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Easton, PA, United States

Lafayette College is a private coeducational liberal arts and engineering college located in Easton, Pennsylvania, USA. The school, founded in 1826 by James Madison Porter, son of General Andrew Porter of Norristown and the citizens of Easton, first began holding classes in 1832. The founders voted to name the school after General Lafayette, who famously toured the country in 1824–25, as "a testimony of respect for talents, virtues, and signal services... in the great cause of freedom".Located on College Hill in Easton, the campus is situated in the Lehigh Valley, about 70 mi west of New York City and 60 mi north of Philadelphia. Lafayette College guarantees campus housing to all enrolled students. The school requires students to live in campus housing unless approved for residing in private off-campus housing or home as a commuter.The student body, consisting entirely of undergraduates, comes from 42 U.S. states and 37 countries. Students at Lafayette are involved in over 250 clubs and organizations including athletics, fraternities and sororities, special interest groups, community service clubs and honor societies. Lafayette College's athletic program is notable for The Rivalry with nearby Lehigh University. Since 1884, the two football teams have met 150 times, making it the most played rivalry in the history of college football. Wikipedia.

Sherma J.,Lafayette College
Central European Journal of Chemistry | Year: 2014

The most important advances in planar chromatography published between November 1, 2011 and November 1, 2013 are reviewed in this paper. Included are an introduction to the current status of the field; student experiments, books, and reviews; theory and fundamental studies; apparatus and techniques for sample preparation and TLC separations (sample application and plate development with the mobile phase); detection and identification of separated zones (chemical and biological detection, TLC/mass spectrometry, and TLC coupled with other spectrometric methods); techniques and instruments for quantitative analysis; preparative layer chromatography; and thin layer radiochromatography. Numerous applications to a great number of compound types and sample matrices are presented in all sections of the review. © 2014 Versita Warsaw and Springer-Verlag Wien. Source

Traldi L.,Lafayette College
Combinatorics Probability and Computing | Year: 2010

The interlace polynomials introduced by Arratia, Bollobs and Sorkin extend to invariants of graphs with vertex weights, and these weighted interlace polynomials have several novel properties. One novel property is a version of the fundamental three-term formula q(G)=q(G-a)+q(Gab-b)+((x-1)^ 2-1)q(Gab-a-b) that lacks the last term. It follows that interlace polynomial computations can be represented by binary trees rather than mixed binary-ternary trees. Binary computation trees provide a description of q(G) that is analogous to the activities description of the Tutte polynomial. If G is a tree or forest then these algorithmic activities are associated with a certain kind of independent set in G. Three other novel properties are weighted pendant-twin reductions, which involve removing certain kinds of vertices from a graph and adjusting the weights of the remaining vertices in such a way that the interlace polynomials are unchanged. These reductions allow for smaller computation trees as they eliminate some branches. If a graph can be completely analysed using pendant-twin reductions, then its interlace polynomial can be calculated in polynomial time. An intuitively pleasing property is that graphs which can be constructed through graph substitutions have vertex-weighted interlace polynomials which can be obtained through algebraic substitutions. © 2009 Cambridge University Press. Source

Traldi L.,Lafayette College
European Journal of Combinatorics | Year: 2011

A theorem of Cohn and Lempel [M. Cohn, A. Lempel, Cycle decomposition by disjoint transpositions, J. Combin. Theory Ser. A 13 (1972) 83-89] gives an equality relating the number of circuits in a directed circuit partition of a 2-in, 2-out digraph to the GF(2)-nullity of an associated matrix. This equality is essentially equivalent to the relationship between directed circuit partitions of 2-in, 2-out digraphs and vertex-nullity interlace polynomials of interlace graphs. We present an extension of the Cohn-Lempel equality that describes arbitrary circuit partitions in (undirected) 4-regular graphs. The extended equality incorporates topological results that have been of use in knot theory, and it implies that if H is obtained from an interlace graph by attaching loops at some vertices then the vertex-nullity interlace polynomial qN(H) is essentially the generating function for certain circuit partitions of an associated 4-regular graph. © 2011 Elsevier Ltd. Source

Traldi L.,Lafayette College
Journal of Combinatorial Theory. Series B | Year: 2013

The generating function that records the sizes of directed circuit partitions of a connected 2-in, 2-out digraph D can be determined from the interlacement graph of D with respect to a directed Euler circuit; the same is true of the generating functions for other kinds of circuit partitions. The interlace polynomials of Arratia, Bollobás and Sorkin [R. Arratia, B. Bollobás, G.B. Sorkin, The interlace polynomial of a graph, J. Combin. Theory Ser. B 92 (2004) 199-233; R. Arratia, B. Bollobás, G.B. Sorkin, A two-variable interlace polynomial, Combinatorica 24 (2004) 567-584] extend the corresponding functions from interlacement graphs to arbitrary graphs. We introduce a multivariate interlace polynomial that is an analogous extension of a multivariate generating function for undirected circuit partitions of undirected 4-regular graphs. The multivariate polynomial incorporates several different interlace polynomials that have been studied by different authors, and its properties include invariance under a refined version of local complementation and a simple recursive definition. © 2012 Elsevier Inc. Source

Xia G.,Lafayette College
SIAM Journal on Computing | Year: 2013

Let S be a finite set of points in the Euclid ean plane. Let D be a Delaunay triangulation of S. The stretch factor (also known as dilation or spanning ratio) of D is the maximum ratio, among all points p and q in S, of the shortest path distance fromp to q in D over the Euclidean distance ||pq||. Proving a tight bound on the stretch factor of the Delaunay triangulation has been a long-standing open problem in computational geometry. In this paper we prove that the stretch factor of the Delaunay triangulation is less than p = 1.998, significantly improving the current best upper bound of 2.42 by Keil and Gutwin ["The Delaunay triangulation closely approximates the complete Euclidean graph," in Proceedings of the 1st Workshop on Algorithms and Data Structures (WADS), 1989, pp. 47-56]. Our bound of 1.998 also improves the upper bound of the best stretch factor that can be achieved by a plane spanner of a Euclidean graph (the current best upper bound is 2). Our result has a direct impact on the problem of constructing spanners of Euclidean graphs, which has applications in the area of wireless computing. © 2013 Society for Industrial and Applied Mathematics. Source

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