Related papers: chi^2 and Linear Fits
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
We discuss the geometry of warped foliations. After examining the Levi-Civita connection, we describe the formulae for sectional, Ricci and scalar curvatures. In the final part of this note, we present some examples.
The paper develops a $(2+2)$-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. The formalism is two-dimensionally covariant, and leads to simple, geometrically…
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
In the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using…
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…
This thesis consists of an introductory text, which is divided into two parts, and six appended research papers. The first part contains a general discussion on conformal and superconformal symmetry in six dimensions, and treats how the…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…