基于均值距离测度的医学图像配准

针对互信息测度在配准医学图像时易陷入局部极值、速度慢的缺点,提出了基于均值不等式的均值距离测度.首先根据均值不等式推导出5种均值距离测度：方根-算术均值距离(SAM)、方根-几何均值距离(SGM)、方根-调和均值距离(SHM)、算术-几何均值距离(AGM)、算术-调和均值距离(AHM).然后通过人体脑部CT/MR和MR-T1/PD图像的刚体配准实验,从函数曲线、配准精度、计算时间和收敛性能方面,对互信息与5种均值距离信息测度进行了比较与分析.实验结果表明,在不损失配准精度的前提下,AHM和SAM测度可以获得更快的配准速度,对噪声有很强的鲁棒性.     

The Natural Philosophy of Economic Information: Autonomous Agents and Physiosemiosis

Information is a core concept in modern economics, yet its definition and empirical specification is elusive. One reason is the intellectual grip of the Shannon paradigm which marginalizes semantic information. However, a precise concept of economic information must be based on a theory of semantics, since what counts economically is the meaning, function and use of information. This paper introduces a new principled approach to information that adopts the paradigm of biosemiotics, rooted in the philosophy of Charles S. Peirce and builds on recent developments of the thermodynamics of information. Information processing by autonomous agents, defined as autopoietic heat engines, is conceived as physiosemiosis operating according to fundamental thermodynamic principles of information processing, as elucidated in recent work by Kolchinsky and Wolpert (KW). I plug the KW approach into a basic conceptual model of physiosemiosis and present an evolutionary interpretation. This approach has far-reaching implications for economics, such as suggesting an evolutionary view of the economic agent, choice and behavior, which is informed by applications of statistical thermodynamics on the brain.     

The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.     

Information Geometric Theory in the Prediction of Abrupt Changes in System Dynamics

Detection and measurement of abrupt changes in a process can provide us with important tools for decision making in systems management. In particular, it can be utilised to predict the onset of a sudden event such as a rare, extreme event which causes the abrupt dynamical change in the system. Here, we investigate the prediction capability of information theory by focusing on how sensitive information-geometric theory (information length diagnostics) and entropy-based information theoretical method (information flow) are to abrupt changes. To this end, we utilise a non-autonomous Kramer equation by including a sudden perturbation to the system to mimic the onset of a sudden event and calculate time-dependent probability density functions (PDFs) and various statistical quantities with the help of numerical simulations. We show that information length diagnostics predict the onset of a sudden event better than the information flow. Furthermore, it is explicitly shown that the information flow like any other entropy-based measures has limitations in measuring perturbations which do not affect entropy.     

A Novel Approach to the Partial Information Decomposition

We consider the “partial information decomposition” (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we propose a general framework for constructing a multivariate PID. Our framework is defined in terms of a formal analogy with intersection and union from set theory, along with an ordering relation which specifies when one information source is more informative than another. Our definitions are algebraically and axiomatically motivated, and can be generalized to domains beyond Shannon information theory (such as algorithmic information theory and quantum information theory). In the second part of this paper, we use our general framework to define a PID in terms of the well-known Blackwell order, which has a fundamental operational interpretation. We demonstrate our approach on numerous examples and show that it overcomes many drawbacks associated with previous proposals.     

Quark interpretation of the combinatorial hierarchy

We propose a physical interpretation of the second level of the combinatorial hierarchy in terms of three quarks, three antiquarks, and the vacuum. This interpretation allows us to introduce a new quantum number, which measures electromagnetic mass splitting of the quarks. We extend our argument by analog to baryons, and find someSU(3) and some new mass formulas for baryons. The generalization of our approach to other hierarchy levels is discussed. We present also an empirical mass formula for baryons, which seems to be loosely connected with the combinatorial hierarchy.     

Information Network Modeling for U.S. Banking Systemic Risk

In this work we investigate whether information theory measures like mutual information and transfer entropy, extracted from a bank network, Granger cause financial stress indexes like LIBOR-OIS (London Interbank Offered Rate-Overnight Index Swap) spread, STLFSI (St. Louis Fed Financial Stress Index) and USD/CHF (USA Dollar/Swiss Franc) exchange rate. The information theory measures are extracted from a Gaussian Graphical Model constructed from daily stock time series of the top 74 listed US banks. The graphical model is calculated with a recently developed algorithm (LoGo) which provides very fast inference model that allows us to update the graphical model each market day. We therefore can generate daily time series of mutual information and transfer entropy for each bank of the network. The Granger causality between the bank related measures and the financial stress indexes is investigated with both standard Granger-causality and Partial Granger-causality conditioned on control measures representative of the general economy conditions.     

一种研究二元对称离散信道平均互信息的新方法

在有干扰(噪声)无记忆信道和有记忆信道两种情况下，运用协同学的方法研究如何分配输入概率获取二元对称离散信道最大的平均互信息. 研究结果表明：对于无记忆二元对称离散信道，最大平均互信息与信息论中相同输入概率使平均互信息最大化的结果是一致的；对于干扰(噪声)有记忆二元对称离散信道，考虑输入、输出符号满足不同程度的记忆度和干扰(噪声)因子情况下，得到符号最佳输入概率. 拓展了一种研究信息论的方法. 关键词： 协同学 二元对称离散信道 互信息 转移概率     

New trends in density matrix renormalization

The density matrix renormalization group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond condensed matter, and is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and nuclear and high-energy physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview of the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite-temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the dynamical mean field method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.     

Disorder and decision cost in spatial networks

We introduce the concept of decision cost of a spatial graph, which measures the disorder of a given network taking into account not only the connections between nodes but their position in a two-dimensional map. The influence of the network size is evaluated and we show that normalization of the decision cost allows us to compare the degree of disorder of networks of different sizes. Under this framework, we measure the disorder of the connections between airports of two different countries and obtain some conclusions about which of them is more disordered. The introduced concepts (decision cost and disorder of spatial networks) can easily be extended to Euclidean networks of higher dimensions, and also to networks whose nodes have a certain fitness property (i.e., one-dimensional).     

Formulation of the Shannon theorem for a discrete noisy channel

In this paper, the Shannon theorem is formulated for a discrete noisy channel in terms used in the Shannon formulation. Proof of the theorem is based on the theory of optimal signals reception, in which the signal intensity with respect to noise has a significant meaning. Although the formulation contains the notions of the channel capacity and the message-source entropy, it substantially differs from the Shannon formulation. The obtained formulation allows us to explain some cases where the information transmission conditions do not satisfy the Shannon theorem.     

Active-space N-representability constraints for variational two-particle reduced density matrix calculations

The ground-state energy of a system of fermions can be calculated by minimizing a linear functional of the two-particle reduced density matrix (2-RDM) if an accurate set of N-representability conditions is applied. In this Letter we introduce a class of linear N-representability conditions based on exact calculations on a reduced active space. Unlike wave-function-based approaches, the 2-RDM methodology allows us to combine information from calculations on different active spaces. By adding active-space constraints, we can iteratively improve our estimate for the ground-state energy. Applying our methodology to a 1D Hubbard model yields a significant improvement over traditional 2-positivity constraints with the same computational scaling.     

Isospectral Twirling and Quantum Chaos

We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).     

Determining Causal Skeletons with Information Theory

Modeling a causal association as arising from a communication process between cause and effect, simplifies the discovery of causal skeletons. The communication channels enabling these communication processes, are fully characterized by stochastic tensors, and therefore allow us to use linear algebra. This tensor-based approach reduces the dimensionality of the data needed to test for conditional independence, e.g., for systems comprising three variables, pair-wise determined tensors suffice to infer the causal skeleton. The only thing needed is a minor extension to information theory, namely the concept of path information.     

Quantum Information in the Frame of Coherent States Representation

In this paper we have showed that the qubit can be expressed through the coherent states. Consequently, a message, i.e. a sequence of qubits, is expressed as a tensor product of coherent states. In the quantum information theory and practice, only the code and key message are expressed as a sequence of qubits, i.e. through a quantum channel, the properly information will be transmitted by using a classical channel. Even if the most used coherent states in the quantum information theory are the coherent states of the harmonic oscillator (particularly, expressing by them the Schrödinger “cat states” and the Bell states), several authors have been demonstrated that other kind of coherent states may be used in quantum information theory. For the ensembles of qubits, we must use the density operator, in order to describe the informational content of the ensemble. The diagonal representation of the density operator, in the coherent state representation, is also useful to examine the entanglement of the states.     

Matrix effects on the surface plasmon resonance of dry supported gold nanocrystals

We present a method to characterize surface-chemical properties of gold nanocrystals. Spherical, 60 nm gold nanocrystals were immobilized on quartz substrates by a coupling agent and cleaned in a hydrogen plasma. The nanocrystals were then functionalized with alkanethiol self-assembled monolayers (SAM) of varying chain lengths by adsorption from the gas phase, and localized surface plasmon resonance (LSPR) spectroscopy was performed on the samples. Depending on the alkanethiol chain length, the adsorption of the SAM redshifted the LSPR to different extents, in accordance with Mie theory. SAM thickness differences below 1 nm could be easily resolved. Our results demonstrate that LSPR spectroscopy can be applied to characterize thin organic layers on dry supported gold particles with high sensitivity.     

Characterizing correlation changes of complex pattern transitions: The case of epileptic activity

We analyze the time-dependent spectrum of eigenvalues of the correlation matrix for multivariate EEG data at the transition to epileptic seizures. By a mechanism of level repulsion between states at both edges of the spectrum of the correlation matrix, relevant information about quantitative correlation changes is reflected in the largest and smallest eigenvalues and corresponding eigenvectors. By the application of measures from random matrix theory we provide evidence that statistically relevant information can be obtained both at the upper and the lower end of the spectrum. In addition, information about spatial characteristics of correlation changes can be extracted.     

The Spread of Ideas in a Network—The Garbage-Can Model

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of the concept of temporal networks allows us to show the dynamics of ideas spreading processes in networks, thanks to the analysis of contacts between agents in networks. The Axelrod culture dissemination model allows us to use the importance of cooperative behavior for the dynamics of ideas disseminated in networks. In the third model decisions on solutions of problems are made as an outcome of sequences of pseudorandom numbers. The origin of this model is the Herbert Simon’s view on bounded rationality. In the Axelrod model, ideas are conveyed by strings of symbols. The outcome of the model should be the diversity of evolving ideas as dependent on the chain length, on the number of possible values of symbols and on the threshold value of Hamming distance which enables the combination.