We present an algorithm for learning the intersection of half-spaces in n dimensions. Over nearly-uniform distributions, it runs in polynomial time for up to O(log n= log log n) half-spaces or, more generally , for any number of half-spaces whose normal vectors lie in an O(log n= log log n) dimensional subspace. Over less restricted \non-concentrated" distributions it runs in polynomial time fo...

1Southern Illinois University Nutrition Department, Carbondale, IL, USA; Department of Nutrition, School of Public Health and Health Sciences, University of Massachusetts, Amherst, MA, USA (Former Affiliation Universities where part of the USDA/NIFA funded work on sensory nutrition education with exotic fruits and vegetables, was completed) 2Department of Computer Science, Southern Illinois Uni...

These are abridged lecture notes from the Spring 2017 course offering of “Principles of Data Analytics” that I offer at Iowa State University annually. This graduate level course offers an introduction to a variety of data analysis techniques, particularly those relevant for electrical and computer engineers, from an algorithmic perspective. Topics include techniques for classification, visuali...

It is well known that search SVP is equivalent to optimization SVP. However, the former reduction from search SVP to optimization SVP by Kannan needs polynomial times calls to the oracle that solves the optimization SVP. In this paper, a new rank-preserving reduction is presented with only one call to the optimization SVP oracle. It is obvious that the new reduction needs the least calls, and i...

The 125th anniversary of the birth of Srinivasa Ramanujan was on December 22, 2012. To mark the occasion, the Notices is publishing a feature article of which this is the second and final installment. This installment contains pieces by Ken Ono, Kannan Soundararajan, Robert Vaughan, and Ole Warnaar on various aspects of Ramanujan’s work. The first installment appeared in the December 2012 issue...

We prove that integer programming with three alternating quantifiers is NPcomplete, even for a fixed number of variables. This complements earlier results by Lenstra and Kannan, which together say that integer programming with at most two alternating quantifiers can be done in polynomial time for a fixed number of variables. As a byproduct of the proof, we show that for two polytopes P,Q ⊂ R, c...

In this paper we present fixed point results for generalized α-ψ-contractive type mappings in dislocated metric spaces. We also provide some examples to illustrate our results. References 1. Banach S., “Surles operations dans les ensembles abstraites et leurs applications”, Fund. Math., 3 (1922), 133-187. 2. Kannan R., “Some results on fixed points”, Bull. Cal. Math. Soc., 60 (1968), 71-76. 3. ...

that fluid type rather than rate had a greater effect on sodium concentration even though the pre-admission fluids received by the patients were not recorded. Kannan, et al. [5], in their randomized controlled trial demonstrated that incidence of hyponatremia was reduced in the group receiving 0.9% saline in 5% dextrose at standard maintenance volume. Similar observations were reported by Coult...

In this paper we study the t-branch split cuts introduced by Li and Richard (2008). They presented a family of mixed-integer programs with n integer variables and a single continuous variable and conjectured that the convex hull of integer solutions for any n has unbounded rank with respect to (n−1)-branch split cuts. It was shown earlier by Cook, Kannan and Schrijver (1990) that this conjectur...