25 papers · ranked by Valyu relevance
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…
Yonghong Li, Miao Hao
Due to the rapid development of quantum computing, the compact representation of quantum operations based on decision diagrams has been received more and more attraction. Since variable orders have a significant impact on the size of the decision diagram, identifying a good variable order is of paramount importance. In…
Ruben A. Martinez-Avendaño
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural generalization for functions whose domain and range are in higher-dimensional…
Nicholas C Chesnaye, Merel van Diepen, Friedo Dekker, Carmine Zoccali + 2 more
'Carmine Zoccali' 'Kitty J Jager' 'Vianda S Stel'] Title: ABSTRACT True linear relationships are rare in clinical data. Despite this, linearity is often assumed during analyses, leading to potentially biased estimates and inaccurate conclusions. In this introductory paper, we aim to first describe-in a non-mathematical…
Natasha Rozhkovskaya
We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of Hall-Littlewood polynomials are described, including preservation of commutation relations…
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…
Alexander Krasavin, Gaukhar Nazenova, Adema Dairbekova, Albina Kadyroldina + 3 more
This article investigates the trajectory tracking control of a differential-drive two-wheeled mobile robot (DDWMR) using its kinematic model, framed in the context of sustainability. A nonlinear-to-linear transformation based on differential flatness is employed to convert the original nonlinear system into two fully…
Sebastián García López, Søren Hauberg, Wouter Boomsma
Multiple Sequence Alignment (MSA) has long been a prominent and critical tool in bioinformatics and computational biology. Its importance lies in its ability to provide valuable insights into the relationships between sequences and the evolutionary pressure leading to amino acid preferences at particular sites in a…
Tony Lindeberg
The property of covariance, also referred to as equivariance, means that an image operator is well-behaved under image transformations, in the sense that the result of applying the image operator to a transformed input image gives essentially a similar result as applying the same image transformation to the output of…
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…
Gabriel E. Hoffman, Christian P. Dillard, Kiran Girdhar, Panos Roussos
Statistical methods often make assumptions about independence between the samples or features of a dataset. Yet correlation structure is ubiquitous in real data, so these assumptions are often not met in practice. Whitening transformations are widely applied to remove this correlation structure. Existing approaches to…
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…
Gabriel E. Hoffman, Panos Roussos
Statistical methods often make assumptions about independence between the samples or features of a dataset. Yet correlation structure is ubiquitous in real data, so these assumptions are often not met in practice. Whitening transformations are widely applied to remove this correlation structure. Existing approaches to…
J. Wu, Chenjia Li, Z. Lei, Tuerdi Wumaier + 3 more
'Zekun Wang'] Abstract—The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless aspect of Legendre transformation, this paper explores 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…
Irina Higgins, Sébastien Racanière, Danilo Rezende
Biological intelligence is remarkable in its ability to produce complex behavior in many diverse situations through data efficient, generalizable, and transferable skill acquisition. It is believed that learning “good” sensory representations is important for enabling this, however there is little agreement as to what…
Heng Ma, Longsheng Jiang, Tao Liu, Jia Liu
Classification constitutes a core cognitive challenge for both biological and artificial intelligence systems, with many tasks potentially reducible to classification problems. Here we investigated how the brain categorizes stimuli that are not linearly separable in the physical world by analyzing the geometry 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…
Ryan A. Williams, David A. Liberles
There is a need for computational approaches to compare molecules based upon chemical similarity or for evaluating biochemical transformations. Here, a new approach to molecular alignment in the Simplified Molecular Input Line Entry System (SMILES) format is introduced. Leveraging dynamic programming and scoring…
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)…
Steven Phillips
Category theorists and cognitive scientists study the structural (analogical) relations between domains of interest albeit in different contexts, that is, formal and psychological systems, respectively. Despite this basic commonality, very few cognitive scientists take a category theory approach toward understanding…
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…