In arbitrary dimension, in the discrete setting of finite-differences we prove a Carleman estimate for a semi-discrete parabolic operator, in which the large parameter is connected to the mesh size. This estimate is applied for the derivation of a (relaxed) observability estimate, that yield some controlability results for semi-linear semi-discrete parabilic equations. Sub-linear and super-line...

We characterize the value function of a discounted, infinite-horizon version of the single-item lot-sizing problem. As corollaries, we show that this value function inherits several properties of finite, mixedinteger program value functions; namely, it is subadditive, lower semicontinuous and piecewise linear.

Let W be an arbitrary subset of IR and posW the positive hull of W . We are concerned with conditions under which one can guarantee continuity properties for posW as a function of W . The results are then applied in the context of semi-infinite linear programs and stochastic programs with recourse.

Lecture Notes taken by Nilufer Koldan In this lecture I will describe one of the most significant achievements of the second half of the XX century – the Atiyah-Singer index theorem. I will also discuss some more recent developments in the area as well as some open problems. 1. The definition of the index 1.1. The finite-dimensional case. Let A : V 1 → V 2 be a linear map between finite dimensi...

An overview is presented of some parametric and semi-parametric models, estimators, and specification tests that can be used to analyze ordered response variables. In particular, limited dependent variable models that generalize ordered probit are compared to regression models that generalize the linear model. These techniques are then applied to analyze how self-reported satisfaction with hous...

In this note we are concerned with the generalization given by Ferris and Philpott [3] of the affine scaling algorithm discovered by Dikin [2] to solve semi-infinite linear programming problems, in which the number of variables is finite, but the number of constraints is not. In [3] a discrepancy is pointed out between the classical algorithm and its generalization. The purpose of this note is ...

This paper is focused on the concept of an eventually periodic linear discrete-time system. We derive a necessary and su4cient analysis condition for checking open-loop stability and performance of such systems, and use this to derive exact controller synthesis conditions given eventually periodic plants. All the conditions derived are provided in terms of semi-de9nite programming problems. The...

To deal with the problem of insufficient labeled data, usually side information – given in the form of pairwise equivalence constraints between points – is used to discover groups within data. However, existing methods using side information typically fail in cases with high-dimensional spaces. In this paper, we address the problem of learning from side information for high-dimensional data. To...

To save the labeling efforts for training a classification model, we can simultaneously adopt Active Learning (AL) to select the most informative samples for human labeling, and Semi-supervised Learning (SSL) to construct effective classifiers using a few labeled samples and a large number of unlabeled samples. Recently, using Transfer Learning (TL) to enhance AL and SSL, i.e., T-SS-AL, has gai...