21 papers · ranked by Valyu relevance
Louis H. Y. Chen
Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general…
Alexandra Dorofeeva, V. Yu. Korolev, Alexander Zeifman
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is practically impossible to check the conditions providing the validity of the…
Omar Eidous, Mohammad Al-Rawash
In this paper, we introduce a new approximation of the cumulative distribution function of the standard normal distribution based on Tocher's approximation. Also, we assess the quality of the new approximation using two criteria namely the maximum absolute error and the mean absolute error. The approximation is…
Zoe Shapcott
In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the ddimensional cube [−1, 1]d and an Lq-ball centred at the origin; this is clearly equivalent to approximating the distribution of the Lq-norm of a random point in a d-dimensional cube centered at 0. The approximations…
Zhangyi He, Wenyang Lyu, Mark Beaumont, Feng Yu
Properly modelling genetic recombination and local linkage has been shown to bring significant improvement to the inference of natural selection from time series data of allele frequencies under a Wright-Fisher model. Existing approaches that can account for genetic recombination and local linkage are built on either…
Xuequan Lu, Scott Schaefer, Jun Luo, Lizhuang Ma + 1 more
We propose a robust normal estimation method for both point clouds and meshes using a low rank matrix approximation algorithm. First, we compute a local isotropic structure for each point and find its similar, non-local structures that we organize into a matrix. We then show that a low rank matrix approximation…
Guangshuai Liu, Xurui Li, Si Sun, Wenyu Yi + 1 more
This paper introduces a robust normal estimation method for point cloud data that can handle both smooth and sharp features. Our method is based on the inclusion of neighborhood recognition into the normal mollification process in the neighborhood of the current point: First, the point cloud surfaces are assigned…
Daisuke Miyazaki, Yuka Onishi, Shinsaku Hiura
One of the main problems faced by the photometric stereo method is that several measurements are required, as this method needs illumination from light sources from different directions. A solution to this problem is the color photometric stereo method, which conducts one-shot measurements by simultaneously…
John Heine, Erin E.E. Fowler, Anders Berglund, Michael J. Schell + 1 more
Proper data modeling in biomedical research requires sufficient data for exploration and reproducibility purposes. A limited sample size can inhibit objective performance evaluation. We are developing a synthetic population (SP) generation technique to address the limited sample size condition. We show how to estimate…
Edmund Weitz
In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in base 2. We generalize this proof to show that almost all numbers are normal. The result is arguably the most elementary proof for this theorem so far and should be accessible to undergraduates in their first year.
Abhranil Das, Wilson S. Geisler
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases where these integrals are easy…
Xu Yang, Cai Cheng, Jin Duan, You-Fei Hao + 3 more
'Sylvain Girard'] There are six possible solutions for the surface normal vectors obtained from polarization information during 3D reconstruction. To resolve the ambiguity of surface normal vectors, scholars have introduced additional information, such as shading information. However, this makes the 3D reconstruction…
Authors not listed
Vibrational exciton models are widely used for the simulation of biomolecular vibrational spectra, in particular of two-dimensional infrared (2D-IR) spectra. The parameters entering such models, specifically harmonic local-mode frequencies and harmonic coupling constants, are provided by vibrational maps, which have…
Jonas Vester, Jógvan Magnus Haugaard Olsen
The partial Hessian approximation is often used to perform vibrational analysis of large QM/MM systems where the high computational cost of calculating the full Hessian is impractical. Here, we investigate the accuracy and applicability of the partial Hessian vibrational analysis (PHVA) approach as it is typically used…
Simon A. Neild, Alan R. Champneys, David J. Wagg, Thomas L. Hill + 1 more
'Andrea Cammarano'] A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent…
Paul M Bays
Simple visual features, such as orientation, are thought to be represented in the spiking of visual neurons using population codes. I show that optimal decoding of such activity predicts characteristic deviations from the normal distribution of errors at low gains. Examining human perception of orientation stimuli, I…
Augustijn A.A. de Boer, Seyed Mostafa Kia, Saige Rutherford, Mariam Zabihi + 7 more
Normative modelling is an emerging technique for parsing heterogeneity in clinical cohorts. This can be implemented in practice using hierarchical Bayesian regression, which provides an elegant probabilistic solution to handle site variation in a federated learning framework. However, applications of this method to…
Denis Tikhonov, Yury Vishnevskiy
In this work we discuss the generally applicableWigner sampling and introduce a new, simplified Wigner sampling method, for computationally effective modeling of molecular properties containing nuclear quantum effects and vibrational anharmonicity. For various molecular systems have been performed test calculations 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…
Shunzhou Wan, Agastya Bhati, David Wright, Ian Wall + 3 more
Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an…
Paul Morris, Cory Simon
In many gas sensing tasks, we simply wish to become aware of gas compositions that deviate from normal, "business-as-usual" conditions. We provide a methodology, illustrated by example, to computationally predict the performance of a gas sensor array design for detecting anomalous gas compositions. Specifically, we…