Visualizing probabilistic models: Intensive Principal Component Analysis

Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in high-dimensions. Inspired by replica theory from statistical mechanics, we consider replicas of the system to tune the dimensionality and take the limit as the number of replicas goes to zero. The result is the intensive embedding, which is not only isometric (preserving local distances) but allows global structure to be more transparently visualized. We develop the Intensive Principal Component Analysis (InPCA) and demonstrate clear improvements in visualizations of the Ising model of magnetic spins, a neural network, and the dark energy cold dark matter ({\Lambda}CDM) model as applied to the Cosmic Microwave Background.Comment: 6 pages, 5 figure

Soft singularity and the fundamental length

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordstr\"om singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.Comment: 5 page

Post-transcriptional regulation of satellite cell quiescence by TTP-mediated mRNA decay.

Skeletal muscle satellite cells in their niche are quiescent and upon muscle injury, exit quiescence, proliferate to repair muscle tissue, and self-renew to replenish the satellite cell population. To understand the mechanisms involved in maintaining satellite cell quiescence, we identified gene transcripts that were differentially expressed during satellite cell activation following muscle injury. Transcripts encoding RNA binding proteins were among the most significantly changed and included the mRNA decay factor Tristetraprolin. Tristetraprolin promotes the decay of MyoD mRNA, which encodes a transcriptional regulator of myogenic commitment, via binding to the MyoD mRNA 3' untranslated region. Upon satellite cell activation, p38α/β MAPK phosphorylates MAPKAP2 and inactivates Tristetraprolin, stabilizing MyoD mRNA. Satellite cell specific knockdown of Tristetraprolin precociously activates satellite cells in vivo, enabling MyoD accumulation, differentiation and cell fusion into myofibers. Regulation of mRNAs by Tristetraprolin appears to function as one of several critical post-transcriptional regulatory mechanisms controlling satellite cell homeostasis

An Exact Solution for Static Scalar Fields Coupled to Gravity in (2+1)(2+1)-Dimensions

We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.Comment: 9 pages. Replaced by a revised versio

Geroch--Kinnersley--Chitre group for Dilaton--Axion Gravity

Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the matrix--valued $SL(2,R)$ formulation and effectively reduces the construction of the Geroch group to the corresponding problem for the vacuum Einstein equations. An infinite hierarchy of potentials is introduced in terms of $2\times 2$ real symmetric matrices generalizing the scalar hierarchy of Kinnersley--Chitre known for the vacuum Einstein equations.Comment: Published in ``Quantum Field Theory under the Influence of External Conditions'', M. Bordag (Ed.) (Proc. of the International Workshop, Leipzig, Germany, 18--22 September 1995), B.G. Teubner Verlagsgessellschaft, Stuttgart--Leipzig, 1996, pp. 228-23

Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder

The effect of a weak three-dimensional (3d) isotropic laser speckle disorder on various thermodynamic properties of a dilute Bose gas is considered at zero temperature. First, we summarize the derivation of the autocorrelation function of laser speckles in 1d and 2d following the seminal work of Goodman. The goal of this discussion is to show that a Gaussian approximation of this function, proposed in some recent papers, is inconsistent with the general background of laser speckle theory. Then we propose a possible experimental realization for an isotropic 3d laser speckle potential and derive its corresponding autocorrelation function. Using a Fourier transform of that function, we calculate both condensate depletion and sound velocity of a Bose-Einstein condensate as disorder ensemble averages of such a weak laser speckle potential within a perturbative solution of the Gross-Pitaevskii equation. By doing so, we reproduce the expression of the normalfluid density obtained earlier within the treatment of Landau. This physically transparent derivation shows that condensate particles, which are scattered by disorder, form a gas of quasiparticles which is responsible for the normalfluid component

Environmental Exposure and Health Effects Associated with Malathion Toxicity

Malathion (O,O-dimethyl-S-1,2-bis ethoxy carbonyl ethyl phosphorodithionate) is a non-systemic, wide-spectrum pesticide. It is widely used throughout the world for agricultural, residential, and public health purposes, mainly to enhance food production and to provide protection from disease vectors. Malathion preference over other organophosphate pesticides relates to its low persistence in the environment as it is highly susceptible to hydrolysis, photolysis, and biodegradation. However, numerous malathion poisoning incidents including acute and chronic cases have been reported among pesticide workers and small children through accidental exposure. Malathion toxicity is compounded by its reactive metabolites and also depends upon the product purity, route of exposure, nutritional status, and gender of exposed individuals. Its metabolic oxidation in mammals, insects, and plants leads to the formation of malaoxon which appears to be several times more acutely toxic and represents the primary cause of malathion’s toxicity. Depending on the level of exposure, several signs and symptoms of toxicity including numbness, tingling sensation, headache, dizziness, difficulty breathing, weakness, irritation of skin, exacerbation of asthma, abdominal cramps, and death have been reported. Similar to other organophosphate pesticides, malathion exerts it toxic action by binding to acetylcholinesterase enzyme and inhibiting its activity, leading to accumulation of acetylcholine in synaptic junctions, which in turn results in overstimulation of cholinergic, muscarinic, and nicotinic receptors, and subsequent induction of adverse biologic effects. This chapter provides an update and analysis of the production and use, environmental occurrence, molecular mechanisms of toxicity, genotoxicity and carcinogenicity, and adverse human health effects associated with malathion exposure