Angiitis with Nodule Formation, Vasomotor Instability and Secondary Cutis Laxa11From the University of Southern California School of Medicine, Department of Medicine (Doctor Winsor) and Section of Dermatology (Doctor Obermayer), Los Angeles, California.

https://nsuworks.nova.edu/nsudigital_harrison/3625/thumbnail.jp

Escalation of error catastrophe for enzymatic self-replicators

It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication, we analyze highly specific enzymatic self-replication mediated through an otherwise neutral recognition region, which leads to frequency-dependent replication rates. We find a significant reduction of the maximally tolerable error rate, because the replication rate of the fittest molecules decreases with the fraction of functional enzymes. Our analysis is extended to hypercyclic couplings as an example for catalytic networks.Comment: 6 pages, 4 figures; accepted at Europhys. Let

A freely relaxing polymer remembers how it was straightened

The relaxation of initially straight semiflexible polymers has been discussed mainly with respect to the longest relaxation time. The biologically relevant non-equilibrium dynamics on shorter times is comparatively poorly understood, partly because "initially straight" can be realized in manifold ways. Combining Brownian dynamics simulations and systematic theory, we demonstrate how different experimental preparations give rise to specific short-time and universal long-time dynamics. We also discuss boundary effects and the onset of the stretch--coil transition.Comment: 14 pages, 5 figures, 3 table

Cellular Structures for Computation in the Quantum Regime

We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking avoids the time-scale problems associated with ground-state relaxation schemes. For quantum computing, the architecture constitutes a novel paradigm whereby the algorithm is embedded in spatial, as opposed to temporal, structure. The architecture can be exploited to produce highly efficient algorithms: for example, a list of length N can be searched in time of order cube root N.Comment: 11 pages (LaTeX), 3 figure

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Two-Bit Gates are Universal for Quantum Computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon reques

A Simple Quantum Computer

We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design which we employ also demonstrates a signature for quantum parallelism which unambiguously delineates the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum optical components calls for the development of several key technologies common to single photonics.Comment: 8 pages RevTeX + 6 figures in postscrip