exhibit diverse neural populations sensitive to diverse visual features. Yet it remains unclear how neural populations in each area partition stimulus space to span these features. One possibility is that neural populations are organized into discrete groups of neurons…
Anders S. Olsen, Rasmus M. T. Høegh, Jesper L. Hinrich, Kristoffer H. Madsen + 1 more
'Kristoffer H. Madsen' 'Morten Mørup'] Metastable microstates in electro- and magnetoencephalographic (EEG and MEG) measurements are usually determined using modified k-means accounting for polarity invariant states. However, hard state assignment approaches assume that the brain traverses microstates in a discrete…
Anthony Onwuli, Keith T. Butler, Aron Walsh
High-dimensional representations of the elements have become common within the field of materials informatics to build useful, structure-agnostic models for the chemistry of materials. However, the characteristics of elements change when they adopt a given oxidation state, with distinct structural preferences and…
H. Robert Frost
We present an approach for modeling single cell RNA-sequencing (scRNA-seq) data using quaternions. Quaternions are four dimensional hypercomplex numbers that, along with real numbers, complex numbers and octonions, represent one of the four normed division algebras. Quaternions have been most widely employed to…
Authors not listed
NMR chemical shifts depend on the applied magnetic flux density, and this becomes more and more important as stronger and stronger magnetic fields are becoming available. Herein, we develop a theory of the field dependence of NMR shifts of paramagnetic molecules in solution. Our derivation leads to two distinct…
Amer El-Samman, Stijn De Baerdemacker
In deep learning methods, especially in the context of chemistry, there is an increasing urgency to uncover the hidden learning mechanisms often dubbed as ``black box." In this work, we show that graph models built on computational chemical data behave similar to natural language processing (NLP) models built on text…