Fluctuation-dissipation relations far from equilibrium

The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the nonequilibrium relaxation dynamics is related to the spontaneous fluctuation at equilibrium. Most processes in Nature are out of equilibrium, for which we have limited theory. Common wisdom believes the F-D theorem is violated in general for systems far from equilibrium. Recently we show that dynamics of a dissipative system described by stochastic differential equations can be mapped to that of a thermostated Hamiltonian system, with a nonequilibrium steady state of the former corresponding to the equilibrium state of the latter. Her we derived the corresponding F-D theorem, and tested with several examples. We suggest further studies exploiting the analogy between a general dissipative system appearing in various science branches and a Hamiltonian system. Especially we discussed the implications of this work on biological network studies.Comment: 12 pages, 4 figures, major revision over the first versio

Intelligent data mining using artificial neural networks and genetic algorithms : techniques and applications

Data Mining (DM) refers to the analysis of observational datasets to find relationships and to summarize the data in ways that are both understandable and useful. Many DM techniques exist. Compared with other DM techniques, Intelligent Systems (ISs) based approaches, which include Artificial Neural Networks (ANNs), fuzzy set theory, approximate reasoning, and derivative-free optimization methods such as Genetic Algorithms (GAs), are tolerant of imprecision, uncertainty, partial truth, and approximation. They provide flexible information processing capability for handling real-life situations. This thesis is concerned with the ideas behind design, implementation, testing and application of a novel ISs based DM technique. The unique contribution of this thesis is in the implementation of a hybrid IS DM technique (Genetic Neural Mathematical Method, GNMM) for solving novel practical problems, the detailed description of this technique, and the illustrations of several applications solved by this novel technique. GNMM consists of three steps: (1) GA-based input variable selection, (2) Multi- Layer Perceptron (MLP) modelling, and (3) mathematical programming based rule extraction. In the first step, GAs are used to evolve an optimal set of MLP inputs. An adaptive method based on the average fitness of successive generations is used to adjust the mutation rate, and hence the exploration/exploitation balance. In addition, GNMM uses the elite group and appearance percentage to minimize the randomness associated with GAs. In the second step, MLP modelling serves as the core DM engine in performing classification/prediction tasks. An Independent Component Analysis (ICA) based weight initialization algorithm is used to determine optimal weights before the commencement of training algorithms. The Levenberg-Marquardt (LM) algorithm is used to achieve a second-order speedup compared to conventional Back-Propagation (BP) training. In the third step, mathematical programming based rule extraction is not only used to identify the premises of multivariate polynomial rules, but also to explore features from the extracted rules based on data samples associated with each rule. Therefore, the methodology can provide regression rules and features not only in the polyhedrons with data instances, but also in the polyhedrons without data instances. A total of six datasets from environmental and medical disciplines were used as case study applications. These datasets involve the prediction of longitudinal dispersion coefficient, classification of electrocorticography (ECoG)/Electroencephalogram (EEG) data, eye bacteria Multisensor Data Fusion (MDF), and diabetes classification (denoted by Data I through to Data VI). GNMM was applied to all these six datasets to explore its effectiveness, but the emphasis is different for different datasets. For example, the emphasis of Data I and II was to give a detailed illustration of how GNMM works; Data III and IV aimed to show how to deal with difficult classification problems; the aim of Data V was to illustrate the averaging effect of GNMM; and finally Data VI was concerned with the GA parameter selection and benchmarking GNMM with other IS DM techniques such as Adaptive Neuro-Fuzzy Inference System (ANFIS), Evolving Fuzzy Neural Network (EFuNN), Fuzzy ARTMAP, and Cartesian Genetic Programming (CGP). In addition, datasets obtained from published works (i.e. Data II & III) or public domains (i.e. Data VI) where previous results were present in the literature were also used to benchmark GNMM’s effectiveness. As a closely integrated system GNMM has the merit that it needs little human interaction. With some predefined parameters, such as GA’s crossover probability and the shape of ANNs’ activation functions, GNMM is able to process raw data until some human-interpretable rules being extracted. This is an important feature in terms of practice as quite often users of a DM system have little or no need to fully understand the internal components of such a system. Through case study applications, it has been shown that the GA-based variable selection stage is capable of: filtering out irrelevant and noisy variables, improving the accuracy of the model; making the ANN structure less complex and easier to understand; and reducing the computational complexity and memory requirements. Furthermore, rule extraction ensures that the MLP training results are easily understandable and transferrable

PLIT: An alignment-free computational tool for identification of long non-coding RNAs in plant transcriptomic datasets

Long non-coding RNAs (lncRNAs) are a class of non-coding RNAs which play a significant role in several biological processes. RNA-seq based transcriptome sequencing has been extensively used for identification of lncRNAs. However, accurate identification of lncRNAs in RNA-seq datasets is crucial for exploring their characteristic functions in the genome as most coding potential computation (CPC) tools fail to accurately identify them in transcriptomic data. Well-known CPC tools such as CPC2, lncScore, CPAT are primarily designed for prediction of lncRNAs based on the GENCODE, NONCODE and CANTATAdb databases. The prediction accuracy of these tools often drops when tested on transcriptomic datasets. This leads to higher false positive results and inaccuracy in the function annotation process. In this study, we present a novel tool, PLIT, for the identification of lncRNAs in plants RNA-seq datasets. PLIT implements a feature selection method based on L1 regularization and iterative Random Forests (iRF) classification for selection of optimal features. Based on sequence and codon-bias features, it classifies the RNA-seq derived FASTA sequences into coding or long non-coding transcripts. Using L1 regularization, 31 optimal features were obtained based on lncRNA and protein-coding transcripts from 8 plant species. The performance of the tool was evaluated on 7 plant RNA-seq datasets using 10-fold cross-validation. The analysis exhibited superior accuracy when evaluated against currently available state-of-the-art CPC tools

YOWOv2: A Stronger yet Efficient Multi-level Detection Framework for Real-time Spatio-temporal Action Detection

Designing a real-time framework for the spatio-temporal action detection task is still a challenge. In this paper, we propose a novel real-time action detection framework, YOWOv2. In this new framework, YOWOv2 takes advantage of both the 3D backbone and 2D backbone for accurate action detection. A multi-level detection pipeline is designed to detect action instances of different scales. To achieve this goal, we carefully build a simple and efficient 2D backbone with a feature pyramid network to extract different levels of classification features and regression features. For the 3D backbone, we adopt the existing efficient 3D CNN to save development time. By combining 3D backbones and 2D backbones of different sizes, we design a YOWOv2 family including YOWOv2-Tiny, YOWOv2-Medium, and YOWOv2-Large. We also introduce the popular dynamic label assignment strategy and anchor-free mechanism to make the YOWOv2 consistent with the advanced model architecture design. With our improvement, YOWOv2 is significantly superior to YOWO, and can still keep real-time detection. Without any bells and whistles, YOWOv2 achieves 87.0 % frame mAP and 52.8 % video mAP with over 20 FPS on the UCF101-24. On the AVA, YOWOv2 achieves 21.7 % frame mAP with over 20 FPS. Our code is available on https://github.com/yjh0410/YOWOv2

Can Hubbard model resist electric current?

It is claimed by a recent quantum Monte Carlo simulation that the linear-in-temperature DC resistivity observed in the high-$T_{c}$ cuprate superconductors can be reproduced in the pure two dimensional Hubbard model\cite{Huang}. Here we show perturbatively that such a translational invariant electronic model can not support a steady state current in the presence of a uniform electric field at any finite temperature. Instead, the Hubbard model is perfectly conducting in the linear response regime and will undergo Bloch oscillation at finite electric field for any finite temperature. Nevertheless, the quantum Monte Carlo simulation can provide us the key information on the temperature dependence of the Drude weight, a quantity of central importance in the holographic description of the transport properties of the strange metal phase.Comment: 5 pages, 0 figures, new arguments based on emergent symmetry and related anomaly adde

Instability of the U(1)U(1) spin liquid with a large spinon Fermi surface in the Heisenberg-ring exchange model on the triangular lattice

It is widely believed that the $U(1)$ spin liquid with a large spinon Fermi surface(SFS state) can be realized in the spin-$\frac{1}{2}$ $J_{1}-J_{4}$ model on the triangular lattice, when the ring exchange coupling $J_{4}$ is sufficiently strong to suppress the 120 degree magnetic ordered state. This belief is supported by many variational studies on this model and seems to be consistent with observations on the organic spin liquid materials such as $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, a system that is close to Mott transition and thus has large ring exchange coupling. Here we show through a systematic variational search that such a state is never favored in the $J_{1}-J_{4}$ model on the triangular lattice. Instead, a state with broken spatial symmetry is favored in the most probable parameter regime for the SFS state, with an energy much lower than that of the SFS state and other previously proposed variational states. More specifically, we find that for $J_{4}\ge 0.09J_{1}$, the system favors a valence bond solid state with a $4\times6$ period in its local spin correlation pattern, with a variational energy that is about $5\%$ lower than that of the SFS state. This state is separated form the $\pi$-flux state for $J_{4}\le 0.045J_{1}$ by an intermediate valence bond solid state with a zigzag pattern in its local spin correlation. We find that the variational phase digram is in qualitative agreement with that obtained from exact diagonalization on a $6\times6$ cluster.Comment: 16 pages, 17 figure

Strong relevance of Zinc impurity in the spin-12\frac{1}{2} Kagome quantum antiferromagnets: a variational study

Copper hydroxyhalide materials herbertsmithite ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ and Zn-barlowite ZnCu$_{3}$(OH)$_{6}$FrBr are thought to be the best realizations of the spin-$\frac{1}{2}$ Kagome quantum antiferromagnetic Heisenberg model and are widely believed to host a spin liquid ground state. However, the exact nature of such a novel state of matter is still under strong debate, partly due to the complication related to the occupation disorder between the Zinc and the Copper ions in these systems. In particular, recent nuclear magnetic resonance measurements indicate that the magnetic response of the Kagome plane is significantly spatial inhomogeneous, even though the content of the misplaced Zinc or Copper ions is believed to be very small. Here we use extensive variational optimization to show that the well known $U(1)$-Dirac spin liquid state is extremely sensitive to the introduction of the nonmagnetic Zinc impurity in the Kagome plane. More specifically, we find that the Zinc impurities can significantly reorganize the local spin correlation pattern around them and induce strong spatial oscillation in the magnetic response of the system. We argue that this is a general trend in highly frustrated quantum magnet systems, in which the nonmagnetic impurity may act as strongly relevant perturbation on the emergent resonating valence bond structure in their spin liquid ground state. We also argue that the strong spatial oscillation in the magnetic response should be attributed to the free moment released by the doped Zinc ions and may serve as the smoking gun evidence for the Dirac node in the $U(1)$ Dirac spin liquid state on the Kagome lattice.Comment: 12 pages, 10 figure