We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community “noise” (inter-community edges) on any “community detection” algorithm’s ability to correctly group nodes assigned to a planted partition, a problem which has been proven to be NP complete in a standard rendition...

A data distribution scheme of sparse arrays on a distributed memory multicomputer, in general, is composed of three phases, data partition, data distribution, and data compression. In the data partition phase, a global sparse array is partitioned into some local sparse arrays. In the data distribution phase, these local sparse arrays are distributed to processors. In the data compression phase,...

Liquid-liquid equilibrium (LLE) occurs at a subzero temperature for the acetonitrilewater binary system.When the equilibrium temperature is below its LLE critical temperature of 1.32 C, the top phase is acetonitrile-rich and the bottom phase water-rich. It was observed that a human growth hormone analog with 191 amino acids partitioned exclusively into the bottom phase and its bioactivity was r...

Occupants of former methamphetamine laboratories, often residences, may experience increased exposure through the accumulation of the methamphetamine in the organic films that coat skin and indoor surfaces. The objectives of this study were to determine equilibrium partition coefficients of vapor-phase methamphetamine with artificial sebum (AS-1), artificial sebum without fatty acids (AS-2), an...

Casein hydrolysis was carried out in PEG-dextran two-phase system by using a-chymotrypsin immobilized on a water soluble polymer Eudragit S-100. This biocatalyst along with the substrate casein was predominantly found to partition into the PEG phase. Under these optimized conditions, the product was found to partition (84%) in the dextran phase. Removal of dextran phase at an appropriate time i...

A quantizer for complex data is defined by a partition of the complex plane and a representation point associated with each cell of the partition. A polar coordinate quantizer independently quantizes the magnitude and phase angle of complex data. We derive design equations for minimum mean-squared error polar coordinate quantizers and report some interesting theoretical results on their perform...

We consider the Sine-Gordon model coupled to 2D gravity. We find a nonperturbative expression for the partition function as a function of the cosmological constant, the SG mass and the SG coupling constant. At genus zero, the partition function exhibits singularities which are interpreted as signals of phase transitions. A semiclassical picture of one of these transitions is proposed. According...