Adsorption assisted translocation of a chain molecule through a pore in a spherical vesicle

We analyze the free energy for translocation of a polymer from the outside of a spherical vesicle to the inside. The process is assumed to be driven by the adsorption of the polymer on the inner surface of the vesicle. We argue that in the case where the polymer is adsorbed on the outer surface too, the entropic barrier for translocation is absent. We analyze the adsorption energy and find the free energy profile for the process. We argue that the motion corresponds to a polymer crossing a region with a change in free energy per segment. Based upon our earlier analsis of the behaviour of kinks in such a problem, we conclude that the translocation can occur with a crossing time $t_{cross}\sim N$

Neuroplasticity of language networks in aphasia: advances, updates, and future challenges

Researchers have sought to understand how language is processed in the brain, how brain damage affects language abilities, and what can be expected during the recovery period since the early 19th century. In this review, we first discuss mechanisms of damage and plasticity in the post-stroke brain, both in the acute and the chronic phase of recovery. We then review factors that are associated with recovery. First, we review organism intrinsic variables such as age, lesion volume and location and structural integrity that influence language recovery. Next, we review organism extrinsic factors such as treatment that influence language recovery. Here, we discuss recent advances in our understanding of language recovery and highlight recent work that emphasizes a network perspective of language recovery. Finally, we propose our interpretation of the principles of neuroplasticity, originally proposed by Kleim and Jones (1) in the context of extant literature in aphasia recovery and rehabilitation. Ultimately, we encourage researchers to propose sophisticated intervention studies that bring us closer to the goal of providing precision treatment for patients with aphasia and a better understanding of the neural mechanisms that underlie successful neuroplasticity.P50 DC012283 - NIDCD NIH HHSPublished versio

Approximation of Entropy Numbers

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction works for a very general class of operators between Banach spaces, in particular reflexive spaces. As a consequence of this technique we also obtain that the entropy number of a bounded linear operator T between two separable Hilbert spaces is equal to the entropy number of the adjoint of T. This gives a complete answer to the question posed by B. Carl [4] in the setting of separable Hilbert spaces.Comment: 10 page

3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction

These are notes of introductory lectures on (a) elements of 2+1 dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein-Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.Comment: 23 pages, Based on talks/lectures by CK at Goteborg, Tehran and Bangkok. v2:acknowledgments and references added, v3:published versio

Strings vs Spins on the Null Orbifold

We study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the $\alpha^\prime\to \infty$ limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.Comment: 27 pages, 5 figures, v2: comments about boundary conditions added, strengthening the conclusio