The fundamental group of reductive Borel-Serre and Satake compactifications

Let $G$ be an almost simple, simply connected algebraic group defined over a number field $k$, and let $S$ be a finite set of places of $k$ including all infinite places. Let $X$ be the product over $v\in S$ of the symmetric spaces associated to $G(k_v)$, when $v$ is an infinite place, and the Bruhat-Tits buildings associated to $G(k_v)$, when $v$ is a finite place. The main result of this paper is an explicit computation of the fundamental group of the reductive Borel-Serre compactification of $\Gamma\backslash X$, where $\Gamma$ is an $S$-arithmetic subgroup of $G$. In the case that $\Gamma$ is neat, we show that this fundamental group is isomorphic to $\Gamma/E\Gamma$, where $E\Gamma$ is the subgroup generated by the elements of $\Gamma$ belonging to unipotent radicals of $k$-parabolic subgroups. Analogous computations of the fundamental group of the Satake compactifications are made. It is noteworthy that calculations of the congruence subgroup kernel $C(S,G)$ yield similar results.Comment: 21 pages, 1 figure, uses Xy-pic 3.8.6; in version 2, title changed to more accurately reflect main result, expository material on congruence subgroup problem removed, many small corrections and improvements in expositio

Flag structure for operators in the Cowen-Douglas class

The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen-Douglas operators possessing a flag structure. These operators are irreducible. We show that the flag structure is rigid in the sense that the unitary equivalence class of the operator and the flag structure determine each other. We obtain a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the Cowen-Douglas class.Comment: Announcement, 6 page

Impaired neurodevelopmental pathways in autism spectrum disorder: a review of signaling mechanisms and crosstalk.

BackgroundThe development of an autistic brain is a highly complex process as evident from the involvement of various genetic and non-genetic factors in the etiology of the autism spectrum disorder (ASD). Despite being a multifactorial neurodevelopmental disorder, autistic patients display a few key characteristics, such as the impaired social interactions and elevated repetitive behaviors, suggesting the perturbation of specific neuronal circuits resulted from abnormal signaling pathways during brain development in ASD. A comprehensive review for autistic signaling mechanisms and interactions may provide a better understanding of ASD etiology and treatment.Main bodyRecent studies on genetic models and ASD patients with several different mutated genes revealed the dysregulation of several key signaling pathways, such as WNT, BMP, SHH, and retinoic acid (RA) signaling. Although no direct evidence of dysfunctional FGF or TGF-β signaling in ASD has been reported so far, a few examples of indirect evidence can be found. This review article summarizes how various genetic and non-genetic factors which have been reported contributing to ASD interact with WNT, BMP/TGF-β, SHH, FGF, and RA signaling pathways. The autism-associated gene ubiquitin-protein ligase E3A (UBE3A) has been reported to influence WNT, BMP, and RA signaling pathways, suggesting crosstalk between various signaling pathways during autistic brain development. Finally, the article comments on what further studies could be performed to gain deeper insights into the understanding of perturbed signaling pathways in the etiology of ASD.ConclusionThe understanding of mechanisms behind various signaling pathways in the etiology of ASD may help to facilitate the identification of potential therapeutic targets and design of new treatment methods

Centrally endo-AIP Modules

In this paper, we introduce the concept of centrally endo-AIP modules. We call a module M centrally endo-AIP, if the left annihilator of any fully invariant submodule N of M in the endomorphism ring S = End(M) is a centrally s-unital ideal of S. We discuss some properties of centrally endo-AIP modules. We also study the endomorphism ring of centrally endo-AIP modules and characterize quasi-Baer modules in terms of centrally endo-AIP module

Deconstruction of Symbols of Reality in Hindi Cinema: A Study on Calendar Girls and Haider

Hindi cinema has always been a better citation for Indian culture. Now it is an accepted proof for the changing scenarios of modern India. The cinema has shaped and portrayed Indian culture to the extent that the sixth art forms could ever achieve. Hindi cinema has a great influence on common man who sees the different symbols of daily life and culture constructed by cinema as real things present in their day-to-day life. Cinema does not only construct the symbols but also deconstruct it. The present research aims to trace and analyze the construction and deconstruction of different social, economic, and psychological symbols created over a period of time through many block buster films. To check this changing perspective of cinema for the society, two films namely ‘Calendar Girls’ and ‘Haider’ discussed in this paper. The focus of the study is on understanding the portrayal of women in Calendar Girls and terrorism in Haider. Keywords: Deconstruction, representation, reality, symbols, Hindi cinem

Accurate Tracking of Manoeuvring Target using Scale Estimation and Detection

Camera zoom operation and fast approaching/receding target causes scaling of acquired target in video frames. Fast moving target manifests in large inter-frame motion. In general, non-uniform background degrades performance of tracking algorithms. Fast Fourier transform (FFT)-based Correlation algorithms improve tracking in this scenario, but their applications is limited to small inter-frame motion. Increasing search region has implication on execution speed of the algorithms. Rapid target scaling, non-uniform background and large inter-frame motion of target hinder accurate and long term visual tracking. These challenges have been addressed for extended target tracking by augmenting fast discriminative scale space tracking (fDSST) algorithm with probable target location prediction and target detection. Localisation of fast motion has been achieved by applying fused outputs of Kalman filter and quadratic regression based prediction before applying fDSST. It has helped in accurate localisation of fast motion without increasing search region. In each frame, target location and size have been estimated using fDSST and further refined by target detection near this location. Smoothing and limiting of trajectory and size of detected target has enhanced tracking performance. Experimental results show considerable improvement of precision, success rate and centre location error tracking performance against state-of-the-art trackers in stringent conditions