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1. Perfect Conditional ε ‐Equilibria of Multi‐Stage Games With Infinite Sets of Signals and Actions

   https://doi.org/10.3982/ECTA13426  

   Myerson, Roger B. ; Reny, Philip J. ( January 2020 , Econometrica)

   We extend Kreps and Wilson's concept of sequential equilibrium to games with infinite sets of signals and actions. A strategy profile is a conditional ε ‐equilibrium if, for any of a player's positive probability signal events, his conditional expected utility is within ε of the best that he can achieve by deviating. With topologies on action sets, a conditional ε ‐equilibrium is full if strategies give every open set of actions positive probability. Such full conditional ε ‐equilibria need not be subgame perfect, so we consider a non‐topological approach. Perfect conditional ε ‐equilibria are defined by testing conditional ε ‐rationality along nets of small perturbations of the players' strategies and of nature's probability function that, for any action and for almost any state, make this action and state eventually (in the net) always have positive probability. Every perfect conditional ε ‐equilibrium is a subgame perfect ε ‐equilibrium, and, in finite games, limits of perfect conditional ε ‐equilibria as ε  → 0 are sequential equilibrium strategy profiles. But limit strategies need not exist in infinite games so we consider instead the limit distributions over outcomes. We call such outcome distributions perfect conditional equilibrium distributions and establish their existence for a large class of regular projective games. Nature's perturbations can produce equilibria that seem unintuitive and so we augment the game with a net of permissible perturbations. 

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2. Fingerprint Distortion Rectification using Deep Convolutional Neural Networks

   Dabouei, Ali ; Kazemi, Hadi ; Iranmanesh, Seyed-Mehdi ; Dawson, Jeremy ; Nasrabadi, Nasser M ( February 2018 , The 11th IAPR International Conference on Biometrics (ICB 2018))

   Elastic distortion of fingerprints has a negative effect on the performance of fingerprint recognition systems. This negative effect brings inconvenience to users in authentication applications. However, in the negative recognition scenario where users may intentionally distort their fingerprints, this can be a serious problem since distortion will prevent recognition system from identifying malicious users. Current methods aimed at addressing this problem still have limitations. They are often not accurate because they estimate distortion parameters based on the ridge frequency map and orientation map of input samples, which are not reliable due to distortion. Secondly, they are not efficient and requiring significant computation time to rectify samples. In this paper, we develop a rectification model based on a Deep Convolutional Neural Network (DCNN) to accurately estimate distortion parameters from the input image. Using a comprehensive database of synthetic distorted samples, the DCNN learns to accurately estimate distortion bases ten times faster than the dictionary search methods used in the previous approaches. Evaluating the proposed method on public databases of distorted samples shows that it can significantly improve the matching performance of distorted samples. 

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3. Investigation and Development of a Three-Dimensional Transmission Tower-Line System Model Using Nonlinear Truss and Elastic Catenary Elements for Wind Loading Dynamic Simulation

   https://doi.org/10.1155/2021/1959683  

   Zhu, Xiao ; Ou, Ge ( December 2021 , Shock and Vibration)

   Tian, Li (Ed.)

   The accuracy of transmission tower-line system simulation is highly impacted by the transmission line model and its coupling with the tower. Owing to the high geometry nonlinearity of the transmission line and the complexity of the wind loading, such analysis is often conducted in the commercial software. In most commercial software packages, nonlinear truss element is used for cable modeling, whereas the initial strain condition of the nonlinear truss under gravity loading is not directly available. Elastic catenary element establishes an analytical formulation for cable structure under distributed loading; however, the nonlinear iteration to reach convergence can be computational expensive. To derive an optimal transmission tower-line model solution with high fidelity and computational efficiency, an open-source three-dimensional model is developed. Nonlinear truss element and elastic catenary element are considered in the model development. The results of the study imply that both elements are suitable for the transmission line model; nevertheless, the initial strain in nonlinear truss element largely impacts the model accuracy and should be calibrated from the elastic catenary model. To cross-validate the developed models on the coupled transmission tower and line, a one-span eight-line system is modeled with different elements and compared with several state-of-the-art commercial packages. The results indicate that the displacement time-history root-mean-square error (RMSE) of the open-source transmission tower-line model is less than 1 % and with a 66 % computational time reduction compared with the ANSYS model. The application of the open-source package transmission tower-line model on extreme wind speed considering the aerodynamic damping is further implemented. 

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4. The Mori–Zwanzig formulation of deep learning

   https://doi.org/10.1007/s40687-023-00390-2  

   Venturi, Daniele ; Li, Xiantao ( May 2023 , Research in the Mathematical Sciences)

   We develop a new formulation of deep learning based on the Mori–Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete dynamical systems, and it allows us to directly propagate quantities of interest (conditional expectations and probability density functions) forward and backward through the network by means of exact linear operator equations. Such new equations can be used as a starting point to develop new effective parameterizations of deep neural networks and provide a new framework to study deep learning via operator-theoretic methods. The proposed MZ formulation of deep learning naturally introduces a new concept, i.e., the memory of the neural network, which plays a fundamental role in low-dimensional modeling and parameterization. By using the theory of contraction mappings, we develop sufficient conditions for the memory of the neural network to decay with the number of layers. This allows us to rigorously transform deep networks into shallow ones, e.g., by reducing the number of neurons per layer (using projection operators), or by reducing the total number of layers (using the decay property of the memory operator).

    

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5. Secure control of networked cyber-physical systems

   https://doi.org/10.1109/CDC.2016.7798283  

   Satchidanandan, Bharadwaj ; Kumar, P. R. ( December 2016 , 55th IEEE Conference on Decision and Control)

   For networked cyber-physical systems to proliferate, it is important to ensure that the resulting control system is secure. We consider a physical plant, abstracted as a single input- single-output stochastic linear dynamical system, in which a sensor node can exhibit malicious behavior. A malicious sensor may report false or distorted sensor measurements. For such compromised systems, we propose a technique which ensures that malicious sensor nodes cannot introduce any significant distortion without being detected. The crux of our technique consists of the actuator node superimposing a random signal, whose realization is unknown to the sensor, on the control law-specified input. We show that in spite of a background of process noise, the above method can detect the presence of malicious nodes. Specifically, we establish that by injecting an arbitrarily small amount of such random excitation into the system, one can ensure that either the malicious sensor is detected, or it is restricted to add distortion that is only of zero-power to the noise entering the system. The proposed technique is potentially usable in applications such as smart grids, intelligent transportation, and process control. 

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