7,271 research outputs found
Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit
In this paper, we derive the Fay-like identities of tau function for the Toda
lattice hierarchy from the bilinear identity. We prove that the Fay-like
identities are equivalent to the hierarchy. We also show that the
dispersionless limit of the Fay-like identities are the dispersionless Hirota
equations of the dispersionless Toda hierarchy.Comment: 20 page
Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
In a certain class of differential-difference equations for dissipative
systems, we show that hyperbolic tangent model is the only the nonlinear system
of equations which can admit some particular solutions of the Toda lattice. We
give one parameter family of exact solutions, which include as special cases
the Toda lattice solutions as well as the Whitham's solutions in the Newell's
model. Our solutions can be used to describe temporal-spatial density patterns
observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur
Modeling error analysis of stationary linear discrete-time filters
The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available
Host resistance does not explain variation in incidence of male-killing bacteria in Drosophila bifasciata
Background
Selfish genetic elements that distort the sex ratio are found widely. Notwithstanding the number of records of sex ratio distorters, their incidence is poorly understood. Two factors can prevent a sex ratio distorter from invading: inability of the sex ratio distorter to function (failure of mechanism or transmission), and lack of drive if they do function (inappropriate ecology for invasion). There has been no test to date on factors causing variation in the incidence of sex ratio distorting cytoplasmic bacteria. We therefore examined whether absence of the male-killing Wolbachia infection in D. bifasciata in Hokkaido island of Japan, in contrast to the presence of infection on the proximal island of Honshu, was associated with failure of the infection to function properly on the Hokkaido genetic background.
Results
The male-killer both transmitted and functioned well following introgression to each of 24 independent isofemale inbred lines carrying Hokkaido genetic backgrounds. This was maintained even under stringent conditions of temperature. We therefore reject the hypothesis that absence of infection is due to its inability to kill males and transmit on the Hokkaido genetic background. Further trap data indicates that D. bifasciata may occur at different densities in Hokkaido and Honshu populations, giving some credence to the idea that ecological differentiation could be important.
Conclusions
The absence of the infection from the Hokkaido population is not caused by failure of the male-killer to function on the Hokkaido genetic background
Algorithms for adaptive stochastic control for a class of linear systems
Control of linear, discrete time, stochastic systems with unknown control gain parameters is discussed. Two suboptimal adaptive control schemes are derived: one is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single input, third order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known
On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy
We give a simple algebraic proof that the two different Lax pairs for the
Kac-van Moerbeke hierarchy, constructed from Jacobi respectively
super-symmetric Dirac-type difference operators, give rise to the same
hierarchy of evolution equations. As a byproduct we obtain some new recursions
for computing these equations.Comment: 8 page
Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models
A system of first-order differential-difference equations with time lag
describes the formation of density waves, called as quasi-solitons for
dissipative systems in this paper. For co-moving density waves, the system
reduces to some exactly solvable lattice models. We construct a shock-wave
solution as well as one-quasi-soliton solution, and argue that there are
pseudo-conserved quantities which characterize the formation of the co-moving
waves. The simplest non-trivial one is given to discuss the presence of a
cascade phenomena in relaxation process toward the pattern formation.Comment: REVTeX, 4 pages, 1 figur
Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold
Thermodynamic interpretation of the uniformity of the phase space probability measure
Uniformity of the probability measure of phase space is considered in the
framework of classical equilibrium thermodynamics. For the canonical and the
grand canonical ensembles, relations are given between the phase space
uniformities and thermodynamic potentials, their fluctuations and correlations.
For the binary system in the vicinity of the critical point the uniformity is
interpreted in terms of temperature dependent rates of phases of well defined
uniformities. Examples of a liquid-gas system and the mass spectrum of nuclear
fragments are presented.Comment: 11 pages, 2 figure
Reductions of the Volterra and Toda chains
The Volterra and Toda chains equations are considered. A class of special
reductions for these equations are derived.Comment: LaTeX, 6 page
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