Regularity conditions and Bernoulli properties of equilibrium states and gg-measures

When T : X -> X is a one-sided topologically mixing subshift of finite type and {varphi} : X -> R is a continuous function, one can define the Ruelle operator L{varphi} : C(X) -> C(X) on the space C(X) of real-valued continuous functions on X. The dual operator Formula always has a probability measure {nu} as an eigenvector corresponding to a positive eigenvalue (Formula = {lambda}{nu} with {lambda} > 0). Necessary and sufficient conditions on such an eigenmeasure {nu} are obtained for {varphi} to belong to two important spaces of functions, W(X, T) and Bow (X, T). For example, {varphi} isin Bow(X, T) if and only if {nu} is a measure with a certain approximate product structure. This is used to apply results of Bradley to show that the natural extension of the unique equilibrium state µ{varphi} of {varphi} isin Bow(X, T) has the weak Bernoulli property and hence is measure-theoretically isomorphic to a Bernoulli shift. It is also shown that the unique equilibrium state of a two-sided Bowen function has the weak Bernoulli property. The characterizations mentioned above are used in the case of g-measures to obtain results on the ‘reverse’ of a g-measure

A natural space of functions for the Ruelle operator theorem

We study a new space, $R(X)$, of real-valued continuous functions on the space $X$ of sequences of zeros and ones. We show exactly when the Ruelle operator theorem holds for such functions. Any $g$-function in $R(X)$ has a unique $g$-measure and powers of the corresponding transfer operator converge. We also show Bow$(X,T)\neq W(X,T)$ and relate this to the existence of bounded measurable coboundaries, which are not continuous coboundaries, for the shift on the space of bi-sequences of zeros and ones

Entropy increase in switching systems

The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switched dynamics, as quantified by the topological entropy, coincide. In this paper we extend the previous framework to pullback attractors with nontrivial components sets in order to gain further insights in that relation. This calls, in particular, for distinguishing two distinct contributions to the complexity of the switched dynamics. One proceeds from trajectory segments connecting different component sets of the attractor; the other contribution proceeds from trajectory segments within the component sets. We call them “macroscopic” and “microscopic” complexity, respectively, because only the first one can be measured by our analytical tools. As a result of this picture, we obtain sufficient conditions for a switching system to be more complex than its unswitched subsystems, i.e., a complexity analogue of Parrondo’s paradox

Impact of solvent on state-to-state population transport in multistate systems using coherences

Understanding the pathways taken by a quantum particle during a transport process is an enormous challenge. There are broadly two different aspects of the problem that affect the route taken. First is obviously the couplings between the various sites, which translates into the intrinsic "strength" of a state-to-state channel. Apart from the inter-state couplings, the solvents affecting the energies of the state, and their relative coupling strengths and time-scales form the second factor. This impact of dissipative media is significantly more difficult to analyze. Building on recently derived relations between coherences and population derivatives, we present an analysis of the transport that allows us to account for both the effects in a rigorous manner. We demonstrate the richness hidden behind the transport even for a relatively simple system, a 4-site coarse-grained model of the Fenna-Matthews-Olson complex. The effect of the local dissipative media is highly non-trivial. We show that while the impact on the total site population may be small, there are dramatic changes to the pathway taken by the transport process. The ability to untangle the dynamics at a greater granularity opens up possibilities in terms of design of novel systems with an eye towards quantum control.Comment: 8 pages, 7 figures, supplementary information file provide

Networks alliances as strategy: A case study of an SME in an emerging economy

This study adopts a qualitative approach to examine key factors to build successful network alliances in emerging economies. A market leader firm in the retail optical industry in China was used in this study. Data from interviews was collected from senior management of the firm, suppliers and customers in relation to effective strategies and factors for successful network alliances. The result in this study showed that relationship management and knowledge sharing management had the highest impact on effective network alliances. That is, trust, relationship and knowledge sharing play a dominant role

The Potential for Xanthine Oxidase Inhibition in the Prevention and Treatment of Cardiovascular and Cerebrovascular Disease

There is a now a wealth of epidemiological, animal, and clinical data to suggest the benefits of uric acid reduction and hxanthine oxidase inhibition in prevention of vascular disease. This review discusses the available epidemiological, preclinical, and clinical data and considers arguments for and against a role for serum uric acid in common cardiovascular disorders. It concludes that large scale trials with clinical endpoints are justified to address this important question and to define whether use of drugs such as allopurinol should be a routine part of preventative strategies

Components of the ubiquitin-proteasome pathway compete for surfaces on Rad23 family proteins

Background: The delivery of ubiquitinated proteins to the proteasome for degradation is a key step in the regulation of the ubiquitin-proteasome pathway, yet the mechanisms underlying this step are not understood in detail. The Rad23 family of proteins is known to bind ubiquitinated proteins through its two ubiquitin-associated (UBA) domains, and may participate in the delivery of ubiquitinated proteins to the proteasome through docking via the Rad23 ubiquitin-like (UBL) domain. Results: In this study, we investigate how the interaction between the UBL and UBA domains may modulate ubiquitin recognition and the delivery of ubiquitinated proteins to the proteasome by autoinhibition. We have explored a competitive binding model using specific mutations in the UBL domain. Disrupting the intramolecular UBL-UBA domain interactions in HHR23A indeed potentiates ubiquitin-binding. Additionally, the analogous surface on the Rad23 UBL domain overlaps with that required for interaction with both proteasomes and the ubiquitin ligase Ufd2. We have found that mutation of residues on this surface affects the ability of Rad23 to deliver ubiquitinated proteins to the proteasome. Conclusions: We conclude that the competition of ubiquitin-proteasome pathway components for surfaces on Rad23 is important for the role of the Rad23 family proteins in proteasomal targeting