The conundrum of stock versus bond prices

In a general way, stock and bond prices do not display any significant correlation. Yet, if we concentrate our attention on specific episodes marked by a crash followed by a rebound, then we observe that stock prices have a strong connection with interest rates on the one hand, and with bond yield spreads on the other hand. That second relationship is particularly stable in the course of time having been observed for over 140 years. Throughout the paper we use a quasi-experimental approach. By observing how markets respond to well-defined exogenous shocks (such as the shock of September 11, 2001) we are able to determine how investors organize their ``flight to safety'': which safe haven they select, how long their collective panic lasts, and so on. As rebounds come to an end the correlation of stock and bond prices fades away, a clear sign that the collective behavior of investors loses some of its coherence; this observation can be used as an objective criterion for assessing the end of a market rebound. Based on the behavior of investors, we introduce a distinction between ``genuine stock market rallies'', as opposed to spurious rallies such as those brought about by the buyback programs implemented by large companies. The paper ends with a discussion of testable predictions.Comment: 19 pages, 8 figures, 3 tables. To appear in "Physica A

Does the price multiplier effect also hold for stocks?

The price multiplier effect provides precious insight into the behavior of investors during episodes of speculative trading. It tells us that the higher the price of an asset is (within a set of similar assets) the more its price is likely to increase during the upgoing phase of a speculative price peak. In short, instead of being risk averse, as is often assumed, investors rather seem to be ``risk prone''. While this effect is known to hold for several sorts of assets, it has not yet been possible to test it for stocks because the price of one share has no intrinsic significance which means that one cannot say that a stock $A$ is more expensive than a stock $B$ on the basis of its price. In this paper we show that the price-dividend ratio gives a good basis for assessing the price of stocks in an intrinsic way. When this alternative measure is used instead, it turns out that the price multiplier effect also holds for stocks, at least if one concentrates on samples of companies which are sufficiently homogeneous.Comment: 11 pages, 5 figures, 1 table To appear in the "International Journal of Modern Physics C

Derivation of the Gutenberg-Richter Empirical Formula from the Solution of the Generalized Logistic Equation

We have written a new equation to study the statistics of earthquake distributions. We call this equation "the generalized logistic equation". The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case in approximation of large magnitudes. To illustrate how the found solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N-25N, 5W-35W), Canary Islands, Magellan Mountains (20N-9S, 148E-170E), and the Sea of Japan. This approximation showed the excellent fit between the theoretical curves and observed data for earthquake magnitudes 1<m<9.Comment: 10 pages, 2 figures, 1 table, 8 references. Submitted to Natural Science, Earthquakes special issu

On the superfluidity of classical liquid in nanotubes

In 2001, the author proposed the ultra second quantization method. The ultra second quantization of the Schr\"odinger equation, as well as its ordinary second quantization, is a representation of the N-particle Schr\"odinger equation, and this means that basically the ultra second quantization of the equation is the same as the original N-particle equation: they coincide in 3N-dimensional space. We consider a short action pairwise potential V(x_i -x_j). This means that as the number of particles tends to infinity, $N\to\infty$, interaction is possible for only a finite number of particles. Therefore, the potential depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite with support $\Omega_V$, then as $N\to\infty$ the support engulfs a finite number of particles, and this number does not depend on N. As a result, it turns out that the superfluidity occurs for velocities less than $\min(\lambda_{\text{crit}}, \frac{h}{2mR})$, where $\lambda_{\text{crit}}$ is the critical Landau velocity and R is the radius of the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop "Idempotent and tropical mathematics and problems of mathematical physics", Independent University of Moscow, Moscow, August 25--30, 2007 and to be published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #

Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Application of Permutation Group Theory in Reversible Logic Synthesis

The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits consisting of gates from the NCT library is described. An algorithm for gate complexity reduction, based on equivalent replacements of gates compositions, is introduced. A new approach for combining a group-theory-based synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is described. Experimental results are presented to show that the proposed synthesis techniques allow a reduction in input lines count, gate complexity or quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016 conferenc

Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude