Symmetry-preserving discretization of variational field theories

The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete bundle, and developed up to the notion of symmetries and conservation laws for solutions of the discrete field equations. The notion of variational integrator for a Cauchy problem associated to this variational principle is also studied. The theory is then connected with the classical (smooth) formulation of variational field theories, describing a functorial method to derive a discrete Lagrangian density from a smooth Lagrangian density on a Riemannian fibered manifold, so that all symmetries of the Lagrangian turn into symmetries of the corresponding discrete Lagrangian. Elements of the discrete and smooth theories are compared and all sources of error between them are identified. Finally the whole theory is illustrated with the discretization of the classical variational formulation of the kinematics of a Cosserat rod

Joint Iterative Power Allocation and Linear Interference Suppression Algorithms in Cooperative DS-CDMA Networks

This work presents joint iterative power allocation and interference suppression algorithms for spread spectrum networks which employ multiple hops and the amplify-and-forward cooperation strategy for both the uplink and the downlink. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to individual and global power constraints and the design of linear receivers for interference suppression. We derive constrained linear minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the linear receivers. In order to solve the proposed optimization problems, we develop cost-effective algorithms for adaptive joint power allocation, and estimation of the parameters of the receiver and the channels. An analysis of the optimization problem is carried out and shows that the problem can have its convexity enforced by an appropriate choice of the power constraint parameter, which allows the algorithms to avoid problems with local minima. A study of the complexity and the requirements for feedback channels of the proposed algorithms is also included for completeness. Simulation results show that the proposed algorithms obtain significant gains in performance and capacity over existing non-cooperative and cooperative schemes.Comment: 9 figures; IET Communications, 201

Fluid dynamics in porous media with Sailfish

In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through in order to calculate permeability and tortuosity. We also present a simple way to obtain the specific superficial area of porous media using Python libraries. To contextualize these concepts, we test the Kozeny--Carman equation, discuss its validity and calculate the Kozeny's constant for our artificial samples.Comment: 13 pages, 12 figure

Low-Rank Signal Processing: Design, Algorithms for Dimensionality Reduction and Applications

We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed to introduce the reader to the fundamentals of reduced-rank signal processing and to describe how dimensionality reduction is performed on an observed discrete-time signal. A unified treatment of dimensionality reduction algorithms is presented with the aid of least squares optimization techniques, in which several techniques for designing the transformation matrix that performs dimensionality reduction are reviewed. Among the dimensionality reduction techniques are those based on the eigen-decomposition of the observed data vector covariance matrix, Krylov subspace methods, joint and iterative optimization (JIO) algorithms and JIO with simplified structures and switching (JIOS) techniques. A number of applications are then considered using a unified treatment, which includes wireless communications, sensor and array signal processing, and speech, audio, image and video processing. This tutorial concludes with a discussion of future research directions and emerging topics.Comment: 23 pages, 6 figure

Study of Sparsity-Aware Distributed Conjugate Gradient Algorithms for Sensor Networks

This paper proposes distributed adaptive algorithms based on the conjugate gradient (CG) method and the diffusion strategy for parameter estimation over sensor networks. We present sparsity-aware conventional and modified distributed CG algorithms using $l_{1}$ and log-sum penalty functions. The proposed sparsity-aware diffusion distributed CG algorithms have an improved performance in terms of mean square deviation (MSD) and convergence as compared with the consensus least-mean square (Diffusion-LMS) algorithm, the diffusion CG algorithms and a close performance to the diffusion distributed recursive least squares (Consensus-RLS) algorithm. Numerical results show that the proposed algorithms are reliable and can be applied in several scenarios.Comment: 1 figure, 7 page

6-cycle double covers of cubic graphs

A cycle double cover (CDC) of an undirected graph is a collection of the graph's cycles such that every edge of the graph belongs to exactly two cycles. We describe a constructive method for generating all the cubic graphs that have a 6-CDC (a CDC in which every cycle has length 6). As an application of the method, we prove that all such graphs have a Hamiltonian cycle. A sense of direction is an edge labeling on graphs that follows a globally consistent scheme and is known to considerably reduce the complexity of several distributed problems. In [9], a particular instance of sense of direction, called a chordal sense of direction (CSD), is studied and the class of k-regular graphs that admit a CSD with exactly k labels (a minimal CSD) is analyzed. We now show that nearly all the cubic graphs in this class have a 6-CDC, the only exception being K4.Comment: This version fixes typos and minor technical problems, and updates reference

Joint Power Adjustment and Interference Mitigation Techniques for Cooperative Spread Spectrum Systems

This paper presents joint power allocation and interference mitigation techniques for the downlink of spread spectrum systems which employ multiple relays and the amplify and forward cooperation strategy. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to an individual power constraint and the design of linear receivers for interference suppression. We derive constrained minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the linear receivers. In order to solve the proposed optimization problem efficiently, we develop joint adaptive power allocation and interference suppression algorithms that can be implemented in a distributed fashion. The proposed stochastic gradient (SG) and recursive least squares (RLS) algorithms mitigate the interference by adjusting the power levels across the relays and estimating the parameters of the linear receiver. SG and RLS channel estimation algorithms are also derived to determine the coefficients of the channels across the base station, the relays and the destination terminal. The results of simulations show that the proposed techniques obtain significant gains in performance and capacity over non-cooperative systems and cooperative schemes with equal power allocation.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1301.009

Low-Complexity Variable Forgetting Factor Techniques for RLS Algorithms in Interference Rejection Applications

We propose a low-complexity variable forgetting factor (VFF) mechanism for recursive least square (RLS) algorithms in interference suppression applications. The proposed VFF mechanism employs an updated component related to the time average of the error correlation to automatically adjust the forgetting factor in order to ensure fast convergence and good tracking of the interference and the channel. Convergence and tracking analyses are carried out and analytical expressions for predicting the mean squared error of the proposed adaptation technique are obtained. Simulation results for a direct-sequence code-division multiple access (DS-CDMA) system are presented in nonstationary environments and show that the proposed VFF mechanism achieves superior performance to previously reported methods at a reduced complexity.Comment: 12 figure

Multi-Feedback Successive Interference Cancellation for Multiuser MIMO Systems

In this paper, a low-complexity multiple feedback successive interference cancellation (MF-SIC) strategy is proposed for the uplink of multiuser multiple-input multiple-output (MU-MIMO) systems. In the proposed MF-SIC {algorithm with shadow area constraints (SAC)}, an enhanced interference cancellation is achieved by introducing {constellation points as the candidates} to combat the error propagation in decision feedback loops. We also combine the MF-SIC with multi-branch (MB) processing, which achieves a higher detection diversity order. For coded systems, a low-complexity soft-input soft-output (SISO) iterative (turbo) detector is proposed based on the MF and the MB-MF interference suppression techniques. The computational complexity of the MF-SIC is {comparable to} the conventional SIC algorithm {since very little additional complexity is required}. {Simulation} results show that the algorithms significantly outperform the conventional SIC scheme and {approach} the optimal detector.Comment: 6 figure

Adaptive Minimum BER Reduced-Rank Interference Suppression Algorithms Based on Joint and Iterative Optimization of Parameters

In this letter, we propose a novel adaptive reduced-rank strategy based on joint iterative optimization (JIO) of filters according to the minimization of the bit error rate (BER) cost function. The proposed optimization technique adjusts the weights of a subspace projection matrix and a reduced-rank filter jointly. We develop stochastic gradient (SG) algorithms for their adaptive implementation and introduce a novel automatic rank selection method based on the BER criterion. Simulation results for direct-sequence code-division-multiple-access (DS-CDMA) systems show that the proposed adaptive algorithms significantly outperform the existing schemes.Comment: 3 figure