Related papers: The Several Complex Variables Problem List
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face.…
Astronomical researchers often think of analysis and visualization as separate tasks. In the case of high-dimensional data sets, though, interactive exploratory data visualization can give far more insight than an approach where data…
Scatter plots carry an implicit if subtle message about causality. Whether we look at functions of one variable in pure mathematics, plots of experimental measurements as a function of the experimental conditions, or scatter plots of…
Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…
Spreadsheets are widely used in industry, even for critical business processes. This implies the need for proper risk assessment in spreadsheets to evaluate the reliability and validity of the spreadsheet's outcome. As related research has…
This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…
In recent years, rather than enclosing data within a single organization, exchanging and combining data from different domains has become an emerging practice. Many studies have discussed the economic and utility value of data and data…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
In Physics, we are generally interested in real solutions involving natural phenomena, where knowledge of real functions of real variables is sufficient to obtain physically relevant results. However, the complexity of phenomena associated…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…
The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
Boxplots and related visualization methods are widely used exploratory tools for taking a first look at collections of univariate variables. In this note an extension is provided that is specifically designed to detect and display…
Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…
Variable importance is central to scientific studies, including the social sciences and causal inference, healthcare, and other domains. However, current notions of variable importance are often tied to a specific predictive model. This is…
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
Data intensive research requires the support of appropriate datasets. However, it is often time-consuming to discover usable datasets matching a specific research topic. We formulate the dataset discovery problem on an attributed…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…