R. Friedberg

Efficient sorting of genomic permutations by translocation, inversion and block interchange

MOTIVATION Finding genomic distance based on gene order is a classic problem in genome rearrangements. Efficient exact algorithms for genomic distances based on inversions and/or translocations have been found but are complicated by special cases, rare in simulations and empirical data. We seek a universal operation underlying a more inclusive set of evolutionary operations and yielding a tractable genomic distance with simple mathematical form. RESULTS We study a universal double-cut-and-join operation that accounts for inversions, translocations, fissions and fusions, but also produces circular intermediates which can be reabsorbed. The genomic distance, computable in linear time, is given by the number of breakpoints minus the number of cycles (b-c) in the comparison graph of the two genomes; the number of hurdles does not enter into it. Without changing the formula, we can replace generation and re-absorption of a circular intermediate by a generalized transposition, equivalent to a block interchange, with weight two. Our simple algorithm converts one multi-linear chromosome genome to another in the minimum distance.

Random lattice field theory: General formulation☆

A new type of lattice field theory is formulated in which the sites are chosen randomly in space. An algorithm is given for linking nearby sites; these links form the edges of non-overlapping simplices which fill the entire volume. All physical quantities averaged over such a lattice can therefore be translationally and rotationally symmetric.

Frequency shifts in emission and absorption by resonant systems ot two-level atoms☆

Abstract The frequency shifts in emission and absorption arising from resonant many-body interactions in a system of two-level atoms are discussed from several points of view: (1) in the language of superradiance, Dicke states, quantum electrodynamics and perturbation theory; (2) in the classical-path treatment of gaseous emission, with emphasis on the impact approximation; (3) by means of diagrams related to the temperature-Greens function formalism; (4) in the semiclassical model using the macroscopic Bloch vector; (5) through ordinary classical electromagnetic theory in a linear medium.

Weights of links and plaquettes in a random lattice

In a random lattice, links and plaquettes have varying sizes and orientations. Therefore, they should enter the action function with different weights. A particularly attractive choice of these weights is presented; its consequences for spin-0, 12 and 1 fields on such a lattice are discussed.

Derivation of Regge's action from Einstein's theory of general relativity

Abstract Regges action for a discrete lattice is derived from Einsteins continuum formula ʃ√ |g| R d D x in general relativity.

Gauge theory on a random lattice

Abstract A general formulation of gauge theory on a random lattice is developed and the strong coupling limit of the Wilson string tension worked out. The confining force found in this strong coupling limit is identical to that predicted by the relativistic string model. In particular, the force between two color-triplet charges is a constant for large separation and the tube of electric flux joining the charges fluctuates, giving it a net thickness proportional to the logarithm of its length.

Lattice gravity near the continuum limit

Abstract We prove that the lattice gravity always approaches the usual continuum limit when the link length l → 0, provided that certain general boundary conditions are satisfied. This result holds for any lattice, regular or irregular. Furthermore, for a given lattice, the deviation from its continuum limit can be expressed as a power series in l 2 . General formulas for such a perturbative calculation are given, together with a number of illustrative examples, including the graviton propagator. The lattice gravity satisfies all the invariance properties of Einsteins theory of general relativity. In addition, it is symmetric under a new class of transformations that are absent in the usual continuum theory. The possibility that the lattice theory (with a nonzero l) may be more fundamental is discussed.

Boson-Fermion model of superconductivity

Abstract We examine the superfluidity properties of a mixed boson-fermion system, with individual bosons unstable. There exists a critical density p c . The superfluid consists of both bosons and fermions for density p > p c , but only fermions for p c . Possible applications to Y-123 and other material are suggested.

Superradiant damping and absorption

Abstract We obtain a relationship between the absorption coefficient and the superradiant lifetime which shows that superradiant damping can be large only in an optically thick sample. Accordingly, we reexamine the recent photon-echo experiment of Compaan and Abella.

The s-channel theory of superconductivity on a one-dimensional lattice of parallel (CuO2) planes

Abstract The recently proposed s -channel theory of high T c superconductivity is applied to a one-dimensional lattice of parallel CuO 2 planes. It is shown that at T T c , the long-range-order parameter is described by the Bose-condensate amplitude B and the electrons (or holes) have a gap energy proportional to B , the same as in the continuum case.