Color superconductivity of QCD at finite density, temperature and flavor asymmetry is studied within an approximation which the interaction is modeled upon four–fermion interactions. We calculate the thermodynamic potential in the socalled NJL-type model and study the phase structure at finite density, temperature and flavor asymmetry. We find that a mixed phase appears at sufficiently large fl...

For a simple connected graph G with n-vertices having Laplacian eigenvalues μ1, μ2, . . . , μn−1, μn = 0, and signless Laplacian eigenvalues q1, q2, . . . , qn, the Laplacian-energy-like invariant(LEL) and the incidence energy (IE) of a graph G are respectively defined as LEL(G) = ∑n−1 i=1 √ μi and IE(G) = ∑n i=1 √ qi. In this paper, we obtain some sharp lower and upper bounds for the Laplacian...

The last two lectures focused on the algorithms and analysis of spectral clustering for Gaussian mixtures in the isotropic case, in which the i-th Gaussian has the distribution Xi ∼ N (μi, σ i I). Note that the covariance matrix is simply a multiple of the identity matrix, so each Gaussian is distributed spherically, as depicted in figure 11.1. Recall that in this case, we reduced dimension by ...

Consider the problem of sampling sequentially from a finite number of N > 2 populations, specified by random variables X i k, i = 1, . . . ,N, and k = 1,2, . . .; where X i k denotes the outcome from population i the k th time it is sampled. It is assumed that for each fixed i, {X i k}k>1 is a sequence of i.i.d. normal random variables, with unknown mean μi and unknown variance σ2 i . The objec...

We consider an overloaded multi-server multi-class queueing model where customers may abandon while waiting to be served. For class i, service is provided at rate μi , and abandonment occurs at rate θi . In a many-server fluid regime, we show that prioritizing the classes in decreasing order of ciμi/θi asymptotically minimizes an ergodic holding cost, where ci denotes the equivalent holding cos...