Related papers: chi^2 and Linear Fits
These notes discuss, in a style intended for physicists, how to average data and fit it to some functional form. I try to make clear what is being calculated, what assumptions are being made, and to give a derivation of results rather than…
Approximate distributions for sum and difference of linearly correlated $\chi^{2}$ distributed random variables are derived. It is shown that they can be reduced to conveniently parametrized gamma and Variance-Gamma distributions,…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
We present a new criterion for the goodness of global fits. It involves an exploration of the variation of \chi^2 for subsets of data.
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
This paper deals with classical solutions of the modified chiral model on $R^{2+1}$. Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
Linear matrix inequalities (LMIs) commonly appear in systems, stability, and control applications. Many analysis and synthesis problems in these areas can be solved as feasibility or optimization problems subject to LMI constraints.…
Regression with $\chi^2$ constructed from the covariance matrix should not be used for some combinations of covariance matrices and fitting functions. Using the technique for unsuitable combinations can amplify systematic errors. This…
These are the notes from my courses on the arithmetic of quadratic forms.
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential…
We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
These pedagogical lectures present some material, classical or more recent, on (Rational) Conformal Field Theories and their general setting ``in the bulk'' or in the presence of a boundary. Two well posed problems are the classification of…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversities has been developed which exhibits many deep analogies to…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…