Optimal quantization for infinite nonhomogeneous distributions on the real line

Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, an infinitely generated nonhomogeneous Borel probability measure $P$ is considered on $\mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th quantization error for every natural number $n$ is given. In addition, using the induction formula we give some results and observations about the optimal sets of $n$-means for all $n\geq 2$.Comment: arXiv admin note: text overlap with arXiv:1512.0037

Classification of Large-Scale Fundus Image Data Sets: A Cloud-Computing Framework

Large medical image data sets with high dimensionality require substantial amount of computation time for data creation and data processing. This paper presents a novel generalized method that finds optimal image-based feature sets that reduce computational time complexity while maximizing overall classification accuracy for detection of diabetic retinopathy (DR). First, region-based and pixel-based features are extracted from fundus images for classification of DR lesions and vessel-like structures. Next, feature ranking strategies are used to distinguish the optimal classification feature sets. DR lesion and vessel classification accuracies are computed using the boosted decision tree and decision forest classifiers in the Microsoft Azure Machine Learning Studio platform, respectively. For images from the DIARETDB1 data set, 40 of its highest-ranked features are used to classify four DR lesion types with an average classification accuracy of 90.1% in 792 seconds. Also, for classification of red lesion regions and hemorrhages from microaneurysms, accuracies of 85% and 72% are observed, respectively. For images from STARE data set, 40 high-ranked features can classify minor blood vessels with an accuracy of 83.5% in 326 seconds. Such cloud-based fundus image analysis systems can significantly enhance the borderline classification performances in automated screening systems.Comment: 4 pages, 6 figures, [Submitted], 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society 201

Holographic charge transport in non commutative gauge theories

In this paper, based on the holographic techniques, we explore the hydrodynamics of charge diffusion phenomena in non commutative $\mathcal{N}=4$ SYM plasma at strong coupling. In our analysis, we compute the $R$ charge diffusion rates both along commutative as well as the non commutative coordinates of the brane. It turns out that unlike the case for the shear viscosity, the DC conductivity along the non commutative direction of the brane differs significantly from that of its cousin corresponding to the commutative direction of the brane. Such a discrepancy however smoothly goes away in the limit of the vanishing non commutativity.Comment: Latex, 11 pages, Version to appear in JHE

Magnetoconductivity in chiral Lifshitz hydrodynamics

In this paper, based on the principles of linear response theory, we compute the longitudinal DC conductivity associated with Lifshitz like fixed points in the presence of chiral anomalies in ($3+1$) dimensions. In our analysis, apart from having the usual anomalous contributions due to chiral anomaly, we observe an additional and pure \textit{parity odd} effect to the magnetoconductivity which has its origin in the broken Lorentz (boost) invariance at a Lifshitz fixed point. We also device a holographic set up in order to compute ($z=2$) Lifshitz contributions to the magnetoconductivity precisely at strong coupling and low charge density limit.Comment: Minor clarifications added, Version To Appear In JHE

Boolean Computation Using Self-Sustaining Nonlinear Oscillators

Self-sustaining nonlinear oscillators of practically any type can function as latches and registers if Boolean logic states are represented physically as the phase of oscillatory signals. Combinational operations on such phase-encoded logic signals can be implemented using arithmetic negation and addition followed by amplitude limiting. With these, general-purpose Boolean computation using a wide variety of natural and engineered oscillators becomes potentially possible. Such phase-encoded logic shows promise for energy efficient computing. It also has inherent noise immunity advantages over traditional level-based logic.Comment: Added a section on energy-efficiency and speed using high-Q harmonic oscillators. Other minor update