The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' CECAM virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience -- covering both analytical and numerical methods -- and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.
Recently developed methods for video analysis, especially models for pose estimation and behavior classification, are transforming behavioral quantification to be more precise, scalable, and reproducible in fields such as neuroscience and ethology. These tools overcome long-standing limitations of manual scoring of video frames and traditional "center of mass" tracking algorithms to enable video analysis at scale. The expansion of open-source tools for video acquisition and analysis has led to new experimental approaches to understand behavior. Here, we review currently available open-source tools for video analysis and discuss how to set up these methods for labs new to video recording. We also discuss best practices for developing and using video analysis methods, including community-wide standards and critical needs for the open sharing of datasets and code, more widespread comparisons of video analysis methods, and better documentation for these methods especially for new users. We encourage broader adoption and continued development of these tools, which have tremendous potential for accelerating scientific progress in understanding the brain and behavior.
Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely defined by the underlying variational formulation and is typically introduced in an ad hoc manner, potentially affecting the numerical response. Stabilization-free and self-stabilized formulations have been proposed to overcome this issue, although their theoretical analysis is still less mature. This paper provides an in-depth numerical investigation into different stabilized and self-stabilized formulations for the p-version of VEM. The results show that self-stabilized and stabilization-free formulations achieve optimal accuracy while suffering from worse conditioning. Moreover, a new projection operator, which explicitly accounts for variable coefficients, is introduced within the framework of standard virtual element spaces. Numerical results show that this new approach is more robust than the existing ones for large values of p.
Models accounting for imperfect detection are important. Single-visit methods have been proposed as an alternative to multiple-visits methods to relax the assumption of closed population. Knape and Korner-Nievergelt (2015) showed that under certain models of probability of detection single-visit methods are statistically non-identifiable leading to biased population estimates. There is a close relationship between estimation of the resource selection probability function (RSPF) using weighted distributions and single-visit methods for occupancy and abundance estimation. We explain the precise mathematical conditions needed for RSPF estimation as stated in Lele and Keim (2006). The identical conditions, that remained unstated in our papers on single-visit methodology, are needed for single-visit methodology to work. We show that the class of admissible models is quite broad and does not excessively restrict the application of the RSPF or the single-visit methodology. To complement the work by Knape and Korner-Nievergelt, we study the performance of multiple-visit methods under the scaled logistic detection function and a much wider set of situations. In general, under the scaled log
In the industries that involved either chemistry or biology, such as pharmaceutical industries, chemical industries or food industry, the analytical methods are the necessary eyes and hear of all the material produced or used. If the quality of an analytical method is doubtful, then the whole set of decision that will be based on those measures is questionable. For those reasons, being able to assess the quality of an analytical method is far more than a statistical challenge; it's a matter of ethic and good business practices. Many regulatory documents have been releases, primarily ICH and FDA documents in the pharmaceutical industry (FDA, 1995, 1997, 2001) to address that issue.
From flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish skin, and wound healing relies on cell migration. Across these examples, scientists are interested in shedding light on the individual behaviors informing spatial group dynamics and in predicting the patterns that will emerge under altered agent interactions. One challenge to these goals is that images of self-organization -- whether empirical or generated by models -- are qualitative. To get around this, there are many methods for transforming qualitative pattern data into quantitative information. In this tutorial chapter, I survey some methods for quantifying self-organization, including order parameters, pair correlation functions, and techniques from topological data analysis. I also discuss some places that I see as especially promising for quantitative data, modeling, and data-driven approaches to continue meeting in the future.
Left-invariant PDE-evolutions on the roto-translation group $SE(2)$ (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour enhancement) proposed by Citti & Sarti, and Petitot, and they include the direction process (for contour completion) proposed by Mumford. This paper presents a thorough study and comparison of the many numerical approaches, which, remarkably, is missing in the literature. Existing numerical approaches can be classified into 3 categories: Finite difference methods, Fourier based methods (equivalent to $SE(2)$-Fourier methods), and stochastic methods (Monte Carlo simulations). There are also 3 types of exact solutions to the PDE-evolutions that were derived explicitly (in the spatial Fourier domain) in previous works by Duits and van Almsick in 2005. Here we provide an overview of these 3 types of exact solutions and explain how they relate to each of the 3 numerical approaches. We compute relative errors of all numerical approaches to the exact solutions, and the Fourier based methods show us the best performance with smallest relative errors. We also p
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical theories, like GR, to quantum mechanics, like in the AdS/CFT correspondence. In this paper, we first make a survey of the most important settings in which geometrical methods have proven useful to quantum information theory. Then, we lay down a general framework for an action principle for quantum resources like entanglement, coherence, and anti-flatness. We discuss the case of a two-qubit system.
This editorial from the PASP Special Focus Issue "Techniques and Methods for Astrophysical Data Visualization" summarizes contributions from authors, their software and tutorials, video abstracts, and 3D content. PASP and IOP have made this Focus Issue an ongoing project and will continue accepting submissions throughout 2017. For more information and to view the video abstract visit: http://iopscience.iop.org/journal/1538-3873/page/Techniques-and-Methods-for-Astrophysical-Data-Visualization
The Atacama Large Millimeter/submillimeter Array with the planned electronic upgrades will deliver an unprecedented amount of deep and high resolution observations. Wider fields of view are possible with the consequential cost of image reconstruction. Alternatives to commonly used applications in image processing have to be sought and tested. Advanced image reconstruction methods are critical to meet the data requirements needed for operational purposes. Astrostatistics and astroinformatics techniques are employed. Evidence is given that these interdisciplinary fields of study applied to synthesis imaging meet the Big Data challenges and have the potentials to enable new scientific discoveries in radio astronomy and astrophysics.
Mammalian cells have about 30,000-fold more protein molecules than mRNA molecules. This larger number of molecules and the associated larger dynamic range have major implications in the development of proteomics technologies. We examine these implications for both liquid chromatography-tandem mass spectrometry (LC-MS/MS) and single-molecule counting and provide estimates on how many molecules are routinely measured in proteomics experiments by LC-MS/MS. We review strategies that have been helpful for counting billions of protein molecules by LC-MS/MS and suggest that these strategies can benefit single-molecule methods, especially in mitigating the challenges of the wide dynamic range of the proteome. We also examine the theoretical possibilities for scaling up single-molecule and mass spectrometry proteomics approaches to quantifying the billions of protein molecules that make up the proteomes of our cells.
In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different ancillary statistics in frequentist inference and of different prior distributions in Bayesian inference. More broadly, choices are made between parametric and nonparametric methods and between frequentist and Bayesian methods. Rather than choosing a single method, it can be safer, in a game-theoretic sense, to combine those that are equally appropriate in light of the available information. Since methods of combining subjectively assessed probability distributions are not objective enough for that purpose, this paper introduces a method of distribution combination that does not require any assignment of distribution weights. It does so by formalizing a hedging strategy in terms of a game between three players: nature, a statistician combining distributions, and a statistician refusing to combine distributions. The optimal move of the first statistician reduces to the solution of a simpler problem of selecting an estimating distribution that minimize
This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlying the mathematical analysis, and some useful variants of the method as well as links to other methods from the literature. The following four present various challenging applications to solid mechanics, including linear elasticity and hyperelasticity, elastodynamics, contact/friction, and plasticity. The last chapter reviews implementation aspects. This book is primarily intended for graduate students, researchers (in applied mathematics, numerical analysis, and computational mechanics), and engineers working in related fields of application. Basic knowledge of the devising and analysis of finite element methods is assumed. Special effort was made to streamline the presentation so as to pinpoint the essential ideas, address key mathematical aspects, present examples, and provide bibliographic pointers.
Sharing diverse genomic and other biomedical datasets is critical to advance scientific discoveries and their equitable translation to improve human health. However, data sharing remains challenging in the context of legacy datasets, evolving policies, multi-institutional consortium science, and international stakeholders. The NIH-funded Polygenic Risk Methods in Diverse Populations (PRIMED) Consortium was established to improve the performance of polygenic risk estimates for a broad range of health and disease outcomes with global impacts. Improving polygenic risk score performance across genetically diverse populations requires access to large, diverse cohorts. We report on the design and implementation of data sharing policies and procedures developed in PRIMED to aggregate and analyze data from multiple, heterogeneous sources while adhering to existing data sharing policies for each integrated dataset. We describe two primary data sharing mechanisms: coordinated dbGaP applications and a Consortium Data Sharing Agreement, as well as provide alternatives when individual-level data cannot be shared within the Consortium (e.g., federated analyses). We also describe technical implem
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches to statistical inference are treated. Resampling methods, particularly the bootstrap, provide valuable procedures when distributions functions of statistics are not known. Several approaches to model selection and good- ness of fit are considered. Applied statistics relevant to astronomical research are briefly discussed: nonparametric methods for use when little is known about the behavior of the astronomical populations or processes; data smoothing with kernel density estimation and nonparametric regression; unsupervised clustering and supervised classification procedures for multivariate problems; survival analysis for astronomical datasets with nondetections; time- and frequency-domain times series analysis for light curves; and spatial statistics to interpret the spatial distributions of points in low dimensions. Two types of resources are presented: about 40 recommended texts and monographs in various fields of statistics, and the public do
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this "interaction" between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two PDE's, with the determination of some conditional and partial symmetries, the construction of group-invariant solutions, and the symmetry classification of a nonlinear PDE.
Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging problems, specifically, their dual problems, for which we develop in detail the relevant coarse-grid problems. We demonstrate the performance of our method on total variation denoising and magnetic resonance imaging.
Two blind source separation methods (Independent Component Analysis and Non-negative Matrix Factorization), developed initially for signal processing in engineering, found recently a number of applications in analysis of large-scale data in molecular biology. In this short review, we present the common idea behind these methods, describe ways of implementing and applying them and point out to the advantages compared to more traditional statistical approaches. We focus more specifically on the analysis of gene expression in cancer. The review is finalized by listing available software implementations for the methods described.
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely on techniques such as the reduced basis method and discrete empirical interpolation. The presence of geometrical parameters in unfitted domain discretizations entails challenges for the application of standard ROMs. Therefore, in this work we propose a methodology based on i) extension of snapshots on the background mesh and ii) localization strategies to decrease the number of reduced basis functions. The method we obtain is computationally efficient and accurate, while it is agnostic with respect to the underlying discretization choice. We test the applicability of the proposed framework with numerical experiments on two model problems, namely the Poisson and linear elasticity problems. In particular, we study several benchmarks formulated on two-dimensional, trimmed domains discretized with splines and we observe a significant reduction of the online computational cost compared to standard ROMs for the same level of accurac
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is used in the form of a piece-wise linear model of the objective function, which provides us with much better prediction abilities as compared with the standard linear model. To the best of our knowledge, this approach was never really applied in Convex Minimization to differentiable functions in view of the high complexity of the corresponding auxiliary problems. However, we show that all necessary computations can be done very efficiently. Consequently, we get new optimization methods, which are better than the usual Gradient Methods both in the number of oracle calls and in the computational time. Our theoretical conclusions are confirmed by preliminary computational experiments.