Surface modeling and rendering with line segments

Master'sMASTER OF SCIENC

Improved Decoding of Expander Codes

We study the classical expander codes, introduced by Sipser and Spielman [M. Sipser and D. A. Spielman, 1996]. Given any constants 0 < ?, ? < 1/2, and an arbitrary bipartite graph with N vertices on the left, M < N vertices on the right, and left degree D such that any left subset S of size at most ? N has at least (1-?)|S|D neighbors, we show that the corresponding linear code given by parity checks on the right has distance at least roughly {? N}/{2 ?}. This is strictly better than the best known previous result of 2(1-?) ? N [Madhu Sudan, 2000; Viderman, 2013] whenever ? < 1/2, and improves the previous result significantly when ? is small. Furthermore, we show that this distance is tight in general, thus providing a complete characterization of the distance of general expander codes. Next, we provide several efficient decoding algorithms, which vastly improve previous results in terms of the fraction of errors corrected, whenever ? < 1/4. Finally, we also give a bound on the list-decoding radius of general expander codes, which beats the classical Johnson bound in certain situations (e.g., when the graph is almost regular and the code has a high rate). Our techniques exploit novel combinatorial properties of bipartite expander graphs. In particular, we establish a new size-expansion tradeoff, which may be of independent interests

Complex phase diagram and supercritical matter

Supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquid-like and gas-like, however, indicate their should-be different belongings. Here, we provide a mathematical description of these phenomena by revisiting the Lee-Yang (LY) theory and using a complex phase diagram, e.g. a 4-D one with complex $T$ and $p$. Beyond the critical point, the 2-D phase diagram with real $T$ and $p$, i.e. the physical plane, is free of LY zeros and hence no criticality emerges. But off-plane zeros in this 4-D scenario still come into play by inducing critical anomalies for different physical properties. This is evidenced by the correlation between the Widom lines and LY edges in van der Waals model and water. The present distinct criteria to distinguish the supercritical matter manifest the high-dimensional feature of the phase diagram: e.g. when the LY zeros of complex $T$ or $p$ are projected onto the physical plane, a boundary defined by isobaric heat capacity $C_p$ or adiabatic compression coefficient $K_T$ emanates. These results demonstrate the incipient phase transition nature of the supercritical matter

Polypropylene based anion exchange fiber for enrichment and determination of trace indium by GFAAS

Indium was enriched and separated by a new polypropylene based anion exchange fiber before determined by graphite furnace atomic absorption spectrometry (GFAAS). Indium can be enriched quantitatively by 0.1 g of fiber at the flow rate within 6 mL·min-1 in the pH 4 and can be desorbed quantitatively with 10 mL of 1.0 M nitric acid from the fiber column. The fibers were soaked in 2 M sodium hydroxide sodium hydroxide solution for activation and were washed with distilled water at least thirty times until neutral for regeneration, The saturated capacity of the fiber for In(III) was 1.32 mg·g-1. The activation energy (Ea) of the fiber adsorption In(III) was 89.3 kJ·mol-1. The method was used to enrich trace In(III) in artificial samples solution and zinc concentrate solution before determination. The method detection limit was 0.08 ng·mL-1, the recoveries were 96.8-101%, and the relative standard deviations (RSD) were 0.1-2.1%. KEY WORDS: Anion exchange fiber, Separation, Enrichment, Indium, GFAAS Bull. Chem. Soc. Ethiop. 2011, 25(2), 295-298