Cayley graphs generated by small degree polynomials over finite fields

We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields

Holomorphic Koszul-Brylinski Homology

In this note, we study the Koszul-Brylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on Koszul-Brylinski homology is nondegenerate. Finally we compute the Koszul-Brylinski homology for Poisson structures on \CP^1\times\CP^1.Comment: 14 page

Old tales, untold : Lu Xun against world literature

World literature has smiled on Lu Xun 魯迅. He stands, if not as the foremost, then as a major representative of modern Chinese literature in anthologies. Though anthologies are not the ultimate arbiters of literary worldliness, they are influential discursive sites because of their accessibility and classroom utility. To wit, he is a common figure on university syllabi in world literature surveys. Professionally, scholarship on Lu Xun’s work reaches far beyond disciplinary Chinese studies. His works have been translated and retranslated many times in less than a century. All this is perhaps fitting considering his extraordinary services rendered to world literature as a reader and translator. Following David Damrosch’s (2003) provisional definition of world literature as circulation beyond a national origin (281), Lu Xun enabled dozens of works to circulate in Chinese, and in turn his works circulate beyond the Sinosphere. But not all of them. If, following Franco Moretti (2013), we were to look at world literature as a market, a work’s circulation has to do with the demands of readers as much as with its innate qualities (69-70). These demands reflect geopolitical realities, to be sure, but can also constitute an apologetics for them

Labeling and purification studies on cancer targeting DOTA-TATE labeled with radiolanthanides

Abstract only availableMolecular imaging and targeted radiotherapy are emerging fields for cancer treatment. DOTA-Tyr (3)-Thr(9)-octreotate (DOTA-TATE) is used for peptide receptor-mediated radionuclide therapy (PRMRT) in neuroendocrine tumours. These biomolecules can be radiolabeled with an appropriated radioisotope to produce radiopharmaceuticals for diagnostic and therapeutic applications. The DOTA-TATE molecule is comprised of a bifunctional chelate (DOTA) that is capable of stably binding a radiolanthanide as well as being covalently attached to a targeting biomolecule (e.g.,octreotate). Among the radiolanthanides, Ho-166, Tb-161 and Lu-177, that were used to label the peptide, Lu-177 was used to obtain optimum conditions. Direct neutron capture on Lu-176 produces Lu-177. The indirect production of Lu-177 proceeds by neutron capture on Yb-176 producing Yb-177, which beta decays to Lu-177. Chromatographic separation yields high specific activity Lu-177 that minimizes the presence of cold Lu-176. Lanthanides have similar chemical properties that allow further studies to apply similar conditions as those developed for Lu-177. In addition, longevity of half-life of Lu-177 enables longer periods of dose delivery to targeted tumors. This research focused on identifying appropriate buffer solutions and volumes that could neutralize the acidic radioisotope to appropriate pH levels to label the peptide in high yield. The sample was purified from the unlabeled peptide by using HPLC separations methods and adding stabilizing agents (ascorbic and gentisic acid) to prevent radiolysis of the radiolabeled peptide. The results for the labeled peptide with various radioisotopes shows that 0.4 M NH4OAc, 0.4 M NaOAc, and 0.01 M HEPES buffer solution in 500 µL yields 99% labeling at pH ranging from 6.0 to 7.5. The labeled ligand at equimolar ratio with the metal yields 3 mCi/µg of the ligand, whereas as high specific activity sample can label up to 6.68 mCi/µg of the ligand. Carrier free Lu-177-DOTA-TATE was labeled using 0.01 M HEPES buffer at pH 6.0 and remains stable after using ascorbic acid; gentisic acid shows interference on HPLC which may cause some purification problems. (Ho- holmium, Tb- terbium Lu- lutetium)U.S. Dept. of Energy Innovations in Nuclear Infrastructure and Education Summer MURR Undergraduate Research Scholarshi

On the sigma-model structure of type IIA supergravity action in doubled field approach

In this letter we describe how to string together the doubled field approach by Cremmer, Julia, Lu and Pope with Pasti-Sorokin-Tonin technique to construct the sigma-model-like action for type IIA supergravity. The relation of the results with that of obtained in the context of searching for Superstring/M-theory hidden symmetry group is discussed.Comment: 9 pp, LATEX; published in JETP Let

A Scalable Null Model for Directed Graphs Matching All Degree Distributions: In, Out, and Reciprocal

Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null model to compare algorithms or perform experimental studies. Furthermore, there are scalable algorithms that implement these models and they are invaluable in the study of graphs. However, networks in the real-world are often directed, and have a significant proportion of reciprocal edges. A stronger relation exists between two nodes when they each point to one another (reciprocal edge) as compared to when only one points to the other (one-way edge). Despite their importance, reciprocal edges have been disregarded by most directed graph models. We propose a null model for directed graphs inspired by the Chung-Lu model that matches the in-, out-, and reciprocal-degree distributions of the real graphs. Our algorithm is scalable and requires $O(m)$ random numbers to generate a graph with $m$ edges. We perform a series of experiments on real datasets and compare with existing graph models.Comment: Camera ready version for IEEE Workshop on Network Science; fixed some typos in tabl