Data-driven decision making has drawn scrutiny from policy makers due to fears of potential discrimination, and a growing literature begun develop fair statistical techniques. However, these techniques are often specialized one model context based on ad hoc arguments, which makes it difficult perform theoretical analysis. This paper develops an optimization hierarchy, is sequence problems with ...

Curcumin is an herbal plant with great therapeutic applications. Although it is useful in treating several diseases, its low solubility in water and low bioavailability in living systems are limiting factors in using curcumin as a medicine. One way to overcome these shortcomings is the production of curcumin micro/nano particles. In this research, the particles of curcumin loaded with polycapro...

We consider optimization problems whose parameters are known only approximately, based on noisy samples. Of particular interest is the high-dimensional regime, where the number of samples is roughly equal to the dimensionality of the problem, and the noise magnitude may greatly exceed the magnitude of the signal itself. This setup falls far outside the traditional scope of Robust and Stochastic...

In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the presentation I will describe in details only the problems related to the coloring of a random graph.

As IC technologies scale to finer feature sizes, it becomes increasingly difficult to control the relative process variations. The increasing fluctuations in manufacturing processes have introduced unavoidable and significant uncertainty in circuit performance; hence ensuring manufacturability has been identified as one of the top priorities of today’s IC design problems. In this paper, we revi...

This work emerged from the following observation: usual search procedures for octrees start from the root to retrieve the data stored at the leaves. But since the leaves are the farthest nodes to the root, why start from the root? With usual octree representations, there is no other way to access a leaf. However, hashed octrees allow direct access to any node, given its position in space and it...

Learning problems, such as logistic regression, are typically formulated as pure optimization problems defined on some loss function. We argue that this view ignores the fact that the loss function depends on stochastically generated data which in turn determines an intrinsic scale of precision for statistical estimation. By considering the statistical properties of the update variables used du...