Evolutionary drive: The effect of microscopic diversity,error making,and noise

In order to model any macroscopic system, it is necessary to aggregate both spatially and taxonomically. If average processes are assumed, then kinetic equations of population dynamics can be derived. Much effort has gone into showing the important effects introduced by non-average effects (fluctuations) in generating symmetry-breaking transitions and creating structure and form. However, the effects of microscopic diversity have been largely neglected. We show that evolution will select for populations which retain variability, even though this is, at any given time, loss-making, predicting that we shall not observe populations with optimal behavior, but populations which can learn. This lesser short-term efficiency may be why natural diversity is so great. Evolution is seen to be driven by the noise to which it leads.     

Semiclassical Behaviour of Expectation Values in Time Evolved Lagrangian States for Large Times

We study the behaviour of time evolved quantum mechanical expectation values in Lagrangian states in the limit 0 and t. We show that it depends strongly on the dynamical properties of the corresponding classical system. If the classical system is strongly chaotic, i.e. Anosov, then the expectation values tend to a universal limit. This can be viewed as an analogue of mixing in the classical system. If the classical system is integrable, then the expectation values need not converge, and if they converge their limit depends on the initial state. An additional difference occurs in the timescales for which we can prove this behaviour; in the chaotic case we get up to Ehrenfest time, t ln (1/), whereas for integrable system we have a much larger time range.     

One massless particle equals two Dirac singletons

The remarkable representations of the 3+2 de Sitter group, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly remarkable property: Each of the direct products Di Di, Di Rac, and Rac Rac decomposes into a direct sum of unitary, irreducible representations, each of which admits an extension to a unitary, irreducible representation of the conformal group SO(4, 2). Therefore, in de Sitter space, every state of a free, massless particle may be interpreted as a state of two free singletons — and vice versa. The term massless is associated with a set of particle-like representations of SO(3, 2) that, besides the noted conformal extension, exhibit other phenomena typical of masslessness, especially gauge invariance.     

Formation of F-centers in Kcl-Rbcl solid solutions with Sr2+ and OH− impurities

The kinetics of F-center formation are studied in crystals of KCl-RbCl. solid solutions, both in the pure state and with Sr²⁺ and OH^– impurities. The crystals were irradiated by electrons at 1.2 MeV at room temperature. The initial stage of coloration in crystals that have been purified of divalent cation impurities is the same as that of pure crystals; only when Sr²⁺ is introduced is this stage sharply accelerated. The efficiency of F-center formation in the second stage of coloration is significantly smaller in purified crystals than in pure crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 38–41, July, 1971.     

A cell dynamical system model of chemical turbulence

A cellular-automaton-like caricature of chemical turbulence on an infinite one-dimensional lattice is studied. The model exhibits apparently turbulent space-time patterns. To make this statement precise, the following problems or points are discussed: (1) The infinite-system-size limit of such cell-dynamical systems and its observability is defined. (2) It is proved that the invariant state in the large-system-size limit of the turbulent phase exhibits spatial patterns governed by a Gibbs random field. (3) Potential characteristics of turbulent space-time patterns are critically surveyed and a working definition of (weak) turbulence is proposed. (4) It is proved that the invariant state of the turbulent phase is actually (weak) turbulent. Furthermore, we conjecture that the turbulent phase of our model is an example of a K system that is not Bernoulli.     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

A relationship between asymmetric Lévy-stable distributions and the dielectric susceptibility

This paper, as a complement to the work of Montroll and Bendler, is concerned with the Lévy-stable distributions and their connection to the dielectric response of dipolar materials in the frequency domain. The necessary and sufficient condition for this connection is found. The presented probabilistic analysis is based on the mathematically correct representation of the meaning of the relaxation function of a system of dipoles and shows why the same form of a distribution of relaxation rates, namely, the completely asymmetric Lévy-stable distribution, should apply in all different relaxing systems. This is in contrast to the traditional definition of the relaxation function, expressed as a weighted average of exponential relaxation functions, which does not explain the universality of the dielectric relaxation law. It also follows from the present considerations that not only is the imaginary part () of the dielectric susceptibility directly related to the Lévy-stable distribution (as was found by Montroll and Bendler), but so is the real part(). As a consequence the relation()/()=cot(n/2) for> _p and 0<n<1, implied by experimental results, is obtained.     

Conditions for Obtaining Stimulated Radiation in Thin‐Film Organic Electroluminescent Structures

This paper analyzes the possibilities of obtaining induced radiation in singlelayer organic electroluminescent structures on the basis of the proposed model of luminophor molecule excitation by hot electrons emitted from the cathode as a result of the tunnel effect. Numerical calculations of the kinetic, spectral, and energy characteristics of radiation in the regime of singlepass superluminescence and in the presence of positive feedback have been made. It has been concluded that, in principle, it is possible to obtain in such systems induced radiation at actually attainable values of the applied electricfield strength, and the conditions for this have been analyzed.     

AN EXTENSION OF “POPPER'S EXPERIMENT” CAN TEST INTERPRETATIONS OF QUANTUM MECHANICS

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics—namely that the state of a particle is merely an expression of what is known about the system—is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called Extension step 1)—which fully serves its original purpose—is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the many-worlds interpretation (MWI) is correct are shown to be identical. Only after a further modification (called Extension step 2) (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because what is known by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus—within the CI—for H they are known not to exist. Yet H can infer their existence by studying the evolution of the ion.     

Nonstationary quantum mechanics. I. Time-irreversible noninstantaneous self-reduction to a stationary state of some quantal wave packets

It is shown that the formalism of quantum theory needs modification in the case of potential fields swiftly varying with time. The necessity of a time-irreversible master equation for such cases is discussed.The underlying idea is that any (sub)system will undergo a spontaneous transition to a state of definiteenergy in the process of separating spatially from the rest of the universe, assuming the universe is isolated and has a definite energy. This requires what might be termed a pragmatic interpretation of the wave function: If a composite, separated system is represented by a linear superposition of product states, we may say that the actual state of the composite system is represented by some particular component of the superpositionfor the purposes of statistical inferences relevant to each subsystem alone, but the entire superposition—and not the corresponding mixture of the product components—must be used to compute the statistics of correlations. The considerations are illustrated with thought experiments which are real enough to make the application of the usual quantum mechanical formalism possible. Cases of disagreement between conventional theory and experiment in the field of interest are indicated.     

Ultimate stochastic entities

We take the view that everything that is known about a physical system can be described by a stochastic entity (Å, ), which consists of a manual Å of experiments that can be performed on the system, and a set of possible stochastic states (probability measures) on the logic of the manual. We next consider what happens when new information about the system is learned and describe precisely how one then obtains a new stochastic entity more elaborate than the first. Finally, we show that as information about the system continues to grow, the increasingly elaborate stochastic entities describing the system necessarily acquire mathematical properties often assumed for mathematical convenience in papers on quantum mechanics.     

Peculiarities of the resonance absorption in the magnetic films magnetized to non-saturated state

The review is devoted to recent investigations in the field of LF FMR in polycrystalline TMF with uniaxial anisotropy and unidirectional antiferro-ferromagnetic exchange anisotropy. The dependence of FMR parameters on magnetization inhomogeneity (mosaic structure, magnetization ripple and magnetization non-uniformity through the film thickness) are considered. Resonance absorption in multi-domain films including films with stripe- structure is examined.     

Information theory and the problem of molecular structure

Recently it has been shown that the classical stick and ball viewpoint of molecules is inconsistent with quantum theory (QT). We suggest an unusual reconciliation: The QT state is not a physical property, but instead reflects our state of knowledge about observable aspects of reality. We show how this perspective is nevertheless objective. Applied to molecules, the view permits structure to exist only when observable evidence is compatible with this feature. Typically one must replace the a priori model (in particular, the dynamical generator) with one consistent with the evidence. We show that such structure is stable in the context of first-order perturbation theory. We also indicate how dynamics can be inferred from scattering data—a process alternative to postulating (field-theoretic) models for environment.     

Strategies for the synthesis of novel indole alkaloid-based screening libraries for drug discovery

A series of diverse indole-based chemotypes were synthesized from -tetrahydrocarboline (-THC) scaffolds prepared from commercially and readily available tryptamines and -ketoesters. Diversity can be generated within these chemotypes through the following strategies: (a) appendage of substituents to the -THC scaffold, prepared in situ or as a template, through further elaboration and (b) skeletal modifications to the -THC scaffold via ring forming or ring breaking reactions. The strategies described here are amenable to high throughput solution-phase parallel synthesis, providing access to novel indole-based screening libraries for drug discovery.Dedicated to Professor Spyros P. Perlepes     

Phase transitions and hysteresis in a cellular automata-based model of opinion formation

A particular case of a cellular automata-based model of two-state opinion formation in social groups with a strong leader is studied. We consider a 2D Euclidian geometry of social space and mutual interactions 1/r ⁿ . The model shows an interesting dynamics which can be analytically calculated. There are two stable states of the system: a cluster around the leader and unification. Unstable clusters may also appear. A variation in parameters such as the leader's strength or the social temperature can change the size of a cluster or, when they reach some critical values, make the system jump into another state. For a certain range of parameters the system exhibits bistability and hysteresis phenomena. We obtained explicit formulas for the cluster size, critical leader's strength, and critical social temperature. These analytical results are verified by computer simulations.     

The rate of growth of the magnetic energy density during a gravitational collapse

It is shown that during an isotropic gravitational collapse of a fluid with infinite electrical conductivity, the magnetic energy density cannot grow faster than ^4/3 no matter the equation of state, where is the total proper energy density. If the equation of state is=c ², where 01, then the rate of growth of the magnetic energy density in such a collapse is proportional to ^4/3(1+). If an isotropic collapse is also locally adiabatic, it is shown, independently of any equation of state, that the rate of increase of the magnetic energy density is proportional tor ^4/3, wherer is the proper material density. If the collapse is nonisotropic, shear can modify these results. Numerical estimates of the magnetic field strength at various stages in the collapse of a magnetic star are given.     

Complexity of Two-Dimensional Patterns

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of regular language or local rule that are equivalent in d=1 lead to distinct classes in d2. We explore the closure properties and computational complexity of these classes, including undecidability and L, NL, and NP-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d2 has a periodic point of a given period, and that certain local lattice languages are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CA's finite-time image cannot decrease faster than t ^–d unless it maps every initial condition to a single homogeneous state.     

Stationary non-equilibrium states of infinite harmonic systems

We investigate the existence, properties and approach to stationary non-equilibrium states of infinite harmonic crystals. For classical systems these stationary states are, like the Gibbs states, Gaussian measures on the phase space of the infinite system (analogues results are true for quantum systems). Their ergodic properties are the same as those of the equilibrium states: e.g. for ordered periodic crystals they are Bernoulli. Unlike the equilibrium states however they are not stable towards perturbations in the potential.We are particularly concerned here with states in which there is a non-vanishing steady heat flux passing through every point of the infinite system. Such superheat-conducting states are of course only possible in systems in which Fourier's law does not hold: the perfect harmonic crystal being an example of such a system. For a one dimensional system, we find such states (explicitely) as limits, whent, of time evolved initial states _i in which the left and right parts of the infinite crystal are in equilibrium at different temperatures, _L ^–L _R ^–1 , and the middle part is in an arbitrary state. We also investigate the limit of these stationary (t) states as the coupling strength between the system and the reservoirs goes to zero. In this limit we obtain a product state, where the reservoirs are in equilibrium at temperatures _L ^–1 and _R ^–1 and the system is in the unique stationary state of the reduced dynamics in the weak coupling limit.On leave of absence from the Fachbereich Physik der Universität München. Work supported by a Max Kade Foundation FellowshipResearch supported in part by NSF Grant MPS75-20638     

Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas

This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states atx=±, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant satisfies 12, then the solution is proved to tend to the rarefaction wave ast under no smallness conditions of both the difference of asymptotic values atx=± and the initial data. The proof is given by an elementaryL ²-energy method.     

A reinterpretation of von Neumann's theory of measurement

Von Neumann's theory of measurement in quantum mechanics is reinterpreted so that the experimental arrangement specifies the location of the cut by calling for the separate observation of the object and the measuring apparatus after the initial measurement interaction. The measurement ascertains which element of the mixture describing the final state of the apparatus is actually present. The relevance and feasibility of observing the final coherent state of the object plus apparatus is criticized and the paradoxes of Schrödinger's cat and Wigner's friend are discussed.Work performed under the auspices of the U.S. Atomic Energy Commission.