Convex Dynamics and Applications

This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. \textit{Digital halftoning} is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A corollary of the theorem is that for \textit{error diffusion}, one of the methods of digital halftoning, averages of colors of the printed dots converge to averages of the colors taken from the same dots of the actual images. Digital printing is a special case of a much wider class of scheduling problems to which the theorem applies. Convex dynamics has roots in classical areas of mathematics such as symbolic dynamics, Diophantine approximation, and the theory of uniform distributions.Comment: LaTex with 9 PostScript figure

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

Spatial, Temporal, and Habitat-Related Variation in Abundance of Pelagic Fishes in the Gulf of Mexico: Potential Implications of the Deepwater Horizon Oil Spill

Time-series data collected over a four-year period were used to characterize patterns of abundance for pelagic fishes in the northern Gulf of Mexico (GoM) before (2007-2009) and after (2010) the Deepwater Horizon oil spill. Four numerically dominant pelagic species (blackfin tuna, blue marlin, dolphinfish, and sailfish) were included in our assessment, and larval density of each species was lower in 2010 than any of the three years prior to the oil spill, although larval abundance in 2010 was often statistically similar to other years surveyed. To assess potential overlap between suitable habitat of pelagic fish larvae and surface oil, generalized additive models (GAMs) were developed to evaluate the influence of ocean conditions on the abundance of larvae from 2007-2009. Explanatory variables from GAMs were then linked to environmental data from 2010 to predict the probability of occurrence for each species. The spatial extent of surface oil overlapped with early life habitat of each species, possibly indicating that the availability of high quality habitat was affected by the DH oil spill. Shifts in the distribution of spawning adults is another factor known to influence the abundance of larvae, and the spatial occurrence of a model pelagic predator (blue marlin) was characterized over the same four-year period using electronic tags. The spatial extent of oil coincided with areas used by adult blue marlin from 2007-2009, and the occurrence of blue marlin in areas impacted by the DH oil spill was lower in 2010 relative to pre-spill years

Standard decomposition of expansive ergodically supported dynamics

In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically supported dynamical system $(X,T)$ with the shadowing property establishes a sufficient criterion for the existence of quasigroup operations defined almost everywhere outside of universally null sets and for which $T$ is an automorphism. Furthermore, we find a decomposition of the dynamics of $T$ in terms of $T$-invariant weak topological subquasigroups.Comment: 18 pages, the conditions on the entropy in Theorem 3.5 was improved. Some small changes in the text, by adding more explanation

Input-state-output representations and constructions of finite-support 2D convolutional codes

Two-dimensional convolutional codes are considered, with codewords having compact support indexed in N^2 and taking values in F^n, where F is a finite field. Input-state-output representations of these codes are introduced and several aspects of such representations are discussed. Constructive procedures of such codes with a designed distance are also presented. © 2010 AIMS-SDU

Endocytic uptake, transport and macromolecular interactions of anionic PAMAM dendrimers within lung tissue

Purpose: Polyamidoamine (PAMAM) dendrimers are a promising class of nanocarrier with applications in both small and large molecule drug delivery. Here we report a comprehensive evaluation of the uptake and transport pathways that contribute to the lung disposition of dendrimers. Methods: Anionic PAMAM dendrimers and control dextran probes were applied to an isolated perfused rat lung (IPRL) model and lung epithelial monolayers. Endocytosis pathways were examined in primary alveolar epithelial cultures by confocal microscopy. Molecular interactions of dendrimers with protein and lipid lung fluid components were studied using small angle neutron scattering (SANS). Results: Dendrimers were absorbed across the intact lung via a passive, size-dependent transport pathway at rates slower than dextrans of similar molecular sizes. SANS investigations of concentration-dependent PAMAM transport in the IPRL confirmed no aggregation of PAMAMs with either albumin or dipalmitoylphosphatidylcholine lung lining fluid components. Distinct endocytic compartments were identified within primary alveolar epithelial cells and their functionality in the rapid uptake of fluorescent dendrimers and model macromolecular probes was confirmed by co-localisation studies. Conclusions: PAMAM dendrimers display favourable lung biocompatibility but modest lung to blood absorption kinetics. These data support the investigation of dendrimer-based carriers for controlled-release drug delivery to the deep lung

An Examination of Not-For-Profit Stakeholder Networks for Relationship Management: A Small-Scale Analysis on Social Media

Using a small-scale descriptive network analysis approach, this study highlights the importance of stakeholder networks for identifying valuable stakeholders and the management of existing stakeholders in the context of mental health not-for-profit services. We extract network data from the social media brand pages of three health service organizations from the U.S., U.K., and Australia, to visually map networks of 579 social media brand pages (represented by nodes), connected by 5,600 edges. This network data is analyzed using a collection of popular graph analysis techniques to assess the differences in the way each of the service organizations manage stakeholder networks. We also compare node meta-information against basic topology measures to emphasize the importance of effectively managing relationships with stakeholders who have large external audiences. Implications and future research directions are also discussed

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Pathways of cellular internalisation of liposomes delivered siRNA and effects on siRNA engagement with target mRNA and silencing in cancer cells

Design of an efficient delivery system is a generally recognised bottleneck in translation of siRNA technology into clinic. Despite research efforts, cellular processes that determine efficiency of siRNA silencing achieved by different delivery formulations remain unclear. Here, we investigated the mechanism(s) of cellular internalisation of a model siRNA-loaded liposome system in a correlation to the engagement of delivered siRNA with its target and consequent silencing by adopting siRNA molecular beacon technology. Probing of cellular internalisation pathways by a panel of pharmacological inhibitors indicated that clathrin-mediated (dynamin-dependent) endocytosis, macropinocytosis (dynamine independent), and cell membrane cholesterol dependent process(es) (clathrin and caveolea-independent) all play a role in the siRNA-liposomes internalization. The inhibition of either of these entry routes was, in general, mirrored by a reduction in the level of siRNA engagement with its target mRNA, as well as in a reduction of the target gene silencing. A dramatic increase in siRNA engagement with its target RNA was observed on disruption of endosomal membrane (by chloroquine), accompanied with an increased silencing. The work thus illustrates that employing molecular beacon siRNA technology one can start to assess the target RNA engagement – a stage between initial cellular internalization and final gene silencing of siRNA delivery systems

Unified treatment algorithm for the management of crotaline snakebite in the United States: results of an evidence-informed consensus workshop

<p>Abstract</p> <p>Background</p> <p>Envenomation by crotaline snakes (rattlesnake, cottonmouth, copperhead) is a complex, potentially lethal condition affecting thousands of people in the United States each year. Treatment of crotaline envenomation is not standardized, and significant variation in practice exists.</p> <p>Methods</p> <p>A geographically diverse panel of experts was convened for the purpose of deriving an evidence-informed unified treatment algorithm. Research staff analyzed the extant medical literature and performed targeted analyses of existing databases to inform specific clinical decisions. A trained external facilitator used modified Delphi and structured consensus methodology to achieve consensus on the final treatment algorithm.</p> <p>Results</p> <p>A unified treatment algorithm was produced and endorsed by all nine expert panel members. This algorithm provides guidance about clinical and laboratory observations, indications for and dosing of antivenom, adjunctive therapies, post-stabilization care, and management of complications from envenomation and therapy.</p> <p>Conclusions</p> <p>Clinical manifestations and ideal treatment of crotaline snakebite differ greatly, and can result in severe complications. Using a modified Delphi method, we provide evidence-informed treatment guidelines in an attempt to reduce variation in care and possibly improve clinical outcomes.</p