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.     

Frobenius manifolds and Frobenius algebra-valued integrable systems

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929–952, 1996), Kontsevich and Manin (Inv Math 124: 313–339, 1996). By specializing this construction, using a fixed Frobenius algebra \({\mathcal {A}},\) one can arrive at such a theory. More generally, one can apply the same idea to construct an \({\mathcal {A}}\)-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an \({\mathcal {A}}\)-valued modified Camassa–Holm equation is constructed.     

Luminescence imaging of biological subjects during X-ray irradiations lower energy than Cerenkov-light threshold

It is commonly thought that UV or visible-light luminescence imaging of biological subjects during X-ray irradiation at the energy below 120 keV is impossible because the secondary electrons produced in this energy range do not emit Cerenkov light. Contrary to this consensus, we found UV or visible-light luminescence imaging of the subjects were possible with X-ray irradiations of this energy range. We placed one of the biological subjects in a black box; visible-light luminescence images were measured with a high-sensitivity, cooled charge coupled device (CCD) camera during X-ray irradiation at energy below 120 keV. We also conducted the imaging of air without subjects during irradiation of the same X-ray. The biological subjects emitted visible-light luminescence, and the imaging was possible with the irradiation of the X-ray below 120 keV. The luminescence images were observed in only the X-ray irradiated areas. Also air luminescence images could be obtained and the intensity of the luminescence measured from the images was proportionally increased with the exposure dose. UV or visible-light luminescence imaging of biological subjects was possible during X-ray irradiations lower energy than the Cerenkov-light threshold. The phenomenon was different from general X-ray fluorescence because wavelength of the luminescence is UV or visible-light. The luminescence imaging method is promising for estimating the irradiated area with X-ray, which could be used for interventional radiology (IVR). Also air luminescence imaging would be applied to the exposure dose distribution measurements for X-ray of diagnostic X-ray systems.     

Distributions of positive correlations in sectoral value added growth in the global economic network*

International trade has grown considerably during the process of globalization. Complex supply chains for the production of goods have resulted in an increasingly connected International Trade Network (ITN). Traditionally, direct trade relations between industries have been regarded as mediators of supply and demand spillovers. With increasing network connectivity the question arises if higher-order relations become more important in explaining a national sector’s susceptibility to supply and demand changes of its trading partner. In this study we address this question by investigating empirically to what extent the topological properties of the ITN provide information about positive correlations in the production of two industry sectors. We observe that although direct trade relations between industries serve as important indicators for correlations in the industries’ value added growth, opportunities of substitution for required production inputs as well as second-order trade relations cannot be neglected. Our results contribute to a better understanding of the relation between trade and economic productivity and can serve as a basis for the improvement of crisis spreading models that evaluate contagion threats in the case of a node’s failure in the ITN.     

Scale-invariant structure of energy fluctuations in real earthquakes

Earthquakes are obviously complex phenomena associated with complicated spatiotemporal correlations, and they are generally characterized by two power laws: the Gutenberg-Richter (GR) and the Omori-Utsu laws. However, an important challenge has been to explain two apparently contrasting features: the GR and Omori-Utsu laws are scale-invariant and unaffected by energy or time scales, whereas earthquakes occasionally exhibit a characteristic energy or time scale, such as with asperity events. In this paper, three high-quality datasets on earthquakes were used to calculate the earthquake energy fluctuations at various spatiotemporal scales, and the results reveal the correlations between seismic events regardless of their critical or characteristic features. The probability density functions (PDFs) of the fluctuations exhibit evidence of another scaling that behaves as a q-Gaussian rather than random process. The scaling behaviors are observed for scales spanning three orders of magnitude. Considering the spatial heterogeneities in a real earthquake fault, we propose an inhomogeneous Olami-Feder-Christensen (OFC) model to describe the statistical properties of real earthquakes. The numerical simulations show that the inhomogeneous OFC model shares the same statistical properties with real earthquakes.     

Enhancing energy harvesting by coupling monostable oscillators

The performance of a ring of linearly coupled, monostable nonlinear oscillators is optimized towards its goal of acting as energy harvester – through piezoelectric transduction – of mesoscopic fluctuations, which are modeled as Ornstein-Uhlenbeck noises. For a single oscillator, the maximum output voltage and overall efficiency are attained for a soft piecewise-linear potential (providing a weak attractive constant force) but they are still fairly large for a harmonic potential. When several harmonic springs are linearly and bidirectionally coupled to form a ring, it is found that counter-phase coupling can largely improve the performance while in-phase coupling worsens it. Moreover, it turns out that few (two or three) coupled units perform better than more.     

Trapping of helium atom by vacancy in tungsten: a density functional theory study

The interaction between helium (He) atom and vacancy defect in tungsten (W) has been investigated by using first-principles simulations. We have obtained that the most stable site for He in tungsten is the substitutional position because He can keep its own electronic structure at this position. In the studied tungsten system, vacancy can act as a trapping center for surrounding He atom with negative trapping energy. The migration behaviors of He atom at tetrahedral interstitial site in W, which can be trapped by vacancy but the final position is almost unchanged comparing with its initial position through structural relaxation, have been predicted and discussed. It is also found that single He atom prefers to go through an octahedral site rather than through a direct path to the vacancy, and the stronger the interaction between He atom and vacancy is, the lower the migration barrier will be.     

Ab initio study of phonon dispersion and thermodynamic properties of pure and doped pyrites

Pyrites (FeS₂) are solid minerals that are found abundantly in Nigeria and are easy to prepare in laboratories. In this work, FeS₂ is studied extensively in its pure state as well as when iron is substitutionally doped with zinc and calcium at concentrations of 0, 0.25, 0.5, 0.75 and 1. Using density functional theory, the eectronic, dynamic and thermodynamic properties were calculated. The results revealed that the lattice parameters and bulk modulus increases with increasing concentration and the obtained values are in agreement with available experimental and theoretical values. Though pyrite, when doped with zinc, obeys Vegard’s law, doping with calcium revealed pronounced deviation from this law. The calculated band structures showed that FeS₂ has an indirect band gap whose size decreases after introducing zinc while doping with calcium increases the band gap. The phonon dispersion of the end members FeS₂ and ZnS₂ indicate that the systems are dynamically stable while CaS₂ is dynamically unstate. Also, the thermodynamic properties of the pure and doped pyrites were calculated and the ranges of temperature at which the lattice and electronic degrees of freedom contribute to the specific heat capacity are presented.