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The financial time series analysis is important access to touch the complex laws of financial markets. Among many goals of the financial time series analysis, one is to construct a model that can extract the information of the future return out of the known historical stock data, such as stock price, financial news, and e.t.c. To design such a model, prior knowledge on how the future return is correlated with the historical stock prices is needed. In this work, we focus on the issue: in what mode the future return is correlated with the historical stock prices. We manually design several financial time series where the future return is correlated with the historical stock prices in pre-designed modes, namely the curve-shape-feature (CSF) and the non-curve-shape-feature (NCSF) modes. In the CSF mode, the future return can be extracted from the curve shapes of the historical stock prices. By applying various kinds of existing algorithms on those pre-designed time series and real financial time series, we show that: (1) the major information of the future return is not contained in the curve-shape features of historical stock prices. That is, the future return is not mainly correlated with the historical stock prices in the CSF mode. (2) Various kinds of existing machine learning algorithms are good at extracting the curveshape features in the historical stock prices and thus are inappropriate for financial time series analysis although they are successful in the image recognition and natural language processing. That is, new models handling the NCSF series are needed in the financial time series analysis.

The fingerprint classification is an important and effective method to quicken the process and improve the accuracy in the fingerprint matching process. Conventional supervised methods need a large amount of pre-labeled data and thus consume immense human resources. In this paper, we propose a new and efficient unsupervised deep learning method that can extract fingerprint features and classify fingerprint patterns automatically. In this approach, a new model named constraint convolutional auto-encoder (CCAE) is used to extract fingerprint features and a hybrid clustering strategy is applied to obtain the final clusters. A set of experiments in the NIST-DB4 dataset shows that the proposed unsupervised method exhibits the efficient performance on fingerprint classification. For example, the CCAE achieves an accuracy of 97.3% on only 1000 unlabeled fingerprints in the NIST-DB4.

This work develops a multiphase thermomechanical model of porous silica aerogel and implements an uncertainty analysis framework consisting of the Sobol methods for global sensitivity analyses and Bayesian inference using a set of experimental data of silica aerogel. A notable feature of this work is implementing a new noise model within the Bayesian inversion to account for data uncertainty and modeling error. The hyper-parameters in the likelihood balance data misfit and prior contribution to the parameter posteriors and prevent their biased estimation. The results indicate that the uncertainty in solid conductivity and elasticity are the most influential parameters affecting the model output variance. Also, the Bayesian inference shows that despite the microstructural randomness in the thermal measurements, the model captures the data with 2% error. However, the model is inadequate in simulating the stress-strain measurements resulting in significant uncertainty in the computational prediction of a building insulation component., Comment: Jingye Tan and Pedram Maleki contributed equally to this work

The exact solution of the interacting many-body system is important and is difficult to solve. In this paper, we introduce a group method to solve the interacting many-body problem using the relation between the permutation group and the unitary group. We prove a group theorem first, then using the theorem, we represent the Hamiltonian of the interacting many-body system by the Casimir operators of unitary group. The eigenvalues of Casimir operators could give the exact values of energy and thus solve those problems exactly. This method maps the interacting many-body system onto an intermediate statistical representation. We give the relation between the conjugacy-class operator of permutation group and the Casimir operator of unitary group in the intermediate statistical representation, called the Gentile representation. Bose and Fermi cases are two limitations of the Gentile representation. We also discuss the representation space of symmetric and unitary group in the Gentile representation and give an example of the Heisenberg model to demonstrate this method. It is shown that this method is effective to solve interacting many-body problems., Comment: 11 pages, 0 figures

In this paper, we convert the lattice configurations into networks with different modes of links and consider models on networks with arbitrary numbers of interacting particle-pairs. We solve the Heisenberg model by revealing the relation between the Casimir operator of the unitary group and the conjugacy-class operator of the permutation group. We generalize the Heisenberg model by this relation and give a series of exactly solvable models. Moreover, by numerically calculating the eigenvalue of Heisenberg models and random walks on network with different numbers of links, we show that a system on lattice configurations with interactions between more particle-pairs have higher degeneracy of eigenstates. The highest degeneracy of eigenstates of a lattice model is discussed.

The quantum system under periodical modulation is the simplest path to understand the quantum non-equilibrium system, because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase can not be gauged out, so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to ultra-high precision and ultra-stability of OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. Finally, by experimentally detecting the eigen-energies, we demonstrate the relation between effective Floquet Hamiltonian and 1-D topological insulator with high winding number. Our experiment not only provides a direction for detecting the phase effect, but also paves a way in simulating quantum topological phase in OLC platform., Comment: 7 pages, 4 figures, almost published version, comments are welcome and more information at http://cqutp.org/users/xfzhang/

In the task of image classification, usually, the network is sensitive to noises. For example, an image of cat with noises might be misclassified as an ostrich. Conventionally, to overcome the problem of noises, one uses the technique of data augmentation, that is, to teach the network to distinguish noises by adding more images with noises in the training dataset. In this work, we provide a noise-resistance network in images classification by introducing a technique of pixel embedding. We test the network with pixel embedding, which is abbreviated as the network with PE, on the mnist database of handwritten digits. It shows that the network with PE outperforms the conventional network on images with noises. The technique of pixel embedding can be used in many tasks of image classification to improve noise resistance.

A deep neural network for classification tasks is essentially consist of two components: feature extractors and function approximators. They usually work as an integrated whole, however, improvements on any components can promote the performance of the whole algorithm. This paper focus on designing a new function approximator. Conventionally, to build a function approximator, one usually uses the method based on the nonlinear activation function or the nonlinear kernel function and yields classical networks such as the feed-forward neural network (MLP) and the radial basis function network (RBF). In this paper, a new function approximator that is effective and efficient is proposed. Instead of designing new activation functions or kernel functions, the new proposed network uses the fractional form. For the sake of convenience, we name the network the ratio net. We compare the effectiveness and efficiency of the ratio net and that of the RBF and the MLP with various kinds of activation functions in the classification task on the mnist database of handwritten digits and the Internet Movie Database (IMDb) which is a binary sentiment analysis dataset. It shows that, in most cases, the ratio net converges faster and outperforms both the MLP and the RBF.

In solving the variational problem, the key is to efficiently find the target function that minimizes or maximizes the specified functional. In this paper, by using the Pade approximant, we suggest a methods for the variational problem. By comparing the method with those based on the radial basis function networks (RBF), the multilayer perception networks (MLP), and the Legendre polynomials, we show that the method searches the target function effectively and efficiently.

A Brownian particle in an ideal quantum gas is considered. The mean square displacement (MSD) is derived. The Bose-Einstein or Fermi-Dirac distribution, other than the Maxwell-Boltzmann distribution, provides a different stochastic force compared with the classical Brownian motion. The MSD, which depends on the thermal wavelength and the density of medium particles, reflects the quantum effect on the Brownian particle explicitly. The result shows that the MSD in an ideal Bose gas is shorter than that in a Fermi gas. The behavior of the quantum Brownian particle recovers the classical Brownian particle as the temperature raises. At low temperatures, the quantum effect becomes obvious. For example, there is a random motion of the Brownian particle due to the fermionic exchange interaction even the temperature is near the absolute zero.

Beyond Bose and Fermi statistics, there still exist various kinds of generalized quantum statistics. Two ways to approach generalized quantum statistics: (1) in quantum mechanics, generalize the permutation symmetry of the wave function and (2) in statistical mechanics, generalize the maximum occupation number of quantum statistics. The connection between these two approaches, however, is obscure. In this paper, we suggest a unified framework to describe various kinds of generalized quantum statistics. We first provide a general formula of canonical partition functions of ideal $N$-particle gases obeying various kinds of generalized quantum statistics. Then we reveal the connection between the permutation phase of the wave function and the maximum occupation number, through constructing a method to obtain the permutation phase and the maximum occupation number from the canonical partition function. In our scheme, the permutation phase of wave functions is generalized to a matrix phase, rather than a number. It is commonly accepted that different kinds of statistics are distinguished by the maximum number. We show that the maximum occupation number is not sufficient to distinguish different kinds of generalized quantum statistics. As examples, we discuss a series of generalized quantum statistics in the unified framework, giving the corresponding canonical partition functions, maximum occupation numbers, and the permutation phase of wave functions. Especially, we propose three new kinds of generalized quantum statistics which seem to be the missing pieces in the puzzle. The mathematical basis of the scheme are the mathematical theory of the invariant matrix, the Schur-Weyl duality, the symmetric function, and the representation theory of the permutation group and the unitary group. The result in this paper builds a bridge between the statistical mechanics and such mathematical theories.

Dealing with a few-fermion system in the canonical ensemble, rather than in the grand canonical ensemble, shows that a few-fermion system with odd number fermions behaves differently from a few-fermion system with even number fermions. An even-number-fermion system behaves like a Bose system rather than a Fermi system.

Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the perspective of data fitting, a stable vector representation, namely, persistence B-spline grid (PBSG), is proposed based on the efficient technique of progressive-iterative approximation for least-squares B-spline function fitting. We theoretically prove that the PBSG method is stable with respect to the metric of 1-Wasserstein distance defined on the PD space. The proposed method was tested on a synthetic data set, data sets of randomly generated PDs, data of a dynamical system, and 3D CAD models, showing its effectiveness and efficiency

Internet of Things (IoT) systems in general consist of a lot of devices with massive connectivity. Those devices are usually constrained with limited energy supply and can only operate at low power and low rate. In this paper, we investigate a cellular-based IoT system combined with energy harvesting and NOMA. We consider all base stations (BS) and IoT devices follow the Poisson Point Process (PPP) distribution in a given area. The unit time slot is divided into two phases, energy harvesting phase in downlink (DL) and data transmission phase in uplink (uplink). That is, IoT devices will first harvest energy from all BS transmissions and then use the harvested energy to do the NOMA information transmission. We define an energy harvesting circle within which all IoT devices can harvest enough energy for NOMA transmission. The design objective is to maximize the total throughput in uplink within the circle by varying the duration T of energy harvesting phase. In our work, we also consider the inter-cell interference in the throughput calculation. The analysis of Probability Mass Function (PMF) for IoT devices in the energy harvesting circle is also compared with simulation results. It is shown that the BS density needs to be carefully set so that the IoT devices in the energy harvesting circle receive relatively smaller interference and energy circles overlap only with a small probability. Our simulations show that there exists an optimal T to achieve the maximum throughput. When the BSs are densely deployed consequently the total throughput will decrease because of the interference., Comment: Accepted by vtc 2019 fall workshop