Long range action in networks of chaotic elements

We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of an arbitrary large network is completely determined by its boundary conditions. This phenomenon takes place under very mild and robust assumptions on local dynamics with short range interactions. However, we show that it is unstable with respect to arbitrarily weak local random perturbations.Comment: 15 page

Stochastic stability versus localization in chaotic dynamical systems

We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's conjecture about the approximation of the dynamics of a chaotic system by a finite state Markov chain. Conditions under which the localization phenomenon (i.e. stabilization of singular invariant measures) takes place are also considered. Our main tools are the so called bounded variation approach combined with the ergodic theorem of Ionescu-Tulcea and Marinescu, and a random walk argument that we apply to prove the absence of ``traps'' under the action of random perturbations.Comment: 27 pages, LaTe

Hysteresis phenomenon in deterministic traffic flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow model being a straightforward generalization to the well known Nagel-Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the ``free-flowing'' (or ``gaseous'') phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the ``jammed'' (or ``liquid'') phase. Between the two critical values each of these phases may take place, which can be interpreted as an ``overcooled gas'' phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles.Comment: 22 pages, 6 figures, corrected and improved version, to appear in the Journal of Statistical Physic

Multicomponent dynamical systems: SRB measures and phase transitions

We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various definitions of SRB measures are considered as well.Comment: 13 pages, LaTeX 2

Exclusion type spatially heterogeneous processes in continuum

We study deterministic discrete time exclusion type spatially heterogeneous particle processes in continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local velocities etc. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to particle and obstacles densities (the so called Fundamental Diagram) is analyzed rigorously. The main technical tool is a "dynamical" coupling construction applied in a nonstandard fashion: instead of proving the existence of the successful coupling (which even might not hold) we use its presence/absence as an important diagnostic tool.Comment: 17 pages, minor corrections, accepted for publication in JSTA

Rapid Assessment of Existing HIV Prevention Programming in a Community Mental Health Center

In preparation for implementation of a comprehensive HIV prevention program in a Community Mental Health Center for persons with mental illness who are also abusing substances, a rapid assessment procedure (RAP) of existing prevention services that may have developed in the setting over time was undertaken at baseline. In addition to an ecological assessment of the availability of HIV-related information that was available on-site, in-depth interviews and focus groups were conducted with Center administrators, direct-care staff, and mental health consumers. Results indicated that responses regarding available services differed depending upon type of respondent, with administration reporting greater availability of preventive programs and educational materials than did direct-care staff or mental health consumers themselves. But overall, formalized training on HIV prevention by case managers is extremely rare. Case managers felt that other providers, such as doctors or nurses, were more appropriate to deliver an HIV prevention intervention

Ruelle-Perron-Frobenius spectrum for Anosov maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (Information on the existence of an SRB measure, its smoothness properties and statistical properties readily follow from such a result.) In dimension $d=2$ we show that the transfer operator associated to smooth random perturbations of the map is close, in a proper sense, to the unperturbed transfer operator. This allows to obtain easily very strong spectral stability results, which in turn imply spectral stability results for smooth deterministic perturbations as well. Finally, we are able to implement an Ulam type finite rank approximation scheme thus reducing the study of the spectral properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe

Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation

We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x)$ and $\Gamma(x) = \Gamma_1(x) \chi_{\{x_1>0\}}(x)+\Gamma_2(x) \chi_{\{x_1<0\}}(x)$ and with $V_1, V_2, \Gamma_1, \Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\min \sigma(-\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\equiv V_1, \Gamma\equiv \Gamma_1$ and $V\equiv V_2, \Gamma\equiv \Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\tfrac{d^2}{dx^2} +V_1(x)$ and $-\tfrac{d^2}{dx^2} +V_2(x)$.Comment: definition of ground and bound states added, assumption (H2) weakened (sign changing nonlinearity is now allowed); 33 pages, 4 figure

Mineral Resources of the Marble Canyon Wilderness Study Area, White Pine County, Nevada, and Millard County, Utah

The 19,150-acre Marble Canyon Wilderness Study Area (NV-040-086) was evaluated for mineral resources (known) and mineral resource potential (undiscovered), and field work was conducted in 1987. The acreage includes 6,435 acres that is now designated as part of the Mount Moriah Wilderness under the Nevada Wilderness Protection Act of 1989 (S. 974), most but not all of which is included in 8,300 acres fro which the U.S. Bureau of Land Management requested a mineral survey. In this report, the wilderness study area, or simply the study area refers to the entire 19,150-acre tract. The area in underlain by quartzite shale and carbonate rocks. The norther Snake Range decollement is a detachment surface within the study area that separates rocks of similar age but different metamorphic grade. Large inferred subeconomic limestone and marble resources i the study area have no special or unique properties. The mineral resource potential for limestone and marble is high in two canyons and is moderate in the rest of the wilderness study area. Parts of the study area above and along the northern Snake Range decollement have low potential for undiscovered deposits of gold, silver, copper, lead, zinc, tungsten, molybdenum, beryllium, and flourite. A zone around barite-bearing rock penetrated by adits inside the southeast boundary of the study area has moderate potential for barite, and the surrounding area has low potential for barite; both areas also have low potential for silver, copper, lead, zinc, and tungsten. The entire study area has moderate potential for oil and gas and low potential for geothermal energy resources

Systematic Analysis of Cell Cycle Effects of Common Drugs Leads to the Discovery of a Suppressive Interaction between Gemfibrozil and Fluoxetine

Screening chemical libraries to identify compounds that affect overall cell proliferation is common. However, in most cases, it is not known whether the compounds tested alter the timing of particular cell cycle transitions. Here, we evaluated an FDA-approved drug library to identify pharmaceuticals that alter cell cycle progression in yeast, using DNA content measurements by flow cytometry. This approach revealed strong cell cycle effects of several commonly used pharmaceuticals. We show that the antilipemic gemfibrozil delays initiation of DNA replication, while cells treated with the antidepressant fluoxetine severely delay progression through mitosis. Based on their effects on cell cycle progression, we also examined cell proliferation in the presence of both compounds. We discovered a strong suppressive interaction between gemfibrozil and fluoxetine. Combinations of interest among diverse pharmaceuticals are difficult to identify, due to the daunting number of possible combinations that must be evaluated. The novel interaction between gemfibrozil and fluoxetine suggests that identifying and combining drugs that show cell cycle effects might streamline identification of drug combinations with a pronounced impact on cell proliferation