Learning Mixtures of Gaussians in High Dimensions

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings

Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.Comment: 7 page

Nonlinear Hodge maps

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Various degrees of smoothness are proven for the sonic limit, high-dimensional flow, and flow having nonzero vorticity. The gradient flow of solutions is estimated. Implications for other quasilinear field theories are suggested.Comment: Slightly modified and updated version; tcilatex, 32 page

MeCP2 interacts with HP1 and modulates its heterochromatin association during myogenic differentiation

There is increasing evidence of crosstalk between epigenetic modifications such as histone and DNA methylation, recognized by HP1 and methyl CpG-binding proteins, respectively. We have previously shown that the level of methyl CpG-binding proteins increased dramatically during myogenesis leading to large-scale heterochromatin reorganization. In this work, we show that the level of HP1 isoforms did not change significantly throughout myogenic differentiation but their localization did. In particular, HP1 relocalization to heterochromatin correlated with MeCP2 presence. Using co-immunoprecipitation assays, we found that these heterochromatic factors interact in vivo via the chromo shadow domain of HP1 and the first 55 amino acids of MeCP2. We propose that this dynamic interaction of HP1 and MeCP2 increases their concentration at heterochromatin linking two major gene silencing pathways to stabilize transcriptional repression during differentiation

The dual role of wild phages for the horizontal gene transfer among Salmonella strains

Horizontal gene transfer (e.g. transduction, transformation, conjugation) has a great impact on the evolution of bacteria. Several transducing phages related P22 have been reported, transfering chromosomal as well as plasmid born determinants (Schicklmaier & Schmieger, 1995)

The New ‘Hidden Abode’: Reflections on Value and Labour in the New Economy

In a pivotal section of Capital, volume 1, Marx (1976: 279) notes that, in order to understand the capitalist production of value, we must descend into the ‘hidden abode of production’: the site of the labour process conducted within an employment relationship. In this paper we argue that by remaining wedded to an analysis of labour that is confined to the employment relationship, Labour Process Theory (LPT) has missed a fundamental shift in the location of value production in contemporary capitalism. We examine this shift through the work of Autonomist Marxists like Hardt and Negri, Lazaratto and Arvidsson, who offer theoretical leverage to prize open a new ‘hidden abode’ outside employment, for example in the ‘production of organization’ and in consumption. Although they can open up this new ‘hidden abode’, without LPT's fine-grained analysis of control/resistance, indeterminacy and structured antagonism, these theorists risk succumbing to empirically naive claims about the ‘new economy’. Through developing an expanded conception of a ‘new hidden abode’ of production, the paper demarcates an analytical space in which both LPT and Autonomist Marxism can expand and develop their understanding of labour and value production in today's economy. </jats:p

Global weak solution and large-time behavior for the compressible flow of liquid crystals

The three-dimensional equations for the compressible flow of liquid crystals are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $\gamma>\frac32$

Preparing to work: dramaturgy, cynicism and normative ‘remote’ control in the socialization of graduate recruits in management consulting

online) This paper examines the socialization of graduate recruits into a knowledge intensive labour process and organizational culture. Theoretically the paper draws upon the idea of ‘preparing for work’ to position this early socialization as a crucial moment in the production of subjectivities suited (and booted) for the labour process of management consulting. Empirically the paper reports on a two-day induction session for new graduate recruits joining a global management consultancy and their responses to this training. Particular attention is given to the use of role-play and a dramaturgical workshop used in part of the training process. The paper argues that the utilization of dramaturgy in training is consistent with the overall approach to control developed in the firm in response to the fact that the labour process of consulting is often conducted on client sites, away from any direct supervisory gaze. As such, the consultants were subjected to a form of cultural control that was designed to function independently of direct supervision. This control did not operate directly upon the new employees professed values, however, but at one step removed so that a ‘cynical distance’ from the content of the organization’s culture was accepted so long as a professional ‘ethic of behaviour’ was established. By focusing on an ‘ethic of behaviour’ these young professionals were encouraged to internalize a self-control akin to that of an actor, rather than internalizing the corporate values entirely