We consider the problem of learning mixtures of distributions via spectral methods and derive a tight characterization of when such methods are useful. Specifically, given a mixture-sample, let μi, Ci, wi denote the empirical mean, covariance matrix, and mixing weight of the i-th component. We prove that a very simple algorithm, namely spectral projection followed by single-linkage clustering, ...

QCD at finite isospin chemical potential μI is studied. This theory has no fermion sign problem and can be simulated on the lattice using present-day techniques. We solve this theory analytically in two limits: low μI where chiral perturbation theory is applicable, and asymptotically high μI where perturbative QCD is at work. At low isospin density the ground state is a superfluid pion condensa...

We present a generalized discontinuous Galerkin method for a multicomponent compressible barotropic Navier-Stokes system of equations. The system presented has a functional viscosity ν which depends on the pressure p = p(ρ, μi) of the flow, with the density ρ and the local concentration μi. High order Runge-Kutta time discretization techniques are employed, and different methods of dealing with...

In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions. In this note we study a fair division problem. Fair divisions problems are sometimes called cake cutting problems. These kinds of problems appear when we study division of land, time or computer memory between different agents with different ...

The states ρi, i = 1, 2 in the state space S of a C-algebra A are absolutely continuous if and only if there exist absolutely continuous probability measures μi on S such that ρi is the barycenter of μi. This technique allows one to study the transformation of conditional expectations under an absolutely continuous change of state using the classical Bayes formula, which can be exploited to obt...

Given three n-tuples {λi}i=1, {μi}i=1, {νi}i=1 of complex numbers, we introduce the problem of when there exists a pair of normal matrices A and B such that σ(A) = {λi}i=1, σ(B) = {μi}i=1, and σ(A+B) = {νi}i=1, where σ(·) denote the spectrum. In the case when λk = 0, k = 2, . . . , n, we provide necessary and sufficient conditions for the existence of A and B. In addition, we show that the solu...

A new analysis and new Molecular Dynamics (MD) simulations of the measurements of the mobility μi of O − 2 ions in dense supercritical Ar gas are reported. μi shows a marked dependence on the distance from the critical temperature Tc. A mobility defect appears as a function of the gas density and its maximum value occurs below the critical density. The locus of points of maximum mobility defect...

Let A and B be bounded linear operators acting on a Hilbert space H. It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense that sup{‖U∗AU + V ∗BV ‖ : U and V are unitaries} = min{‖A+ μI‖+ ‖B − μI‖ : μ ∈ C}. Consequences of the result related to spectral sets, the von Neumann inequality, and normal dilations a...

We note that the inequality expressed by Eq. 4 is consistent with experimental observation (Fig. S1). The inequality in Eq. 4 implies that Ωexp increases with the difference in chemical potentials, i.e. μfi −μi, between the two geometries. Conversely, it means that if the guiding is negligible, then attaching a voltage probe at c would not impact the chemical potential at i i.e. μfi ≈ μi. Howev...

We consider the problem of Bose condensation of charged pions in QCD at finite isospin chemical potential μI using the O(4)-symmetric linear sigma model as an effective field theory for twoflavor QCD. Using the 2PI 1/N-expansion, we determine the quasiparticle masses as well as the pion and chiral condensates as a function of the temperature and isospin chemical potential in the chiral limit an...