With the goal of explaining the maldistribution of evil in the world, Asha Lancaster-Thomas has recently (2023) expounded upon the idea of a fluctuating maximal God (FMG) that she and others developed (Jeffrey et al. (2020)) from the idea of a maximal God originally proposed by Yujin Nagasawa ( 2017 ). Lancaster-Thomas uses this model to answer what I and my co-author, Daniel Linford, have called the problem of geography (Linford and Patterson (2015)). The problem of geography points to the (...) geographically unequal distribution of suffering in the world and argues that this aggravates the original problem of evil (POE) and undermines the primary theodicies offered as solutions to it. I subsequently (2021) added to this problem by pointing out that evil is also maldistributed across race, gender and time. This larger problem may be referred to as the problem of the distribution of evil (PODE). Lancaster-Thomas argues that the FMG, especially under her modified version, is not susceptible to the problem of geography or to temporal inequalities of well-being. In this article I will demonstrate how the FMG, even on Lancaster-Thomas? updated model, fails to undermine either the problem of geography or the more broadly conceived PODE. (shrink)

Fluctuating asymmetry (FA) is small deviations from perfect symmetry in normally bilaterally symmetrical traits. We examined the relationship between FA of five body traits (ear height, length of three digits, and ankle circumference) and self-reported scores of physical and verbal aggression in a sample of 90 boys aged 10 to 15 years. The relationships between FA and scores of aggression (particularly physical aggression) were found to be negative; in other words, the most symmetrical boys showed highest aggression. One trait (ankle (...) circumference) showed the characteristics of “ideal” FA—parametric mean of zero and a normal distribution. Mean asymmetries calculated from six repeated measures of ankle FA in 30 subjects taken over a period of five months showed strong negative associations with scores of physical aggression which were independent of age, height, and weight.It is argued that soft tissue “cyclical” FA (as opposed to “fixed” bony FA) is dependent on the secretion of hormones: for example, cortisol. Causal associations between behavioral traits such as aggresion and hormones will lead to similar correlations between FA and behavior. (shrink)

The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution 'from within'. This analysis sheds light on two views on thermodynamic equilibrium, the 'ergodic' and the 'thermodynamic (...) limit' schools, and the relations between them. It also provides an outline for a new definition of equilibrium that is weaker than full ergodicity. Finally, we briefly discuss the possibility that the distribution can be determined by external observers. (shrink)

We investigate several fluctuation effects in high-energy hadronic and nuclear collisions through the analysis of different observables. To introduce fluctuations in the initial stage of collisions, we use the interacting gluon model (IGM) modified by the inclusion of the impact parameter. The inelasticity and leading-particle distributions follow directly from this model. The fluctuation effects on rapidity distributions are then studied using Landau's hydrodynamic model in one dimension. To investigage further the effects of the multiplicity fluctuation, we use (...) the longitudinal phase-space model, with the multiplicity distribution calculated within the hydrodynamic model, and the initial conditions given by the IGM. Forward-backward correlation is obtained in this way. (shrink)

The traditional formalism of quantum mechanics is mainly used to describe ensembles of identical systems (with a density-operator formalism) or single isolated systems, but is not capable of describing single open quantum objects with many degrees of freedom showing pure-state stochastic dynamical behaviour. In particular, stochastic 'line-migration' as in single-molecule spectroscopy of defect molecules in a molecular matrix is not adequately described. Starting with the Bohr scenario of stochastic quantum jumps (between strict energy eigenstates), we try to incorporate more general (...) pure-state stochastic dynamical behaviour into the quantum mechanical formalism.Probability distributions of (approximately) pure states, arising through the stochastic pure-state dynamics for long times, give rise to appropriate decompositions of thermal density operators. These decompositions of density operators into pure states mediate between quantum mechanics for ensembles of molecules and quantum theory for single molecules (or single dressed quantum objects). We suggest that such decompositions should be consistent with infinite limits (e.g. the Born-Oppenheimer limit for infinite nuclear masses) in the sense that quantum fluctuations (around classical behaviour in the infinite limit) die out asymptotically. (shrink)

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, (...) and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future. (shrink)

This paper investigates the behavior of conformal fluctuations of space-time geometry that are admissible under the quantized version of Einstein's general relativity. The approach to quantum gravity is via path integrals. It is shown that considerable simplification results when only the conformal degrees of freedom are considered under this scheme, so much so that it is possible to write down a formal kernel in the most general case where the space-time contains arbitrary distributions of particles with no other interaction except (...) gravity. The behavior of this kernel near the classical space-time singularity then shows that quantum fluctuations inevitably diverge near the singularity. It is shown further that the root cause of this divergence lies in the fact that the Green's function for the conformally invariant scalar wave equation diverges at the singularity. The limitations on the validity of classical general relativity near the space-time singularity are discussed and it is argued that the notion of singularity itself needs to be radically modified once the quantum effects are taken into account. (shrink)

Electrical membrane fluctuations are treated as due to sequences of ion pulses passing through the membrane. A mathematical procedure is developed which permits calculation of the power spectra for sequences in which the pulses can have Poisson or non-Poisson interval distributions and may or may not have coupled pulse parameters. It is shown that there probably exist specific sequences which are intimately related to membrane 1/f and burst noise. In particular, emphasis is placed upon sequences with non-Poisson interval distributions and (...) their implications for membrane structure. A variety of experiments is suggested which will help to distinguish among the alternatives presented. (shrink)

The social and cognitive science replication crisis is partly due to the limitations of commonly used statistical tools. Inferential statistics require that unsystematic measurement variation is independent of system history, and weak relative to systematic or causal sources of variation. However, contemporary systems research underscores the dynamic, adaptive nature of social, cognitive, and behavioral systems. Variation in human activity includes the influences of intrinsic dynamics intertwined with changing contextual circumstances. Conventional inferential techniques presume milder forms of variability, such as unsystematic (...) measurement error, as in a Gaussian distribution. Inferential statistics indicate an elementary Newtonian cause-effect metaphor for change that is inconsistent with known principles of change in complex systems. Pattern formation in self-organizing systems and quantum probability are used to illustrate theoretical metaphors that instantiate alternative notions of change in complex systems. Inferential statistics and related techniques are crucial scientific resources. However, in the social and behavioral sciences, they must be practiced in conjunction with an appropriate general systems framework that accommodates intrinsic fluctuations and contextual adaptation. (shrink)

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F ¦ –¦dF/dt=gG =k 1,G=k 2 as ¦– ¦ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower.A solution of the system satisfying the boundary conditions is constructed so that specified limiting conditions are fulfilled.

Power provision is coming to be the most important constraint to data center development. The efficient management of power consumption according to the loads of the data center is urgent. As the load for every application hosted in every server node of the data center and corresponding Service Level Agreement requirements can be quite different, it is hard to deploy a power strategy at application. The asynchronies and abruptness characteristics of workload fluctuation make power management policymaking using periodic resource (...) scheduling method invalid. In this article, the design and implementation of the request–response distributed power management scheme is elaborated. Bound by linear time complexity, the method proposed integrates dynamic voltage/frequency scaling, power-on–power-off, and virtual machine migration mechanisms and dynamically optimizes the power consumption of a cloud data center. The significant advantage of the scheme is that it does not need synchronous scheduling between all SNs. Simulation results showed that the scheme could effectively decrease the power consumption of the data center, with a tiny reduction in performance as centralized control methods. (shrink)

Two-classes of phase-space spin quasi-distribution functions are introduced and discussed. The first class of these distributions is based on the delta function construction. It is shown that such a construction can be carried out for an arbitrary spin s and an arbitrary ordering of the spin operators. The second class of the spin distributions is constructed with the help of the spin coherent states. The connection of the spin coherent states to the Stratonovich formalism is established and discussed. It (...) is shown that the c-number phase-space description of quantum fluctuations provides a simple statistical picture of quantum fluctuations of spinoperators in terms of random directions on a unit sphere. For quantum states of the spin system the statistics of these random orientations is given by non-positive spin quasi-distribution functions. It is shown that the application of these spin quasi-distribution functions to the Einstein-Podolsky-Rosen correlations provide an insight into the quantum theory of measurement. (shrink)

We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity (GR) in vacuum regions. This is an investigation of a possible scenario of spacetime emergence from quantum interactions directly in the spacetime, and of how effective quantum behaviour might provide a useful link between detailed properties of quantum interactions and GR. The quantum fluctuations are assumed to entangle (...) sufficiently for a cohesive spacetime to form, so that their effective properties can be described relative to a D-dimensional reference frame. To obtain the desired features of a smooth metric with a vanishing Ricci tensor, the quantum fluctuations are modelled as Gaussian probability distributions, with a shape set relative to the interactions coming from the surroundings. At small scales, the propagation through the spacetime is modelled by a Gaussian random walk. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

This 1974 collection of six essays in economic theory represents a major contribution to the field. The first contains the formulation of the Ricardian system, whilst the next two contain, respectively, the author's synthetic treatment of the complex problems of fluctuations and economic growth, and his well-known theorem that in the long run the rate of profit and income distribution are independent of the propensities to save of the working class. The essays that follow provide the missing links: a (...) coherent picture of the macroeconomic theories that have originated in Cambridge and a discussion of their deep foundations in classical economic analysis. Finally, the author evaluates some economic controversies and draws his conclusions on the basic forces determining rate of profit in the process of economic growth. Although the arguments are highly theoretical, they require no knowledge of mathematics beyond elementary calculus and algebra. (shrink)

Not all of the studies cited in the target article as evidence that fluctuating asymmetry (FA) predicts male mating success demonstrate that the observed asymmetry is, in fact, FA. FA is a population-level pattern of differences between sides. Unless the population-level distributional criteria of bilateral traits are reported, the meaning of asymmetry in individuals is unknown.

Randomness, uncertainty, and lack of regularity had concerned savants for a long time. As early as the seventeenth century, Blaise Pascal conceived the arithmetic of chance for gambling. At the height of positional astronomy, mathematicians developed a theory of errors to cope with random deviations in astronomical observations. In the nineteenth century, pioneers of statistics employed probabilistic calculus to define “normal” and “pathological” in the distribution of social characters, while physicists devised the statistical-mechanical interpretation of thermodynamic effects. By the (...) end of the century, a probabilistic worldview—as historians Lorrain Daston, Theodore Porter, and Stephen Stigler. (shrink)

A classical gas at equilibrium satisfies the locality conditionif the correlations between local fluctuations at a pair of remote small regions diminish in the thermodynamic limit. The gas satisfies a strong locality conditionif the local fluctuations at any number of remote locations have no (pair, triple, quadruple....) correlations among them in the thermodynamic limit. We prove that locality is equivalent to a certain factorizability condition on the distribution function. The analogous quantum condition fails in the case of a freeBose (...) gas. Next we prove that strong locality is equivalent to the total factorizability of the distribution function, and thus (given Liourille’s theorem) to the Maxwell Boltzmann distribution for an ideal gas. (shrink)

Metagenomics is a culture‐ and PCR‐independent approach that is now widely exploited for directly studying microbial evolution, microbial ecology, and developing biotechnologies. Observations and discoveries are critically dependent on DNA extraction methods, sequencing technologies, and bioinformatics tools. The potential pitfalls need to be understood and, to some degree, mastered if the resulting data are to survive scrutiny. In particular, methodological variations appear to affect results from different ecosystems differently, thus increasing the risk of biological and ecological misinterpretation. Part of the (...) difficulty is derived from the lack of knowledge concerning the true microbial diversity and because no approach can guarantee accessing microorganisms in the same proportion in which they exist in the environment. However, the variation between different approaches (e.g. DNA extraction techniques, sequence annotation systems) can be used to evaluate whether observations are meaningful. These methodological variations can be integrated into the error analysis before comparing microbial communities. (shrink)

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is studied as an analytically tractable example, and a kinetic theory is formulated for describing the states of the particle. What is peculiar here is that the (inverse) temperature is treated as a dynamical variable. Dynamical hierarchy is introduced in conformity with the adiabatic scheme. Then, a (...) new analytical method is developed to show how the Fokker–Planck equation admits as a stationary solution the Maxwellian distribution modulated by the temperature fluctuations, the distribution of which turns out to be determined by the drift term. A careful comment is also made on so-called superstatistics. (shrink)

The neutral theory of biodiversity purports that patterns in the distribution and abundance of species do not depend on adaptive differences between species (i.e. niche differentiation) but solely on random fluctuations in population size (“ecological drift”), along with dispersal and speciation. In this framework, the ultimate driver of biodiversity is speciation. However, the original neutral theory made strongly simplifying assumptions about the mechanisms of speciation, which has led to some clearly unrealistic predictions. In response, several recent studies have combined (...) neutral community models with more elaborate speciation models. These efforts have alleviated some of the problems of the earlier approaches, while confirming the general ability of neutral theory to predict empirical patterns of biodiversity. However, the models also show that the mode of speciation can have a strong impact on relative species abundances. Future work should compare these results to diversity patterns arising from non‐neutral modes of speciation, such as adaptive radiations. (shrink)

This paper discusses the possibility of wealth adjustment through a credit network. The discussed credit network in this paper is a kind of loaning with no interest rate (its value is zero). It explains the influence of existence or inexistence of a cooperation originated from the credit network on wealth distribution and adjustment in an artificial society. To show how the wealth may distribute, environment agents in terms of their obtained wealth have been classified into ten wealth categories; thus, (...) the share of each category in terms of population has been determined. In addition, the survival of population in the environment has been studied. Findings and results show more balanced distribution of agents among the categories of wealth and higher survival of the population in the existence of the credit network. More over, the curve of population has fewer fluctuations. In other words, the population is more stable due to the ability of credit network in making more survival and stability in the population of environment in periods of time by providing the possibility of cooperation and wealth better distribution. (shrink)

The continual background awareness of duration is an essential structure of consciousness, conferring temporal extension to the many objects of awareness within the evanescent sensory present. Seeking the possible neural correlates of ubiquitous temporal awareness, this article reexamines fMRI data from off-task “default mode” periods in 25 healthy subjects studied by Grady et al. , 2005). “Brain reading” using support vector machines detected information specifying elapsed time, and further analysis specified distributed networks encoding implicit time. These networks fluctuate; none are (...) continuously active during DM. However, the aggregate regions of greatest variability closely resemble the default mode network. It appears that the default mode network has an important role as a state-dependent monitor of temporality. (shrink)

The time taken to react voluntarily to a stimulus is far longer than can be accounted for by ordinary processes of nerve conduction and synaptic delay, and varies unpredictably from trial to trial. Though random, the distribution of reaction times usually follows a relatively simple law, which in turn can be explained by the LATER model, in which a decision signal, representing belief in the existence of the target, rises in response to incoming sensory evidence from an initial value (...) to a criterion level at which action is initiated. But the rate of rise fluctuates randomly from trial, to an extent that cannot be explained by sensory noise at the input. These conclusions, confirmed by recording from neurons in the frontal eye fields, suggest that the randomness of reaction time is due to a deliberate, gratuitous, neural process which confers certain biological advantages as well as having implications for general ideas about the nature of ‘free will'. (shrink)

Darwin's theory of evolution brought to an end the static view of nature. It was no longer possible to think of species as immortal, with secure places in nature. Fluctuation of population could no longer be thought of as occurring within definite limits which had been set at the time of creation. Nor was it any longer possible to generalize from the differential reproductive potentials, or from a few cases of mutualism between species, that everything in nature was “fitted (...) to produce general ends, and reciprocal uses.” 134 The appeal to “design” could no longer be substituted for answers to questions concerning animal demography. Instead, the dynamics of a population had to be viewed as the outcome of species' struggle against animate and inanimate factors in the environment. Both the members of a species and the environmental factors tend to vary randomly, and therefore neither evolution nor population dynamics could be fully understood alone. For this reason Darwin's linking of the two subjects was inevitable and not merely an historical accident. Since Darwin had shown that no automatic equilibrium existed, he demonstrated the importance of closer study of the causes of population dynamics and extinction. He also indicated that an understanding of population depends upon the development of a broad knowledge in ecology.Viewed from another direction, Darwin's work ended the early modern era of population studies by clarifying three interrelated problems which were important for understanding population: extinction, distribution, and the nature of species. The components of his answer had been discussed in the eighteenth century, but there had not existed enough evidence for the completion of the revolution in thought which had then begun. At the beginning of the nineteenth century, Playfair found the evidence for extinction conclusive, and, in spite of Lamarck, Curvier convinced the scientific world that there could no longer be any doubt about it. This was a step the importance of which, with his limited knowledge of biogeography and population, Cuvier could not have fully realized. Lamarck attempted, with his evolutionary theory, to circumvent the necessity for admitting extinction, but he overestimated the adaptability of organisms and in doing so he underestimated the importance of competition and the whole field of ecology. On the other hand, he was not willing to let questions such as the origin of species remain taboo to science. The origin of species was a biogeographical as well as a paleontological question. Humboldt correlated environment with the distribution of species and conveyed the impression that plant communities are subject to change. De Candolle, following the lead of Linnaeus and Humboldt, emphasized the ecological aspects of biogeography, not only the importance of habitat and range, clearly showing the ecological effects of competition. The entomologists Kirby and Spence took a faltering step toward understanding the relationship between population and ecological role, but they fell short of any significant new conclusions. Neither they nor Swainson could fully comprehend the new perspective of De Candolle.Lyell was able to bring together the evidence from these three lines of investigation and weave them into an important synthesis that almost accomplished that Darwin later did. Although opposing Lamarck's theory of evolution, Lyell had a dynamic view of ecology. He realized that population dynamics offered an important key to the understanding of biogeography. Since he knew that species become extinct, he investigated closely the factors which could either preserve or extinguish species. While explaining these factors, he described the interrelationships of species in greater detail than had ever been done before. Forbes continued to develop Lyell's ecological concepts, and his first-hand field experience enabled him to describe biotic communities more concretely than Lyell had.Having the advantages of Lyell's understanding and his own experience from a global voyage, Darwin could take the final step from the static to the dynamic concept of life. He had seen populations fluctuating and also fossil species in South America, and on the Galapagos Islands he had encountered a biogeographical problem that could not be credibly solved without the idea of evolution. However, the bare idea of evolution did not fully answer his questions. He sought physiological causes of extinction before he read Malthus and realized that De Candolle and Lyell had correctly emphasized the importance of competition. Darwin found that, in order to understand evolution, he needed to improve his understanding of ecology. He wanted to know when populations were most easily decimated, how extensive were competition and cooperation, what effects parasites have upon populations, and what changes occur in biotic communities when a species is either added or subtracted. He contributed to some extent to answering these questions. Though there remained much for others to do, there was now a new and more secure theoretical framework within which later studies could be interpreted. As Ernst Mayr has observed, Darwin's “consistent thinking in terms of population has had an impact on biological theory and practice which is second only to his sponsorship of natural selection as the mechanism of evolution.” 135. (shrink)

Reality exists independently of human observers, but does the same apply to its structure? Realist ontologies usually assume so: according to them, the world consists of objects, these have properties and enter into relations with each other, more or less as we are accustomed to think of them. Against this view, Rein Raud develops a radical process ontology that does not credit any vantage point, any scale or speed of being, any range of cognitive faculties with the privilege to judge (...) how the world ‘really’ is. In his view, what we think of as objects are recast as fields of constitutive tensions, cross-sections of processes, never in complete balance but always striving for it and always reconfiguring themselves accordingly. The human self is also understood as a fluctuating field, not limited to the mind but distributed all over the body and reaching out into its environment, with different constituents of the process constantly vying for control. The need for such a process philosophy has often been voiced, but rarely has there been an effort to develop it in a systematic and rigourous manner that leads to original accounts of identity, continuity, time, change, causality, agency and other topics. Throughout his new book, Raud engages with an unusually broad range of philosophical schools and debates, from New Materialism and Object-Oriented Ontology to both phenomenological and analytical philosophy of mind, from feminist philosophy of science to neurophilosophy and social ontology. Being in Flux will be of interest to students and scholars in philosophy and the humanities generally and to anyone interested in current debates about realism, materialism and ontology. (shrink)

A similarity index allowing comparisons of human populations has been defined as the common “Percentage of Isoactive Genes” or PIG, which can be calculated from any gene frequency distribution characterizing two populations. The complement to one of this value has been proved to be a distance, a measure which can be used in most techniques of cluster analysis as well as in usual representations of multivariated data (dendrograms, etc...). Furthermore, the formula can be generalized to a set of populations. (...) From a biological point of vue, PIG values are particularly meaningful, whereas other previously defined indices which tend to measure similarity or difference between populations neither have such an advantage, nor can they be expressed by a single and clear number like a percentage. Moreover,comparisons using PIG indices depend at first on the fluctuations of the most frequent genes of a distribution; on the other hand, different measures principally reflect the variations of low frequency genes, which unfortunately are nearly always poorly estimated, due to weak samples of populations.Interestingly, PIG values can be applied to any frequency distribution of any kind of objects. They can also extend to a whole set of distributions by using a mean value. When applying these measures to a series of polymorphic genetical systems such as ABO, Rhesus, MNSs, Gm and HLA, one can account for the variability or the homogeneity particular to the different human groups, with simple and objective criteria. (shrink)

Two of the most influential evaluations of Charles Lyell's geological ideas were those of the philosophers of science, John F. W. Herschel and William Whewell. In this paper I shall argue that the great difference between these evaluations—whereas Herschel was fundamentally sympathetic to Lyell's geologizing, Whewell was fundamentally opposed—is a function of the fact that Herschel was an empiricist and Whewell a rationalist. For convenience, I shall structure the discussion around the three key elements in Lyell's approach to geology. First, (...) he was anactualist: he wanted to explain past geological phenomena in terms of causes of the kind that are operating at present. Second, he was auniformitarian: he wanted to explain only in terms of causes of the degree operating at present; that is, he wanted to avoid ‘catastrophes’. Third, as a geologist he saw the earth as being in asteady-state, in which all periods are essentially similar to one another. Because they will prove important, I draw attention also to two major features of Lyell's programme. First, there is his theory of climate, which suggests, ‘without help from a comet’, that earthly temperature fluctuations are primarily a function of the constantly changing distribution of land and sea. Clearly this theory is actualistic, for it is based on such present phenomena as the Gulf Stream; it is also uniformitarian and supports a steady-state world picture. Second, there is Lyell's denial that the fossil record is progressive, his criticism of Lamarckian evolutionism, ostensibly on the grounds that modern evidence is against it (i.e. it fails actualistically), and his rather veiled claim that the origins of species will nevertheless prove in some way natural, that is, subject to causes falling beneath lawlike regularities in principle discernible by us. (shrink)

In this paper, we take a data-driven approach to analyse intellectual trends over the first five decades of theJournal of Medical Ethics(JME). Our data set, comprising all texts published in theJMEsince 1975, reveals not only the most distinctive topics of theJMEin comparison to other key journals with similar profiles but also diachronic fluctuations in the prominence of certain topics. Overall, the distribution of topics shifted gradually, with each editorial period at theJMEshowing continuity with its immediate predecessor. However, a significant (...) drift in topic distribution is evident over the 50 years, with some editorial periods being more ‘disruptive’ than others. These disruptions were influenced by external events (eg,Public health emergencies), broader trends in bioethics (eg, the recent growth of topics such asRace,PrivacyandVaccination) or editors’ preferences (eg,Ethics education). Additionally, our data provides insights into editorials where editors outlined their visions for the journal or reflected retrospectively on their past editorship. (shrink)

Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A theory in which most observers are of the Boltzmann Brain type is generally thought to be unacceptable, although opinions differ. I argue that such theories are indeed unacceptable: the real problem is with fluctuations into observers who are locally identical to ordinary observers, and their existence cannot be swept under the rug (...) by a choice of probability distributions over observers. The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed. (shrink)

The main characteristic of the modern environment is the negative change by its people – destruction and pollution. Man is part of the biosphere and the technogenic transformations of the biosphere inevitably affect him. Under the influence of technogenic civilization, all spheres of human activity undergo changes, and science above all. Ecology is especially keenly aware of the challenges of technogenic civilization. It focuses on anthropogenic factors, works with the human environment. At the same time, its problem field is expanding (...) due to interdisciplinary research and the allocation of knowledge of new environmental disciplines into an independent industry. The interdisciplinarity of modern ecology is most clearly visible on the example of such a direction as informational ecology. The presence of the digital environment in human life has grown so much that it requires the separation of the digital information environment into a separate subsystem. Information ecology studies the laws of the influence of information on the formation and functioning of man. In turn, interdisciplinarity, assuming the use of knowledge from various branches of science, brings us to the problems of the collective agent of cognition and distributed knowledge. In ecology, the problems of the collective agent of cognition are implemented through crowd-sourcing technology. Ecology is a science that requires massive collection of observation data (samples of water, air, soil pollution in various, sometimes hard-to-reach corners of the planet, observation of fluctuations in the number of species of animals and plants). The popularity of crowdsourcing projects in the field of ecology is explained by the fact that the challenges and threats of anthropogenic civilization have generated such a trend of our time as environmental orientation or environmentalism. Ecological crowdsourcing projects, inspired by the philosophy of environmentalism, can serve as an answer to the challenges of technogenic civilization. (shrink)

The identification and analysis of the spatiotemporal dynamic traffic patterns in citywide road networks constitute a crucial process for complex traffic management and control. However, city-scale and synchronal traffic data pose challenges for such kind of quantification, especially during peak hours. Traditional studies rely on data from road-based detectors or multiple communication systems, which are limited in not only access but also coverage. To avoid these limitations, we introduce real-time, traffic condition digital maps as our input. The digital maps keep (...) spatiotemporal urban traffic information in nature and are open to access. Their pixel colors represent traffic conditions on corresponding road segments. We propose a stacked convolutional autoencoder-based method to extract a low-dimension feature vector for each input. We compute and analyze the distances between vectors. The statistical results show different traffic patterns during given periods. With the actual data of Chongqing city, we compare the feature extraction performance between our proposed method and histogram. The result shows our proposed method can extract spatiotemporal features better. For the same data set, there is little difference in the number distribution of red pixels found in the statistics result of the histogram, while differences do exist in the results of our proposed method. We find the most fluctuated morning is on Friday; the most fluctuated evening is on Tuesday; and the most stable evening is on Wednesday. The distance captured by our method can represent the evolution of different traffic conditions during the morning and evening peak hours. Our proposed method provides managers with assistance to sense the dynamics of citywide traffic conditions in quantity. (shrink)

According to the modern widespread approaches to the nature of external debt and its effects on economic processes, debt financing is among the distinctive features of the liberalization-oriented world of nowadays. Accordingly, unrestricted capital flows signify orientation at macroeconomic balance, since under the conditions when administrative barriers are absent capital distribution is even and symmetric, enabling leveling of factor prices. Associated with these arguments is a claim that prices of goods and services do not indicate non-negligible fluctuations and a (...) financial system gains economic agents' confidence. This research addresses the issues of the phenomenon of external debt and provides an insight into the U.S. external debt and its effects on both the U.S. and world economy. The findings show that the U.S. external debt is of no considerable threat to the world economy in the short-term, since the peace of the world's economic leader's growth exceeds that of debt servicing expenditures. However, an economic decline may turn the status-quo upside down, since the country may face inability to raise enough funds in time to discharge its financial liabilities, especially to non-residents. (shrink)

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can be assigned only to systems in thermal isolation, thus excluding the simultaneous determination of its temperature. Rosenfeld (...) extended this analogy with quantum mechanics and obtained a quantitative uncertainty relation in the form ΔU Δ(1/T) ≥ k, where k is Boltzmann's constant. The two “extreme” cases of this relation would then characterize this complementarity between isolation (U definite) and contact with a heat bath (T definite). Other formulations of the thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989), Lindhard (1986), and Lavenda (1987, 1991). This work, however, has not led to a consensus in the literature. It is shown here that the uncertainty relation for temperature and energy in the version of Mandelbrot is indeed exactly analogous to modern formulations of the quantum mechanical uncertainty relations. However, his relation holds only for the canonical distribution, describing a system in contact with a heat bath. There is, therefore, no complementarily between this situation and a thermally isolated system. (shrink)

In the last decades, streams within posthumanism and new materialism, have turned their attention to the phenomenon of agency. And they have done so in ways which open the phenomenon for social and cultural historical investigations, relevant for cultural studies and literary studies alike. This article uses a concrete case—the melodramatic novel Koloss by Norwegian author Finn Alnæs—in order to speculate on how a literary form can be seen to co-evolve—or in this case, clash—with fluctuations in the cultural history of (...) agency. In the 1960s—the heydays of cybernetics—a discrepancy can be observed, between the nourishment of individualism in politics and advertisement, and the distribution of individual agency in the new emerging technologies of cybernetics, which pushed agency as a question in the forefront of a series of novels, Koloss included. However, the novel’s discussion of agency was ignored by the critics, as well as in the scholarly literature to follow. In an effort to get closer to the co-development of ideas of agency and aesthetic form, the article asks why this has been the case. Did the melodramatic form of the novel stand in the way of its aesthetic reflection on agency? And could the novel and its reception therefore be seen as an example of the existence of complex feedback-loops, between ideas of agency in a given culture and aesthetic form? (shrink)

This study is to explore the optimization of the adaptive genetic algorithm in the backpropagation neural network, so as to expand the application of the BPNN model in nonlinear issues. Traffic flow prediction is undertaken as a research case to analyse the performance of the optimized BPNN. Firstly, the advantages and disadvantages of the BPNN and genetic algorithm are analyzed based on their working principles, and the AGA is improved and optimized. Secondly, the optimized AGA is applied to optimize the (...) standard BPNN, and the optimized algorithm is named as OAGA-BPNN. Finally, three different cases are proposed based on the actual scenario of traffic flow prediction to analyse the optimized algorithm on the matrix laboratory platform by simulation. The results show that the average error distribution of the GA-BPNN algorithm is about 1% with small fluctuation range, better calculation accuracy, and generalization performance in contrast to the BPNN. The average output error of the AGA-BPNN fluctuates around 0 and remains in a relatively stable range as a whole in contrast to that of GA-BPNN; the maximum fitness level keeps increasing during the evolution process but approaches the average value in later process, so the population diversity is hard to be guaranteed. The output error of the OAGA-BPNN fluctuates little compared with that of AGA-BPNN, and its maximum fitness continues to increase in the evolution process with guaranteed population diversity. In short, the OAGA-BPNN algorithm can achieve the best performance in terms of calculation accuracy, generalization performance, and population evolution. (shrink)

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the de Broglie–Bohm theory. However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the wave-function. (...) In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm’s trajectory, that is a single realization of the time dependent configuration which should be representative of a single realization of the quantum system. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm’s trajectory, but in this case there is no room for the Born’s rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm’s trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm’s trajectory description of the model system of six confined planar rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor, the others representing the environment, along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born’s rule when the pilot wave theory is applied at the level of single Bohm’s trajectory. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm’s coordinate of a single rotor and, under this condition, it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified. (shrink)

In business and government, databases contain large quantities of digital transactional data (purchases made, services used, finances transferred, benefits received, licences acquired, borders crossed, tickets purchased). The data can be understood as ongoing and dynamic measurements of the activities and doings of people. In government, numerous database devices have been developed to connect such data across services to discover patterns and identify and evaluate the performance of individuals and populations. Under the UK’s New Labour government, the development of such devices (...) was part of a broader policy known as ‘joined-up thinking and government’. Analyses of this policy have typically understood joining up as an operation of adding together distributed data about subjects, which can then be used in the service of government surveillance, the database state or informational capitalism. But rather than such technical or managerialist analytics, I argue that topological analytics capture what these database devices enact and do: they materialize the ‘individuality’ of subjects in intensified, distributed and fluctuating ways and materialize and intensify a logic of what Deleuze describes as modulating controls. Through examples of UK New Labour social policy initiatives over the past decade, I argue that topological analytics can account for these as immanent rather than exceptional properties of database devices and, as such, part and parcel of a governmental logic and ontology of subjects. (shrink)

The introduction by Dirac of a new aether model based on a stochastic covariant distribution of subquantum motions (corresponding to a “vacuum state” alive with fluctuations and randomness) is discussed with respect to the present experimental and theoretical discussion of nonlocality in EPR situations. It is shown (1) that one can deduce the de Broglie waves as real collective Markov processes on the top of Dirac's aether; (2) that the quantum potential associated with this aether's modification, by the presence (...) of EPR photon pairs, yields a relativistic causal action at a distance which interprets the superluminal correlations recently established by Aspect et al.; (3) that the existence of the Einstein-de Broglie photon model (deduced from Dirac's aether) implies experimental predictions which conflict with the Copenhagen interpretation in certain specific testable interference experiments. (shrink)

This study investigates global properties of three categories of English text: canonical fiction, non-canonical fiction, and non-fictional texts. The central hypothesis of the study is that there are systematic differences with respect to structural design features between canonical and non-canonical fiction, and between fictional and non-fictional texts. To investigate these differences, we compiled a corpus containing texts of the three categories of interest, the Jena Corpus of Expository and Fictional Prose. Two aspects of global structure are investigated, variability and self-similar (...) patterns, which reflect long-range correlations along texts. We use four types of basic observations, the frequency of POS-tags per sentence, sentence length, lexical diversity, and the distribution of topic probabilities in segments of texts. These basic observations are grouped into two more general categories, the lower-level properties and, which are observed at the level of the sentence, and the higher-level properties and, which are observed at the textual level. The observations for each property are transformed into series, which are analyzed in terms of variance and subjected to Multi-Fractal Detrended Fluctuation Analysis, giving rise to three statistics: the degree of fractality () of the fractal spectrum. The statistics thus obtained are compared individually across text categories and jointly fed into a classification model. Our results show that there are in fact differences between the three text categories of interest. In general, lower-level text properties are better discriminators than higher-level text properties. Canonical fictional texts differ from non-canonical ones primarily in terms of variability in lower-level text properties. Fractality seems to be a universal feature of text, slightly more pronounced in non-fictional than in fictional texts. On the basis of our results obtained on the basis of corpus data we point out some avenues for future research leading toward a more comprehensive analysis of textual aesthetics, e.g., using experimental methodologies. (shrink)

Financial internationalization leads to similar fluctuations and spillover effects in financial markets around the world, resulting in cross-border financial risks. This study examines comovements across G20 international stock markets while considering the volatility similarity and spillover effects. We provide a new approach using an ICA- based ARMA-APARCH-M model to shed light on whether there are spillover effects among G20 stock markets with similar dynamics. Specifically, we first identify which G20 stock markets have similar volatility features using a fuzzy C-means time (...) series clustering method and then investigate the dominant source of volatility spillovers using the ICA-based ARMA-APARCH-M model. The evidence has shown that the ICA method can more accurately capture market comovements with nonnormal distributions of the financial time series data by transforming the multivariate time series into statistically independent components. Our findings indicate that the G20 stock markets are clustered into three categories according to volatility similarity. There are spillover effects in stock market comovements of each group and the dominant source can be identified. This study has important implications for investors in international financial markets and for policymakers in G20 countries. (shrink)

A large number of modern communication technologies and sensing technologies are incorporated into the smart grid, which makes its structure unique. The centralized optimized dispatch method of traditional power grids is difficult to achieve effective dispatch of smart grids. Based on the analysis of power generation plan and maintenance plan optimization model, this paper establishes a smart grid power generation and maintenance collaborative optimization model with distributed renewable energy. The objective function of this collaborative optimization problem is the operating cost (...) of conventional units, the cost of wind power generation, and the cost of overhauling units; the constraints considered mainly include system constraints and overhaul constraints. The solution method of combinatorial optimization is analyzed, and the genetic optimization algorithm adopted in this paper is selected and discussed. According to the characteristics of the system, various loads are modeled, and power supply constraints are considered. By establishing an effective objective function, the adjustable load scheduling problem is transformed into a solvable optimal control problem. Taking into account the uncertain factors in the system, the advantage of the real-time control system is that it can realize the dynamic update scheduling of the load, so it is more in line with the requirements of the actual system. The real-time algorithm proposed in the paper is based on a distributed control strategy, which can not only realize dynamic compensation for random fluctuations in renewable energy power generation but also satisfy the load curve optimization under the premise of making full use of power supply resources. In addition, simulation experiments compare the load dispatching capabilities of the proposed algorithm with the existing algorithms, thereby verifying the performance of the proposed method. (shrink)

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification of the (...) topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought. (shrink)

The year 1905 has been called Einstein's annus mirabilis in virtue of three ground-breaking works completed over the span of a few months --- the light quantum paper (Einstein, 1905a), the Brownian motion paper (Einstein, 1905c), and the paper on the electrodynamics of moving bodies introducing the special theory of relativity (Einstein, 1905d). There are prima facie reasons for thinking that the origins of these papers cannot be understood in isolation from one another. Due to space limitations, we concentrate primarily (...) on the light quantum paper, since, in key respects, it marks the turning point for the annus mirabilis. The task is to probe, not just how the idea of the light quantum might have occurred to Einstein, but, more importantly, what convinced him that the idea was not just a quixotic hypothesis, but an unavoidable and demonstrable feature of radiation. The crucial development, we suggest, arose from comparing the energy fluctuations that following rigorously from the Stefan-Boltmann law, as well as from Wien's distribution formula for blackbody radiation, with what it is reasonable to expect from Maxwell's electromagnetic theory of light. A special case of this is addressed in (Einstein, 1904). The outcome for the general case leads naturally to the central theoretical argument of the light quantum paper, the expectation of Brownian-like motion, and several of the key results for the electrodynamics of moving bodies. (shrink)

Have the large-scale evolutionary patterns illustrated by the fossil record been driven by fluctuations in environmental opportunity, by biotic factors, or by changes in the types of phenotypic variants available for evolutionary change? Since the Modern Synthesis most evolutionary biologists have maintained that microevolutionary processes carrying on over sufficient time will generate macroevolutionary patterns, with no need for other pattern-generating mechanisms such as punctuated equilibrium or species selection. This view was challenged by paleontologists in the 1970s with proposals that the (...) differential sorting and selection of species and clades, and the effects of biotic crises such as mass extinctions, were important extensions to traditional evolutionary theory. More recently those interested in macroevolution have debated the relative importance of abiotic and biotic factors in driving macroevolutionary patterns and have introduced comparative phylogenetic methods to analyze the rates of change in taxonomic diversity. Applying Peter Godfrey-Smith’s distinction between distributional explanations and explanations focusing on the origin of variation, most macroevolutionary studies have provided distributional explanations of macroevolutionary patterns. Comparative studies of developmental evolution, however, have implicated the origin of variants as a driving macroevolution force. In particular, the repatterning of gene regulatory networks provides new insights into the origins of developmental novelties. This raises the question of whether macroevolution has been pulled by the generation of environmental opportunity, or pushed by the introduction of new morphologies. The contrast between distributional and origination scenarios has implications for understanding evolutionary novelty and innovation and how macroevolutionary process may have evolved over time. (shrink)

The Yangtze River Economic Zone is a major corridor of national science and innovation culture, an innovation-driven region that fosters new drivers of growth and leads transformation and development, and plays an important strategic support and exemplary leading role in the overall pattern of regional development. This paper analyzes the spatiotemporal differentiation characteristics of innovation output of 110 cities of YREZ from 2008 to 2018 by using Gini coefficient, coefficient of variation, geographical weighted regression, and other methods. The factors affecting (...) innovation output are selected from the perspective of innovation ecosystem. The results show the following. Innovation output showed an increasing trend, and the high-value concentration cities in downstream areas gradually became prominent, the geographical concentration degree fluctuated and declined, and the distribution of innovation output gradually became balanced. The global Moran’s I index of innovation output shows a fluctuation pattern of “M” shape and an overall upward trend. The analysis of local spatial correlation indicates that spatial distribution pattern of innovation output has not changed significantly. There is obvious regional heterogeneity under different impacts of factors of innovation ecosystem on innovation output. Enterprises have the greatest impact, followed by financial resources and infrastructure environment. (shrink)

The sixth volume of the Collected Works of Micha/l Kalecki, one of the twentieth-century's pre-eminent economists, contains his empirical studies of the capitalist economy, published primarily in pre-war Poland. The first part of the book collects together reviews of business conditions in commodity markets, studies of the structure and operations of large companies and cartels, and articles on international economic relations. These studies, written between 1928 and 1935, demonstrate Kalecki's keen insight into the international consequences of the Great Crisis of (...) 1929-33, and into the developments in Nazi Germany. The second part contains Kalecki's papers on the methodological problems of examining business fluctuations and on constructing indicators of economic trends. Part 3 comprises, Kalecki's estimates of the national income in Poland and of its structure. These studies, conducted between 1931 and 1935, were unique at the time in taking into account the distribution of aggregate income between the main social classes. The editorial notes and annexes at the end of the volume not only provide invaluable background information and explanatory glosses on the main text, but also give invaluable insights into the development of Kalecki's thought. (shrink)

Face à la question des modes de distribution inégalitaire de l’honneur social et de la lutte pour la reconnaissance chez des populations objets de mépris social, le « savoir-être avec » l’Autre est devenu pour le sociologue un enjeu scientifique, méthodologique et épistémologique important. Est proposée ici une ethnographie de la reconnaissance où l’Autre est regardé et reconnu avec son expérience, sa compétence, et son identité plurielle, fluctuante, réversible, inscrit dans une diversité de mondes sociaux organisée par des processus (...) culturels producteurs de hiérarchies et d’inégalités.When faced with unequal forms of distribution of social honour and with the struggle for recognition among populations subject to social contempt, knowing how to be with the Other has become a major methodological and epistemological scientific issue. Here, we are proposing an ethnography of recognition, in which the Other is regarded and recognized with his experience, his competence, and his fluctuating, reversible and varied identity, anchored in a diversity of social worlds organized on the basis of structural processes which produce hierarchy and inequalities. (shrink)

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector (...) potential that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)