Bound on the graviton mass from Chandra X-ray cluster sample

We present new limits on the graviton mass using a sample of 12 relaxed galaxy clusters, for which temperature and gas density profiles were derived by Vikhlinin et al (astro-ph/0507092) using Chandra X-ray observations. These limits can be converted to a bound on the graviton mass, assuming a non-zero graviton mass would lead to a Yukawa potential at these scales. For this purpose, we first calculate the total dynamical mass from the hydrostatic equilibrium equation in Yukawa gravity and then compare it with the corresponding mass in Newtonian gravity. We calculate a 90 % c.l. lower/upper limit on the graviton Compton wavelength/ mass for each of the 12 clusters in the sample. The best limit is obtained for Abell 2390, corresponding to $\lambda_g > 3.58\times 10^{19}$ km or $m_g<3.46 \times 10^{-29}$ eV. This is the first proof of principles demonstration of setting a limit on the graviton mass using a sample of related galaxy clusters with X-ray measurements and can be easily applied to upcoming X-ray surveys such as eRosita.Comment: 6 pages, 1 figur

A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement

A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PI{\lambda}D{\mu}) controller have been approximated in this paper vis-\`a-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PI{\lambda}D{\mu} controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as "M-curve". This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller's effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.Comment: 23 pages, 7 figures, in press; Communications in Nonlinear Science and Numerical Simulations, 201

Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PI{\lambda}D{\mu} Controllers to Handle a Class of Fractional Order Systems

A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique that minimizes the change in trajectories of the state variables and the control signal. A class of fractional order systems having single non-integer order element which show highly sluggish and oscillatory open loop responses have been tuned with an LQR based FOPID controller. The proposed controller design methodology is compared with the existing time domain optimal tuning techniques with respect to change in the trajectory of state variables, tracking performance for change in set-point, magnitude of control signal and also the capability of load disturbance suppression. A real coded genetic algorithm (GA) has been used for the optimal choice of weighting matrices while designing the quadratic regulator by minimizing the time domain integral performance index. Credible simulation studies have been presented to justify the proposition.Comment: 6 pages, 5 figure

Privacy-Preserving Secret Shared Computations using MapReduce

Data outsourcing allows data owners to keep their data at \emph{untrusted} clouds that do not ensure the privacy of data and/or computations. One useful framework for fault-tolerant data processing in a distributed fashion is MapReduce, which was developed for \emph{trusted} private clouds. This paper presents algorithms for data outsourcing based on Shamir's secret-sharing scheme and for executing privacy-preserving SQL queries such as count, selection including range selection, projection, and join while using MapReduce as an underlying programming model. Our proposed algorithms prevent an adversary from knowing the database or the query while also preventing output-size and access-pattern attacks. Interestingly, our algorithms do not involve the database owner, which only creates and distributes secret-shares once, in answering any query, and hence, the database owner also cannot learn the query. Logically and experimentally, we evaluate the efficiency of the algorithms on the following parameters: (\textit{i}) the number of communication rounds (between a user and a server), (\textit{ii}) the total amount of bit flow (between a user and a server), and (\textit{iii}) the computational load at the user and the server.\BComment: IEEE Transactions on Dependable and Secure Computing, Accepted 01 Aug. 201

Estimation, Analysis and Smoothing of Self-Similar Network Induced Delays in Feedback Control of Nuclear Reactors

This paper analyzes a nuclear reactor power signal that suffers from network induced random delays in the shared data network while being fed-back to the Reactor Regulating System (RRS). A detailed study is carried out to investigate the self similarity of random delay dynamics due to the network traffic in shared medium. The fractionality or selfsimilarity in the network induced delay that corrupts the measured power signal coming from Self Powered Neutron Detectors (SPND) is estimated and analyzed. As any fractional order randomness is intrinsically different from conventional Gaussian kind of randomness, these delay dynamics need to be handled efficiently, before reaching the controller within the RRS. An attempt has been made to minimize the effect of the randomness in the reactor power transient data with few classes of smoothing filters. The performance measure of the smoothers with fractional order noise consideration is also investigated into.Comment: 6 pages, 6 figure