Sharif Digital Repository

We consider d-dimensional simplicial complexes which can be PL embedded in the 2d-dimensional Euclidean space. In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in the (2 d- 1 ) -dimensional Euclidean space. In addition, we use similar considerations on links of vertices to derive a new asymptotic upper bound on the total number of d-simplices in an (continuously) embeddable complex in 2d-space with n vertices, improving known upper bounds, for all d≥ 2. Moreover, we show that the same asymptotic bound also applies to the size of d-complexes linklessly embeddable in the (2 d+ 1 ) -dimensional... 

We consider d-dimensional simplicial complexes which can be PL embedded in the 2d-dimensional Euclidean space. In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in the (Formula presented.)-dimensional Euclidean space. In addition, we use similar considerations on links of vertices to derive a new asymptotic upper bound on the total number of d-simplices in an (continuously) embeddable complex in 2d-space with n vertices, improving known upper bounds, for all (Formula presented.). Moreover, we show that the same asymptotic bound also applies to the size of d-complexes linklessly embeddable in the... 

Radiofrequency coils provide high-resolution magnetic resonance (MR) imaging of human tissues. A small RF coil produces MR images with a higher resolution compared to the commercial volume MR coils from mass limited samples. Signal to noise ratio (SNR) plays a key role in the optimal design of receiver radiofrequency coils. In this work, we present a three-loop saddle coil suitable for MR imaging of digits of the human body. The geometry of the introduced coil is optimized to achieve the highest SNR. The coil performance is evaluated through comparing the measured SNR maps of the optimal coil derived from MR images of a saline phantom with the corresponding measured SNR maps of a commercial... 

This paper presents a new technique for almost sure asymptotic state tracking, stability and reference tracking of nonlinear dynamic systems by remote controller over the packet erasure channel, which is an abstract model for transmission via WiFi and the Internet. By implementing a suitable linearization method, a proper encoder and decoder are presented for tracking the state trajectory of nonlinear systems at the end of communication link when the measurements are sent through the packet erasure channel. Then, a controller for reference tracking of the system is designed. In the proposed technique linearization is applied when the error between the states and an estimate of these states... 

This paper presents a new technique for mean square asymptotic reference tracking of nonlinear dynamic systems over Additive White Gaussian Noise (AWGN) channel. The nonlinear dynamic system has periodic outputs and sinusoidal inputs and is cascaded with a bandpass filter acting as an encoder. By using the describing function method, the nonlinear dynamic system is represented by an equivalent linear dynamic system. Then, for this system, a mean square asymptotic reference tracking technique, including an encoder, a decoder, and a controller, is presented. It is shown that the proposed reference tracking technique results in mean square asymptotic reference tracking of nonlinear dynamic... 

This paper presents a new technique for mean square asymptotic reference tracking of nonlinear dynamic systems over Additive White Gaussian Noise (AWGN) channel. The nonlinear dynamic system has periodic outputs and sinusoidal inputs and is cascaded with a bandpass filter acting as an encoder. By using the describing function method, the nonlinear dynamic system is represented by an equivalent linear dynamic system. Then, for this system, a mean square asymptotic reference tracking technique, including an encoder, a decoder, and a controller, is presented. It is shown that the proposed reference tracking technique results in mean square asymptotic reference tracking of nonlinear dynamic... 

This paper presents a new technique for the state estimation and reference tracking of nonlinear dynamic systems over the packet erasure channel, which is an abstract model for transmission via the Internet, WiFi wireless network and ZigBee modules. A new encoder and decoder for real time state estimation of nonlinear dynamic systems at the end of communication link when the measurements are sent through the limited capacity erasure channel, are presented. Then, using the available results from control theory, a controller for reference tracking and hence the stability of the system is also designed. That is, for nonlinear systems, almost sure asymptotic state estimation and reference... 

This paper is concerned with the tele-operation of autonomous vehicles over analog Additive White Gaussian Noise (AWGN) channel, which is subject to transmission noise and power constraint. The nonlinear dynamic of autonomous vehicles is described by the unicycle model and is cascaded with a bandpass filter acting as encoder. Using the describing function method, the nonlinear dynamic of autonomous vehicles is represented by an approximate linear system. Then, the available results for linear control over analog AWGN channel are extended to account for linear continuous time systems with non-real valued and multiple real valued eigenvalues and for tracking a non-zero reference signal.... 

This paper presents a new technique for the state estimation and reference tracking of nonlinear dynamic systems over the packet erasure channel, which is an abstract model for transmission via the Internet, WiFi wireless network and ZigBee modules. A new encoder and decoder for real time state estimation of nonlinear dynamic systems at the end of communication link when the measurements are sent through the limited capacity erasure channel, are presented. Then, using the available results from control theory, a controller for reference tracking and hence the stability of the system is also designed. That is, for nonlinear systems, almost sure asymptotic state estimation and reference... 

This paper offers a mathematical solution based on queuing theory and a generalized stochastic Petri net model to minimize the total makespan of the grid computing environments. A grid manager could minimize the total makespan through cautious distribution of subtasks to the grid resources. Subtask arrival rates depend on the arrival rate of the grid tasks submitted to the grid manager, local tasks directly submitted to the grid resources and the processing speed of the resources. Modeling the grid environment using queuing network, the steady state analysis of the network will result in the mean response time of the resources. Therefore, the total makespan could be minimized by minimizing... 

In this paper we deal with ray tracing acceleration problem in wave propagation simulation as a separate problem from its computer graphical counterpart and try to review accelerating techniques with this point of view. We build a classical kd-tree adapted to the special geometry of the problem. Then we mention the main differences between these two problems and devise algorithms that use these differences for accelerating intersection test in this problem even further  

Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward problems, however, pose significant challenges, mainly because of the complex non-convex and multi-objective loss function. In this work, we present a PINN approach to solving the equations of coupled flow and deformation in porous media for both single-phase and multiphase flow. To this end, we construct the solution space using multi-layer neural networks. Due to the dynamics of the problem, we find that incorporating multiple differential relations into the...