scholarly journals Computing Classification of Interacting Fermionic Symmetry-Protected Topological Phases Using Topological Invariants*

2021 ◽  
Vol 38 (12) ◽  
pp. 127101
Author(s):  
Yunqing Ouyang ◽  
Qing-Rui Wang ◽  
Zheng-Cheng Gu ◽  
Yang Qi
Keyword(s):  
Computational Cost ◽  
Discrete Symmetry ◽  
Cohomology Theory ◽  
Explicit Calculation ◽  
Topological Invariants ◽  
Symmetry Groups ◽  
Great Success ◽  
Generalized Cohomology ◽  
Symmetry Protected

In recent years, great success has been achieved on the classification of symmetry-protected topological (SPT) phases for interacting fermion systems by using generalized cohomology theory. However, the explicit calculation of generalized cohomology theory is extremely hard due to the difficulty of computing obstruction functions. Based on the physical picture of topological invariants and mathematical techniques in homotopy algebra, we develop an algorithm to resolve this hard problem. It is well known that cochains in the cohomology of the symmetry group, which are used to enumerate the SPT phases, can be expressed equivalently in different linear bases, known as the resolutions. By expressing the cochains in a reduced resolution containing much fewer basis than the choice commonly used in previous studies, the computational cost is drastically reduced. In particular, it reduces the computational cost for infinite discrete symmetry groups, like the wallpaper groups and space groups, from infinity to finity. As examples, we compute the classification of two-dimensional interacting fermionic SPT phases, for all 17 wallpaper symmetry groups.

A Study on the Auxiliary Diagnosis of Thyroid Disease Images Based on Multiple Dimensional Deep Learning Algorithms

2020 ◽  
Vol 16 (3) ◽  
pp. 199-205
Author(s):  
Yuejun Liu ◽  
Yifei Xu ◽  
Xiangzheng Meng ◽  
Xuguang Wang ◽  
Tianxu Bai
Keyword(s):  
Deep Learning ◽  
Learning Algorithms ◽  
Region Of Interest ◽  
Classification Performance ◽  
Thyroid Diseases ◽  
Great Success ◽  
Learning Models ◽  
Good Classification Performance ◽  
Spect Images

Background: Medical imaging plays an important role in the diagnosis of thyroid diseases. In the field of machine learning, multiple dimensional deep learning algorithms are widely used in image classification and recognition, and have achieved great success. Objective: The method based on multiple dimensional deep learning is employed for the auxiliary diagnosis of thyroid diseases based on SPECT images. The performances of different deep learning models are evaluated and compared. Methods: Thyroid SPECT images are collected with three types, they are hyperthyroidism, normal and hypothyroidism. In the pre-processing, the region of interest of thyroid is segmented and the amount of data sample is expanded. Four CNN models, including CNN, Inception, VGG16 and RNN, are used to evaluate deep learning methods. Results: Deep learning based methods have good classification performance, the accuracy is 92.9%-96.2%, AUC is 97.8%-99.6%. VGG16 model has the best performance, the accuracy is 96.2% and AUC is 99.6%. Especially, the VGG16 model with a changing learning rate works best. Conclusion: The standard CNN, Inception, VGG16, and RNN four deep learning models are efficient for the classification of thyroid diseases with SPECT images. The accuracy of the assisted diagnostic method based on deep learning is higher than that of other methods reported in the literature.

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
Author(s):  
Samuel Monnier
Keyword(s):  
Topological Field Theories ◽  
Geometric Quantization ◽  
Discrete Symmetry ◽  
Local System ◽  
Field Theories ◽  
Simons Theory ◽  
General Point ◽  
Topological Field ◽  
Generalized Cohomology ◽  
Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

scholarly journals A CAUSAL HIERARCHICAL MARKOV FRAMEWORK FOR THE CLASSIFICATION OF MULTIRESOLUTION AND MULTISENSOR REMOTE SENSING IMAGES

2020 ◽  
Vol V-3-2020 ◽  
pp. 269-277
Author(s):  
A. Montaldo ◽  
L. Fronda ◽  
I. Hedhli ◽  
G. Moser ◽  
S. B. Serpico ◽  
...  
Keyword(s):  
High Resolution ◽  
Markov Chain Model ◽  
Computational Cost ◽  
Order Relation ◽  
Boosted Regression Trees ◽  
Chain Model ◽  
Remotely Sensed Data ◽  
Space Filling Curve ◽  
Very High

Abstract. In this paper, a multiscale Markov framework is proposed in order to address the problem of the classification of multiresolution and multisensor remotely sensed data. The proposed framework makes use of a quadtree to model the interactions across different spatial resolutions and a Markov model with respect to a generic total order relation to deal with contextual information at each scale in order to favor applicability to very high resolution imagery. The methodological properties of the proposed hierarchical framework are investigated. Firstly, we prove the causality of the overall proposed model, a particularly advantageous property in terms of computational cost of the inference. Secondly, we prove the expression of the marginal posterior mode criterion for inference on the proposed framework. Within this framework, a specific algorithm is formulated by defining, within each layer of the quadtree, a Markov chain model with respect to a pixel scan that combines both a zig-zag trajectory and a Hilbert space-filling curve. Data collected by distinct sensors at the same spatial resolution are fused through gradient boosted regression trees. The developed algorithm was experimentally validated with two very high resolution datasets including multispectral, panchromatic and radar satellite images. The experimental results confirm the effectiveness of the proposed algorithm as compared to previous techniques based on alternate approaches to multiresolution fusion.

scholarly journals Classification of rough transformations of a circle from a modern point of view

2018 ◽  
Vol 20 (4) ◽  
pp. 408-418
Author(s):  
A. E. Kolobyanina ◽  
E. V. Nozdrinova ◽  
O. V. Pochinka
Keyword(s):  
Invariant Manifolds ◽  
Sufficient Conditions ◽  
Periodic Points ◽  
Point Of View ◽  
Topological Classification ◽  
Topological Invariants ◽  
Modern Theory ◽  
Ambient Manifold ◽  
Periodic Data

In this paper the authors use modern methods and approaches to present a solution to the problem of the topological classification of circle’s rough transformations in canonical formulation. In the modern theory of dynamical systems such problems are understood as the complete topological classification: finding topological invariants, proving the completeness of the set of invariants found and constructing a standard representative from a given set of topological invariants. Namely, in the first theorem of this paper the type of periodic data of circle’s rough transformations is established. In the second theorem necessary and sufficient conditions of their conjugacy are proved. These conditions mean coincidence of periodic data and rotation numbers. In the third theorem the admissible set of parameters is implemented by a rough transformation of a circle. While proving the theorems, we assume that the results on the local topological classification of hyperbolic periodic points, as well as the results on the global representation of the ambient manifold as a union of invariant manifolds of periodic points, are known.

scholarly journals Watching a Small Portion could be as Good as Watching All: Towards Efficient Video Classification

2018 ◽  
Author(s):  
Hehe Fan ◽  
Zhongwen Xu ◽  
Linchao Zhu ◽  
Chenggang Yan ◽  
Jianjun Ge ◽  
...  
Keyword(s):  
Large Scale ◽  
Sampling Rate ◽  
Computational Cost ◽  
Confidence Score ◽  
Video Content ◽  
Video Classification ◽  
Video Frames ◽  
Similar Accuracy ◽  
Efficient Video

We aim to significantly reduce the computational cost for classification of temporally untrimmed videos while retaining similar accuracy. Existing video classification methods sample frames with a predefined frequency over entire video. Differently, we propose an end-to-end deep reinforcement approach which enables an agent to classify videos by watching a very small portion of frames like what we do. We make two main contributions. First, information is not equally distributed in video frames along time. An agent needs to watch more carefully when a clip is informative and skip the frames if they are redundant or irrelevant. The proposed approach enables the agent to adapt sampling rate to video content and skip most of the frames without the loss of information. Second, in order to have a confident decision, the number of frames that should be watched by an agent varies greatly from one video to another. We incorporate an adaptive stop network to measure confidence score and generate timely trigger to stop the agent watching videos, which improves efficiency without loss of accuracy. Our approach reduces the computational cost significantly for the large-scale YouTube-8M dataset, while the accuracy remains the same.

scholarly journals Ternary and n-ary f-distributive structures

2018 ◽  
Vol 16 (1) ◽  
pp. 32-45 ◽  
Author(s):  
Indu R. U. Churchill ◽  
M. Elhamdadi ◽  
M. Green ◽  
A. Makhlouf
Keyword(s):  
Cohomology Theory ◽  
Extension Theory ◽  
Low Dimensions

AbstractWe introduce and study ternary f-distributive structures, Ternary f-quandles and more generally their higher n-ary analogues. A classification of ternary f-quandles is provided in low dimensions. Moreover, we study extension theory and introduce a cohomology theory for ternary, and more generally n-ary, f-quandles. Furthermore, we give some computational examples.

Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

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