Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address

Finding the Center of Mass of a Soft Spring

This article shows how to use calculus to find the center of mass position of a soft cylindrical helical spring that is suspended vertically. The spring is non-uniformly stretched by the action of gravity. A general expression for the vertical position of the center of mass is obtained.Comment: LaTeX, 7 pages, 2 figures. Minor changes to agree with published versio

Dihedral symmetry of periodic chain: quantization and coherent states

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian dihedral group D_n - is taken as its symmetry group. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.Comment: 13 pages; minor changes of the tex

Weighted Mean Field Theory for the Random Field Ising Model

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe critical behavior arising from the weighted sum. The resulting exponents are calculated.Comment: 15 pages of tex using harvmac. 8 postscript figures (fig3.ps is large) in a separate .uu fil

Economical (k,m)-threshold controlled quantum teleportation

We study a (k,m)-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over GF(p) with prime p > m-1 needs to distribute a d-dimensional qudit with d >= p to each controller for this purpose. We propose a scheme using m qubits (two-dimensional qudits) for the controllers' portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.Comment: 11 pages, 2 figures, v2: minor revision, discussions improved, an equation corrected in procedure (A) of section 4.3, v3: major revision, protocols extended, citations added, v4: minor grammatical revision, v5: minor revision, discussions extende

Effect of Impurity Scattering on the Nonlinear Microwave Response in High-Tc Superconductors

We theoretically investigate intermodulation distortion in high-Tc superconductors. We study the effect of nonmagnetic impurities on the real and imaginary parts of nonlinear conductivity. The nonlinear conductivity is proportional to the inverse of temperature owing to the dependence of the damping effect on energy, which arises from the phase shift deviating from the unitary limit. It is shown that the final-states interaction makes the real part predominant over the imaginary part. These effects have not been included in previous theories based on the two-fluid model, enabling a consistent explanation for the experiments with the rf and dc fields

Ground state properties of solid-on-solid models with disordered substrates

We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain wall energy of a boundary induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to infinitesimal variations of the quenched disorder is analyzed.Comment: 4 pages RevTeX, 3 eps-figures include

Form-function relationship in the amplitude and frequency modulations of infant - directed speech: A predictive processing perspective

Infants prefer infant-directed speech (IDS) over adult-directed speech (ADS). IDS is thought to serve specific functions compared to ADS: - Attracting infant attention to the speech signal - Conveying clear opportunities for easier word segmentation. Two independent domains of complexity that are embedded in the speech stream: - Amplitude complexity: Lower amplitude complexity associates with greater ease in identifying word boundaries ​ - ​Frequency complexity: Higher fre q uency complexity associates with more attention eliciting speech attention by inducing uncertaint

Minimal Model for Sand Dunes

We propose a minimal model for aeolian sand dunes. It combines an analytical description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The model provides a qualitative understanding of important features of real dunes, such as their longitudinal shape and aspect ratio, the formation of a slip face, the breaking of scale invariance, and the existence of a minimum dune size.Comment: 4 pages, 4 figures, replaced with publishd versio