Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted I$\alpha$), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative $\alpha$-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative $\alpha$-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum R{\'{e}}nyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I$\alpha$-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I$\alpha$-projection is studied.

Department of Mathematics

World University root node

Fulltext

IEEE Transactions on Information Theory

Minimization problems based on relative $\alpha$-entropy I: Forward projection

Department of Physics

Applied Physics Letters

Electronic transport in graphene-based heterostructures

There are many aspects of urban transportation that represent sources of uncertainty in the design of roadways, such as the level of capacity needed to ensure efficient traffic flow. As a result of uncertainty in roadway capacity, an urban road network can be deemed to operate at different capacity levels. Some of these levels will have unused capacity, whereas some others will not be enough to cater traffic from all origins to all destinations. Past models assume knowledge over the pattern of these uncertainties. However, it is difficult to gather such knowledge from field observations, and it is absent for majority of the world's urban areas. We present an alternative methodology in which the capacities are considered as variables that can take any value from zero to a practically realizable maximum. Using a minimax optimization formulation, we determine bounds on urban roadway capacity levels, below which the traffic demand will go unmet. We call this the critical state, and define it as a state of link capacities which effects in the maximum irreducible operational cost on the network with the demand getting fulfilled. We prove that at a critical state, the total travel time (or cost) of the system will be a unique value; i.e. for a given urban road network and a given traffic demand, there is an associated unique critical travel time. We illustrate that this unique travel time-which is an aggregate value of the travel times from all roads on the network-can be used as a benchmark to create various metrics for the urban road network. As an illustrative example on the applicability of critical state, we compare the unique travel time with the best possible travel time on the network, and develop a metric for network resilience. Network resilience is calculated as a normalized difference of the critical and best operation costs. Two-space genetic algorithm is used to solve the problem formulation. The formulation and the solution methodology are illustrated on test networks and results are presented. © 2015 Elsevier Ltd.

Department of Civil Engineering

Computers, Environment and Urban Systems

Capacity uncertainty on urban road networks: A critical state and its applicability in resilience quantification

Hilbert functions and Hilbert polynomials of Zs-graded admissible filtrations of ideals {F(n)}n∈Zs such that λ(R/F(n)) is finite for all n∈Zs are studied. Conditions are provided for the Hilbert function HF(n):=λ(R/F(n)) and the corresponding Hilbert polynomial PF(n) to be equal for all n∈Ns. A formula for the difference HF(n)-PF(n) in terms of local cohomology of the extended Rees algebra of F is proved which is used to obtain sufficient linear relations analogous to the ones given by Huneke and Ooishi among coefficients of PF(n) so that HF(n)=PF(n) for all n∈Ns. A theorem of Rees about joint reductions of the filtration {IrJs}r,s∈Z is generalised for admissible filtrations of ideals in two-dimensional Cohen-Macaulay local rings. Necessary and sufficient conditions are provided for the multi-Rees algebra of an admissible Z2-graded filtration F to be Cohen-Macaulay. © 2015 Elsevier Inc.

Journal of Algebra

Hilbert polynomials of multigraded filtrations of ideals

Rigidity And Regularity Of Holomorphic Mappings

In this paper, we develop a new HOC based immersed interface scheme in cylindrical polar coordinates for solving viscous, incompressible, laminar flow past a circular cylinder. This new scheme is developed by clubbing the recently developed higher order compact (HOC) methodology with with special interface treatment for the points just next to the points of discontinuity. Non uniform grid in polar coordinates (r, $\theta$) is used for the discretization, where the surface of the cylinder is considered as an interface immersed in the fluid. Streamfunction-Vorticity formulation of Navier-Stokes equation in cylindrical polar coordinates is considered with an assumption that solution inside the immersed boundary is zero. Quantitative and qualitative results are shown for various values of Reynolds number Re ≤ 100 and an excellent agreement with existing numerical and experimental results is found in each case.

Procedia Engineering

An HOC Based Immersed Interface Scheme for Uniform Flow Past a Circular Cylinder

Department of Mechanical Engineering

Mechanical Engineering Graduate Research Symposium (MEGRES 2015)

Steady state wall heat flux distribution for impinging laminar methane-air flame jet

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z⊆Y⊆X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proximinal subspace Y of X is strongly proximinal in X if and only if Y⊥⊥ is strongly proximinal in X**. We also prove that in an abstract L1-space, the notions of strongly subdifferentiable points and quasi-polyhedral points coincide. We also give an example to show that M-ideals need not be ball proximinal. Moreover, we prove that in an L1-predual space, M-ideals are ball proximinal. © 2015 Elsevier Inc.

Journal of Mathematical Analysis and Applications

Strong proximinality and intersection properties of balls in Banach spaces

This paper addresses the inverse dynamics of three degrees of freedom (DOF) U-shaped planar parallel manipulator having three legs consisting of prismatic-prismatic-revolute (PPR) joint arrangement in which each leg has one active prismatic joint. This paper also proposes a proportional-derivative (PD) like adaptive sliding mode control combined with a disturbance observer for the motion control of the proposed manipulator. Using this control scheme, the controlled robotic manipulator is transformed into decoupled dynamics, and thus the motion performance is very convenient to quantify. Based on Lyapunov like argument the global asymptotic stability of the proposed closed loop system is proved. Real time experiments performed on the in-house fabricated prototype of the proposed manipulator are provided to substantiate the effectiveness and the improved performance of the proposed controller. The proposed controller performances are also compared with traditional controllers such as proportional integral derivative (PID) controller, sliding mode controller (SMC) and computed torque controller (CTC) © 2015 Elsevier Ltd.

Robotics and Computer-Integrated Manufacturing

Inverse dynamics and control of a 3-DOF planar parallel (U-shaped 3-PPR) manipulator

This article investigates a new robust nonlinear proportional integral derivative (PID) position tracking control applied on a serial underwater spatial manipulator with three degrees of freedom. The proposed controller integrates the known approximated inverse dynamic model output as a model-base portion of the controller. It uses a feed forward term to enhance the control activity with indulgence from known desired acceleration vector. The proposed control scheme carries an estimated perturbed term to compensate for the unknown effects namely external disturbances and unmodelled dynamics. Finally, it has a decoupled nonlinear PID controller as a feedback portion to enhance closed-loop stability and account for the estimation error of uncertainties. The usefulness and competency of the proposed approach are demonstrated with the help of numerical simulations. © 2015 IEEE.