arXiv subjects

Jorge Cisneros

Publications and source records attributed to Jorge Cisneros.

4 recordsLinked to original sources

arXiv2025

Developing synthetic microdata through machine learning for firm-level business surveys

Public-use microdata samples (PUMS) from the United States (US) Census Bureau on individuals have been available for decades. However, large increases in computing power and the greater availability of Big Data have dramatically increased the probability of re-identifying anonymized data, potentially violating the pledge of confidentiality given to survey respondents. Data science tools can be used to produce synthetic data that preserve critical moments of the empirical data but do not contain the records of any existing individual respondent or business. Developing public-use firm data from surveys presents unique challenges different from demographic data, because there is a lack of anonymity and certain industries can be easily identified in each geographic area. This paper briefly describes a machine learning model used to construct a synthetic PUMS based on the Annual Business Survey (ABS) and discusses various quality metrics. Although the ABS PUMS is currently being refined and results are confidential, we present two synthetic PUMS developed for the 2007 Survey of Business Owners, similar to the ABS business data. Econometric replication of a high impact analysis published in Small Business Economics demonstrates the verisimilitude of the synthetic data to the true data and motivates discussion of possible ABS use cases.

cs.LG↗

arXiv2022

The analytic extension of solutions to initial-boundary value problems outside their domain of definition

We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation for solutions to half-line and finite-interval initial-boundary value problems as integrals of kernels with explicit spatial and temporal dependence. These solution representations are defined within the spatial domain of the problem. We obtain the extension of these representation formulae via Taylor series outside these spatial domains and find the extension of the initial condition that gives rise to a whole-line initial-value problem solved by the extended solution. In general, the extended initial condition is not differentiable or continuous unless the boundary and initial conditions satisfy compatibility conditions. We analyze dissipative and dispersive problems, and problems with continuous and discrete spatial variables.

math.AP↗

arXiv2021

The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method

We study a semidiscrete analogue of the Unified Transform Method introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equations with constant coefficients on the finite interval $x \in (0,L)$. The semidiscrete method is applied to various spatial discretizations of several first and second-order linear equations, producing the exact solution for the semidiscrete problem, given appropriate initial and boundary data. From these solutions, we derive alternative series representations that are better suited for numerical computations. In addition, we show how the Unified Transform Method treats derivative boundary conditions and ghost points introduced by the choice of discretization stencil and we propose the notion of "natural" discretizations. We consider the continuum limit of the semidiscrete solutions and compare with standard finite-difference schemes.

math.NA↗

arXiv2021

The numerical solutions of linear semi-discrete evolution problems on the half-line using the Unified Transform Method

We discuss a semi-discrete analogue of the Unified Transform Method, introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equations of constant coefficients. The semi-discrete method is applied to various spacial discretizations of several first and second-order linear equations on the half-line $x \geq 0$, producing the exact solution for the semi-discrete problem, given appropriate initial and boundary data. We additionally show how the Unified Transform Method treats derivative boundary conditions and ghost points introduced by the choice of discretization stencil. We consider the continuum limit of the semi-discrete solutions and provide several numerical examples.

math.NA↗