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Where Tutte and Holant meet: a view from counting complexity
Published in Joanna A. Ellis-Monaghan, Iain Moffatt, Handbook of the Tutte Polynomial and Related Topics, 2022
The Holant framework is a natural and powerful setting to express a broad class of counting problems. In the study of counting complexity, a primary goal is to achieve complexity classifications. Such a classification often takes the form of a dichotomy theorem, which says that for any set of local constraint functions that defines a counting problem, the problem is either solvable in polynomial time or is ♯P -hard. The complexity of Holant problems are a generalization of counting constraint satisfaction problems, graph homomorphisms, and partition functions of spin systems. It is essentially equivalent to computing the contraction of a tensor network.
Electroerosion resistant composite materials and coatings of electrical contacts
Published in Denis A. Romonov, Stanislav V. Moskovskii, Viktor E. Gromov, Surface Structure Modification nd Hardening of Al-Si Alloys, 2020
Denis A. Romonov, Stanislav V. Moskovskii, Viktor E. Gromov
The susceptibility of the pin socket to vibration loads is one of the achievements of electrical engineering. Electrical engineering alone is not enough to solve this complex problem. Multiphysics analysis is expected to be the solution to analyze this electromechanical pin-socket dynamic structure. Studies [57–59] develop dynamic contact multiphysical analysis with the formalism of tensor network analysis. The multiphysical model combines the relative speed and position of the pin in combination with instantaneous contact resistance implemented in an RC network. An innovative method has been developed that allows one to determine the signature of vibrational voltage by the signal-to-noise amplitude. The relevance of the model of multiphysical tensor analysis of networks is illustrated by the example of a 10 mm long socket with uniaxial vibrational voltage of an arbitrary waveform with a passband of 20 kHz. It has been shown that contact resistance can fluctuate more than a thousand times. The vibration-stress state of the pin-socket depending on the parameters of the RC network is also discussed. The proposed multiphysical analysis can be potentially applied to the study of electromagnetic compatibility and signal integrity of assembled electronic equipment and printed circuit boards under conditions of vibrational stresses.
An Overview of Deep Learning in Industry
Published in Jay Liebowitz, Data Analytics and AI, 2020
Quan Le, Luis Miralles-Pechuán, Shridhar Kulkarni, Jing Su, Oisín Boydell
One of the advantages of deep learning approaches is their ability to handle sparse data types. News sources are essential driving forces for stock market activities and may be even more influential than the current and past stock prices (Fama, 1965). Ding et al. (2015) proposed a CNN-based framework to model the influence of news events on stock market prices. The proposed framework has two key features. First, a neural tensor network (NTN) is applied to learn event embeddings from word embeddings in an automatic way. Second, a CNN model covering both short-term and long-term events is used to predict a binary output indicating whether a stock price is rising or falling. This CNN-based architecture is demonstrated to show increased prediction accuracy over state-of-the-art non-deep learning baseline methods (Ding et al. 2015). A later modification to this approach (Ding et al. 2016) integrates knowledge graph information during the learning process of event embeddings to predict stock prices even more accurately.
Tensor networks for MIMO LPV system identification
Published in International Journal of Control, 2020
Bilal Gunes, Jan-Willem van Wingerden, Michel Verhaegen
In this paper, we present the following novel contributions. Firstly, the LPV identification problem is recast and optimised using tensor networks to make the proposed refinement method ‘curse-of-dimensionality’-free in memory and computation. This is done by circumventing the explicit construction of the LPV sub-Markov parameters. Namely, operations can be performed directly on the tensor network decompositions. In detail, the used class of tensor network (Batselier, Chen, & Wong, 2017) is a generalisation of tensor trains (Oseledets, 2011). They inherit tensor train efficiency results, and become tensor trains for single-output problems. These decompositions allow efficient storage and computation in the tensor network domain. This recast in tensor networks includes not only the LPV sub-Markov parameters, but also the data and state-revealing matrix. More specifically, the LPV sub-Markov parameters are shown to admit exact tensor network representation with ranks equal to the model order, and the data tensor admits exact and sparse tensor network representation. Secondly, these properties are exploited to obtain a condensed tensor network parametrisation which can be optimised ‘curse-of-dimensionality’-free in memory and computation. Thirdly, we propose an efficient way to obtain the estimate state sequence from the estimate tensor networks without explicitly constructing the LPV sub-Markov parameters. Additionally, we provide an upper bound on the condition numbers of its sub-problems.