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- Sophia Yancopoulos, Oliver Attie, Richard Friedberg
- Bioinformatics
- 2005

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… (More)

- Richard Friedberg
- J. Symb. Log.
- 1957

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… (More)

- Sophia Yancopoulos, Richard Friedberg
- Journal of Computational Biology
- 2009

We extend the double cut and join operation (DCJ) paradigm to perform genome rearrangements on pairs of genomes having unequal gene content and/or multiple copies by permitting genes in one genome which are completely or partially unmatched in the other. The existence of unmatched gene ends introduces new kinds of paths in the adjacency graph, since some… (More)

- Sophia Yancopoulos, Richard Friedberg
- RECOMB-CG
- 2008

- Richard Friedberg, Aaron E. Darling, Sophia Yancopoulos
- Methods in molecular biology
- 2008

The Double Cut and Join is an operation acting locally at four chromosomal positions without regard to chromosomal context. This chapter discusses its application and the resulting menu of operations for genomes consisting of arbitrary numbers of circular chromosomes, as well as for a general mix of linear and circular chromosomes. In the general case the… (More)

Decades of scientific advances have brought modern healthcare to a level of complexity that is having a negative impact on care delivery. “American healthcare is falling short on basic dimensions of quality, outcomes, costs, and equity....The traditional systems for transmitting new knowledge-the ways clinicians are educated, deployed, rewarded, and… (More)

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1.… (More)

- Richard Friedberg, Pierre Hohenberg
- Reports on progress in physics. Physical Society
- 2014

Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the… (More)

We present a new convergent iterative solution for the two lowest quantum wave functions ψev and ψod of the Hamiltonian with a quartic double well potential V in one dimension. By starting from a trial function, which is by itself the exact lowest even or odd eigenstate of a different Hamiltonian with a modified potential V + δV , we construct the Green’s… (More)