Protein Design is NP-hard

Biologists working in the area of computational protein design have never doubted the seriousness of the algorithmic challenges that face them in attempting in silico sequence selection. It turns out that in the language of the computer science community, this discrete optimization problem is NP-hard. The purpose of this paper is to explain the context of this observation, to provide a simple illustrative proof and to discuss the implications for future progress on algorithms for computational protein design

Spiral wave drift in an electric field and scroll wave instabilities

I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. In contrast to earlier results, the drift speed presents a strong variation close to the parameter value where the drift speed component along the field changes direction. Using a simple phenomenological model and results from a numerical linear stability analysis of scroll waves, I show this behavior can be attributed to a resonance of the meander modes with the translation modes of the spiral wave. Extending this phenomenological model to scroll waves also clarifies the link between the drift and long wavelength instabilities of scroll waves.Comment: Phys Rev E accepte

COLLECTIVE REPUTATION AND QUALITY

Firms who sell a regional or specialty product often share a common or collective reputation, which is based on the group's aggregate quality. The dynamic problem of collective reputation is similar to the natural resource extraction problems. Therefore, for the analysis of this particular problem, we use differential games. If there is unrestricted access to a common property resource (the reputation stock), agents perceive its shadow value to be zero and extract too rapidly; i.e, they all "cheat" on quality, "milking" the rents generated by the existence of the resource (reputation stock). We show that when there exists a collective product reputation without firm traceability, the firms will extract too much from the stock of reputation. A firm is said to "extract" reputation from the reputation stock when it sells low-quality products at high prices given by the high past levels of quality. The firm builds on the group's reputation when it provides a product with a quality level which is higher than the expected level of quality. The results from this work support minimum quality standards for producer groups and regional and specialty products. This is in contrast to the findings of previous work. Finally, the implications of these results are discussed as they relate to the case study of Washington apples. We present the case of Washington apples in light of the results of the analytical model.Agribusiness,

On propagation failure in 1 and 2 dimensional excitable media

We present a non-perturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behaviour of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity and scaling behavior. The results are compared with numerical simulations and show good agreement.Comment: accepted for publication in Chao

Phase Synchronization and Polarization Ordering of Globally-Coupled Oscillators

We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and a polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement can not take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results

Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability

We analyze the way topological constraints and inhomogeneity in the excitability influence the dynamics of spiral waves on spheres and punctured spheres of excitable media. We generalize the definition of an index such that it characterizes not only each spiral but also each hole in punctured, oriented, compact, two-dimensional differentiable manifolds and show that the sum of the indices is conserved and zero. We also show that heterogeneity and geometry are responsible for the formation of various spiral wave attractors, in particular, pairs of spirals in which one spiral acts as a source and a second as a sink -- the latter similar to an antispiral. The results provide a basis for the analysis of the propagation of waves in heterogeneous excitable media in physical and biological systems.Comment: 5 pages, 6 Figures, major revisions, accepted for publication in Phys. Rev.

Using synchronism of chaos for adaptive learning of network topology

In this paper we consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology, i.e., identify the time evolution of the couplings between the network nodes. To this aim, we present an adaptive strategy that, based on a potential that the network systems seek to minimize in order to maintain synchronization, can be successfully applied to identify the time evolution of the network from limited information. This strategy takes advantage of the properties of synchronism of chaos and of the presence of different communication delays over the network links. As a motivating example we consider a network of sensors surveying an area, in which information regarding the time evolution of the network connections can be used, e.g., to detect changes taking place within the area. We propose two different setups for our strategy. In the first one, synchronization has to be achieved at each node (as well as the identification of the couplings over the network links), based solely on a single scalar signal representing a superposition of signals from the other nodes in the network. In the second one, we incorporate an additional node, termed the maestro, having the function of maintaining network synchronization. We will see that when such an arrangement is realized, it will become possible to effectively identify the time evolution of networks that are much larger than would be possible in the absence of a maestro.Comment: 22 pages, 12 figures, accepted for publication on Physical Review

College Athletes and NCAA Violations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94513/1/capp850.pd

Paradigms for computational nucleic acid design

The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCR‐based applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensively studied thermodynamic model, we perform a detailed study of several criteria for designing sequences intended to adopt a target secondary structure. We conclude that superior design methods should explicitly implement both a positive design paradigm (optimize affinity for the target structure) and a negative design paradigm (optimize specificity for the target structure). The commonly used approaches of sequence symmetry minimization and minimum free‐energy satisfaction primarily implement negative design and can be strengthened by introducing a positive design component. Surprisingly, our findings hold for a wide range of secondary structures and are robust to modest perturbation of the thermodynamic parameters used for evaluating sequence quality, suggesting the feasibility and ongoing utility of a unified approach to nucleic acid design as parameter sets are refined further. Finally, we observe that designing for thermodynamic stability does not determine folding kinetics, emphasizing the opportunity for extending design criteria to target kinetic features of the energy landscape

Spiral Waves in Media with Complex Excitable Dynamics

The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken symmetry and complex temporal dynamics. The main structural features of such waves, synchronization defect lines, are demonstrated to be similar to those of spiral waves in systems with complex-oscillatory dynamics.Comment: to appear in International Journal of Bifurcation and Chao