How real are virtual realities,how virtual is reality?—Constructive re-interpretation of physical undecidability

Throughout the ups and downs of scientific world conception there has been a persistent vision of a world which is understandable by human reasoning. In a contemporary, recursion theoretic, comprehension, the term “reasoning” is interpretable as “constructive” or, more specifically, “mechanically computable.” An expression of this statement is the assumption that our universe is generated by the action of some deterministic computing agent; or, stated pointedly, that we are living in a computer-generated universe. Physics then reduces to the investigation of the intrinsic, “inner view” of a particular virtual reality which happens to be our universe. In this interpretation, formal logic, mathematics and the computer sciences are just the physical sciences of more general “virtual” realities, irrespective of whether they are “really” realized or not. We shall study several aspects of this conception, among them the conjecture that randomness in physics can be constructively reinterpreted to correspond to uncomputability and undecidability in mathematics. We shall also attack the nonconstructive feature of classical physics by showing its inconsistency. Another concern is the modeling of interfaces, i.e., the means and methods of communication between two universes. On a speculative level, this may give some clue on such notorious questions such as the occurrence of “miracles” or on the “mind-body problem.”     

Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones

We consider the log-likelihood function of hidden Markov models, its derivatives and expectations of these (such as different information functions). We give explicit expressions for these functions and bound them as the size of the chain increases. We apply our bounds to obtain partial second order asymptotics and some qualitative properties of a special model as well as to extend some results of [19].     

Radioactive Decay and the Structure of e (∞) Quantum Spacetime

Some theoretical arguments and some experimental evidence are given for the hypothesis that the form of the spectra of the Beta radioactive decay, as well as the micro background radiation and related phenomena, can be traced back to the geometrical–topological structure of spacetime itself. It is argued that this structure obeys the same Aufbau principle upon which Plancks black body radiation law is based. The main conclusion here is that the universe is four-dimensional but every point in this space, however small, is again also four-dimensional and that this accounts for the form of classical and quantum behaviour observed.     

Oscillations of particles in the Standard Model

We construct Hilbert spaces of particle states such that all neutrinos and also charged leptons and up and down quarks are united into multiplets and their components can be treated as different quantum states of a single particle. The phenomenon of neutrino oscillations arises in a theory based on the Lagrangian of the fermionic sector of the Standard Model modified according to the proposed approach.     

The strength of Martin-Löf type theory with a superuniverse. Part I

Universes of types were introduced into constructive type theory by Martin-L?f [12]. The idea of forming universes in type theory is to introduce a universe as a set closed under a certain specified ensemble of set constructors, say . The universe then “reflects”. This is the first part of a paper which addresses the exact logical strength of a particular such universe construction, the so-called superuniverse due to Palmgren (cf. [16, 18, 19]). It is proved that Martin-L?f type theory with a superuniverse, termed MLS, is a system whose proof-theoretic ordinal resides strictly above the Feferman-Schütte ordinal but well below the Bachmann-Howard ordinal. Not many theories of strength between and the Bachmann-Howard ordinal have arisen. MLS provides a natural example for such a theory. Received: 14 October 1997     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

Stability and bifurcation in two species predator–prey models

Changes in the number and stability of equilibrium points in the Lotka–Volterra model as well as some of its generalizations that lead to qualitative changes in the behavior of the system as a function of some of its parameters are studied by bifurcation analysis. A generalization involving a cubic interaction as proposed by Nutku is shown to change the stability properties in a simple way and in particular cases introduce additional stability. Numerical methods and the approach provided by approximate techniques near equilibrium points are used in the analysis.     

Neutrino emission from a one-dimensional hydrogen-like atom

We find the probability and intensity of the neutrino emission from a hydrogen-like atom in a strong magnetic field. We analyze the dependence of the neutrino emission intensity on the temperature of the ensemble of atoms.     

Large Deviations in Generalized Random Graphs with Node Weights

Generalized random graphs are considered where the presence or absence of an edge depends on the weights of its nodes. Our main interest is to investigate large deviations for the number of edges per node in such a generalized random graph, where the node weights are deterministic under some regularity conditions, as well as chosen i.i.d. from a finite set with positive components. When the node weights are random variables, obstacles arise because the independence among edges no longer exists, our main tools are some results of large deviations for mixtures. After calculating, our results show that the corresponding rate functions for the deterministic case and the random case are very different.     

连续论域上Fuzzy集的信息熵

在文献[1]的基础上,把模糊熵从离散论域推广到连续论域,给出连续论域上Fuzzy集的偏熵、关联熵等概念。对其主要性质进行讨论,取得了一些令人满意的结果。拓宽信息熵的研究领域,对不确定复杂系统的信息处理、知识学习、归纳学习、模糊信息学的进一步研究打下一定基础。     

Detection of incipient gear failures using statistical techniques

Gears are important components in most power transmission mechanisms.Failures of gears can cause heavy losses in industry. Conditionmonitoring and fault diagnosis of gears is therefore importantto improve safety and reliability of gearbox operations andreduce losses caused by gear failures. This research proposesa new diagnostic approach based on the statistical analysisof data. It investigates the use of Principal Components Analysis(PCA) to detect growing local faults in a two-stage industrialhelical gearbox. In this research, the vibration signal is usedto monitor fault conditions and a broken tooth is simulatedas a local fault. Since the early detection of faults is a challenge,small fault conditions were tested first as well as severe faultconditions. In order to examine the ability of the PCA to detectfault conditions, first the PCA-based model was created fornormal operating conditions. Any unexpected event such as afault condition causes a significant deviation from the PCAmodel, which is obtained from the normal condition data of thegearbox. The Square Prediction Error (SPE) was calculated todetect the fault conditions. When the vibration signal fromthe gearbox is representative of normal operation, the valueof the SPE shows very little fluctuation and remains under acertain threshold value. However, in the presence of the faultthe SPE fluctuates considerably beyond the threshold value.It is shown that the PCA-based statistical approach cannot onlybe used to detect severe fault conditions, but that it alsoreveals small growing fault conditions at very early stage.The technique also provides information about the state of thefault such as the location of the fault as well as its severity. Received 5 March 2001. Revised 12 December 2001. Accepted 17 January 2002.     

连续论域上混合集的熵

在连续论域上定义了包含模糊性和随机性的混合集。并给出了混合熵、混合偏熵与混合关联熵、混合偏关联系数和混合关联系数等概念,拓宽了熵的应用范围,对研究一类随机性和模糊性共存的复杂系统开辟了一条新的途径。     

A mixed ODE–PDE model for vehicular traffic

We present a traffic flow model consisting of a gluing between the Lighthill–Whitham and Richards macroscopic model with a first‐order microscopic following the leader model. The basic analytical properties of this model are investigated. Existence and uniqueness are proved, as well as the basic estimates on the dependence of solutions from the initial data. Moreover, numerical integrations show some qualitative features of the model, in particular the transfer of information among regions where the different models are used. Copyright © 2014 John Wiley & Sons, Ltd.     

Exploring the dynamics of financial markets: from stock prices to strategy returns

Exploring the dynamics of financial time-series is an exciting and interesting challenge because of the many truly complex interactions that underly the price formation process. In this contribution we describe some of the anomalous statistical features of such time-series and review models of the price dynamics both across time and across the universe of stocks. In particular we discuss a non-Gaussian statistical feedback process of stock returns which we have developed over the past years with the particular application of option pricing. We then discuss a cooperative model for the correlations of stock dynamics which has its roots in the field of synergetics, where numerical simulations and comparisons with real data are presented. Finally we present summarized results of an empirical analysis probing the dynamics of actual trading strategy return streams.     

Positive periodic solutions for a neutral impulsive delayed Lotka–Volterra competition system with the effect of toxic substance

Based on the coincidence degree theory and its related continuation theorem as well as some a priori estimates, we explore the existence of periodic solutions with strictly positive components of a neutral delayed Lotka–Volterra competitive system with impulse. Easily verifiable sufficient criteria are established for the existence of positive periodic solution for the neutral impulsive system. When the results reduce to neutral system without impulse, they generalize the results in Yang and Cao [Positive periodic solutions of neutral Lotka–Volterra system with periodic delays, Appl. Math. Comput. 149 (2004) 661–687].     

Bifurcations of a Leslie-Gower prey-predator system with ratio-dependent Holling IV functional response and prey harvesting

The dynamics of a Leslie-Gower prey-predator system with ratio-dependent Holling IV functional response and constant harvesting rate of prey are taken into account. The results developed in this article reveal far richer dynamics compared with the system without harvesting. We first make qualitative and bifurcation analysis of the system without harvesting and show that the system has a weak focus of multiplicity at most 2, at which a Hopf bifurcation occurs. However, the system with harvesting has four nonhyperbolic equilibria for some parameter values, such as two saddle-node, a cusp, and a weak focus of multiplicity at most 4, and exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension 2, and a Hopf bifurcation. It reveals that there exist some critical harvesting values such that the species are in danger of extinction when the harvesting rate is greater than the critical values, which indicates that the dynamics of the system are sensitive to the constant prey harvesting. Moreover, numerical simulations are presented to illustrate our theoretical results.     

Algorithms for Commutative Algebras Over the Rational Numbers

The algebras considered in this paper are commutative rings of which the additive group is a finite-dimensional vector space over the field of rational numbers. We present deterministic polynomial-time algorithms that, given such an algebra, determine its nilradical, all of its prime ideals, as well as the corresponding localizations and residue class fields, its largest separable subalgebra, and its primitive idempotents. We also solve the discrete logarithm problem in the multiplicative group of the algebra. While deterministic polynomial-time algorithms were known earlier, our approach is different from previous ones. One of our tools is a primitive element algorithm; it decides whether the algebra has a primitive element and, if so, finds one, all in polynomial time. A methodological novelty is the use of derivations to replace a Hensel–Newton iteration. It leads to an explicit formula for lifting idempotents against nilpotents that is valid in any commutative ring.     

Improved upwind discretization of the advection equation

The simplest upwind discretization of the advection equation is only first‐order accurate in time and space and very diffusive. In this article, the first‐order upwind method is improved by changing its basis functions. The resulting scheme, called exponentially fitted, proves to be more accurate in both space and time. In addition, it inherits some qualitative behaviors of the advection equation. The proposed approach is able to be generalized for more complicated problems provided that appropriate relations between the fitting parameters of the method are imposed. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 773–787, 2014     

Joint cumulative distribution functions for Dempster–Shafer belief structures using copulas

We first introduce the Dempster–Shafer belief structure and highlight its role in the representation of information about a random variable for which our knowledge of the probabilities is interval-valued. We investigate the formation of the cumulative distribution function (CDF) for these types of variables. It is noted that this is also interval-valued and is expressible in terms of plausibility and belief measures. The class of aggregation operators known as copulas are introduced and a number of their properties are provided. We discuss Sklar’s theorem, which provides for the use of copulas in the formulation of joint CDFs from the marginal CDFs of classic random variables. We then look to extend these ideas to the case of joining the marginal CDFs associated with Dempster–Shafer belief structures. Finally we look at the formulation CDFs obtained from functions of multiple D–S belief structures.