The classifying space of a bound quiver

We associate to a bound quiver (Q,I) a CW-complex which we denote by B(Q,I), and call the classifying space of (Q,I). We show that the fundamental group of B(Q,I) is isomorphic to the fundamental group of (Q,I). Moreover, we show that this construction behaves well with respect to coverings. On the other hand, we study the (co)homology groups of B(Q,I), and compare them with the simplicial and the Hochschild (co)homology groups of the algebra A=kQ/I. More precisely, we give sufficient conditions for these groups to be isomorphic. This generalizes a theorem due to Gerstenhaber and Schack.Comment: Revised version. To appear in J. Algebra. 22 pages, 3 postscript figure

Multilevel variance components and brain volume mediation of life stress on post-traumatic stress disorder symptoms in children via regularization

Alterations of volume in brain regions of interest (ROIs) are associated with post-traumatic stress disorder (PTSD). Most of the extant neuroimaging research in PTSD has studied adults. The present study extends this research by using data from children (N=11,869, M age =9.92) from the ABCD study, a multisite longitudinal long-term study of brain development and childhood health in the U.S. Traumatic events (TEs) and PTSD symptoms were measured through the K- SADS for DSM-5. Values of brain ROIs were assessed using structural MRI measures. The unidirectional model was able to detect the small differences from site variance in sMRI mediators (subc: VS\u3c.009, SE\u3c.004; cort: VS\u3c.009, SE\u3c.004). Additive genetic factors explained 23.49% of the variance in TEs, 41.73% in subcortical and 19.94% in cortical mediators, and residual 21.01% in PTSD symptoms. Environmental factors explained most of the variance in TEs (C=.61, E=.16) and PTSD symptoms (resC=.19, resE=.21), as well as unique environmental factors in the cortical mediators (cort=.66). TEs highly influenced PTSD symptoms (.92). However, the indirect effect of TEs on PTSD symptoms through the mediation of volume in brain ROIs was small to non-influential at this age (subc=-.0003-.001, cort=-.001- .002). Several estimates of mediation effects were notably higher than most. Regularization via elastic net is implemented to train the mediation model to reduce bias and noise from overfitting, and to select the ROIs with mediation effects that explain the data with increased sparsity.https://scholarscompass.vcu.edu/gradposters/1102/thumbnail.jp

The attractive nonlinear delta-function potential

We solve the continuous one-dimensional Schr\"{o}dinger equation for the case of an inverted {\em nonlinear} delta-function potential located at the origin, obtaining the bound state in closed form as a function of the nonlinear exponent. The bound state probability profile decays exponentially away from the origin, with a profile width that increases monotonically with the nonlinear exponent, becoming an almost completely extended state when this approaches two. At an exponent value of two, the bound state suffers a discontinuous change to a delta-like profile. Further increase of the exponent increases again the width of the probability profile, although the bound state is proven to be stable only for exponents below two. The transmission of plane waves across the nonlinear delta potential increases monotonically with the nonlinearity exponent and is insensitive to the sign of its opacity.Comment: submitted to Am. J. of Phys., sixteen pages, three figure

The response of Musa cultivar root systems to a tree shade gradient

Poster presented at Tropentag 2011 - Development on the Margin. Bonn (Germany), 3-7 Oct 2011

A two-state kinetic model for the unfolding of single molecules by mechanical force

We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate), and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results (Liphardt, J., et al. (2002) {\em Science}, {\bf 296} 1832-1835). We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within $k_BT$, from non-equilibrium experiments using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, \bar{\Wdis}, to $k_BT$.}Comment: PDF file, 5 page

Force induced stretched state: Effects of temperature

A model of self avoiding walks with suitable constraint has been developed to study the effect of temperature on a single stranded DNA (ssDNA) in the constant force ensemble. Our exact calculations for small chains show that the extension (reaction co-ordinate) may increase or decrease with the temperature depending upon the applied force. The simple model developed here which incorporates semi-microscopic details of base direction provide an explanation of the force induced transitions in ssDNA as observed in experiments.Comment: 5 pages, 8 figures, RevTex