Exponentially Accurate Approximations to Periodic Lipschitz Functions Based on Fourier Series Partial Sums

The problem of accurately reconstructing a piecewise smooth. 2-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. The locations of the singularities are approximated to within O(N ^–M–2), and the associated jump of the kth derivative of f is approximated to within O(N ^–M–1+k ), as N , and the method is robust. These estimates are then used with a class of singular basis functions, which have certain built-in singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M . The technique is illustrated with several examples.     

A self-configurable large-scale virtual manufacturing environment for collaborative designers

As manufacturing environments are getting distributed and increasing in size, the related virtual environments are getting larger and more closely networked together. This trend has led to a new paradigm—large-scale virtual manufacturing environment (LSVME). It supports networked and distributed virtual manufacturing to meet manufacturing system requirements. Since it contains a large number of virtual components, an effective data structure and collaborative construction methodology are needed. A metaearth architecture is proposed as the data structure for representing LSVME. This architecture consists of virtual space layer, mapping layer, library layer and ontology layers, which describe interaction among virtual components and has the ability to analyze the characteristics of virtual environment. In addition, it increases reusability of virtual components and supports self-reconfiguration for manufacturing simulation. A heuristic construction method based on graph theory is proposed using this architecture. It prevents redundant design of virtual components and contributes to an effective construction scheduling technique for collaborative designers.     

Architectural design and FPGA implementation of radix-4 CORDIC processor

A new scaled radix-4 CORDIC architecture that incorporates pipelining and parallelism is presented. The latency of the architecture is n/2 clock cycles and throughput rate is one valid result per n/2 clocks for n bit precision. A 16 bit radix-4 CORDIC architecture is implemented on the available FPGA platform. The corresponding latency of the architecture is eight clock cycles and throughput rate is one valid result per eight clock cycles. The entire scaled architecture operates at 56.96 MHz of clock rate with a power consumption of 380 mW. The speed can be enhanced with the upgraded version of FPGA device. A speed-area optimized processor is obtained through this architecture and is suitable for real time applications.     

Inventory model for seasonal demand with option to change the market

In real life, when bulk purchase becomes convenient or even mandatory, it is a common practice for distributors to explore an alternative market in order to maximize the revenue earned. In this paper, we consider an inventory model for a product having seasonal demand with two potential markets, say, primary and alternate. The distributor has a single opportunity of procurement prior to multiple demand seasons in the primary and the alternate market. Both the markets have similar demand patterns, with time lag between their demand seasons. The demand is a price and time dependent function with increasing, constant and declining phases within each demand season. The scale parameter of demand rate depends upon the market. In each market, successive seasons are separated by random time. In one replenishment cycle, the distributor has a single option to exit the primary market by transferring the inventory, with or without change in selling price. This option can be exercised at the end of any complete season at the primary market. Our investigations indicate that it will be beneficial for the distributor to shift to the alternate market even at a slightly lower selling price if demand rate in the alternate market is higher. Optimal number of seasons at the primary market before change of price or market is obtained. Optimal policy is obtained for jointly determining the order quantity and price. Concavity of the profit function is discussed. Solution procedure, numerical examples and sensitivity analysis are presented.     

A general framework for efficient geographic routing in wireless networks

We propose a new link metric called normalized advance (NADV) for geographic routing in multihop wireless networks. NADV selects neighbors with the optimal trade-off between proximity and link cost. Coupled with the local next hop decision in geographic routing, NADV enables an adaptive and efficient cost-aware routing strategy. Depending on the objective or message priority, applications can use the NADV framework to minimize various types of link cost.We present efficient methods for link cost estimation and perform detailed experiments in simulated environments. Our results show that NADV outperforms current schemes in many aspects: for example, in high noise environments with frequent packet losses, the use of NADV leads to 81% higher delivery ratio. When compared to centralized routing under certain settings, geographic routing using NADV finds paths whose cost is close to the optimum. We also conducted experiments in Emulab testbed and the results demonstrate that our proposed approach performs well in practice.     

Differential regulation of redox proteins and chaperones in HbEβ-thalassemia erythrocyte proteome

Purpose: In (hemoglobin, Hb) HbEβ‐thalassemia, HbE (β‐26 Glu→Lys) interacts with β‐thalassemia to produce clinical manifestation of varying severity. This is the first proteomic effort to study changes in protein levels of erythrocytes isolated from HbEβ‐thalassemic patients compared to normal. Experimental design: We have used 2‐DE and MALDI‐MS/MS‐based techniques to investigate the differential proteome profiling of membrane and Hb‐depleted fraction of cytosolic proteins of erythrocytes isolated from the peripheral blood samples of HbEβ‐thalassemia patients and normal volunteers. Results: Our study showed that redox regulators such as peroxiredoxin 2, Cu‐Zn superoxide dismutase and thioredoxin and chaperones such as α‐hemoglobin stabilizing protein and HSP‐70 were upregulated in HbEβ‐thalassemia. We have also observed larger amounts of membrane associated globin chains and indications of disruption of spectrin‐based junctional complex in the membrane skeleton of HbEβ‐thalassemic erythrocytes upon detection of low molecular weight fragments of β‐spectrin and decrease in β‐actin and dematin content. Conclusion and clinical relevance: We have observed interesting changes in the proteomic levels of redox regulators and chaperons in the thalassemic hemolysates and have observed strong correlation or association of the extent of such proteomic changes with HbE levels. This could be important in understanding the role of HbE in disease progression and pathophysiology.     

Effect of numerical integration on meshless methods

In this paper, we present the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k1. The meshless method was used on a second order Neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of numerical integration. This estimate was obtained under the assumption that the numerical integration scheme satisfied a form of Green’s formula. We also indicated how to obtain numerical integration schemes satisfying this property.     

Semantics-driven annotation of patient-specific 3D data: a step to assist diagnosis and treatment of rheumatoid arthritis

In the digital era, patient-specific 3D models (3D-PSMs) are becoming increasingly relevant in computer-assisted diagnosis, surgery training on digital models, or implant design. While advanced imaging and reconstruction techniques can create accurate and detailed 3D models of patients’ anatomy, software tools that are able to fully exploit the potential of 3D-PSMs are still far from being satisfactory. In particular, there is still a lack of integrated approaches for extracting, coding, sharing and retrieving medically relevant information from 3D-PSMs and use it concretely as a support to diagnosis and treatment. In this article, we propose the SemAnatomy3D framework, which demonstrates how the ontology-driven annotation of 3D-PSMs and of their anatomically relevant features (parts of relevance) can assist clinicians to document more effectively pathologies and their evolution. We exemplify the idea in the context of the diagnosis of rheumatoid arthritis of the hand district, and show how feature extraction tools and semantic 3D annotation can provide a rich characterization of anatomical landmarks (e.g., articular facets, prominent features, ligament attachments) and pathological markers (erosions, bone loss). The core contributions are an ontology-driven part-based annotation method for the 3D-PSMs and a novel automatic localization of erosion and quantification of the OMERACT RAMRIS erosion score. Finally, our results have been compared against a medical ground truth.     

Experimental realization of quantum cheque using a five-qubit quantum computer

Quantum cheques could be a forgery-free way to make transaction in a quantum networked banking system with perfect security against any no-signalling adversary. Here, we demonstrate the implementation of quantum cheque, proposed by Moulick and Panigrahi (Quantum Inf Process 15:2475–2486, 2016), using the five-qubit IBM quantum computer. Appropriate single qubit, CNOT and Fredkin gates are used in an optimized configuration. The accuracy of implementation is checked and verified through quantum state tomography by comparing results from the theoretical and experimental density matrices.