STRUCTURAL AND FUNCTIONAL STUDIES ON GABAA RECEPTOR SUBTYPES: A COMPUTATIONAL PATHWAY FOR DESIGNING NOVEL NON-SEDATIVE MODULATORS

In this stressful era, maintaining the proper balance of neuronal excitation and inhibition remains the central demand of human brain. To harmonize the optimal brain functioning, γ-Amino Butyric Acid type A Receptors (GABAA-Rs) play a vital role by mediating the fast inhibitory neurotransmissions. These GABA-gated chloride ion channels maintain the delicate balance between neuronal excitation and inhibition. The formation of GABAA-R uses repertoire of 19 different subunit subtypes α1-6, β1-3, γ1-3, δ, ε, π, θ and ρ1-3, out of which two α1, two β2 and one γ2 form the most abundant native GABAA-R structure. In the absence of heteropentameric human GABAA-R structure the structural biology remains yet to be fully explored. Manipulation of GABAergic transmission is aimed to provide the benefits in the treatment of a host of neurological and psychiatric disorders. We utilised the existing experimental data and carried out a computational study to obtain the structural details of different GABAA-Rs. This computational pathway sequentially proceeds for : i) obtaining the different GABAA-R states and subtypes; ii) understanding the logic of their existence and correlating structure-function details for each of them; iii) unravelling the complete journey of molecular events that fine tune the state dependent channel transitions in normal conditions including ligand unoccupied closed, open, uncapped receptive states and GABA occupied singly and doubly bound states; iv) understanding the nature of cross-talk between two orthosteric sites and third allosteric BZD-site when we brought it into consideration; v) identifying a set of governing rules/markers forming the structural basis of selective modulation for BZD-site agonists at α1- and α2-GABAA-R subtypes. Accordingly, to fulfil the deliberate demand of clinically efficacious α2-selective non-sedative modulator/s the underlying logic is systematically demarcated under single platform. The crux from the early stage modulatory pathways of subtype selective actions provides newer avenues to guide the designing of novel modulator/s having desired pharmacological endpoints in diseased states. Overall, this channelled study is bound to track the structure-function-novel drug designing, based on the understanding of GABAA-R modulatory pathways

Long Term Contracting in a Changing World

I study the properties of optimal long-term contracts in an environment in which the agent’s type evolves stochastically over time. The model stylizes a buyer-seller relationship but the results apply quite naturally to many contractual situations including regulation and optimal income-taxation. I …first show, through a simple discrete example, that distortions need not vanish over time and need not be monotonic in the shock to the buyer’s valuation. These results are in contrast to those obtained in the literature that assumes a Markov process with a binary state space e.g. Battaglini, 2005. I then show that the study of the dynamics of the optimal mechanism can be significantly simplified by assuming the shocks are independent over time. When the sets of possible types in any two adjacent periods satisfy a certain overlapping condition (which is always satisfied with a continuum of types) and some additional regularity conditions hold, then the optimal mechanism is the same irrespective of whether the shocks are the buyer’s private information or are observed also by the seller. These conditions are satisfied, for example, in the case of an AR(1) process, a Brownian motion, but also when shocks have a multiplicative effect as it is often the case in financial applications. Furthermore, the distortions in the optimal quantities are independent of the distributions of the shocks and, when the buyer’s payoff is additively separable, they are also independent of whether the shocks are transitory or permanent. Finally, I show that assuming the shocks are independent not only does it greatly simplify the analysis, it is actually without loss of generality.asymmetric information, stochastic process, dynamic mechanism design, long-term contracting

Long-Term Contracting in a Changing World

I study the properties of optimal long-term contracts in an environment in which the agents type evolves stochastically over time. The model stylizes a buyer-seller relationship but the results apply quite naturally to many contractual situations including regulation and optimal income-taxation. I …rst show, through a simple example, that distortions need not vanish over time and need not be monotonic in the shock to the buyers valuation. These results are in contrast to those obtained in the literature that assumes a Markov process with a binary state space e.g. Battaglini, 2005. I then show that when the sets of possible types in any two adja- cent periods satisfy a certain overlapping condition (which is always satis…ed with a continuum of types), then the dynamics of the optimal mechanism can be signi…cantly simpli…ed by as- suming the shocks are independent over time. Under certain regularity conditions, the optimal mechanism is then the same irrespective of whether the shocks are the buyers private informa- tion or are observed also by the seller. These conditions are satis…ed, for example, in the case of an AR(1) process, a Brownian motion, but also when shocks have a multiplicative e¤ect as it is often the case in …nancial applications. Furthermore, the distortions in the optimal quantities are independent of the distributions of the shocks and, when the buyers valuation is additively separable, they are also independent of whether the shocks are transitory or permanent. Finally, I show that assuming the shocks are independent not only greatly simpli…es the analysis but is actually without loss of generality with a continuum of types.asymmetric information, stochastic process, dynamic mechanism design, long-term contracting

Doppler sodar observations of the winds and structure in the lower atmosphere over Fairbanks, Alaska

Thesis (M.S.) University of Alaska Fairbanks, 2007Fairbanks, Alaska (64°49ʹ N, 147°52ʹ W) experiences strong temperature inversions which when combined with the low wind speeds prevailing during the winter cause serious air pollution problems. The SODAR (Sound Detection And Ranging) or acoustic sounder is a very useful instrument for studying the lower atmosphere as it can continuously and reliably measure the vertical profiles of wind speed and direction,vertical motions, turbulence and the thermal structure in the lower part of the troposphere. A Doppler sodar was operated from December 2005 to April 2006 at the National Weather Service site in Fairbanks. The wind observations from the sodar indicate that the majority of the winds during the winter months were from the North, Northeast or the East, which is in good agreement with the radiosonde measurements and the long term trends in the wind patterns over Fairbanks area. Case studies were carried out using the sodar data depicting drainage winds, low-level jets, formation and breakup of inversions and estimation of the mixing layer height.1. Introduction -- 1.1. Climatic features in Fairbanks during winter -- 1.1.1. Temperature inversions -- 1.1.2. Valley winds and drainage winds -- 1.1.3. Urban heat island -- 1.1.4. Air pollution and ice fog -- 1.2. SODAR and its applications -- 1.2.1 Acoustic sounder observations at Fairbanks in the past -- 2. Theory and instrumentation 2.1. Estimation of Ct² -- 2.1.1. Scattering theory -- 2.1.2. Sodar equation -- 2.2. Wind speed and direction -- 2.3. Sodar installation and data acquisition -- 2..4. Sodar dataset and additional sources of data -- 2.5. Algorithm to detect strong layers of temperature inversion -- 3. Results and discussion -- 3.1. Results from the inversion detection algorithm -- 3.1.1. Diurnal variations in inversion characteristics -- 3.1.2. Effect of cloud cover on inversion characteristics -- 3.2. Wind observations from sodar data -- 3.3. Case studies from sodar observations -- 3.3.1. Drainage winds overflowing the stable layer of air beneath -- 3.3.2. Nocturnal jet associated with a temperature inversion -- 3.3.3. Destruction of an inversion due to forced mixing and increasing cloud cover -- 3.3.4. Estimation of the mixing layer height from the backscatter intensity -- 4. Conclusions and future work -- References

Learning Invariant Riemannian Geometric Representations Using Deep Nets

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric constraints can be expressed in the language of Riemannian geometry, where conventional vector space machine learning does not apply directly. The central question this paper deals with is: How does one train deep neural nets whose final outputs are elements on a Riemannian manifold? To answer this, we propose a general framework for manifold-aware training of deep neural networks -- we utilize tangent spaces and exponential maps in order to convert the proposed problem into a form that allows us to bring current advances in deep learning to bear upon this problem. We describe two specific applications to demonstrate this approach: prediction of probability distributions for multi-class image classification, and prediction of illumination-invariant subspaces from a single face-image via regression on the Grassmannian. These applications show the generality of the proposed framework, and result in improved performance over baselines that ignore the geometry of the output space. In addition to solving this specific problem, we believe this paper opens new lines of enquiry centered on the implications of Riemannian geometry on deep architectures.Comment: Accepted at International Conference on Computer Vision Workshop (ICCVW), 2017 on Manifold Learning: from Euclid to Rieman

Control of flexible joint robotic manipulator using tuning functions design

The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified