Black Hole Geometries in Noncommutative String Theory

We obtain a generalized Schwarzschild (GS-) and a generalized Reissner-Nordstrom (GRN-) black hole geometries in (3+1)-dimensions, in a noncommutative string theory. In particular, we consider an effective theory of gravity on a curved $D_3$-brane in presence of an electromagnetic (EM-) field. Two different length scales, inherent in its noncommutative counter-part, are exploited to obtain a theory of effective gravity coupled to an U(1) noncommutative gauge theory to all orders in $\Theta$. It is shown that the GRN-black hole geometry, in the Planckian regime, reduces to the GS-black hole. However in the classical regime it may be seen to govern both Reissner-Nordstrom and Schwarzschild geometries independently. The emerging notion of 2D black holes evident in the frame-work are analyzed. It is argued that the $D$-string in the theory may be described by the near horizon 2D black hole geometry, in the gravity decoupling limit. Finally, our analysis explains the nature of the effective force derived from the nonlinear EM-field and accounts for the Hawking radiation phenomenon in the formalism.Comment: 30 pages, 2 figure

The Generalised Raychaudhuri Equations : Examples

Specific examples of the generalized Raychaudhuri Equations for the evolution of deformations along families of $D$ dimensional surfaces embedded in a background $N$ dimensional spacetime are discussed. These include string worldsheets embedded in four dimensional spacetimes and two dimensional timelike hypersurfaces in a three dimensional curved background. The issue of focussing of families of surfaces is introduced and analysed in some detail.Comment: 8 pages (Revtex, Twocolumn format). Corrected(see section on string worldsheets), reorganised and shortened slightl

Collaborative Uploading in Heterogeneous Networks: Optimal and Adaptive Strategies

Collaborative uploading describes a type of crowdsourcing scenario in networked environments where a device utilizes multiple paths over neighboring devices to upload content to a centralized processing entity such as a cloud service. Intermediate devices may aggregate and preprocess this data stream. Such scenarios arise in the composition and aggregation of information, e.g., from smartphones or sensors. We use a queuing theoretic description of the collaborative uploading scenario, capturing the ability to split data into chunks that are then transmitted over multiple paths, and finally merged at the destination. We analyze replication and allocation strategies that control the mapping of data to paths and provide closed-form expressions that pinpoint the optimal strategy given a description of the paths' service distributions. Finally, we provide an online path-aware adaptation of the allocation strategy that uses statistical inference to sequentially minimize the expected waiting time for the uploaded data. Numerical results show the effectiveness of the adaptive approach compared to the proportional allocation and a variant of the join-the-shortest-queue allocation, especially for bursty path conditions.Comment: 15 pages, 11 figures, extended version of a conference paper accepted for publication in the Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), 201

Path integrals and wavepacket evolution for damped mechanical systems

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational field with linearly or quadratically damped motion. In each case, we study the evolution of Gaussian wavepackets and discuss the characteristic features that help us distinguish between different types of damping. For quadratic damping, we show that the action and equation of motion of such a system has a connection with the zero dimensional version of a currently popular scalar field theory. Furthermore we demonstrate that the equation of motion (for quadratic damping) can be identified as a geodesic equation in a fictitious two-dimensional space.Comment: 15 pages, 6 figure

Development of attentional processes in ADHD and normal children

Attention Deficit Hyperactivity Disorder (ADHD) is a developmental disorder. Typical development of attentional processes is rapid during early childhood. ADHD results in impairment in response inhibition, error monitoring, attentional disengagement, executive attention, and delay aversion and may effect the ongoing development of these processes during childhood. We examined the development of attentional processes in children with ADHD and normal children. Two hundred forty children (120 in each group) in the age range of 6–9 years participated in the study. Four tasks: Stop-Signal, attentional disengagement, attention network, and choice delay task were administered. Stop signal reaction time, switch costs, conflict effect, and percentage choice of short delay reward was higher in ADHD group compared to normal group. Post error of slowing was less in ADHD children. Endogenous orienting effect was more in normal children compared to ADHD children. Different developmental trajectories were observed for control functions in normal children. Major development in response inhibition occurred in 7–8 years, error monitoring in 6–9 years, and attentional disengagement in 7–9 years. Late development in alerting network was observed in normal children at age 9 years. No developmental changes occurred on these control functions in ADHD children aged 6–9 years. Age related changes were observed on delay aversion between 6 and 9 years in normal children, while it changed between 6 and 7 years in ADHD children. Performance was not changed on orienting and conflict attentional networks in both the children except conflict effect reduced between 7 and 9 years in ADHD children under double cue condition. Conflict network was interacted with the alerting and orienting network in normal children; specifically conflict network interacted with the orienting network in younger children (age 6 years) and with alerting network in older children (age 9 years). In ADHD group interaction between alerting and conflict network was observed only in the double cue condition. Together these results indicated that the deficits in control processes accumulate with age in ADHD children Present study favors the conceptual view of ADHD as a stable deficit in cognitive control functions, which are implicated in the pathology of ADHD. These results have theoretical implication for the theories of executive control and ADHD

Interpretative Bias: Indicators of Cognitive Vulnerability to Depression

Objectives: The study aimed at testing the existence of interpretative bias in remitted depressives as compared to unipolar depressives and never-depressed individuals. Method: Cognitive Bias Questionnaire was administered on 10 individuals each with unipolar depression, remitted depression, and never-depressed participants. Participants were presented with vague and ambiguous vignettes of potentially problematic situation that individuals often encounter their daily lives. Each vignette is followed by four questions with four response options reflecting a depressed-distorted, depressed-nondistorted, nondepressed-distorted, or nondepressed- nondistorted option. Participants choose the response option that best represents how they would respond to the situation if it actually happened to them. Results: Unipolar depressives interpret their condition as high on depressive mood symptoms as well as distorted thoughts whereas remitted depressives interpret their condition as high on distorted thoughts alone. Conclusions: It may suggest that despite of reduction in level of symptomatic severity of depression, cognitive errors are still maintained during remission, can increase one’s vulnerability for relapse. It implies that management of depression should focus on reducing cognitive vulnerability to depression, rather than only targeting a reduction in the symptoms