Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $N$ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running top to bottom in figures, to appear in J. Math. Phy

Reversible skew laurent polynomial rings and deformations of poisson automorphisms

A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1). We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field F. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in F-3 and the ring of invariants S-theta of the reversing automorphism is a deformation of B and is a factor of a deformation of F[x(1), x(2), x(3)] for a Poisson bracket determined by the appropriate surface

Calculations of Neutron Reflectivity in the eV Energy Range from Mirrors made of Heavy Nuclei with Neutron-Nucleus Resonances

We evaluate the reflectivity of neutron mirrors composed of certain heavy nuclei which possess strong neutron-nucleus resonances in the eV energy range. We show that the reflectivity of such a mirror for some nuclei can in principle be high enough near energies corresponding to compound neutron-nucleus resonances to be of interest for certain scientific applications in non-destructive evaluation of subsurface material composition and in the theory of neutron optics beyond the kinematic limit.Comment: 18 pages, 5 figures, 1 tabl

Cryptographic requirements for chaotic secure communications

In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.Comment: 13 pages, 3 figure

A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schroedinger systems

An explanation is given for previous numerical results which suggest a certain bifurcation of `vector solitons' from scalar (single-component) solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation in question is nonlocal in the sense that the vector soliton does not have a small-amplitude component, but instead approaches a solitary wave of one component with two infinitely far-separated waves in the other component. Yet, it is argued that this highly nonlocal event can be predicted from a purely local analysis of the central solitary wave alone. Specifically the linearisation around the central wave should contain asymptotics which grow at precisely the speed of the other-component solitary waves on the two wings. This approximate argument is supported by both a detailed analysis based on matched asymptotic expansions, and numerical experiments on two example systems. The first is the usual coupled NLS system involving an arbitrary ratio between the self-phase and cross-phase modulation terms, and the second is a coupled NLS system with saturable nonlinearity that has recently been demonstrated to support stable multi-peaked solitary waves. The asymptotic analysis further reveals that when the curves which define the proposed criterion for scalar nonlocal bifurcations intersect with boundaries of certain local bifurcations, the nonlocal bifurcation could turn from scalar to non-scalar at the intersection. This phenomenon is observed in the first example. Lastly, we have also selectively tested the linear stability of several solitary waves just born out of scalar nonlocal bifurcations. We found that they are linearly unstable. However, they can lead to stable solitary waves through parameter continuation.Comment: To appear in Nonlinearit

Increased expression of a microRNA correlates with anthelmintic resistance in parasitic nematodes

Resistance to anthelmintic drugs is a major problem in the global fight against parasitic nematodes infecting humans and animals. While previous studies have identified mutations in drug target genes in resistant parasites, changes in the expression levels of both targets and transporters have also been reported. The mechanisms underlying these changes in gene expression are unresolved. Here, we take a novel approach to this problem by investigating the role of small regulatory RNAs in drug resistant strains of the important parasite Haemonchus contortus. microRNAs (miRNAs) are small (22 nt) non-coding RNAs that regulate gene expression by binding predominantly to the 3′ UTR of mRNAs. Changes in miRNA expression have been implicated in drug resistance in a variety of tumor cells. In this study, we focused on two geographically distinct ivermectin resistant strains of H. contortus and two lines generated by multiple rounds of backcrossing between susceptible and resistant parents, with ivermectin selection. All four resistant strains showed significantly increased expression of a single miRNA, hco-miR-9551, compared to the susceptible strain. This same miRNA is also upregulated in a multi-drug-resistant strain of the related nematode Teladorsagia circumcincta. hco-miR-9551 is enriched in female worms, is likely to be located on the X chromosome and is restricted to clade V parasitic nematodes. Genes containing predicted binding sites for hco-miR-9551 were identified computationally and refined based on differential expression in a transcriptomic dataset prepared from the same drug resistant and susceptible strains. This analysis identified three putative target mRNAs, one of which, a CHAC domain containing protein, is located in a region of the H. contortus genome introgressed from the resistant parent. hco-miR-9551 was shown to interact with the 3′ UTR of this gene by dual luciferase assay. This study is the first to suggest a role for miRNAs and the genes they regulate in drug resistant parasitic nematodes. miR-9551 also has potential as a biomarker of resistance in different nematode species

UK commercial real estate valuation practice: does it now build in sustainability considerations?

Purpose This paper investigates the extent to which commercial property valuers in the UK refer to Royal Institution of Chartered Surveyors (RICS) professional standards and guidance on the inclusion of sustainability in valuation reports. Data collection, analysis and reporting related to sustainability attributes is examined, as well as the perceived importance of these attributes to clients and any value impacts that are associated with them. Design/methodology/approach An online survey of UK commercial property valuers was conducted from July to September 2019. The survey included both structured and open-ended questions. Findings Reference to RICS standards and guidance on sustainability has improved since earlier research. However, progress on data collection is still limited. At the time of the survey, UK valuers indicated that sustainability attributes were of more importance to owner-occupiers than investors and lenders. UK valuers also indicated that, out of a range of sustainability attributes, only certification was influencing market value (MV) and investment value (IV) to any great extent. Research limitations/implications The online survey had 53 responses and this limited the ability to draw definitive conclusions. Hence, whilst the results may be indicative of the perceptions of some valuers of the significance of sustainability-related matters in the UK, the sample is not large enough to be considered representative of the opinions of property valuers per se in the UK. Practical implications Explicit reflection of sustainability in market or investment values is still limited in the UK valuation practice, but there are challenges faced by valuers that need further investigation, including difficulties in pricing sustainability attributes. Originality/value This is the first empirical investigation of the perception of sustainability by valuers in the UK commercial property market since the 2012 survey reported by Michl et al. (2016)

Liquidity and the drivers of search, due diligence and transaction times for UK commercial real estate investments

Trading commercial real estate involves a process of exchange that is costly and which occurs over an extended and uncertain period of time. This has consequences for the performance and risk of real estate investments. Most research on transaction times has occurred for residential rather than commercial real estate. We study the time taken to transact commercial real estate assets in the UK using a sample of 578 transactions over the period 2004 to 2013. We measure average time to transact from a buyer and seller perspective, distinguishing the search and due diligence phases of the process, and we conduct econometric analysis to explain variation in due diligence times between assets. The median time for purchase of real estate from introduction to completion was 104 days and the median time for sale from marketing to completion was 135 days. There is considerable variation around these times and results suggest that some of this variation is related to market state, type and quality of asset, and type of participants involved in the transaction. Our findings shed light on the drivers of liquidity at an individual asset level and can inform models that quantify the impact of uncertain time on market on real estate investment risk

Early Surgical Morbidity and Mortality in Adults with Congenital Heart Disease: The University of Michigan Experience

Objectives.  To review early surgical outcomes in a contemporary series of adults with congenital heart disease (CHD) undergoing cardiac operations at the University of Michigan, and to investigate possible preoperative and intraoperative risk factors for morbidity and mortality. Methods.  A retrospective medical record review was performed for all patients ≥18 years of age who underwent open heart operations by a pediatric cardiothoracic surgeon at the University of Michigan Congenital Heart Center between January 1, 1998 and December 31, 2004. Records from a cohort of pediatric patients ages 1–17 years were matched to a subset of the adult patients by surgical procedure and date of operation. Results.  In total, 243 cardiac surgical operations were performed in 234 adult patients with CHD. Overall mortality was 4.7% (11/234). The incidence of major postoperative complications was 10% (23/234) with a 19% (45/23) minor complication rate. The most common postoperative complication was atrial arrhythmias in 10.8% (25/234). The presence of preoperative lung or liver disease, prolonged cardiopulmonary bypass and aortic cross clamp times, and postoperative elevated inotropic score and serum lactates were significant predictors of mortality in adults. There was no difference between the adult and pediatric cohorts in terms of mortality and morbidity. Conclusions.  The postoperative course in adults following surgery for CHD is generally uncomplicated and early survival should be expected. Certain risk factors for increased mortality in this patient population may include preoperative presence of chronic lung or liver dysfunction, prolonged cardiopulmonary bypass and aortic cross-clamp times, and postoperative elevated inotropic score and serum lactate levels.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75596/1/j.1747-0803.2008.00170.x.pd