3,050 research outputs found
Randomly Charged Polymers, Random Walks, and Their Extremal Properties
Motivated by an investigation of ground state properties of randomly charged
polymers, we discuss the size distribution of the largest Q-segments (segments
with total charge Q) in such N-mers. Upon mapping the charge sequence to
one--dimensional random walks (RWs), this corresponds to finding the
probability for the largest segment with total displacement Q in an N-step RW
to have length L. Using analytical, exact enumeration, and Monte Carlo methods,
we reveal the complex structure of the probability distribution in the large N
limit. In particular, the size of the longest neutral segment has a
distribution with a square-root singularity at l=L/N=1, an essential
singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near
l=1 is related to a another interesting RW problem which we call the "staircase
problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
Collapse of Randomly Linked Polymers
We consider polymers in which M randomly selected pairs of monomers are
restricted to be in contact. Analytical arguments and numerical simulations
show that an ideal (Gaussian) chain of N monomers remains expanded as long as
M<<N. This result is inconsistent with results obtained from free energy
considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).Comment: 1 page, 1 postscript figure, LaTe
Citizens United v. Federal Election Commission, and the Inherent Unfairness to the “Un-united” American Citizen
Among contemporary United States Supreme Court rulings that have impacted the structure of our nation, the 2010 case Citizens United v. Federal Election Commission resulted in significant political campaign finance reform that gave rise to an election system influenced by money, corporations, and powerful individuals. The ruling of Citizens United allows for the unlimited spending of corporations and labor unions on political expenditures and the limited disclosures of these campaign donors. This overturned precedent established in the 1990 case Austin v. Michigan Chamber of Commerce and the 2003 case McConnell v. Federal Election Commission, the respective rulings of which shaped the way campaign donations were regulated and maintained in political elections. The subsequent deregulation of corporate money financing political campaigns as a result of this ruling places Citizens United among the most iniquitous and decadent rulings of the Supreme Court of the United States
Theta-point universality of polyampholytes with screened interactions
By an efficient algorithm we evaluate exactly the disorder-averaged
statistics of globally neutral self-avoiding chains with quenched random charge
in monomer i and nearest neighbor interactions on
square (22 monomers) and cubic (16 monomers) lattices. At the theta transition
in 2D, radius of gyration, entropic and crossover exponents are well compatible
with the universality class of the corresponding transition of homopolymers.
Further strong indication of such class comes from direct comparison with the
corresponding annealed problem. In 3D classical exponents are recovered. The
percentage of charge sequences leading to folding in a unique ground state
approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl
New control strategies for neuroprosthetic systems
The availability of techniques to artificially excite paralyzed muscles opens enormous potential for restoring both upper and lower extremity movements with\ud
neuroprostheses. Neuroprostheses must stimulate muscle, and control and regulate the artificial movements produced. Control methods to accomplish these tasks include feedforward (open-loop), feedback, and adaptive control. Feedforward control requires a great deal of information about the biomechanical behavior of the limb. For the upper extremity, an artificial motor program was developed to provide such movement program input to a neuroprosthesis. In lower extremity control, one group achieved their best results by attempting to meet naturally perceived gait objectives rather than to follow an exact joint angle trajectory. Adaptive feedforward control, as implemented in the cycleto-cycle controller, gave good compensation for the gradual decrease in performance observed with open-loop control. A neural network controller was able to control its system to customize stimulation parameters in order to generate a desired output trajectory in a given individual and to maintain tracking performance in the presence of muscle fatigue. The authors believe that practical FNS control systems must\ud
exhibit many of these features of neurophysiological systems
From Collapse to Freezing in Random Heteropolymers
We consider a two-letter self-avoiding (square) lattice heteropolymer model
of N_H (out ofN) attracting sites. At zero temperature, permanent links are
formed leading to collapse structures for any fraction rho_H=N_H/N. The average
chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H -->
0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H <
1, entropy approaches zero as N --> infty (being finite for a homopolymer). An
abrupt decrease in entropy occurs at the phase boundary between the swollen (R
~ N^nu) and collapsed region. Scaling arguments predict different regimes
depending on the ensemble of crosslinks. Some implications to the protein
folding problem are discussed.Comment: 4 pages, Revtex, figs upon request. New interpretation and emphasis.
Submitted to Europhys.Let
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