The Experts below are selected from a list of 9456 Experts worldwide ranked by ideXlab platform
Nguyen Kim Thang - One of the best experts on this subject based on the ideXlab platform.
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np hardness of pure nash equilibrium in scheduling and Connection games
2010Co-Authors: Nguyen Kim ThangAbstract:We prove NP-hardness of pure Nash equilibrium for some problems of scheduling games and Connection games. The technique is standard: first, we construct a gadget without the desired property and then embed it to a larger game which encodes a NP-hard problem in order to prove the complexity of the desired property in a game. This technique is very efficient in proving NP-hardness for deciding the existence of Nash equilibria. In the paper, we illustrate the efficiency of the technique in proving the NP-hardness of deciding the existence of pure Nash equilibria of Matrix Scheduling Games and Weighted Connection Games. Moreover, using the technique, we can settle the complexity not only of the existence of equilibrium but also of the existence of good cost-sharing protocol.
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mathcal np hardness of pure nash equilibrium in scheduling and Connection games
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science, 2009Co-Authors: Nguyen Kim ThangAbstract:We prove $\mathcal{NP}$-hardness of pure Nash equilibrium for some problems of scheduling games and Connection games. The technique is standard: first, we construct a gadget without the desired property and then embed it to a larger game which encodes a $\mathcal{NP}$-hard problem in order to prove the complexity of the desired property in a game. This technique is very efficient in proving $\mathcal{NP}$-hardness for deciding the existence of Nash equilibria. In the paper, we illustrate the efficiency of the technique in proving the $\mathcal{NP}$-hardness of deciding the existence of pure Nash equilibria of Matrix Scheduling Games and Weighted Connection Games. Moreover, using the technique, we can settle the complexity not only of the existence of equilibrium but also of the existence of good cost-sharing protocol.
Dmytro Yeroshkin - One of the best experts on this subject based on the ideXlab platform.
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the Weighted Connection and sectional curvature for manifolds with density
Journal of Geometric Analysis, 2019Co-Authors: Lee Kennard, William Wylie, Dmytro YeroshkinAbstract:In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a Weighted torsion-free Connection introduced recently by the last two authors. We develop two new tools for studying Weighted sectional curvature bounds: a new Weighted Rauch comparison theorem and a modified notion of convexity for distance functions. As applications we prove generalizations of theorems of Preissman and Byers for negative curvature, the (homeomorphic) quarter-pinched sphere theorem, and Cheeger’s finiteness theorem. We also improve results of the first two authors for spaces of positive Weighted sectional curvature and symmetry.
Lichtner-bajjaoui Aisha - One of the best experts on this subject based on the ideXlab platform.
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A Mathematical Introduction to Neural Networks
2021Co-Authors: Lichtner-bajjaoui AishaAbstract:Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2020, Director: Josep Vives i Santa EulàliaIn this work, we are going to introduce Neural Networks. First, we are going to give a mathematical formulation of the concept of Neural Networks. Later on, we will examine some important properties of Neural Networks and make a Connection to common statistical methods such as Principal Component Analysis and Singular Value Decomposition. In the last chapter, we will give a practical application of a neural network for a regression problem. The concept of a Neural Network is inspired by the activities of a human brain. Neurons receive information, if the information is relevant to the neuron, a signal is sent to other neurons via synapses. The main difference between Neural Networks and rule-based statistical methods, is the learning ability of Neural Networks. At the beginning of a training phase a network has no explicit information. During the training phase the inter-neural Connections are changed in a way that the network solves the given problem best. Therefore Neural Networks can provide solutions to a wide spectrum of problems. A Neural Network is an abstract model consisting of one or more layers, that are connected in a certain way. The Weighted Connection between the layers plays the role of synapses. Each layer consists of units modelling neurons in the human brain. The units carry activation functions, modelling the impulses, that the real neurons send when being triggered. Just like the brain, the network will be trained to learn a specific task and later should perform a similar task in an unknown situation, using the experience that it gained before. For that matter, during the training phase already-observed information is passed to the model and the model produces an output. The output is evaluated on its ability to approximate the observed information. Depending on the result, the model is then changed to improve performance
Lee Kennard - One of the best experts on this subject based on the ideXlab platform.
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the Weighted Connection and sectional curvature for manifolds with density
Journal of Geometric Analysis, 2019Co-Authors: Lee Kennard, William Wylie, Dmytro YeroshkinAbstract:In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a Weighted torsion-free Connection introduced recently by the last two authors. We develop two new tools for studying Weighted sectional curvature bounds: a new Weighted Rauch comparison theorem and a modified notion of convexity for distance functions. As applications we prove generalizations of theorems of Preissman and Byers for negative curvature, the (homeomorphic) quarter-pinched sphere theorem, and Cheeger’s finiteness theorem. We also improve results of the first two authors for spaces of positive Weighted sectional curvature and symmetry.
Joerg Appenzeller - One of the best experts on this subject based on the ideXlab platform.
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spin torque devices with hard axis initialization as stochastic binary neurons
Scientific Reports, 2018Co-Authors: Vaibhav Ostwal, Punyashloka Debashis, Rafatul Faria, Zhihong Chen, Joerg AppenzellerAbstract:Employing the probabilistic nature of unstable nano-magnet switching has recently emerged as a path towards unconventional computational systems such as neuromorphic or Bayesian networks. In this letter, we demonstrate proof-of-concept stochastic binary operation using hard axis initialization of nano-magnets and control of their output state probability (activation function) by means of input currents. Our method provides a natural path towards addition of Weighted inputs from various sources, mimicking the integration function of neurons. In our experiment, spin orbit torque (SOT) is employed to “drive” nano-magnets with perpendicular magnetic anisotropy (PMA) -to their metastable state, i.e. in-plane hard axis. Next, the probability of relaxing into one magnetization state (+mi) or the other (−mi) is controlled using an Oersted field generated by an electrically isolated current loop, which acts as a “charge” input to the device. The final state of the magnet is read out by the anomalous Hall effect (AHE), demonstrating that the magnetization can be probabilistically manipulated and output through charge currents, closing the loop from charge-to-spin and spin-to-charge conversion. Based on these building blocks, a two-node directed network is successfully demonstrated where the status of the second node is determined by the probabilistic output of the previous node and a Weighted Connection between them. We have also studied the effects of various magnetic properties, such as magnet size and anisotropic field on the stochastic operation of individual devices through Monte Carlo simulations of Landau Lifshitz Gilbert (LLG) equation. The three-terminal stochastic devices demonstrated here are a critical step towards building energy efficient spin based neural networks and show the potential for a new application space.