24 papers · ranked by Valyu relevance
Danushka Bollegala, Kohei Hayashi, Ken-ichi Kawarabayashi, Sergio Gómez
'Sergio Gómez'] Despite the growing interest in prediction-based word embedding learning methods, it remains unclear as to how the vector spaces learnt by the prediction-based methods differ from that of the counting-based methods, or whether one can be transformed into the other. To study the relationship between…
Mario Lezcano-Casado
| 1 | Coordinate-free Linear Algebra | | 2 | | --- | --- | --- | --- | | | 1.1 | Vector spaces | 2 | | | 1.2 | Vector subspaces and bases | 2 | | | 1.3 | Linear maps | 3 | | | 1.4 | n Differences between a real vector space and R | 4 | | 2 | | Multivariable Calculus | 5 | | 3 | | Forward Mode ad | 7 | | | 3.1 | The…
Alessio Basti, Marieke Mur, Nikolaus Kriegeskorte, Vittorio Pizzella + 3 more
'Laura Marzetti' 'Olaf Hauk' 'Claus C Hilgetag'] Most connectivity metrics in neuroimaging research reduce multivariate activity patterns in regions-of-interests (ROIs) to one dimension, which leads to a loss of information. Importantly, it prevents us from investigating the transformations between patterns in…
Alessio Basti, Marieke Mur, Nikolaus Kriegeskorte, Vittorio Pizzella + 2 more
Most connectivity metrics in neuroimaging research reduce multivariate activity patterns in regions-of-interests (ROIs) to one dimension, which leads to a loss of information. Importantly, it prevents us from investigating the transformations between patterns in different ROIs. Here, we applied linear estimation theory…
Kendra K. Schmid, David B. Marx, Ashok Samal
Shape analysis is useful for a wide variety of disciplines and has many applications. There are many approaches to shape analysis, one of which focuses on the analysis of shapes that are represented by the coordinates of predefined landmarks on the object. This paper discusses Tridimensional Regression, a technique…
R. N. Garifullin, R. I. Yamilov, D. Levi
We discuss aspects of the theory of non-invertible transformations which enter in the problem of classification of differential-difference equations and, in particular, the notion of Miura type transformation. We introduce the concept of non–Miura type linearizable transformation and we present techniques which allow…
V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan
In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second order nonlinear ODEs. We show that besides the conventional point, Sundman and generalized linearizing transformations one can also find a large class of mixed or hybrid…
Viola Mocz, Maryam Vaziri-Pashkam, Marvin Chun, Yaoda Xu
In everyday life, we have no trouble recognizing and categorizing objects as they change in position, size, and orientation in our visual fields. This phenomenon is known as object invariance. Previous fMRI research suggests that higher-level object processing regions in the human lateral occipital cortex may link…
Joakim Ekstrand, Albert Westergren, Kristofer Årestedt, Amanda Hellström + 1 more
'Amanda Hellström' 'Peter Hagell'] Background The Rasch model allows for linear measurement based on ordinal item responses from rating scales commonly used to assess health outcomes. Such linear measures may be inconvenient since they are expressed as log-odds units (logits) that differ from scores that users may be…
José F. Cariñena, Eduardo Martı́nez, Miguel C. Muñoz-Lecanda
Jos´e F. Cari˜nena1∗ , Eduardo Mart´ınez2† and Miguel C. Mu˜noz-Lecanda3‡ 1Departamento de F´ısica Te´orica and IUMA, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain 2Departamento de Matem´atica Aplicada and IUMA, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain 3Departament de…
Ludwig Lausser, Robin Szekely, Attila Klimmek, Florian Schmid + 1 more
'Hans A. Kestler'] Analysing molecular profiles requires the selection of classification models that can cope with the high dimensionality and variability of these data. Also, improper reference point choice and scaling pose additional challenges. Often model selection is somewhat guided by ad hoc simulations rather…
Supaporn Suksern, Sergey V. Meleshko
The problem of linearization of a nonlinear ordinary differential equation has attracted a lot of attention of scientists. The first linearization problem for ordinary differential equations was solved by S.Lie [1]. He found the general form of all ordinary differential equations of second-order which can be reduced to…
A. Aslam, F. M. Mahomed
Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic…
Judith Hoeller, Lin Zhong, Marius Pachitariu, Sandro Romani
As we move through the world, we see the same visual scenes from different perspectives. Although we experience perspective deformations, our perception of a scene remains stable. This raises the question of which neuronal representations in visual brain areas are perspective-tuned and which are invariant. Focusing on…
Jian Zhou, Olga G. Troyanskaya
Scaling single-cell data exploratory analysis with the rapidly growing diversity and quantity of single-cell omics datasets demands more interpretable and robust data representation that is generalizable across datasets. To address this challenge, here we developed a novel ‘quasilinear’ framework that combines the…
Jayme Vaz, Stephen Mann
We introduce the concept of paravectors to describe the geometry of points in a three dimensional space. After defining a suitable product of paravectors, we introduce the concepts of biparavectors and triparavectors to describe line segments and plane fragments in this space. A key point in this product of paravectors…
Mazen Ahmad, Volkhard Helms, Olga V. Kalinina, Thomas Lengauer
A new method termed “Relative Principal Components analysis” (RPCA) is introduced that extracts optimal relevant principal components to describe the change between two data samples representing two macroscopic states. The method is applicable in all areas of data-driven science. Mining of the components is based on a…
Authors not listed
Deciphering the correct mechanism governing certain phenomenon in polyelectrolyte (PE) brush grafted systems, revealed through atomistic simulations, is an extremely challenging problem. In a recent study, our all-atom molecular dynamics (MD) simulations revealed a non-linearly large electroosmotic flow (in the…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Authors not listed
Ongoing research involving electronic spin-dependent dynamics, such as chiral- induced spin selectivity, is providing impetus to revise our understanding of nuclear en- tanglement with electronic spatial and spin degrees of freedom. In a spin-independent setting, non-adiabatic couplings are well-known mediators of…
Andrew McCluskey
The use of mathematical transformations to reduce non-linear functions to linear problems, which can be tackled with analytical linear regression, is commonplace in the chemistry curriculum. The linearization procedure, however, assumes an incorrect statistical model for real experimental data; leading to biased…
Yoshio Nishimoto
Complete active space second-order perturbation theory (CASPT2) is useful for accurately predicting properties of complex electronic structures, but it is well known that it systematically underestimates excitation energies. The underestimation can be corrected using the ionization potential--electron affinity (IPEA)…
Authors not listed
In these Notes we present a new perspective on the exact-factorization expression of a molecular wavefunction, which does not rely of the probabilistic interpretation of the molecular wavefunction as a joint probability amplitude. Instead, we demonstrate a close relation with the traditional Born-Huang representation…
Yan Yang, Yan Zhuo, Zhentao Zuo, Tiangang Zhuo + 1 more
We quickly and accurately recognize the dynamic world by extracting invariances from highly variable scenes, a process can be continuously optimized through visual perceptual learning (VPL). While it is widely accepted that the visual system prioritizes the perception of more stable invariants, the influence of the…