Thorsten Gerber

Bio: Thorsten Gerber is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 2181 citations.

Handbook Of Mathematical Functions

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Recent developments in GEANT4

Abstract: Geant4 is a software toolkit for the simulation of the passage of particles through matter. It is used by a large number of experiments and projects in a variety of application domains, including high energy physics, astrophysics and space science, medical physics and radiation protection. Over the past several years, major changes have been made to the toolkit in order to accommodate the needs of these user communities, and to efficiently exploit the growth of computing power made available by advances in technology. The adaptation of Geant4 to multithreading, advances in physics, detector modeling and visualization, extensions to the toolkit, including biasing and reverse Monte Carlo, and tools for physics and release validation are discussed here.

Optimal Hamiltonian Simulation by Quantum Signal Processing.

Abstract: The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d-sparse Hamiltonian H[over ^] for time-interval t with error e is O[td∥H[over ^]∥_{max}+log(1/e)/loglog(1/e)], which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H[over ^] into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.

Mutual information between discrete and continuous data sets.

Abstract: Mutual information (MI) is a powerful method for detecting relationships between data sets. There are accurate methods for estimating MI that avoid problems with “binning” when both data sets are discrete or when both data sets are continuous. We present an accurate, non-binning MI estimator for the case of one discrete data set and one continuous data set. This case applies when measuring, for example, the relationship between base sequence and gene expression level, or the effect of a cancer drug on patient survival time. We also show how our method can be adapted to calculate the Jensen–Shannon divergence of two or more data sets.

Meta-regression approximations to reduce publication selection bias

Abstract: Publication selection bias is a serious challenge to the integrity of all empirical sciences We derive meta-regression approximations to reduce this bias Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution A quadratic approximation without a linear term, precision-effect estimate with standard error (PEESE), is shown to have the smallest bias and mean squared error in most cases and to outperform conventional meta-analysis estimators, often by a great deal Monte Carlo simulations also demonstrate how a new hybrid estimator that conditionally combines PEESE and the Egger regression intercept can provide a practical solution to publication selection bias PEESE is easily expanded to accommodate systematic heterogeneity along with complex and differential publication selection bias that is related to moderator variables By providing an intuitive reason for these approximations, we can also explain why the Egger regression works so well and when it does not These meta-regression methods are applied to several policy-relevant areas of research including antidepressant effectiveness, the value of a statistical life, the minimum wage, and nicotine replacement therapy

Computational Methods for Linear Matrix Equations

Abstract: Given the square matrices $A, B, D, E$ and the matrix $C$ of conforming dimensions, we consider the linear matrix equation $A{\mathbf X} E+D{\mathbf X} B = C$ in the unknown matrix ${\mathbf X}$. Our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing.