About the projection of kinematical quantities within the FE2-approach

Within the FE²-approach strain–like quantities are projected to the boundary of the attached microstructure yielding Dirichlet boundary conditions for the microscopic boundary value problem. By use of the divergence theorem one can show that the projection of gradient information to the boundary of the attached microstructure fulfills the condition that the volumetrical average of the strain–like quantities in the inner of the microstructure is exactly the same as the projected quantity, provided that the microstructure is continous. However, within the Cosserat continuum theory [1] the strain tensor depends directly on the extra rotation and not on the gradient of it. Thus, the projection can not be carried out in the same way as for gradient information. The present approach shows how to circumvent this problem by giving the extra–rotation within the Cosserat continuum theory a strong kinematical interpretation in the form of a displacement field, which shows the same effects as the extra–rotation itself. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase-locking and chaos in a silent Hodgkin–Huxley neuron exposed to sinusoidal electric field

Neuronal firing patterns are related to the information processing in neural system. This paper investigates the response characteristics of a silent Hodgkin–Huxley neuron to the stimulation of externally-applied sinusoidal electric field. The neuron exhibits both p:q phase-locked (i.e. a periodic oscillation defined as p action potentials generated by q cycle stimulations) and chaotic behaviors, depending on the values of stimulus frequencies and amplitudes. In one-parameter space, a rich bifurcation structure including period-adding without chaos and phase-locking alternated with chaos suggests frequency discrimination of the neuronal firing patterns. Furthermore, by mapping out Arnold tongues, we partition the amplitude–frequency parameter space in terms of the qualitative behaviors of the neuron. Thus the neuron’s information (firing patterns) encodes the stimulus information (amplitude and frequency), and vice versa.     

Information sets in abelian codes: defining sets and Groebner basis

In Bernal and Simón (IEEE Trans Inf Theory 57(12):7990–7999, 2011) we introduced a technique to construct information sets for every semisimple abelian code by means of its defining set. This construction is a non trivial generalization of that given by Imai (Inf Control 34:1–21, 1977) in the case of binary two-dimensional cyclic (TDC) codes. On the other hand, Sakata (IEEE Trans Inf Theory IT-27(5):556–565, 1981) showed a method for constructing information sets for binary TDC codes based on the computation of Groebner basis which agrees with the information set obtained by Imai. Later, Chabanne (IEEE Trans Inf Theory 38(6):1826–1829, 1992) presents a generalization of the permutation decoding algorithm for binary abelian codes by using Groebner basis, and as a part of his method he constructs an information set following the same ideas introduced by Sakata. In this paper we show that, in the general case of q-ary multidimensional abelian codes, both methods, that based on Groebner basis and that defined in terms of the defining sets, also yield the same information set.     

An inverse-free Newton-Jarratt-type iterative method for solving equations under the gamma condition

A local as well as a semilocal convergence analysis for Newton–Jarratt–type iterative method for solving equations in a Banach space setting is studied here using information only at a point via a gamma-type condition (Argyros in Approximate Solution of Operator Equations with Applications, [2005]; Wang in Chin. Sci. Bull. 42(7):552–555, [1997]). This method has already been examined by us in (Argyros et al. in J. Comput. Appl. Math. 51:103–106, [1994]; Argyros in Comment. Mat. XXIII:97–108, [1994]), where the order of convergence four was established using however information on the domain of the operator. In this study we also establish the same order of convergence under weaker conditions. Moreover we show that all though we use weaker conditions the results obtained here can be used to solve equations in cases where the results in (Argyros et al. in J. Comput. Appl. Math. 51:103–106, [1994]; Argyros in Comment. Mat. XXIII:97–108, [1994]) cannot apply. Our method is inverse free, and therefore cheaper at the second step in contrast with the corresponding two–step Newton methods. Numerical Examples are also provided.     

A mathematical model of the systemic circulatory system with logistically defined nervous system regulatory mechanisms

A mathematical model is developed that accurately describes the pressure, volume and flow dynamics of the systemic circulatory system over the full physiological range of human pressures and volumes. At the heart of this model are mathematical representations for the autonomic and central nervous system reflexes which maintain arterial pressure, cardiac output and cerebral blood flow. These representations involve functions in which a maximum effect and a minimum effect are smoothly connected by a logistic transition. A new approach to modelling the pressure – volume relationship in a vessel with smooth muscle contraction is also presented. To test the model, simulations of cardiac arrest and various haemorrhagic situations were conducted, and predicted results were compared with clinical observations. Near-perfect agreement was obtained between predicted and observed values of the mean circulatory filling pressure, cardiac output and arterial pressure decay in the face of significant haemorrhage, and the critical values delineating progressive from non-progressive hypovolaemic shock.     

Cubic graphs without cut‐vertices having the same path layer matrix

The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all possible paths in G. The entry (i,j) of this matrix is the number of paths in G having initial vertex i and length j. It is known that there are cubic graphs on 62 vertices having the same path layer matrix (A. A. Dobrynin. J Graph Theory 17 (1993) 1–4). A new upper bound of 36 vertices for the least order of such cubic graphs is established. This bound is realized by cubic graphs without cut‐vertices. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 177–182, 2001     

Integral representations of the TT-transform

The TT-transform of a signal is defined to be the time–time representation of the Stockwell transform that gives the time–frequency information of the signal. Two integral representations of the TT -transform are given.     

SIS epidemic model-based optimization

To solve complicated function optimization problems, a function optimization algorithm is constructed based on the Susceptible–Infective–Susceptible (SIS) epidemic model, the function optimization algorithm is called SIS algorithm, or SISA in short. The algorithm supposes that some male and female organisms exist in an ecosystem; each individual is characterized by a number of features; an infectious disease exists in the ecosystem and infects among individuals, the infection rule is that female individuals infect male individuals or male individuals infect female individuals, the disease attacks a part of features of an individual. The infected individuals can be cured; the cured individuals can be infected again after a period of time. The physique strength of an individual is decided synthetically by the infection, cure and susceptibility of certain features. The S–I operator is used to transfer feature information from male to female or female to male, the I–S operator is used to transfer feature information from male to male or female to female, the I–S operator and S–S operator are used to transfer feature information among individuals without sex difference. The individuals with strong physique can continue to grow, while the individuals with weak physique stop growing. Results show that the algorithm has characteristics of global convergence and high convergence speed for the complicated functions optimization problems, especially for high dimensional function optimization problems.     

Effects of information-dependent vaccination behavior on coronavirus outbreak: insights from a SIRI model

A mathematical model is proposed to assess the effects of a vaccine on the time evolution of a coronavirus outbreak. The model has the basic structure of SIRI compartments (susceptible–infectious–recovered–infectious) and is implemented by taking into account of the behavioral changes of individuals in response to the available information on the status of the disease in the community. We found that the cumulative incidence may be significantly reduced when the information coverage is high enough and/or the information delay is short, especially when the reinfection rate is high enough to sustain the presence of the disease in the community. This analysis is inspired by the ongoing outbreak of a respiratory illness caused by the novel coronavirus COVID-19.

     

On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems

In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time series data. In Sinha and Vaidya (in: IEEE conference on decision and control, pp 7329–7334, 2016), we have shown that the existing measures of information transfer, namely directed information, Granger causality and transfer entropy, fail to capture the causal interaction in a dynamical system and proposed a new definition of information transfer that captures direct causal interactions. The novelty of the information transfer definition used in this paper is the fact that it can differentiate between direct and indirect influences Sinha and Vaidya (2016). The main contribution of this paper is to show that the proposed definition of information transfers in Sinha and Vaidya (2016) and Sinha and Vaidya (in: Indian control conference, pp 303–308, 2017) can be computed from time series data, and thus, the direct influences in a dynamical system can be identified from time series data. We use transfer operator theoretic framework, involving Perron–Frobenius and Koopman operators for the data-driven approximation of the system dynamics and computation of information transfer. Several examples, involving linear and nonlinear system dynamics, are presented to verify the efficiency of the developed algorithm.

     

A note on optimal investment–consumption–insurance in a Lévy market

In Shen and Wei (2014) an optimal investment, consumption and life insurance purchase problem for a wage earner with Brownian information has been investigated. This paper discusses the same problem but extend their results to a geometric Itô–Lévy jump process. Our modelling framework is very general as it allows random parameters which are unbounded and involves some jumps. It also covers parameters which are both Markovian and non-Markovian functionals. Unlike in Shen and Wei (2014) who considered a diffusion framework, ours solves the problem using a novel approach, which combines the Hamilton–Jacobi–Bellman (HJB) and a backward stochastic differential equation (BSDE) in a Lévy market setup. We illustrate our results by two examples.     

On the Incorporation of Residual Stresses in Arterial Walls

The present work deals with the incorporation of residual stresses existing in circumferential direction of arterial walls. For the consideration of the residual stresses a novel model will be presented. This model is based on the assumption that residual stresses decrease the stress gradients through the thickness of the arterial wall. Since arterial walls exhibit a pronounced material behavior in fiber direction, the radial gradients of the fiber stresses are considered for the definition of the residual stresses. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Space–time fractal properties of the forest-fire series in central Italy

The space–time fractality of the forest-fire sequence (1997–2003) occurred in the Tuscany Region (central Italy), one of the most vulnerable to wildfires in Italy, has been approached by using spatial and temporal fractal tools. The fractal exponent α, estimated by the Fano factor method, characterises the time-clustering behaviour of the set of fires, while the correlation dimension D_c, calculated by means of the correlation integral method, gives information on the space-clustering behaviour of the sequence of fires. We found that (i) the investigated fire set is globally characterized by space–time clustering behaviour; (ii) α and D_c decreases and increases, respectively with the increase of the threshold size of burned area; (iii) the time variation of α shows a tendency towards Poissonian processes in correspondence of the largest events.     

The iterative instrumental variables method and the full information maximum likelihood method for estimating interdependent systems

The “iterative instrumental variables” (IIV) method for estimating interdependent systems, originally referred to as a symmetric counterpart to the “fix-point” (FP) method, shares its symmetry properties with Durbin's iterative method for performing the “full information maximum likelihood” (FIML) estimation. Classical interdependent systems are considered and identities may occur among the structural equations. Alternative symmetric procedures for obtaining FIML estimates are also dealt with, including the sequential maximization of the likelihood function with respect to the coefficients of one structural equation at a time.Two recent estimation methods developed by Brundy and Jorgenson (1971, Review of Economics and Statistics53, 207–224) as well as Dhrymes (1971, Austral. J. Statist.13, 168–175) can be considered the second approximation of the IIV method and Durbin's method respectively with the first approximation obtained by the “ordinary instrumental variables” (OIV) method. In practice the second approximation depends heavily on the choice of initial instrumental variables, although the asymptotic distribution is not changed by the continued iteration.     

Numerical aspects of the XFEM — The XFEM p–Version

The XFEM is known to approximate the displacements and stresses around a crack tip in a very efficient way. But as we will present in this paper we have to deal with a phenomenon coming along with this method that compels us to use higher order shape functions for those elements that are enriched by the crack tip functions. For the computation of the stress–intensity–factors we are using a J–integral over a circular domain Ω. The accuracy of the results depend on • the radius of Ω • the number of elements used in the XFEM computation • the number of nodes which were enriched by the crack tip functions (number of layers) and • the shape functions which were used for the standard FE term For more information about the XFEM we refer to [1]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the lower semicontinuity of the solution mappings to a parametric generalized strong vector equilibrium problem

In this paper, under new assumptions, which do not contain any information about the solution set, the lower semicontinuity of solution mappings to a parametric generalized strong vector equilibrium problem are established by using a scalarization method. These results extend and generalize the corresponding ones in Gong and Yao (J Optim Theory Appl 138:197–205, 2008), Chen and Li (Pac J Optim 6:141–151, 2010) and Li et al. (2012, submitted). Some examples are given to illustrate our results.     

New algorithms for determining the inertial orientation of an object

Kinematic equations and algorithms for the operation of strapdown inertial navigation systems intended for the high-accuracy determination of the inertial orientation parameters (the Euler (Rodrigues–Hamilton) parameters) of a moving object are considered. Together with classical orientation equations, Hamilton's quaternions and new kinematic differential equations in four-dimensional (quaternion) skew-symmetric operators are used that are matched with the classical rotation quaternion and the quaternion rotation matrix using Cayley's formulae. New methods for solving the synthesized kinematic equations are considered: a one-step quaternion orientation algorithm of third-order accuracy and two-step algorithms of third- and fourth-order accuracy in four-dimensional skew-symmetric operators for calculating the parameters of the spatial position of an object. The algorithms were constructed using the Picard method of successive approximations and employ primary integral information from measurements of the absolute angular velocity of the object as the input information, and have advantages over existing algorithms of a similar order with respect to their accuracy and simplicity.     

Information-based Parameterization of the Log-linear Model for Categorical Data Analysis

Zighera (App Stoch Mod Data Anal 1:93–108 1985) introduced a new parameterization of log-linear models for analyzing categorical data, directly linked to a thorough analysis of discrimination information through Kullback-Leibler divergence. The method mainly aims at quantifying in terms of information the variations of a binary variable of interest, by comparing two contingency tables – or sub-tables – through effects of explanatory categorical variables. The present paper settles the mathematical background necessary to rigorously apply Zighera’s parameterization to any categorical data. In particular, identifiability and good properties of asymptotically χ ²-distributed test statistics are proven to hold. Determination of parameters and all tests of effects due to explanatory variables are simultaneous. Application to classical data sets illustrates contribution with respect to existing methods.     

An axiomatic derivation of the coding-theoretic possibilistic entropy

We re-take the possibilistic (strictly non-probabilistic) model for information sources and information coding put forward in (Fuzzy Sets and Systems 132–1 (2002) 11–32); the coding-theoretic possibilistic entropy is defined there as the asymptotic rate of compression codes, which are optimal with respect to a possibilistic (not probabilistic) criterion. By proving a uniqueness theorem, in this paper we provide also an axiomatic derivation for such a possibilistic entropy, and so are able to support its use as an adequate measure of non-specificity, or rather of “possibilistic ignorance”, as we shall prefer to say. We compare our possibilistic entropy with two well-known measures of non-specificity: Hartley measure as found in set theory and U-uncertainty as found in possibility theory. The comparison allows us to show that the latter possesses also a coding-theoretic meaning.     

An individual loss reserving model with independent reporting and settlement

The main purpose of this paper is to assess and demonstrate the advantage of claims reserving models based on individual data in forecasting future liabilities over traditional models on aggregate data both theoretically and numerically. The available information consists of the reporting delays, settlement delays and claim payments. The model settings include Poisson distributed frequency of claims produced by each policy, claims payable at the settlement time, and the amount of payment depending only on its settlement delay. While such settings are applicable to certain but not all practical cases, the principal purpose of the paper is to examine the efficiency of individual data against aggregate data. We refer to loss reserving as to estimate the projections of the outstanding liabilities on observed information. The efficiency of the individual loss reserving against classical aggregate loss reservings, namely Chain-Ladder (C-L) and Bornhuetter–Ferguson (B–F), is assessed by comparing the asymptotic variances of the errors in estimating the conditional expectation (projection) of the outstanding liability between individual, C-L and B–F reservings. The research shows a significant increase in the accuracy of loss reserving by using individual data compared with aggregate data.