Financial Return Distributions: Past,Present, and COVID-19

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.     

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable — which plays a role similar to price — whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the “thermodynamic” limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even “infinitesimally” for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a “price taker” behavior if agents account for their market impact.     

Methods for evaluating the performance of emitters in plane parallel diodes

The curvature seen in Child's law plots of current-voltage characteristics measured using plane parallel diodes may be analysed in a number of ways to give information about the work function distribution of a cathode. This paper suggests a simple technique for characterising a cathode based on the assumption it has a “top-hat” work function distribution. The technique allows synthetic current/voltage characteristics to be generated which agree well with the practical characteristics from which the parameters of the work function distribution were derived. The parameters of the “top-hat” model may also be used to obtain an equivalent Gaussian work function distribution which gives almost identical synthetic characteristics and Schottky enhancement may be modelled in a rather empirical manner. Since either model gives good predictions, synthetic characteristics may be used to investigate other methods used to characterise cathodes. It is found that there is generally reasonable agreement which could be improved, for most practical work function distributions, by the choice of parameters slightly different from those normally used.     

De-Pake-ing transform analysis of fully deuterated malonic acid

The analysis of deuterium wideline NMR spectra has been an essential step in characterizing the dynamics of molecules in the solid-state. Although clearly important, the identification of quadrupolar coupling constants (QCCs) from the powder patterns is often complicated by poor sensitivity and/or spectral overlap. Previously, others have demonstrated the utility of “de-Pake-ing”, a mathematical transform that yields the QCCs in a straightforward manner for symmetric (η = 0) sites. In this short paper, we describe our analysis of a powder sample of perdeutero-malonic acid, a molecule with two distinct deuteron environments and asymmetries. The methylene sites are immediately amenable to the standard de-Pake-ing transform analysis due to their low asymmetry. However, the de-Pake-ing methodology for the acid deuterons, for which the asymmetry deviates significantly from zero, requires more analysis to extract their QCCs. The impact of this work on the future application of de-Pake-ing to a wider range of samples is also discussed.     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Novel comprehension of “common path” principle

The idea of “common path” has been widely applied in optical instrument design for 30 years and even today. But the meaning of “common path” has not yet been explained clearly and sometimes confusion has been created. In this paper an “adaptive principle” is proposed and recommended on optical instrument system. It suggests that the designer not only arranges the measurement system to obtain measurement signal but also sets a channel to give prediction of noise or disturbance in real time or short term. Such a recommendation is based on the recent studies on nonlinear dynamics and atmospheric disturbance by means of experiments as well as theoretical analysis.     

The Inertial Transformations and the Relativity Principle

Our recently proposed inertial transformations of the space and time variables based on absolute simultaneity imply the existence of a single isotropic inertial reference system (“privileged system”). We show, however, that aresynchronization of clocks in all inertial systems is possible leading to a different, arbitrarily chosen,isotropic “privileged” system. Such a resynchronization does not modify any one of the empirical consequences of the theory,which is thus compatible with a formulation of the relativity principle weaker than adopted in Einstein’s theory of special relativity.     

Wave Node Dynamics and Revival Symmetry in Quantum Rotors

Symmetries and dynamics of wave nodes in space and time expose principles of quantum theory and its relativistic underpinning. Among these are key principles behind recently discovered dephasing and rephasing phenomena known as revivals. A reexamination of basic Eberly revivals, Berry “quantum fractal” landscapes, and the “quantum carpets” of Schleich and co-workers reveals a simple Farey arithmetic and C_n-group revival structure in one of the earliest quantum wave models, the Bohr rotor. These principles may be useful for interpreting modern time-dependent rovibrational spectra. The nodal dynamics of the Bohr rotor is seen to have a quasi-fractal structure similar to that of earlier systems involving chaotic circle maps. The fractal structure is an overlay of discrete versions of Bohr's rotor model. Each N-point Bohr rotor acts like a base-N quantum “odometer” which performs rational fraction arithmetic. Such systems may have applications for optical information technology and quantum computing.     

Beyond nanosizing: an approach to shape analysis of fluorescent nanostructures by SMI-microscopy

Using spatially modulated illumination (SMI) light microscopy it is possible to measure the sizes of fluorescent structures that have an extension far below the conventional optical resolution limit (“subresolution size”). Presently, the sizes are determined as the object extension along the optical axis of the SMI microscope. For this, however, “a priori” assumptions on the fluorochrome distribution (“shape”) within the examined fluorescent structure have to be made. Usually it is assumed that the fluorochrome follows a Gauss-distribution or a spherical distribution. In this report we overcome the necessity to make an assumption on the shape of the fluorochrome distribution. We introduce two new experimentally obtained parameters which allow the determination of a shape measure to describe the spatial distribution of the fluorescent dye. This becomes possible by independent measurements with different excitation wavelengths. As an example, we present shape parameter measurements on individual fluorescent microspheres with a nominal geometrical diameter (“size”) of 190 nm. In the case investigated, the experimental shape correlated well with a homogeneous fluorochrome distribution (“spherical shape”) but not with a variety of other “shapes”.     

Nucleation and growth mechanism for flame synthesis of MoO2 hollow microchannels with nanometer wall thickness

The growth and morphological evolution of molybdenum-oxide microstructures formed in the high temperature environment of a counter-flow oxy-fuel flame using molybdenum probes is studied. Experiments conducted using various probe retention times show the sequence of the morphological changes. The morphological row begins with micron size objects exhibiting polygonal cubic shape, develops into elongated channels, changes to large structures with leaf-like shape, and ends in dendritic structures. Time of probe–flame interaction is found to be a governing parameter controlling the wide variety of morphological patterns; a molecular level growth mechanism is attributed to their development. This study reveals that the structures are grown in several consecutive stages: material “evaporation and transportation”, “transformation”, “nucleation”, “initial growth”, “intermediate growth”, and “final growth”. XRD analysis shows that the chemical compositions of all structures correspond to MoO₂.     

Development of Matlab filtering techniques in digital speckle pattern interferometry

In interferometric fringe pattern analysis, specular and speckle fringe patterns are the two main divisions. While specular fringes are characterized by quality fringes, speckle (that obtains due to the diffuse scattering of the coherent radiation from an optically rough surface) fringe patterns are characterized by noisy fringes. This paper concentrates on this aspect and the Matlab based filtering methods to improve the quality of speckle fringe patterns by developing the appropriate software. Further, the newly developed software “Macurv” will be presented which can give the second order derivative (curvature) fringe information. A software with several functions is written using Matlab. The objective of the software is to provide a more effective way for the post-processing of speckle interferometric fringes. The algorithm and functions of the developed software “Macurv” will be explained.     

The symmetries of the Manton superconductivity model

The symmetries and conserved quantities of Manton’s modified superconductivity model with non-relativistic Maxwell–Chern–Simons dynamics (also related to the Quantized Hall Effect) are obtained in the “Kaluza–Klein type” framework of Duval et al.     

Optical Entropy Network Mapped from Binary Feature Tree

The concept of a binary feature tree (BFT) and the principle of its formation are described. A pattern is divided into sub-parts by comparing its similarity with other patterns. The BFT is established by sub-parts of a group of patterns and mapped into a three layered neural network which Sethi called an entropy network. The interconnection pattern between the first and hidden layers is formed according to the “AND“ relationship of node feature patterns determined by BFT. The interconnection pattern between the hidden and last layers is obtained by training. The advantage of the proposed network is that the scale is small because a feature neuron is adopted and the interconnection is local instead of full; therefore, it is easily implemented by either hardware or software. Two simulation examples show the success of the entropy network for pattern recognition. A feature extraction by an optical inner product method is also described.Presented at 1996 International Topical Meeting on Optical Computing (OC ‘96), April 21-25, Sendai, Japan.     

Dynamical behavior of the phase transition of strained from atomistic simulations

Using an atomistic shell model we study the temperature dependence of the ferroelectric properties of BaTiO₃ under biaxial compressive strain applicable to growth on perovskites substrate. Molecular dynamics simulations show a “r→c→p” sequence of phase transitions when temperature is increased, and the absence of an “ac phase”. The first-order paraelectric-to-ferroelectric phase transition presents in bulk changes to a second-order one as a consequence of the in-plane constraint imposed by the mechanical boundary conditions. From the tetragonal ferroelectric c phase, the transition takes place in a finite range of temperature where the lattice parameter normal to the plane keeps approximately constant until T_c is reached. Analysis of the local polarization behavior reveals an order–disorder dynamics as the dominant mechanism of the transition.     

Model of a Neuron with Afterdepolarization and Short-Term Memory

In this paper, we propose a model describing the dynamics of a neuron capable of storing the so-called short-term memory. From the dynamical viewpoint, the effect of short-term memory means that the neuron “ remembers” the fact of its short-pulse excitation and the action potential is periodically generated for a long time after it. This mechanism of memory storage is realized due to the property of afterdepolarization included in the model. This property is well known in real (live)neurons of cortex and hippocampus.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 228–237, March 2005.     

Optical transitions in a vanishing conduction-band-offset superlattice

Optical transitions in the strained superlattice ZnSe/ZnS (001) have been calculated within an empirical tight-binding model followed by an appropriate evaluation of the momentum matrix elements. Vanishing conduction-band-offset has been previously established for this system, which can be considered as a realistic candidate for obtaining an “effective-mass” superlattice. Oscillator strengths, calculated for different superlattice periods, show that the usual δn=0 selection rule breaks down.     

Unidirectional transmission of electrons in a magnetic field gradient

This work presents an experimental demonstration of time-reversal asymmetry of electron states propagating along the boundary separating areas with opposite magnetic fields. For this purpose we have fabricated a hybrid ferromagnet– semiconductor device in the form of a Hall cross with two ferromagnets deposited on top. The magnets generated two narrow magnetic barriers of opposite polarity in the active Hall area. We have observed that if the signs of the barriers are reversed, the bend resistance changes its sign. Using the Landauer–Büttiker theory, we have demonstrated that this is a direct consequence of asymmetric transmission of the “snake” and the “cycloidal” trajectories formed at the boundary separating the regions with opposite magnetic field directions.     

What the inflaton might tell us about RHIC/LHC

Topical phenomena in high-energy physics related to collision experiments of heavy nuclei (“Little Bang”) and early universe cosmology (“Big Bang”) involve far-from-equilibrium dynamics described by quantum field theory. One example concerns the role of plasma instabilities for the process of thermalization in heavy-ion collisions. The reheating of the early universe after inflation may exhibit rather similar phenomena following a tachyonic or parametric resonance instability. Certain universal aspects associated to nonthermal fixed points even quantitatively agree, and considering these phenomena from a common perspective can be fruitful.