Sharif Digital Repository

Motivated by the bus escape routing problem in printed circuit boards, we revisit the following problem: given a set of n axis-parallel rectangles inside a rectangular region R, find the maximum number of rectangles that can be extended toward the boundary of R, without overlapping each other. We provide an efficient algorithm for solving this problem in O(n2 log3 n log log n) time, improving over the current best O(n3)-time algorithm available for the problem  

We explore the dictionary learning problem for sparse representation when the signals are dependent. In this paper, a first-order Markovian model is considered for dependency of the signals, that has many applications especially in medical signals. It is shown that the considered dependency among the signals can degrade the performance of the existing dictionary learning algorithms. Hence, we propose a method using the Maximum Log-likelihood Estimator (MLE) and the Expectation Minimization (EM) algorithm to learn the dictionary from the signals generated under the first-order Markovian model. Simulation results show the efficiency of the proposed method in comparison with the... 

Data are presented on the solidification of aluminum alloys and their macro segregation behavior. Three alloys with different solidification ranges were prepared in two temperatures. Two types of molds were also prepared by sand and metallic materials. The solidification of Al alloys were studied and the effects of four parameters were determined, including cooling rate, casting temperature, degassing and nucleation effects on solidification and a comparison was conducted to Scheil model performance. Three types of aluminum alloys (Al-12.1%Si, Al-6.9%Si and Al-4.4% Cu) with short, medium and wide solidification ranges were studied and the results showed that degassing, nucleation, increasing... 

Motivated by the bus escape routing problem in printed circuit boards, we study the following rectangle escape problem: given a set S of n axis-aligned rectangles inside an axis-aligned rectangular region R, extend each rectangle in S toward one of the four borders of R so that the maximum density over the region R is minimized. The density of each point p∈R is defined as the number of extended rectangles containing p. We show that the problem is hard to approximate to within a factor better than 3/2 in general. When the optimal density is sufficiently large, we provide a randomized algorithm that achieves an approximation factor of 1+ε with high probability improving over the current best... 

Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For this purpose we use the Bismut local index formula in the context of noncommutative geometry. This paper uses heavily the methods and technical results developed by E. Leichtnam and P. Piazza  

In this paper we show how the higher index theory can be used to prove results concerning the non-existence of a complete Riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods to prove such non-existence theorems  

In this paper we state and prove delocalized Morse type inequalities for Morse functions as well as for closed differential 1-forms. These inequalities involve delocalized Betti numbers. As an immediate consequence, we prove the vanishing of delocalized Betti numbers of manifolds fibering over the circle under a vanishing condition on the delocalizing conjugacy class  

Development of novel engineering techniques that can promote new clinical treatments requires implementing multidisciplinary in-vitro and in-vivo approaches. In this study, we have implemented microfluidic devices and in-vivorat model to study the mechanism of neural stem cell migration and differentiation.These studies can result in the treatment of damages to the neuronal system. In this research, we have shown that by applying appropriate ranges of biochemical and biomechanical factors as well as by exposing the cells to electromagnetic fields, it is possible to improve viability, proliferation, directional migration and differentiation of neural stem cells. The results of this study can... 

In this short note we apply methods introduced by B. Hanke and T. Schick to prove the vanishing of (low degree) higher Â-genera for spin manifolds admitting a positive scalar curvature metric. Our aim is to provide a short proof for this beautiful result  

We revisit the problem of finding (Formula presented.) paths with a minimum number of shared edges between two vertices of a graph. An edge is called shared if it is used in more than one of the (Formula presented.) paths. We provide a (Formula presented.)-approximation algorithm for this problem, improving the best previous approximation factor of (Formula presented.). We also provide the first approximation algorithm for the problem with a sublinear approximation factor of (Formula presented.), where (Formula presented.) is the number of vertices in the input graph. For sparse graphs, such as bounded-degree and planar graphs, we show that the approximation factor of our algorithm can be... 

We revisit the problem of finding k paths with a minimum number of shared edges between two vertices of a graph. An edge is called shared if it is used in more than one of the k paths. We provide a ⌊k/2⌋-approximation algorithm for this problem, improving the best previous approximation factor of k - 1. We also provide the first approximation algorithm for the problem with a sublinear approximation factor of O(n3/4), where n is the number of vertices in the input graph. For sparse graphs, such as bounded-degree and planar graphs, we show that the approximation factor of our algorithm can be improved to O(√n). While the problem is NP-hard, and even hard to approximate to within an O(log n)... 

Integrating high spatial resolution of functional magnetic resonance imaging (fMRI) and high temporal resolution of electroencephalogram (EEG) is promising in simultaneous EEG and fMRI analysis, especially for epileptic patients. The EEG recorded inside an MR scanner is interfered with MR artifacts. In this article, we propose new artifact reduction approaches and compare them with the conventional artifact reduction methods. Our proposed approaches are based on generalized eigenvalue decomposition (GEVD) and median filtering. The proposed methods are applied on experimental simultaneous EEG and fMRI recordings of an epileptic patient. The results show significant improvement over... 

In this paper, we address theoretical limitations in estimating the mixing matrix in noisy Sparse Component Analysis (SCA) in the two-sensor case. We obtain the Cramér-Rao Bound (CRB) error estimation of the mixing matrix based on the observation vector x=(x1,x2)T. Using the Bernoulli-Gaussian (BG) sparse distribution for sources, and some reasonable approximations, the Fisher Information Matrix (FIM) is approximated by a diagonal matrix. Then, the effect of off-diagonal terms in computing the CRB is investigated. Moreover, we compute an oracle CRB versus the blind uniform CRB and show that this is only 3 dB better than the blind uniform CRB. Finally, the CRB, the approximated CRB, the... 

In this paper, we address recovery of sparse signals from compressed measurements, and sparse signal approximation, which have received considerable attention over the last decade. First, we revisit smoothed L0 (SL0), a well-known sparse recovery algorithm, and give some insights into it that have not been noticed previously. Specifically, we re-derive the SL0 algorithm based on proximal methods, and using recent results in solving nonconvex problems by proximal algorithms, we provide a convergence guarantee for it. In addition, inspired by this derivation, we propose a general family of algorithms, which we call iterative sparsification-projection (ISP), having SL0 as a special member. Our... 

In this study, a detector/estimator is proposed for compressed sensing radars, which does not need to reconstruct the radar signal, and which works directly from compressive measurements. More precisely, through direct processing of the measurements, and without the need for reconstructing the original radar signal, the system performs target detection, and then estimates range, Doppler frequency shift and radar cross section in the presence of a Gaussian clutter. It can be seen that for large compression ratios, the detection performance and estimation quality is comparable with a common radar system while having a much lower data rate and with less computational load  

This letter is concerned with designing incoherent unit-norm frames, i.e., a set of vectors in a finite dimensional Hilbert space with unit norms and very low absolute pairwise correlations. Due to their widespread use in a variety of applications, including compressed sensing and coding theory, incoherent frame design has received considerable attention, and many algorithms have been proposed to this aim. In this letter, a new algorithm is presented which constructs incoherent frames by minimizing the maximum absolute pairwise correlations (mutual coherence) of the frame vectors. Our strategy is based on an alternating minimization penalty method, which admits efficient solvers using...