23 papers · ranked by Valyu relevance
Mikhail Khovanov
| 1. | Linearization | 1 | | --- | --- | --- | | 1.1. | The Price map | 2 | | 1.2. | PageRank | 3 | | 1.3. | Representation theory as linearization | 4 | | 2. | Euler characteristic and homology of topological spaces | 4 | | 3. | Jones polynomial and its categorification | 8 | | 3.1. | Jones polynomial and the Kauffman…
Wen-Hao Zhang, Lin Dai, Wang Chen, Anyu Sun + 3 more
'Bing-Feng Ju' 'Michele Norgia'] A noise-resistant linearization model that reveals the true nonlinearity of the sensor is essential for retrieving accurate physical displacement from the signals captured by sensing electronics. In this paper, we propose a novel information-driven smoothing spline linearization method…
Milo Orlich
We introduce a construction, called linearization, that associates to any monomial ideal I ⊂ K[x1, . . . , xn] an ideal Lin(I) in a larger polynomial ring. The main feature of this construction is that the new ideal Lin(I) has linear quotients. In particular, since Lin(I) is generated in a single degree, it follows…
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…
Sepideh Sharif, Chihiro Hasegawa, Stephen B. Duffull
Nonlinear ordinary differential equations (ODEs) are common in pharmacokinetic-pharmacodynamic systems. Although their exact solutions cannot generally be determined via algebraic methods, their rapid and accurate solutions are desirable. Thus, numerical methods have a critical role. Inductive Linearization was…
Maria Filipa Pinto, Jorge Ripoll-Rozada, Helena Ramos, Emma E. Watson + 7 more
Enzymes are among the most important drug targets in the pharmaceutical industry. The bioassays used to screen enzyme modulators can be affected by unaccounted interferences such as time-dependent inactivation and inhibition effects. Using procaspase-3, caspase-3, and α-thrombin as model enzymes, we show that some of…
Takaki Akiba, Youhi Morii, Kaoru Maruta
The Harrow, Hassidim, Lloyd (HHL) algorithm, known as the pioneering algorithm for solving linear equations in quantum computers, is expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To efficiently combine classical and quantum computers for high-cost chemical problems…
Vladimir P. Gerdt, Dmitry Lyakhov
to the derivative it can be always linearized by a suitable point transformation. However, in this case the linearization procedure is not efficient since finding the linearizing transformation is as hard as solving the equation under consideration. For the second order ODEs the situation is different. In this case…
Sajid Ali, Hassan Azad, Said Waqas Shah, F. M. Mahomed
A characterization of the symmetry algebra of the Nth-order ordinary differential equations (ODEs) with maximal symmetry and all third-order linearizable ODEs is given. This is used to show that such an algebra g determines – up to a point transformation – only one linear equation whose symmetry algebra is g and an…
Sangyeon Lee, Hanjin Kim, Doheon Lee
Regression analysis is one of the most widely applied methods in many fields including bio-medical study. Dimensionality reduction is also widely used for data preprocessing and feature selection analysis, to extract high-impact features from the predictions. As the complexity of both data and prediction models…
Erfan Nozari, Jennifer Stiso, Lorenzo Caciagli, Eli J. Cornblath + 5 more
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. One may therefore expect the collective dynamics of massive networks…
Fangzhou Xiao, Mustafa Khammash, John C. Doyle
Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely…
Jason Rader, Terry Lyons, Patrick Kidger
We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses general linear operators, and unifies linear solves and least-squares into a single, autodifferentiable API. Solvers and operators are user-extensible, without requiring the user…
Duncan Bossion, Sutirtha Chowdhury, Pengfei Huo
We present the rigorous theoretical framework of the generalized spin mapping representation for non- adiabatic dynamics. This formalism is based on the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space in the state representation. The…
Wylie Stroberg, Santiago Schnell
The simple bimolecular ligand–receptor binding interaction is often linearized by assuming pseudo-first-order kinetics when one species is present in excess. Here, a phase-plane analysis allows the derivation of a new condition for the validity of pseudo-first-order kinetics that is independent of the initial receptor…
John Herbert
Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and (in many contexts) semiquantitative accuracy. This Perspective describes various ways in which excited states from TD-DFT calculations can be…
Łukasz Komsta, Katarzyna Wicha-Komsta, Tomasz Kocki, Joaquim Jaumot + 2 more
'Michal Daszykowski' 'Hadi Parastar'] This is an introductory tutorial and review about the uncertainty problem in chromatographic calibration. It emphasizes some unobvious, but important details influencing errors in the calibration curve estimation, uncertainty in prediction, as well as the connections and…
Ikechukwu I. Udema
A burning concern among researchers studying enzyme kinetics has been ways of improving the accuracy of initial rates (v) with much greater precision. The goal of this study was to establish a formal (mathematical) way of achieving more accurate v values in enzyme assay. By adopting Bernfeld method of assay, the v…
Authors not listed
Rapid and robust simulation of chemical processes is critical to conduct process design, optimization, techno-economic analysis, and sustainability analysis. Yet, efficiently solving simulation models remains a challenge due to the highly coupled and nonlinear nature of the underlying algebraic equations that capture…
Jonathan Fine, Prageeth R Wijewardhane, Sheik Dawood Beer Mohideen, Katelyn Smith + 6 more
Chemical and physical stabilities are two key features considered in pharmaceutical development. Chemical stability is typically reported as a combination of potency and degradation product. For peptide products, it is common to measure physical stability via aggregation or fibrillation using the fluorescent reporter…
Alberto Herrera‐Gómez, R. Michael Porter
The problem of fitting experimental data to a given model function f(t; p1, p2, . . . , pN ) is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the χ 2 measure of discrepancy by a quadratic function. Such nonlinear iterative methods are usually…
Yanfei Lu, Shiqing Zhang, Futian Weng, Hongli Sun
In this study, we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm. Considering the ELM algorithm, sine-cosine basis functions, and several classes of integral equations, the improved model is…
D. J. Ewins, B. Weekes, A. delli Carri
Model validation using data from modal tests is now widely practiced in many industries for advanced structural dynamic design analysis, especially where structural integrity is a primary requirement. These industries tend to demand highly efficient designs for their critical structures which, as a result, are…