Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000

Following our investigation of the USA Standard and Poor index anti-bubble that started in August 2000 (Quant. Finance 2 (2002) 468), we analyze 38 world stock market indices and identify 21 “bearish anti-bubbles” and six “bullish anti-bubbles”. An “anti-bubble” is defined as a self-reinforcing price trajectory with self-similar expanding log-periodic oscillations. Mathematically, a bearish anti-bubble is characterize by a power law decrease of the price (or of the logarithm of the price) as a function of time and by expanding log-periodic oscillations. We propose that bearish anti-bubbles are created by positive price-to-price feedbacks feeding overall pessimism and negative market sentiment further strengthened by inter-personal interactions. Bullish anti-bubbles are here identified for the first time. The most striking discovery is that the majority of European and Western stock market indices as well as other stock indices exhibit practically the same log-periodic power law anti-bubble structure as found for the USA S&P500 index. These anti-bubbles are found to start approximately at the same time, August 2000, in all these markets. This shows a remarkable degree of worldwide synchronization. The descent of the worldwide stock markets since 2000 is thus an international event, suggesting the strengthening of globalization.     

A concise proof of the “geometric” construction of inertial manifolds

By employing the standard strong squeezing property, the “geometric” existence proof of Constantin et al. is considerably simplified, and the parallels between this and other methods thereby emphasised.     

Completeness of “good” Bethe ansatz solutions of a quantum-group-invariant Heisenberg model

The sl_q(2) quantum-group-invariant Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into “good” and “bad” states. A “good” state may be described by a path of only “good” representations. It is shown that the “good” states are given by all “good” Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive-parity strings (in the language of Takahashi) are allowed. Applying Bethe's string-counting technique completeness of the “good” Bethe states is proven, i.e. the same number of states is found as the number of all restricted paths on the sl_q(2) Bratteli diagram. It is the first time that a “completeness” proof for an anisotropic quantum-invariant reduced Heisenberg model is performed.     

Formation model of bulk etching rate for polymer detectors

Any detector is composed of an enormous number of sensitive microscopic volumes (SMV) mainly in the state “NO” (Katz 1970. Unified Track Theory. In: Seventh International Colloquium on Corpuscular Photography and Visual Solid Detectors. Barcelona, pp. 1–29.). Irradiation evokes some spatial distribution of SMV in the state “Yes”. It can be described by the many-hit model of the SMV response (Ditlov, 1980. Theory of spatial calculation of primary action of d-electrons in track detectors with account of multiple scattering. In: Francois, H., et al. (Eds.), Solid State Nuclear Track Detectors. Pergamon Press, Oxford, pp. 131–141.). It appears that the process of etching can be described by its own many-hit model too, when the etching molecule attacks SMV in the state “Yes”. As a first our step of research, only the bulk rate V_b was considered.     

Landau-Pomeranchuk-Migdal effect for nuclear matter in QCD

Soft photon and gluon radiation off a fast quark propagating through nuclear matter is discussed. The close analogy between the Landau-Pomeranchuk-Migdal (LPM) effect in QED and the emission of soft gluons, suggested by Baier et al. [R. Baier, Yu.L. Dokshitzer, S. Peigne and D. Schiff, LPTHE-Orsay 94/98] for “hot” plasma, is confirmed and the relation between Mueller's approach and traditional calculations is established. It is shown that perturbative QCD can be applied to take into account the LPM coherent suppression both for photon and gluon induced radiation. The formulae for the photon and gluon radiation densities are presented.     

Rotational, internal rotational, and translational motion of acetic acid and dimethyl sulfoxide in their liquid mixture (with some results for DMSO dissolved in MeOH)

The proton magnetic relaxation rate of DMSO in the mixture 33.3 mole % DMSO + 66.7 mole % CD₃COOD has been measured in the temperature range 3.5 < 1000/T < 6.0 K and at six frequencies 6 < ν < 144 MHz. The intramolecular relaxation rate was determined by the aid of the isotopic substitution technique. The rotational correlation time of “the molecule” and the time constant of the internal motion have been extracted from these experimental results. The corresponding measurements were also performed on DMSO in the solvent CD₃OD (71 mole %) where no internal motion effect appeared in the temperature dependence of the relaxation rate. Furthermore, proton relaxation rates of the acetic acid methyl group and deuteron relaxation rates of the acid methyl and OD group are reported. Again, the data are given in the temperature range as above and for a number of frequencies. Rotational time correlation functions g(t) for the axid molecule are derived. Finally we present experimental results for the self-diffusion coefficients of both mixture partners DMSO and AcH and of DMSO in the solvent MeOH.     

Retrieval of cirrus particle sizes using a split-window technique: a sensitivity study

This paper examines the sensitivity of retrieved ice particle sizes using split-window method to the light scattering program for the single scattering calculation. We find that for randomly oriented hexagonal ice particles the retrieval algorithm using the anomalous diffraction theory (ADT) significantly overestimates the mean effective ice particle sizes, D_ge. The retrieved D_ge based on the geometric optics method (GOM) and Mie theory agrees with reference results within 20% when D_ge<30 μm. Based on the speculation that there is no “tunneling” for complex particles, some recent studies suggest that the ADT is an appropriate method to simulate the absorption coefficient for irregularly shaped particles in the infrared. In this study, however, we find that the overestimation of D_ge due to the ADT is largely caused by the neglect of refraction and reflection processes, instead of by the neglect of “tunneling” in the absorption calculations. By considering complex particle shapes such as aggregates with surface roughness, we further find that the retrieved D_ge based on the GOM is not sensitive to the particle shapes. Note that both ADT and GOM do not consider the “tunneling”, but the retrieved D_ge based on the ADT is about two times larger than those based on the GOM. “Tunneling” plays a significant role in the retrieved D_ge only when the D_ge is larger than 30–35 μm. In this study, we also examine the sensitivities of retrieved D_ge to the ice particle size distributions assumed in the retrieval algorithm and to the errors in the emissivities. It is found that when the D_ge is larger than 30–40 μm, the retrieved D_ge becomes very sensitive to the uncertainties related to the ice particle size distributions and to the errors in cirrus emissivities derived from measurements.     

Simulation of dc magnetic effects due to geometrically defined grain boundaries in type-II superconductors

A Bean model-based program (“Trazacorrientes”^®) has been used to simulate the current distribution in the saturated remanent state of type-II superconducting bicrystal-like squared samples. The grain boundary was modeled by a set of periodically spaced holes geometrically defining the current transparency. Current simulations performed as a function of the boundary transparency, width and geometry are analyzed. Current distributions agree qualitatively with previously reported imaging measurements, while quantitative results can be obtained with an accuracy of 5% due to present computing resolution limits. Thanks to “Trazacorrientes”^® easy way of implementing irregular defects, meandering grain boundaries formed by straight facets of different local transparency could be simulated. The advantages and disadvantages of the program for the simulation of type-II superconductors with defects, among which GB’s, are discussed.     

Interlaboratory calibration of track-etch detectors for the measurement of radon and radon daughter levels

This paper reports the results of the second interlaboratory calibration experiments, which were carried out in two parts. In the first, five types of commercially available and economically cheap membranes were tested as the barrier against thoron for “radon-only” measurements. It was found that all the membranes tested are good barriers against thoron and can be used in the “radon-only” device. In the second, actual calibration experiments were performed with LR-115 type-II and CR-39 track-etch detectors for different radon measuring configurations in a radon exposure chamber.     

Methane activation over Ag-exchanged ZSM-5 zeolites: A theoretical study

Methane activation catalyzed over Ag-exchanged ZSM-5 zeolites was investigated by using the density functional theory (DFT) with a cluster model. Two different pathways were taken into account in this work: the “alkyl” and the “carbenium” pathways. The activation barriers obtained are 34.09 and 66.63 kcal/mol for the “alkyl” and the “carbenium” pathway, respectively. The calculated results show that the activation barrier of the “alkyl” pathway is smaller than that of “carbenium” pathway. Consequently, the “alkyl” pathway is the preferential reaction pathway. A new mechanism of methane conversion in the presence of ethene was proposed. In the catalytic cycle, the initial step of methane activation proceeds with the “alkyl” pathway and the Ag⁺ cation acts as an acceptor of the methyl group, then ethene reacts with the Ag⁺CH₃⁻ group to form propene. In addition, it is found that the Ag⁺ cations play an important role in the methane activation, compared with the reaction of methane activation over H-ZSM-5.     

Vulnerability in one-dimensional excitable media

Potentially life-threatening cardiac arrhythmias can be iniated with stimuli timed to occur during the “vulnerable window (VW)”. We defined VW as the time interval between the “conditioning” and “test” stimuli following in sequence, during which the test stimulus response propagates in only one direction. We show that the VW is a generic feature of excitable media and describe the relationship between the properties of an excitable medium and the VW. We present asymptotic results that reveal the sensitivity of the VW to both the propagation velocity of the conditioning wavefront and the recovery process parameters. We also have identified a critical length of medium that must be excited in order to reveal vulnerability. Analytical results are in agreement with numerical studies.     

Outer curvature and conformal geometry of an imbedding

The differential geometry of an imbedded (e.g. string or membrane world sheet) surface in a higher-dimensional background is shown to be conveniently describable (except in the null limit case) in terms of what are designated as its first, second, and third fundamental tensors, which will have the respective symmetry properties η_μν = η_(μν) as a trivial algebraic identity, K_μν^ρ = K_(μν)^ρ as the “generalised Weingarten identity”, which is the (Frobenius type) integrability condition for the imbedding, and Ξ_λμν^ρ = Ξ_(λμν)^ρ as a “generalised Codazzi equation”, which depends on the background geometry being flat or of constant curvature, needing replacement by a more complicated expression for a generic value of the background curvature B_κλ^μ_ν. The “generalised Gauss equation” expressing the dependence on this background curvature of the internal curvature tensor R_κλ^μ_ν of the imbedded surface is converted into terms of the first and second fundamental tensors, and it is thereby demonstrated that the vanishing of the (conformally invariant) “conformation tensor”, i.e. the trace free part C_μν^ρ of the second fundamental tensor K_μv^ρ, is a sufficient condition for conformal flatness of the imbedded surface (and thus in particular for the vanishing of its (Weyl type) conformal curvature tensor C_κλ^μ_ν) provided the background is itself conformally flat. In a trio of which the first two members are the generalised Gauss and Codazzi equations, the “third” member is shown to give an expression in terms of C_μν^ρ for the (trace free, conformally invariant) “outer curvature” tensor Ω_κλ^μ_ν whose vanishing is the condition for feasibility of the natural generalisation of the Walker frame transportation ansatz. The vanishing of C_μν^ρ is shown to be sufficient in a conformally flat background for the vanishing also of Ω_κλ^μ_ν.     

Time-periodic solutions of multidimensional Hamilton systems

A simple method is proposed to determine the time-periodic solutions of a non-separable hamiltonian system in the regular domain of a phase space. This method is applied for the quantization of gauge-invariant time-dependent Hartree-Fock solutions for the deformed oscillator (DO) and SU(3) models. Energies of quantized states and the “collective” variables for decoupled modes are compared with the corresponding RPA results.     

Stable heavy pentaquark states

If the Θ⁺(1540) is interpreted as a bound state of a quark and two (ud) diquarks in a relative P-wave, then it is very likely that there exist pentaquark states with a heavy antiquark, or , and two “light” diquarks in a relative S-wave which are stable against strong decays. We make a mass estimate for exotic states of this type and discuss their weak decays. Isospin relations are constructed which test their flavor quantum numbers.     

Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory — I

Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of “M-theory”) and a four-dimensional physical theory (using the “F-theory” construction). A key issue in both theories is the calculation of the “superpotential” of the theory, which by a result of Witten is determined by the divisors D on the 4-fold satisfying X( _D = 1. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold.

When B is Fano, we show how divisors contributing to the superpotential are always “exceptional” (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, i.e., birational tranformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. The singularities which occur are “canonical”, the same type of singularities of a (singular) Weierstrass model. We work out the transitions. If a smoothing exists, then the Hodge numbers change.

We speculate that divisors contributing to the superpotential are always “exceptional” (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which are toric varieties.     

Vacuum renormalization of the chiral-sigma model and the structure of neutron stars

Vacuum renormalization corrections are calculated for normal nuclear matter and neutron star matter in the chiral-sigma model. The theory is generalized to include hyperons in equilibrium with nucleons and leptons. The equations of state corresponding to two compression moduli, a “stiff” and “soft” one for nuclear matter, are studied. It is shown that fully one half the mass of a neutron star at the limiting mass is composed of matter at less than twice nuclear density. Neutron star masses are therefore moderately sensitive to the properties of matter near saturation and to the domain of the hyperons, but dominated by neither. The predictions for the two equations of state are compared with observed neutron star masses, and only the stiffer is compatible.     

The influence of abrupt electric field variations on the distribution function of hot electrons

Some analytical models of quiescent hot electron distributions are extended to the transient conditions, in order to describe the response of hot electrons to step changes in the magnitude of the electric field. These models apply to semiconductors having one or several equivalent energy minima in the conduction band, and isotropic lattice scattering due to low-energy acoustic phonons (elastic in-valley scattering) and to high energy single-level acoustic phonons (inelastic inter-valley scattering) or dispersionless optical phonons (inelastic in-valley scattering). Step changes in the field magnitude are considered with respect to the time and space (one-dimensional) variables, separately. In both cases, the spherically-symmetrical term ƒ_O of the electron distribution function may be expressed using a Laguerre polynomial expansion in the energy variable. For a positive step change in field magnitude, transient electron drift velocities in excess of the steady-state “scattering-limited” values are found in both silicon and germanium.     

Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping

We present a framework aimed to reveal directed interactions of activated brain areas using time-resolved fMRI and vector autoregressive (VAR) modeling in the context of Granger causality. After describing the underlying mathematical concepts, we present simulations helping to characterize the conditions under which VAR modeling and Granger causality can reveal directed interactions from fluctuations in BOLD-like signal time courses. We apply the proposed approach to a dynamic sensorimotor mapping paradigm. In an event-related fMRI experiment, subjects performed a visuomotor mapping task for which the mapping of two stimuli (“faces” vs “houses”) to two responses (“left” or “right”) alternated periodically between the two possible mappings. Besides expected activity in sensory and motor areas, a fronto-parietal network was found to be active during presentation of a cue indicating a change in the stimulus-response (S-R) mapping. The observed network includes the superior parietal lobule and premotor areas. These areas might be involved in setting up and maintaining stimulus-response associations. The Granger causality analysis revealed a directed influence exerted by the left lateral prefrontal cortex and premotor areas on the left posterior parietal cortex.     

Acoustic Analyses of Developmental Changes and Emotional Expression in the Preverbal Vocalizations of Infants

The nonverbal vocal utterances of seven normally hearing infants were studied within their first year of life with respect to age- and emotion-related changes. Supported by a multiparametric acoustic analysis it was possible to distinguish one inspiratory and eleven expiratory call types. Most of the call types appeared within the first two months; some emerged in the majority of infants not until the 5th (“laugh”) or 7th month (“babble”). Age-related changes in acoustic structure were found in only 4 call types (“discomfort cry,” “short discomfort cry,” “wail,” “moan”). The acoustic changes were characterized mainly by an increase in harmonic-to-noise ratio and homogeneity of the call, a decrease in frequency range and a downward shift of acoustic energy from higher to lower frequencies. Emotion-related differences were found in the acoustic structure of single call types as well as in the frequency of occurrence of different call types. A change from positive to negative emotional state was accompanied by an increase in call duration, frequency range, and peak frequency (frequency with the highest amplitude within the power spectrum). Negative emotions, in addition, were characterized by a significantly higher rate of “crying,” “hic” and “ingressive vocalizations” than positive emotions, while positive emotions showed a significantly higher rate of “babble,” “laugh,” and “raspberry.”     

Consequences for nuclear physics of a NNγ and A NNγ time reversal violating vertex

This paper studies the effects in low energy nuclear physics of a possible time reversal invariance (TRI) violation in the electromagnetic interaction. It is shown that this effect appears as a two body short range TRI violating transition operator or as a two and three body TRI violating potential. Two cases are studied. Firstly a TRI violating NNγ vertex is considered and found to have very little effect. Secondly the TRI violation is assumed to occur in the NN^*γ vertex and it is shown that if the violation is “maximal” the contribution to the imaginary part of the “mixing ratio” δ is Im δ ≈ ¦δ¦ × 10⁻³. This should be measurable.