Markov Chain Model with Catastrophe to Determine Mean Time to Default of Credit Risky Assets

This article deals with the problem of probabilistic prediction of the time distance to default for a firm. To model the credit risk, the dynamics of an asset is described as a function of a homogeneous discrete time Markov chain subject to a catastrophe, the default. The behaviour of the Markov chain is investigated and the mean time to the default is expressed in a closed form. The methodology to estimate the parameters is given. Numerical results are provided to illustrate the applicability of the proposed model on real data and their analysis is discussed.     

Modulated photoemission spectroscopy: Application to Au

We describe modulated photoemission spectroscopy, in which an internal (sample) parameter such as temperature, or an external (apparatus) parameter such as wavelength is varied. A general formalism is developed for modulated photoemission spectroscopy and then illustrated using temperature modulated photoemission spectra and yields for Au obtained in the ～ 6 to 11.6 eV photon energy range. Modulated s-p band photoemission data are described in terms of photoemission critical points in order to explain the nature of the modulated structures in the s-p band region and relate experiment to energy band thresholds obtained from a recent band calculation for Au. Application of the formalism to modulated d-band emission leads to a method for extracting d-band deformation potentials. For example, we find that the upper d band edge moves upward with respect to E_F at a rate of 2 to 6 × 10^?4 eV/K. Modulation of the quantum yield is described and our measurements are compared with modulated optical data.     

Dynamic Analyses of Contagion Risk and Module Evolution on the SSE A-Shares Market Based on Minimum Information Entropy

The interactive effect is significant in the Chinese stock market, exacerbating the abnormal market volatilities and risk contagion. Based on daily stock returns in the Shanghai Stock Exchange (SSE) A-shares, this paper divides the period between 2005 and 2018 into eight bull and bear market stages to investigate interactive patterns in the Chinese financial market. We employ the Least Absolute Shrinkage and Selection Operator (LASSO) method to construct the stock network, compare the heterogeneity of bull and bear markets, and further use the Map Equation method to analyse the evolution of modules in the SSE A-shares market. Empirical results show that (1) the connected effect is more significant in bear markets than bull markets and gives rise to abnormal volatilities in the stock market; (2) a system module can be found in the network during the first four stages, and the industry aggregation effect leads to module differentiation in the last four stages; (3) some stocks have leading effects on others throughout eight periods, and medium- and small-cap stocks with poor financial conditions are more likely to become risk sources, especially in bear markets. Our conclusions are beneficial to improving investment strategies and making regulatory policies.     

Quantum Contagion: A Quantum-Like Approach for the Analysis of Social Contagion Dynamics with Heterogeneous Adoption Thresholds

Modeling the information of social contagion processes has recently attracted a substantial amount of interest from researchers due to its wide applicability in network science, multi-agent-systems, information science, and marketing. Unlike in biological spreading, the existence of a reinforcement effect in social contagion necessitates considering the complexity of individuals in the systems. Although many studies acknowledged the heterogeneity of the individuals in their adoption of information, there are no studies that take into account the individuals’ uncertainty during their adoption decision-making. This resulted in less than optimal modeling of social contagion dynamics in the existence of phase transition in the final adoption size versus transmission probability. We employed the Inverse Born Problem (IBP) to represent probabilistic entities as complex probability amplitudes in edge-based compartmental theory, and demonstrated that our novel approach performs better in the prediction of social contagion dynamics through extensive simulations on random regular networks.     

A Markov Process Associated with a Boltzmann Equation Without Cutoff and for Non-Maxwell Molecules

Tanaka,⁽¹⁸⁾ showed a way to relate the measure solution {P _t } _t of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: {P _t } is the flow of time marginals of the solution of this stochastic equation. In the present paper, we extend this probabilistic interpretation to much more general spatially homogeneous Boltzmann equations. Then we derive from this interpretation a numerical method for the concerned Boltzmann equations, by using easily simulable interacting particle systems.     

One-Way Markov Process Approach to Repeat Times of Large Earthquakes in Faults

One of the uses of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid??s elastic rebound theory. We propose a general one-way Markovian model in which the waiting time distribution, its first moments, coefficient of variation, and functions of error and alarm (related to the predictability of the model) can be obtained analytically. The fact that in any one-way Markov cycle the coefficient of variation of the corresponding distribution of cycle lengths is always lower than one concurs with observations of large earthquakes in seismic faults. The waiting time distribution of one of the limits of this model is the negative binomial distribution; as an application, we use it to fit the Parkfield earthquake series in the San Andreas fault, California.     

A Markov chain approach to renormalization group transformations

We aim at an explicit characterization of the renormalized Hamiltonian after decimation transformation of a one-dimensional Ising-type Hamiltonian with a nearest-neighbor interaction and a magnetic field term. To facilitate a deeper understanding of the decimation effect, we translate the renormalization flow on the Ising Hamiltonian into a flow on the associated Markov chains through the Markov–Gibbs equivalence. Two different methods are used to verify the well-known conjecture that the eigenvalues of the linearization of this renormalization transformation about the fixed point bear important information about all six of the critical exponents. This illustrates the universality property of the renormalization group map in this case.     

Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition

Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.     

Heat Transport of Non-Local Effect with Modulated SMBI on HL-2A

Modulated supersonic molecular beam （SMB） injection is introduced to study transport features of non-local transport phenomenon on HL-2A. Repetitive non-local effect induced by modulated SMBI allows Fourier trans-formation of the temperature perturbation, yielding detailed investigation of the pulse propagation. Fourier analysis provides evidence for existence of internal transport barriers. Meanwhile, experimental progress of nonlocal effect was made in the HL-2A Tokamak in 200Z The core electron temperature Te rise increases from 18% to more than 40% and the duration of the Te rise could be prolonged by changing the conditions of SMB injection.     

动态故障树在主蒸汽管道破裂事故风险评价中的初步应用研究

冗余设计使核电厂系统广泛存在复杂时序失效行为,而基于静态故障树(Static fault tree, SFT)的事故风险评价无法对时序失效行为进行准确模拟。为解决这一问题,本工作提出一种基于事件树+动态故障树(Dynamic Fault Tree, DFT)的事故风险分析框架,并以典型三代压水堆主蒸汽管道破裂事故为例,开展动态事故风险案例分析。首先,建立主蒸汽管道破裂事故的事件树模型以及相关系统的DFT模型;其次,将系统故障树分为DFT模块和SFT模块,并将DFT树模块替换为超级事件参与后续计算;最后,采用割集法计算案例结果,并在相同条件下与传统SFT方法进行对比。案例分析结果表明：(1)相较于SFT方法,所提方法更为贴近系统的真实失效场景;(2)针对文中案例所提方法可以降低相关系统失效概率与部分事故序列的发生频率、有助于释放保守风险。     

A definition of metastability for Markov processes with detailed balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach [1]. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.     

Multilayer Markov Chains with Applications to Polymers in Shear Flow

We present an analysis of multilayer Markov chains and apply the results to a model of a tethered polymer chain in shear flow. We find that the stationary probability measure in the direction of the flow is nonmonotonic, and has several maxima and minima for sufficiently high shear rates. This is in agreement with the experimental observation of cyclic dynamics for such polymer systems. Estimates for the stationary variance and expectation value were obtained and showed to be in accordance with our numerical results.     

Credit risk—A structural model with jumps and correlations

We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump-diffusion process for the risk factors, i.e. for the company assets. We also include correlations between the companies. We discuss that models of this type have much in common with other problems in statistical physics and in the theory of complex systems. We study a simplified version of our model analytically. Furthermore, we perform extensive numerical simulations for the full model. The observables are the loss distribution of the credit portfolio, its moments and other quantities derived thereof. We compile detailed information about the parameter dependence of these observables. In the course of setting up and analyzing our model, we also give a review of credit risk modeling for a physics audience.     

Jarzyski’s Equality and Crooks’ Fluctuation Theorem for General Markov Chains with Application to Decision-Making Systems

We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski’s equality and Crooks’ fluctuation theorem in this setup. In particular, we regard the discrete-time case, which leads to an asymmetry in the definition of work that appears in the usual formulation of Crooks’ fluctuation theorem. We show how this asymmetry can be avoided with an additional condition regarding the energy protocol. The general formulation in terms of Markov chains allows transferring the results to other application areas outside of physics. Here, we discuss how this framework can be applied in the context of decision-making. This involves the definition of the relevant quantities, the assumptions that need to be made for the different fluctuation theorems to hold, as well as the consideration of discrete trajectories instead of the continuous trajectories, which are relevant in physics.     

A singular perturbation approach to first passage times for Markov jump processes

We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods.     

A Bayesian Networks approach to Operational Risk

A system for Operational Risk management based on the computational paradigm of Bayesian Networks is presented. The algorithm allows the construction of a Bayesian Network targeted for each bank and takes into account in a simple and realistic way the correlations among different processes of the bank. The internal losses are averaged over a variable time horizon, so that the correlations at different times are removed, while the correlations at the same time are kept: the averaged losses are thus suitable to perform the learning of the network topology and parameters; since the main aim is to understand the role of the correlations among the losses, the assessments of domain experts are not used. The algorithm has been validated on synthetic time series. It should be stressed that the proposed algorithm has been thought for the practical implementation in a mid or small sized bank, since it has a small impact on the organizational structure of a bank and requires an investment in human resources which is limited to the computational area.     

Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings

For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter . The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.     

High-Power Modulated Intense Relativistic Electron Sources with Applications to RF Generation and Controlled Thermonuclear Fusion

Recent advances in the physics and technology of the modulated intense relativistic electron beams (IREB's) are reviewed in this paper. Bunched dense electron beams can be used to construct high-power RF sources, which may critically affect future progress in fusion technology. In this paper a system is described in which electrical energy can be converted from a single pulse of relatively long duration into a series of subpulses of short duration (nanosecond and subnanosecond) and of high power (~1010 W). This electrical system consists of an IREB propagating through passive structures. The mutual interaction between the electron beam and one passive structure modifies the IREB so that power compression and beam modulation occur. When the modified IREB interacts with the next passive structure, the kinetic energy of the electrons is converted into electrical energy or RF energy. The beam current modulation depends on the injected IREB and the structure parameters. A 100-percent modulation of the current has been achieved. A single-beam source may be used for exciting radiation in a frequency range of 60 MHz to 10 GHz. In the frequency range of 60-750 MHz a modulated beam with power ~1010 W has already been achieved. IREB modulation at a frequency of ~3 GHz was performed and RF energy was extracted from the bunched beam with power output of 5 × 108 W.     

A Comparison of Lineshape Models in the Analysis of Modulated and Natural Rotational Line Profiles: Application to the Pressure Broadening of OCS and CO

We report on the self and pressure broadening of the J=9←8 transition of O¹²CS and O¹³CS and the J+1←J, with J=0, 1, 2, 3, rotational transitions of ¹²CO and ¹³CO. In particular, the J=9← 8 of OCS and J=1← 0 of CO have been investigated for a detailed comparison of lineshape models in the analysis of natural and modulated line profiles. Since the frequency modulation technique improves the instrumental sensitivity, allowing the study of weak transition line profiles, a thorough test of this technique applied to lineshape analysis has been carried out. Finally, the self and pressure broadening coefficients are also given. Due to the important role covered by CO in the atmospheric chemistry field, we have paid particular attention to the N₂ and O₂ broadening.     

A Process Algebra Approach to Quantum Electrodynamics

The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.