The Rigidity Conjecture

A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps with a break point. More recent developments show that under similar topological conditions, rigidity does not hold for slightly more general systems. In this paper we state a conjecture which describes how topological classes are organized into rigidity classes.Comment: 6 page

Towards a positive welfare protocol for cattle: A critical review of indicators and suggestion of how we might proceed

Current animal welfare protocols focus on demonstrating the absence (or at least low levels) of indicators of poor welfare, potentially creating a mismatch between what is expected by society (an assurance of good animal welfare) and what is actually being delivered (an assurance of the absence of welfare problems). This paper explores how far we have come, and what work still needs to be done, if we are to develop a protocol for use on commercial dairy farms where the aim is to demonstrate the presence of positive welfare. Following conceptual considerations around a perceived “ideal” protocol, we propose that a future protocol should be constructed (i) of animal-based measures, (ii) of indicators of affective state, and (iii) be structured according to indicators of short-term emotion, medium-term moods and long-term cumulative assessment of negative and positive experiences of an animal's life until now (in contrast to the current focus on indicators that represent different domains/criteria of welfare). These three conditions imposed the overall structure within which we selected our indicators. The paper includes a critical review of the literature on potential indicators of positive affective states in cattle. Based on evidence about the validity and reliability of the different indicators, we select ear position, play, allogrooming, brush use and QBA as candidate indicators that we suggest could form a prototype positive welfare protocol. We emphasise that this prototype protocol has not been tested in practice and so it is perhaps not the protocol itself that is the main outcome of this paper, but the process of trying to develop it. In a final section of this paper, we reflect on some of the lessons learnt from this exercise and speculate on future perspectives. For example, while we consider we have moved towards a prototype positive welfare protocol for short-term affective states, future research energy should be directed towards valid indicators for the medium and long-term

A renormalization fixed point for Lorenz maps

A Lorenz map is a Poincar\'e map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a hyperbolic fixed point. The proof is computer assisted and we include a detailed exposition on how to make rigorous estimates using a computer as well as the implementation of the estimates.Comment: 29 pages, 2 figure

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated unstable manifold. An unstable manifold defines a family of Lorenz maps and we prove that each infinitely renormalizable combinatorial type (satisfying the above conditions) has a unique representative within such a family. We also prove that each infinitely renormalizable map has no wandering intervals and that the closure of the forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure

Eolian dust input to the Subarctic North Pacific

Eolian dust is a significant source of iron and other nutrients that are essential for the health of marine ecosystems and potentially a controlling factor of the high nutrient-low chlorophyll status of the Subarctic North Pacific. We map the spatial distribution of dust input using three different geochemical tracers of eolian dust, 4He, 232Th and rare earth elements, in combination with grain size distribution data, from a set of core-top sediments covering the entire Subarctic North Pacific. Using the suite of geochemical proxies to fingerprint different lithogenic components, we deconvolve eolian dust input from other lithogenic inputs such as volcanic ash, ice-rafted debris, riverine and hemipelagic input. While the open ocean sites far away from the volcanic arcs are dominantly composed of pure eolian dust, lithogenic components other than eolian dust play a more crucial role along the arcs. In sites dominated by dust, eolian dust input appears to be characterized by a nearly uniform grain size mode at ∼4 μm. Applying the 230Th-normalization technique, our proxies yield a consistent pattern of uniform dust fluxes of 1–2 g/m2/yr across the Subarctic North Pacific. Elevated eolian dust fluxes of 2–4 g/m2/yr characterize the westernmost region off Japan and the southern Kurile Islands south of 45° N and west of 165° E along the main pathway of the westerly winds. The core-top based dust flux reconstruction is consistent with recent estimates based on dissolved thorium isotope concentrations in seawater from the Subarctic North Pacific. The dust flux pattern compares well with state-of-the-art dust model predictions in the western and central Subarctic North Pacific, but we find that dust fluxes are higher than modeled fluxes by 0.5–1 g/m2/yr in the northwest, northeast and eastern Subarctic North Pacific. Our results provide an important benchmark for biogeochemical models and a robust approach for downcore studies testing dust-induced iron fertilization of past changes in biological productivity in the Subarctic North Pacific

Oral Microbiota and Risk for Esophageal Squamous Cell Carcinoma in a High-Risk Area of China.

Poor oral health has been linked with an increased risk of esophageal squamous cell carcinoma (ESCC). We investigated whether alteration of oral microbiota is associated with ESCC risk. Fasting saliva samples were collected from 87 incident and histopathologicallly diagnosed ESCC cases, 63 subjects with dysplasia and 85 healthy controls. All subjects were also interviewed with a questionnaire. V3-V4 region of 16S rRNA was amplified and sequenced by 454-pyrosequencing platform. Carriage of each genus was compared by means of multivariate-adjusted odds ratios derived from logistic regression model. Relative abundance was compared using Metastats method. Beta diversity was estimated using Unifrac and weighted Unifrac distances. Principal coordinate analysis (PCoA) was applied to ordinate dissimilarity matrices. Multinomial logistic regression was used to compare the coordinates between different groups. ESCC subjects had an overall decreased microbial diversity compared to control and dysplasia subjects (P<0.001). Decreased carriage of genera Lautropia, Bulleidia, Catonella, Corynebacterium, Moryella, Peptococcus and Cardiobacterium were found in ESCC subjects compared to non-ESCC subjects. Multinomial logistic regression analyses on PCoA coordinates also revealed that ESCC subjects had significantly different levels for several coordinates compared to non-ESCC subjects. In conclusion, we observed a correlation between altered salivary bacterial microbiota and ESCC risk. The results of our study on the saliva microbiome are of particular interest as it reflects the shift in microbial communities. Further studies are warranted to verify this finding, and if being verified, to explore the underlying mechanisms