Singular Masas and Measure-Multiplicity Invariant

In this paper we study relations between the \emph{left-right-measure} and properties of singular masas. Part of the analysis is mainly concerned with masas for which the \emph{left-right-measure} is the class of product measure. We provide examples of Tauer masas in the hyperfinite $\rm{II}_{1}$ factor whose \emph{left-right-measure} is the class of Lebesgue measure. We show that for each subset $S\subseteq \mathbb{N}$, there exist uncountably many pairwise non conjugate singular masas in the free group factors with \emph{Puk\'{a}nszky invariant} $S\cup\{\infty\}$.Comment: 24 pages, to appear in Houston. J. Mat

International Trade and Manufacturing Employment Outcomes in India: A Comparative Study

The Indian economy has observed significant trade reforms since the mid 1980s, and the Indian manufacturing sector has rapidly increased its integration with the world economy. In this paper, we ask the question: did the increased trade integration create or destroy jobs in the Indian manufacturing sector? We attempt to answer this question by employing a variety of methodological approaches ? factor content, growth accounting and econometric modelling. We also compare India?s employment outcomes with four other countries ? Bangladesh, Kenya, South Africa, and Vietnam ? where similar methodological approaches were used. We find that the impact of international trade on manufacturing employment seems to be similar to those found for the two African countries ? Kenya and South Africa ? rather than the two Asian countries ? Bangladesh and Vietnam. Thus, the overall effect of international trade on manufacturing employment has been minimal, a surprising result for a country with an apparent comparative advantage in labour-intensive manufacturing goods, and a large excess supply of unskilled labour.international trade, manufacturing, employment, India

Fast and Accurate Bilateral Filtering using Gauss-Polynomial Decomposition

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires $O(\sigma^2)$ operations per pixel, where $\sigma$ is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to $O(1)$ per pixel for any arbitrary $\sigma$ (constant-time implementation). This is based on the observation that the range kernel operates via the translations of a fixed Gaussian over the range space, and that these translated Gaussians can be accurately approximated using the so-called Gauss-polynomials. The overall algorithm emerging from this approximation involves a series of spatial Gaussian filtering, which can be implemented in constant-time using separability and recursion. We present some preliminary results to demonstrate that the proposed algorithm compares favorably with some of the existing fast algorithms in terms of speed and accuracy.Comment: To appear in the IEEE International Conference on Image Processing (ICIP 2015

Inequality and Growth in a Knowledge Economy

We develop a two sector growth model to understand the relation between inequality and growth. Agents, who are endowed with different levels of knowledge, select either into a retail or a manufacturing sector. Agents in the manufacturing sector match to carry out production. A by-product of production is creation of ideas that spill over to the retail sector and improve productivity, thereby causing growth. Ideas are generated according to an idea production function that takes the knowledge of all the agents in a firm as arguments. We go on to study how an increase in the inequality of the knowledge distribution affects the growth rate. A change in the distribution not only affects the occupational choice of agents, but also the way agents match within the manufacturing sector. We show that if the idea generation function is sufficiently convex, an increase in inequality raises the growth rate of the economy.Inequality, growth, idea generation, matching, knowledge

Approximating Hereditary Discrepancy via Small Width Ellipsoids

The Discrepancy of a hypergraph is the minimum attainable value, over two-colorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a restriction of the hypergraph to a subset of its vertices, is a measure of its complexity. Lovasz, Spencer and Vesztergombi (1986) related the natural extension of this quantity to matrices to rounding algorithms for linear programs, and gave a determinant based lower bound on the hereditary discrepancy. Matousek (2011) showed that this bound is tight up to a polylogarithmic factor, leaving open the question of actually computing this bound. Recent work by Nikolov, Talwar and Zhang (2013) showed a polynomial time $\tilde{O}(\log^3 n)$-approximation to hereditary discrepancy, as a by-product of their work in differential privacy. In this paper, we give a direct simple $O(\log^{3/2} n)$-approximation algorithm for this problem. We show that up to this approximation factor, the hereditary discrepancy of a matrix $A$ is characterized by the optimal value of simple geometric convex program that seeks to minimize the largest $\ell_{\infty}$ norm of any point in a ellipsoid containing the columns of $A$. This characterization promises to be a useful tool in discrepancy theory