Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

Incidence and Characteristics of Total Stroke in the United States

BACKGROUND AND PURPOSE: Stroke, increasingly referred to as a "brain attack", is one of the leading causes of death and the leading cause of adult disability in the United States. It has recently been estimated that there were three quarters of a million strokes in the United States in 1995. The aim of this study was to replicate the 1995 estimate and examine if there was an increase from 1995 to 1996 by using a large administrative claims database representative of all 1996 US inpatient discharges. METHODS: We used the Nationwide Inpatient Sample of the Healthcare Cost and Utilization Project, release 5, which contains ≈ 20 percent of all 1996 US inpatient discharges. We identified stroke patients by using the International Classification of Diseases, 9th Revision, Clinical Modification (ICD-9-CM) codes from 430 to 438, and we compared the 1996 database with that of 1995. RESULTS: There were 712,000 occurrences of stroke with hospitalization (95% CI 688,000 to 737,000) and an estimated 71,000 occurrences of stroke without hospitalization. This totaled 783,000 occurrences of stroke in 1996, compared to 750,000 in 1995. The overall rate for occurrence of total stroke (first-ever and recurrent) was 269 per 100,000 population (age- and sex-adjusted to 1996 US population). CONCLUSIONS: We estimate that there were 783,000 first-ever or recurrent strokes in the United States during 1996, compared to the figure of 750,000 in 1995. This study replicates and confirms the previous annual estimates of approximately three quarters of a million total strokes. This slight increase is likely due to the aging of the population and the population gain in the US from 1995 to 1996

Towards quantifying uncertainty in predictions of Amazon 'dieback'.

This is the final version of the article. It first appeared from The Royal Society via http://dx.doi.org/10.1098/rstb.2007.0028Simulations with the Hadley Centre general circulation model (HadCM3), including carbon cycle model and forced by a 'business-as-usual' emissions scenario, predict a rapid loss of Amazonian rainforest from the middle of this century onwards. The robustness of this projection to both uncertainty in physical climate drivers and the formulation of the land surface scheme is investigated. We analyse how the modelled vegetation cover in Amazonia responds to (i) uncertainty in the parameters specified in the atmosphere component of HadCM3 and their associated influence on predicted surface climate. We then enhance the land surface description and (ii) implement a multilayer canopy light interception model and compare with the simple 'big-leaf' approach used in the original simulations. Finally, (iii) we investigate the effect of changing the method of simulating vegetation dynamics from an area-based model (TRIFFID) to a more complex size- and age-structured approximation of an individual-based model (ecosystem demography). We find that the loss of Amazonian rainforest is robust across the climate uncertainty explored by perturbed physics simulations covering a wide range of global climate sensitivity. The introduction of the refined light interception model leads to an increase in simulated gross plant carbon uptake for the present day, but, with altered respiration, the net effect is a decrease in net primary productivity. However, this does not significantly affect the carbon loss from vegetation and soil as a consequence of future simulated depletion in soil moisture; the Amazon forest is still lost. The introduction of the more sophisticated dynamic vegetation model reduces but does not halt the rate of forest dieback. The potential for human-induced climate change to trigger the loss of Amazon rainforest appears robust within the context of the uncertainties explored in this paper. Some further uncertainties should be explored, particularly with respect to the representation of rooting depth

Minimization of free radical damage by metal catalysis of multivitamin/multimineral supplements

Multivitamin/multimineral complexes are the most common dietary supplements. Unlike minerals in foods that are incorporated in bioorganic structures, minerals in dietary supplements are typically in an inorganic form. These minerals can catalyze the generation of free radicals, thereby oxidizing antioxidants during digestion. Here we examine the ability of a matrix consisting of an amino acid and non-digestible oligosaccharide (AAOS) to blunt metal-catalyzed oxidations. Monitoring of ascorbate radical generated by copper shows that ascorbate is oxidized more slowly with the AAOS matrix than with copper sulfate. Measurement of the rate of oxidation of ascorbic acid and Trolox® by catalytic metals confirmed the ability of AAOS to slow these oxidations. Similar results were observed with iron-catalyzed formation of hydroxyl radicals. When compared to traditional forms of minerals used in supplements, we conclude that the oxidative loss of antioxidants in solution at physiological pH is much slower when AAOS is present

Multidimensional treatment foster care for preschoolers: early findings of an implementation in the Netherlands

Multidimensional Treatment Foster Care (MTFC) has been shown to be an evidence based alternative to residential rearing and an effective method to improve behavior and attachment of preschool foster children in the US. This preliminary study investigated an application of MTFC for preschoolers (MTFC-P) in the Netherlands focusing on behavioral outcomes in course of the intervention. To examine the following hypothesis: “the time in the MTFC-P intervention predicts a decline in problem behavior, as this is the desired outcome for children assigned to MTFC-P”, we assessed the daily occurrence of 38 problem behaviors via telephone interviews. Repeated measures revealed significant reduced problem behavior in course of the program. MTFC-P promises to be a treatment model suitable for high-risk foster children, that is transferable across centres and countries

Breaking the superfluid speed limit in a fermionic condensate

Coherent condensates appear as emergent phenomena in many systems. They share the characteristic feature of an energy gap separating the lowest excitations from the condensate ground state. This implies that a scattering object, moving through the system with high enough velocity for the excitation spectrum in the scatterer frame to become gapless, can create excitations at no energy cost, initiating the breakdown of the condensate—the well-known Landau velocity. Whereas, for the neutral fermionic superfluid 3He-B in the T = 0 limit, flow around an oscillating body displays a very clear critical velocity for the onset of dissipation, here we show that for uniform linear motion there is no discontinuity whatsoever in the dissipation as the Landau critical velocity is passed and exceeded. Given the importance of the Landau velocity for our understanding of superfluidity, this result is unexpected, with implications for dissipative effects of moving objects in all coherent condensate systems

The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches

We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branch's individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.Comment: 22 pages, 15 figure

Assessment of low-dose cisplatin as a model of nausea and emesis in beagle dogs, potential for repeated administration

Cisplatin is a highly emetogenic cancer chemotherapy agent, which is often used to induce nausea and emesis in animal models. The cytotoxic properties of cisplatin also cause adverse events that negatively impact on animal welfare preventing repeated administration of cisplatin. In this study, we assessed whether a low (subclinical) dose of cisplatin could be utilized as a model of nausea and emesis in the dog while decreasing the severity of adverse events to allow repeated administration. The emetic, nausea-like behavior and potential biomarker response to both the clinical dose (70 mg/m2) and low dose (15 mg/m2) of cisplatin was assessed. Plasma creatinine concentrations and granulocyte counts were used to assess adverse effects on the kidneys and bone marrow, respectively. Nausea-like behavior and emesis was induced by both doses of cisplatin, but the latency to onset was greater in the low-dose group. No significant change in plasma creatinine was detected for either dose groups. Granulocytes were significantly reduced compared with baseline (P = 0.000) following the clinical, but not the low-dose cisplatin group. Tolerability of repeated administration was assessed with 4 administrations of an 18 mg/m2 dose cisplatin. Plasma creatinine did not change significantly. Cumulative effects on the granulocytes occurred, they were significantly decreased (P = 0.03) from baseline at 3 weeks following cisplatin for the 4th administration only. Our results suggest that subclinical doses (15 and 18 mg/m2) of cisplatin induce nausea-like behavior and emesis but have reduced adverse effects compared with the clinical dose allowing for repeated administration in crossover studies