Min-Max formulae for the speeds of pulsating travelling fronts in periodic excitable media

This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations in a periodic framework. It deals with travelling wave solutions of the equation $$u_t =\nabla\cdot(A(z)\nabla u) +q(z)\cdot\nabla u+ f(z,u), t \in \mathbb{R}, z \in \Omega,$$ propagating with a speed $c.$ In the case of a "combustion" nonlinearity, the speed $c$ exists and it is unique, while the front $u$ is unique up to a translation in $t.$ We give a $\min-\max$ and a $\max-\min$ formula for this speed $c.$ On the other hand, in the case of a "ZFK" or a "KPP" nonlinearity, there exists a minimal speed of propagation $c^{*}.$ In this situation, we give a $\min-\max$ formula for $c^{*}.$ Finally, we apply this $\min-\max$ formula to prove a variational formula involving eigenvalue problems for the minimal speed $c^{*}$ in the "KPP" case

SAT Modulo Monotonic Theories

We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories arise from many common problems, e.g., graph properties such as reachability, shortest paths, connected components, minimum spanning tree, and max-flow/min-cut, and then demonstrate our framework by building SMT solvers for each of these theories. We apply these solvers to procedural content generation problems, demonstrating major speed-ups over state-of-the-art approaches based on SAT or Answer Set Programming, and easily solving several instances that were previously impractical to solve

Downlink Power Control in Massive MIMO Networks with Distributed Antenna Arrays

In this paper, we investigate downlink power control in massive multiple-input multiple-output (MIMO) networks with distributed antenna arrays. The base station (BS) in each cell consists of multiple antenna arrays, which are deployed in arbitrary locations within the cell. Due to the spatial separation between antenna arrays, the large-scale propagation effect is different from a user to different antenna arrays in a cell, which makes power control a challenging problem as compared to conventional massive MIMO. We assume that the BS in each cell obtains the channel estimates via uplink pilots. Based on the channel estimates, the BSs perform maximum ratio transmission for the downlink. We then derive a closed-form spectral efficiency (SE) expression, where the channels are subject to correlated fading. Utilizing the derived expression, we propose a max-min power control algorithm to ensure that each user in the network receives a uniform quality of service. Numerical results demonstrate that, for the network considered in this work, optimizing for max-min SE through the max-min power control improves the sum SE of the network as compared to equal power allocation.Comment: Accepted to appear in ICC 2018, Kansas City, M

The effect of data preprocessing on the performance of artificial neural networks techniques for classification problems

The artificial neural network (ANN) has recently been applied in many areas, such as medical, biology, financial, economy, engineering and so on. It is known as an excellent classifier of nonlinear input and output numerical data. Improving training efficiency of ANN based algorithm is an active area of research and numerous papers have been reviewed in the literature. The performance of Multi-layer Perceptron (MLP) trained with back-propagation artificial neural network (BP-ANN) method is highly influenced by the size of the data-sets and the data-preprocessing techniques used. This work analyzes the advantages of using pre-processing datasets using different techniques in order to improve the ANN convergence. Specifically Min-Max, Z-Score and Decimal Scaling Normalization preprocessing techniques were evaluated. The simulation results showed that the computational efficiency of ANN training process is highly enhanced when coupled with different preprocessing techniques

Centralized and Distributed Power Allocation for Max-Min Fairness in Cell-Free Massive MIMO

Cell-free Massive MIMO systems consist of a large number of geographically distributed access points (APs) that serve users by coherent joint transmission. Downlink power allocation is important in these systems, to determine which APs should transmit to which users and with what power. If the system is implemented correctly, it can deliver a more uniform user performance than conventional cellular networks. To this end, previous works have shown how to perform system-wide max-min fairness power allocation when using maximum ratio precoding. In this paper, we first generalize this method to arbitrary precoding, and then train a neural network to perform approximately the same power allocation but with reduced computational complexity. Finally, we train one neural network per AP to mimic system-wide max-min fairness power allocation, but using only local information. By learning the structure of the local propagation environment, this method outperforms the state-of-the-art distributed power allocation method from the Cell-free Massive MIMO literature