[1] Robert J. Adler, Omer Bobrowski, and Shmuel Weinberger. Crackle: The Homology of Noise. Discrete & Computational Geometry, 52(4):680–704, December 2014. [2] Noga Alon. On the edge-expansion of graphs. Combinatorics, Probability and Computing, 6(02):145–152, 1997. [3] Noga Alon and Joel H. Spencer. The probabilistic method. John Wiley & Sons, 2004. [4] Lior Aronshtam and Nathan Linial. The t...

This talk is based primarily on the paper Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees by Marcus, Spielman, and Srivastava [6]. By proving a variant of a conjecture of Bilu and Linial [1], they show that there exist infinite families of d-regular bipartite Ramanujan graphs for d ≥ 3. Of particular interest in the paper by Marcus, Spielman, and Srivastava is their “method of...

The present thesis consists of three independent parts. In the first part we employ an elementary counting method to study the eigenvalues of the adjacency matrices of some special families of graphs. The main example is provided by the directed graph D(G), constructed by Propp on the vertex set of oriented spanning rooted trees of a given directed graph G. We describe the eigenvalues of D(G) i...

Congen ita l hypomyelinati on neu ro path y is a rare co ndi t ion in a ll spec ies , includ ing human beings. In the ve terina ry lit erature relating to domesti c a ni ma ls, the re is on ly a sing le report , whi ch in vol ved two Golde n Retriever puppies in a litt er o f seven." T he present re po rt is th e fi rst o f a co nge ni ta l hypom yeli nati on ne uropa thy in a lamb. A 2month-o ...

1. D. R. Young, J. N. Johnson, A. Soutar, J. D. Isaacs, Nature (Lond.) 244, 273 (1973); T. J. Chow, K. W. Bruland, K. Bertine, A. Sotitar, M. Koide, E. D. Goldberg, Science 181, 551 (1973). 2. D. H. Klein and E. D. Goldberg, Environ. Sci. Technol. 4, 765 (1970); K. K. Turekian, in Impingement of Man on thle Oceais, D. W. Hood, Ed. (Wiley-Interscience, New York, 1971), p. 9. 3. The Ecology of th...

The cytochemical technique using the in situ precipitation of orthophosphate ions liberated specifically by the aspartate carbamoyltransferase (ATCase) (EC 2 .1 .3 .2) reaction indicated that in Saccharomyces cerevisiae this enzyme is confined to the nucleus. This observation is in accordance with the result reported by Bernhardt and Davis (1972), Proc . Nati . Acad . Sci. U. S. A. 69:1868-1872...

The phase problem of membrane diffraction is usually solved by the swelling method; however, this method does not always resolve the phases unambiguously. An alternative method of phase determination using anomalous dispersion is illustrated by the multiplewavelength diffraction of membranes containing gramicidin ion channels. The anomalously scattering atoms are thallium ions bound to the chan...


 Those words reverberate in our minds as we remember how Dr. Nati Almazan, president of the Philippine Board Otolaryngology- Head and Neck Surgery, bid Jake goodbye on many occasions, also being a member board.
 Jacob Sadang Matubis, colleague, brother Mu Sigma Phi fraternity, batchmate during residency Otolaryngology-Head Surgery at University Philippines-Philippine General Hospital...

Given a monotone graph property P consider p P the proba bility that a random graph with edge probability p will have P The function d p P dp is the key to understanding the threshold behavior of the property P We show that if d p P dp is small corresponding to a non sharp threshold then there is a list of graphs of bounded size such that P can be approximated by the property of having one of t...

1. 0. Diels and K. Alder, Justus Liebigs Ann. Chem. 460, 98 (1928); 0. Diels, J. H. Blom, W. Koll, ibid. 443, 242 (1925); B. M. Trost, I. Fleming, L. A. Paquette, Comprehensive Organic Synthesis (Pergamon, Oxford, 1991), vol. 5, pp. 316; F. Friguelli and A. Tatichi, Dienes in the Diels-Alder Reaction (Wiley, New York, 1990), and references therein; W. Carruthers, Cycloaddition Reactions in Orga...