In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...
Let (X,B) be a pair, and let f :X S be a contraction with -(K-x+B) nef over S. A conjecture, known as the Shokurov-Kollar connectedness principle, predicts thatf(-1) (s) boolean AND Nklt(X,B) has at most two connected components, where s is an element of ...
We present a new analysis of finite element methods for partial differential equations over curved domains. In many applications, a change of variables translates a physical Poisson problem over a curved physical domain into a parametric Poisson problem ov ...
Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently, the algorithm off ...
In this paper, we explore the wall crossing phenomenon for K-stability, and apply it to explain the wall crossing for K -moduli stacks and K-moduli spaces. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY li ...
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...
In this thesis we present three closed form approximation methods for portfolio valuation and risk management.The first chapter is titled ``Kernel methods for portfolio valuation and risk management'', and is a joint work with Damir Filipovi'c (SFI and ...
Using data on international equity portfolio allocations by U.S. mutual funds, we estimate a portfolio expression derived from a standard mean-variance portfolio model extended with portfolio frictions. The optimal portfolio depends on the previous month a ...
The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...
In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and we provide a priori error estimates for them. The abstract analysis is exemplified by considering spline s ...
We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...
We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures ...
This thesis contains four chapters, each of which utilizes new or unusual data sources to analyze a different area of financial economics. In the first chapter, I construct a novel dataset linking individual bankers to large borrowers in the U.S. syndicate ...
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...
This thesis uses machine learning techniques and text data to investigate the relationships that arise between the Fed and financial markets, and their consequences for asset prices.The first chapter, entitled Market Expectations and the Impact of Unconv ...
With the advent of emerging technologies and the Internet of Things, the importance of online data analytics has become more pronounced. Businesses and companies are adopting approaches that provide responsive analytics to stay competitive in the global ma ...
In many signal processing, machine learning and computer vision applications, one often has to deal with high dimensional and big datasets such as images, videos, web content, etc. The data can come in various forms, such as univariate or multivariate time ...
This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and
considerations of statistical and com ...
We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...
We give a criterion for a nef divisor D to be semi-ample on a Calabi-Yau threefold X when D3 = 0 = c2 (X)center dot D and c3 (X) 6= 0. As a direct consequence, we show that on such a variety X, if D is strictly nef and.(D) 6= 1, then D is ample; we also sh ...
