Universal Framework for Quantum Error-Correcting Codes

We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes.     

A General Rate-Distortion Optimization Method for Block Compressed Sensing of Images

Block compressed sensing (BCS) is a promising technology for image sampling and compression for resource-constrained applications, but it needs to balance the sampling rate and quantization bit-depth for a bit-rate constraint. In this paper, we summarize the commonly used CS quantization frameworks into a unified framework, and a new bit-rate model and a model of the optimal bit-depth are proposed for the unified CS framework. The proposed bit-rate model reveals the relationship between the bit-rate, sampling rate, and bit-depth based on the information entropy of generalized Gaussian distribution. The optimal bit-depth model can predict the optimal bit-depth of CS measurements at a given bit-rate. Then, we propose a general algorithm for choosing sampling rate and bit-depth based on the proposed models. Experimental results show that the proposed algorithm achieves near-optimal rate-distortion performance for the uniform quantization framework and predictive quantization framework in BCS.     

Signal-Pressure Curves of Cascaded Four-Wave Mixing in Gas-Filled Capillary by fs Pulses

The theoretical framework for the cascaded four waves mixing (CFWM) in gas-filled capillary by fs pulses is constructed. Based on the theoretical framework, the signal-pressure curves (SPC) of the CFWM in gas-filled capillary by fs pulses are calculated. With a comparison between the theoretical and experimental SPC we have discussed the influence of the walk-off and phase modulation on the SPC. At the same time, we have discussed the possible origin of the first three peaks of the SPC.     

BOTDA光纤传感技术在光纤环圈质量评估中的应用

在分析光纤环对陀螺整体性能影响的基础上,提出将BOTDA光纤传感技术用于光纤环质量检测。通过对光纤环的在线检测、热应力检测和骨架性能影响测试,能及时发现并消除光纤绕制中的应力尖峰及换层现象,消除由骨架、热应力引起的光纤应力曲线反转现象。     

Colossal resistivity change associated with the charge ordered/disordered transition:Monte Carlo study

Earlier theoretical approaches to manganites mainly stem from magnetic framework in which the electronic transports are thought to be spin-dependent and the double exchange plays a vital role. However, quite a number of experimental observations cannot be explained in the magnetic framework, yet. For example, multiplicate insulator-metal transitions and resistivity reduction induced by perturbations other than magnetic field, such as electric current, are not well understood in this framework. Here we present a comprehensive analysis on the magnetic framework and give a Monte Carlo study on the resistivity of a charge ordered/disordered model without accounting for the spin degree of freedom. The result shows a colossal resistivity change as a resultant of the transition between two types of insulated states. This transition has intrinsic difference from the popular insulated-to-metallic transition in the magnetic framework. The present scenario can be used to explain some experimental facts for electronic transports in manganites, which are not accessible in the magnetic framework.     

How to utilize a Grover search in general programming

It is widely believed that quantum computers (if realized) will be more powerful than today’s computers from the viewpoint of computational complexity. However, it is not obvious how to utilize quantum computers in practical situations. For practical purposes, a Grover search may be one of the most promising quantum algorithms known so far. Thus, in this paper, we propose an efficient framework where we can use Grover search for general programming. Our framework has the following steps. (1) A programmer writes a program by using standard C++ programming language. (2) Some if expressions within for loops in the C++ source code are chosen as candidates to be performed as a Grover search on a quantum computer. (3) The framework automatically generates a corresponding quantum circuit for each Grover search chosen in (2). Unlike the existing quantum circuit design methods, we can treat large problems in our quantum circuit design. (4) By evaluating the number of primitive quantum gates in the quantum circuit generated in (3), the framework determines whether the processing time of the quantum circuit is faster than the processing time of the corresponding if expression on a classical computer. If the framework determines that the quantum circuit is faster, it generates some interface source codes for a classical computer. Thus, in our framework, a programmer can use a Grover search with almost no effort.     

A thermodynamic description of the adsorption-induced structural transitions in flexible MIL-53 metal-organic framework

We briefly review the concept of temperature-loading phase diagram that we derived from an osmotic statistical ensemble analysis of the adsorption-induced structural transitions observed in the MIL-53 family of metal-organic framework nanoporous materials. We highlight the generic nature of this diagram and comment on the occurrence of breathing transitions depending on the guest fluid, the framework functionalisation and the nature of the metal centre.     

Colossal resistivity change associated with the charge ordered/disordered transition: Monte Carlo study

Earlier theoretical approaches to manganites mainly stem from magnetic framework in which the electronic transports are thought to be spin-dependent and the double exchange plays a vital role. However, quite a number of experimental observations cannot be explained in the magnetic framework, yet. For example, multiplicate insulator-metal transitions and resistivity reduction induced by perturbations other than magnetic field, such as electric current, are not well understood in this framework. Here we present a comprehensive analysis on the magnetic framework and give a Monte Carlo study on the resistivity of a charge ordered/disordered model without accounting for the spin degree of freedom. The result shows a colossal resistivity change as a resultant of the transition between two types of insulated states. This transition has intrinsic difference from the popular insulated-to-metallic transition in the magnetic framework. The present scenario can be used to explain some experimental facts for electronic transports in manganites, which are not accessible in the magnetic framework.     

Towards a Theory of Conservative Computing

We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation of conservativeness in terms of conservation of the energy associated to the data used during the computation is given. Moreover, we define conservative computations, and we show that they naturally induce a new NP-complete decision problem. Finally, we present a framework that can be used to explicit the movement of energy occurring during a computation, and we provide a quantum implementation of the primitives of such framework using creation and annihilation operators on the Hilbert space ℂ^d, where d is the number of energy levels considered in the framework.     

PEPS as ground states: Degeneracy and topology

We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries.     

Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing

Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with “fat” tails, which can exactly be described with the q-Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.     

Investigating Multi-Level Semantic Extraction with Squash Capsules for Short Text Classification

At present, short text classification is a hot topic in the area of natural language processing. Due to the sparseness and irregularity of short text, the task of short text classification still faces great challenges. In this paper, we propose a new classification model from the aspects of short text representation, global feature extraction and local feature extraction. We use convolutional networks to extract shallow features from short text vectorization, and introduce a multi-level semantic extraction framework. It uses BiLSTM as the encoding layer while the attention mechanism and normalization are used as the interaction layer. Finally, we concatenate the convolution feature vector and semantic results of the semantic framework. After several rounds of feature integration, the framework improves the quality of the feature representation. Combined with the capsule network, we obtain high-level local information by dynamic routing and then squash them. In addition, we explore the optimal depth of semantic feature extraction for short text based on a multi-level semantic framework. We utilized four benchmark datasets to demonstrate that our model provides comparable results. The experimental results show that the accuracy of SUBJ, TREC, MR and ProcCons are 93.8%, 91.94%, 82.81% and 98.43%, respectively, which verifies that our model has greatly improves classification accuracy and model robustness.     

Transmit power and bits/channel use adaption in competitive cognitive radio networks

In this paper, we propose an optimization framework to determine the distribution of power and bits/channel use to secondary users in a competitive cognitive radio networks. The objectives of the optimization framework are to minimize total transmission power, maximize total bits/channel use and also to maintain quality of service. An upper bound on probability of bit error and lower bound on bits/channel use requirement of secondary users are considered as quality of service. The optimization problem is also constrained by total power budget across channels for a user. Simulating the framework in a centralized manner shows that more transmit power is required to allocate in a channel with higher noise power. However, allocation of bits/channel use is directly proportional to signal to interference plus noise power ratio. The proposed framework is more capable of supporting high bits/channel use requirement than existing resource allocation framework. We also develop the game theoretic user based distributed approach of the proposed framework. We see that user based distributed solution also follows centralized solution.     

A high accuracy flow segmentation method in crowded scenes based on streakline

Flow segmentation based on similar motion patterns in crowded scenes remains an open problem in computer vision due to inherent complexity and vast diversity found in such scenes. To solve this problem, the streakline framework based on Lagrangian fluid dynamics had been proposed recently. However, this framework computed optical flow field using conventional optical flow method (Lucas Kanade method) which has poor anti-interference performance, and serious deviation would be brought to the computation of optical flow field. Moreover, our experimental results show that using the formulation of streak flow similarity in this framework can result in incorrect flow segmentation. Therefore, we combine this framework with a high accurate variational model, and modify the corresponding formulation of streak flow similarity after analyzing the streakline framework in detail. Finally, an improved method is proposed to solve flow segmentation in crowded scenes. Experiments are done to compare these two methods and results verify the validity and accuracy of our method.     

Accounting for outliers and calendar effects in surrogate simulations of stock return sequences

Surrogate data analysis (SDA) is a statistical hypothesis testing framework for the determination of weak chaos in time series dynamics. Existing SDA procedures do not account properly for the rich structures observed in stock return sequences, attributed to the presence of heteroscedasticity, seasonal effects and outliers. In this paper we suggest a modification of the SDA framework, based on the robust estimation of location and scale parameters of mean-stationary time series and a probabilistic framework which deals with outliers. A demonstration on the NASDAQ Composite index daily returns shows that the proposed approach produces surrogates that faithfully reproduce the structure of the original series while being manifestations of linear-random dynamics.     

An Information Theoretic Interpretation to Deep Neural Networks

With the unprecedented performance achieved by deep learning, it is commonly believed that deep neural networks (DNNs) attempt to extract informative features for learning tasks. To formalize this intuition, we apply the local information geometric analysis and establish an information-theoretic framework for feature selection, which demonstrates the information-theoretic optimality of DNN features. Moreover, we conduct a quantitative analysis to characterize the impact of network structure on the feature extraction process of DNNs. Our investigation naturally leads to a performance metric for evaluating the effectiveness of extracted features, called the H-score, which illustrates the connection between the practical training process of DNNs and the information-theoretic framework. Finally, we validate our theoretical results by experimental designs on synthesized data and the ImageNet dataset.     

Non-relativistic holography and singular black hole

We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton–Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza–Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be non-zero.     

Correspondence between holographic and Gauss–Bonnet dark energy models

In the present work we investigate the cosmological implications of holographic dark energy density in the Gauss–Bonnet framework. By formulating independently the two cosmological scenarios, and by enforcing their simultaneous validity, we show that there is a correspondence between the holographic dark energy scenario in flat universe and the phantom dark energy model in the framework of Gauss–Bonnet theory with a potential. This correspondence leads consistently to an accelerating universe. However, in general one has not full freedom of constructing independently the two cosmological scenarios. Specific constraints must be imposed on the coupling with gravity and on the potential.