DNA loop statistics and torsional modulus

The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the concept of writhe. This letter presents a unified model for DNA establishing a relation between the different approaches. I show that the writhe created by the loops of DNA is at the origin of the discrepancy. To take this into account, I propose a new treatment of loop statistics based on numerical simulations using the most general formula for the writhe, and on analytic calculations with only one fit parameter. One can then compute the value of the torsional modulus of DNA without the need of any cut-off.Comment: 8 pages, 1 figure. Accepted by Europhysics Letter

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page

How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity

Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existance of a deep connection between quantum gravity and knot theory at a dynamical level.Comment: 7p

Molecular elasticity and the geometric phase

We present a method for solving the Worm Like Chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4 pi. We develop an analogy between WLC elasticity and the geometric phase of a spin half system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's comments, to appear in PR

The formula ABA=Tr(A)A for matrices

We prove that this formula characterizes the square matrices over commutative rings for which all 2 x 2 minors equal zero

Legal Valences of Public-Private Partnership in the Republic of Moldova as an Economic Tool for Innovative Directions of Development

The current economic situation leads to significant changes in the social sector of society. Formerly owned by the state, the infrastructure objects are transferred to private companies, the state reserving the right to regulate and monitor the subsequent activities of these objects. The public-private partnership is based on the cooperation between the public partner and the private partner to increase the efficiency of the public patrimony, each partner assuming concrete risks, innovations, and responsibilities.The Republic of Moldova development required the introduction of innovative management tools for implementing state and regional development strategies, such as the new format of specific programs, strategies for developing regional clusters, the introduction of public-private partnership principles. Governments understood that PPPs could help overcome the situation in the Republic of Moldova when medium and long-term financing sources with a maturity of 3 years are virtually inaccessible within the existing banking system. This situation, combined with a constant lack of financial resources in the budget, suggests that the initiation of the PPP is an alternative tool to further the country's infrastructure development.The article reviews the local legal valences on the public-private partnerships as an economic tool for innovative directions of development and the main weaknesses of the Republic of Moldova framework

The BF Formalism for QCD and Quark Confinement

Using the BF version of pure Yang-Mills, it is possible to find a covariant representation of the 't Hooft magnetic flux operator. In this framework, 't Hooft's pioneering work on confinement finds an explicit realization in the continuum. Employing the Abelian projection gauge we compute the expectation value of the magnetic variable and find the expected perimeter law. We also check the area law behaviour for the Wilson loop average and compute the string tension which turns out to be of the right order of magnitude.Comment: Various changes, version to appear in Nucl.Phys.

On perspective Abelian groups

As a special case of perspective R-modules, an Abelian goup is called perspective if isomorphic summands have a common complement. In this paper we describe many classes of such groups

Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe