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Mahmood A.,University of Punjab | Khan S.,LUMS
IEEE Transactions on Image Processing | Year: 2010

Elimination Algorithms are often used in template matching to provide a significant speed-up by skipping portions of the computation while guaranteeing the same best-match location as exhaustive search. In this work, we develop elimination algorithms for correlation-based match measures by exploiting the transitivity of correlation. We show that transitive bounds can result in a high computational speed-up if strong autocorrelation is present in the dataset. Generally strong intrareference local autocorrelation is found in natural images, strong inter-reference autocorrelation is found if objects are to be tracked across consecutive video frames and strong intertemplate autocorrelation is found if consecutive video frames are to be matched with a reference image. For each of these cases, the transitive bounds can be adapted to result in an efficient elimination algorithm. The proposed elimination algorithms are exact, that is, they guarantee to yield the same peak location as exhaustive search over the entire solution space. While the speed-up obtained is data dependent, we show empirical results of up to an order of magnitude faster computation as compared to the currently used efficient algorithms on a variety of datasets. © 2006 IEEE.

Hussain N.,King Abdulaziz University | Shah M.H.,LUMS
Computers and Mathematics with Applications | Year: 2011

In this paper we establish some topological properties of the cone b-metric spaces and then improve some recent results about KKM mappings in the setting of a cone b-metric space. We also prove some fixed point existence results for multivalued mappings defined on such spaces. © 2011 Elsevier Ltd. All rights reserved.

Naz R.,Lahore School of Economics | Naeem I.,LUMS | Mahomed F.M.,University of Witwatersrand
Mathematical Problems in Engineering | Year: 2011

We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators. © 2011 R. Naz et al.

Brkic Z.,Erasmus University Rotterdam | Maria N.I.,Erasmus University Rotterdam | Van Helden-Meeuwsen C.G.,Erasmus University Rotterdam | Van De Merwe J.P.,Erasmus University Rotterdam | And 6 more authors.
Annals of the Rheumatic Diseases | Year: 2013

Objective To determine the prevalence of upregulation of interferon (IFN) type I inducible genes, the so called "IFN type I signature", in CD14 monocytes in 69 patients with primary Sjögren's syndrome (pSS) and 44 healthy controls (HC) and correlate it with disease manifestations and expression of B cell activating factor (BAFF). Methods Expression of IFI44L, IFI44, IFIT3, LY6E and MX1 was measured using real time quantitative PCR in monocytes. Expression values were used to calculate IFN type I scores for each subject. pSS patients positive for the IFN type I signature (IFN score≥10) and patients negative for the signature (IFN score<10) were then compared for clinical disease manifestations and BAFF expression. A bioassay using a monocytic cell line was performed to study whether BAFF mRNA expression was inducible by IFN type I activity in serum of patients with pSS. Results An IFN type I signature was present in 55% of patients with pSS compared with 4.5% of HC. Patients with the IFN type I signature showed: (a) higher EULAR Sjögren's Syndrome Disease Activity Index scores; higher anti-Ro52, anti-Ro60 and anti-La autoantibodies; higher rheumatoid factor; higher serum IgG; lower C3, lower absolute lymphocyte and neutrophil counts; (b)higher BAFF gene expression in monocytes. In addition, serum of signature-positive patients induced BAFF gene expression in monocytes. Conclusions The monocyte IFN type I signature identifies a subgroup of patients with pSS with a higher clinical disease activity together with higher BAFF mRNA expression. Such patients might benefit from treatment blocking IFN type I production or activity.

Basit A.,LUMS | Mustafa N.H.,LUMS | Ray S.,Ecole Polytechnique Federale de Lausanne | Raza S.,LUMS
Discrete and Computational Geometry | Year: 2010

The so-called first selection lemma states the following: given any set P of n points in ℝd, there exists a point in ℝd contained in at least cdnd+1-O(nd) simplices spanned by P, where the constant cd depends on d. We present improved bounds on the first selection lemma in ℝ3. In particular, we prove that c3≥0. 00227, improving the previous best result of c3≥0. 00162 by Wagner (On k-sets and applications. Ph. D. thesis, ETH Zurich, 2003). This makes progress, for the three-dimensional case, on the open problems of Bukh et al. (Stabbing simplices by points and flats. Discrete Comput. Geom., 2010) (where it is proven that c3≤1/44≈0. 00390) and Boros and Füredi (The number of triangles covering the center of an n-set. Geom. Dedic. 17(1):69-77, 1984) (where the two-dimensional case was settled). © 2010 Springer Science+Business Media, LLC.

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