Euclidean TSP with few inner points in linear space

Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$ is significantly smaller than $n$, i.e., when there are just few inner points, works in $O(k^{11\sqrt{k}} k^{1.5} n^{3})$ time [Knauer and Spillner, WG 2006], but also requires space of order $k^{c\sqrt{k}}n^{2}$. The best linear space algorithm takes $O(k! k n)$ time [Deineko, Hoffmann, Okamoto, Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space $O(nk^2+k^{O(\sqrt{k})})$ time algorithm. The new insight is extending the known divide-and-conquer method based on planar separators with a matching-based argument to shrink the instance in every recursive call. This argument also shows that the problem admits a quadratic bikernel.Comment: under submissio

Is meaning fraught with ought?

According to Normativism, what an expression means has immediate implications for how a subject should or may (not) employ that expression. Many view this thesis as imposing substantive constraints upon theories of linguistic meaning. In this paper, I shall not consider that view; instead, I shall address the prior issue of whether or not one should accept Normativism. Against certain recent prominent lines of attack common to a number of different anti-Normativist discussions, I shall defend both the Normativist thesis and an attempt to appeal to a certain platitude in its support

Approximating Tverberg Points in Linear Time for Any Fixed Dimension

Let P be a d-dimensional n-point set. A Tverberg-partition of P is a partition of P into r sets P_1, ..., P_r such that the convex hulls conv(P_1), ..., conv(P_r) have non-empty intersection. A point in the intersection of the conv(P_i)'s is called a Tverberg point of depth r for P. A classic result by Tverberg implies that there always exists a Tverberg partition of size n/(d+1), but it is not known how to find such a partition in polynomial time. Therefore, approximate solutions are of interest. We describe a deterministic algorithm that finds a Tverberg partition of size n/4(d+1)^3 in time d^{O(log d)} n. This means that for every fixed dimension we can compute an approximate Tverberg point (and hence also an approximate centerpoint) in linear time. Our algorithm is obtained by combining a novel lifting approach with a recent result by Miller and Sheehy (2010).Comment: 14 pages, 2 figures. A preliminary version appeared in SoCG 2012. This version removes an incorrect example at the end of Section 3.

The colonization history of British water vole (Arvicola amphibius (Linnaeus, 1758)): origins and development of the Celtic fringe.

The terminal Pleistocene and Early Holocene, a period from 15 000 to 18 000 Before Present (BP), was critical in establishing the current Holarctic fauna, with temperate-climate species largely replacing cold-adapted ones at mid-latitudes. However, the timing and nature of this process remain unclear for many taxa, a point that impacts on current and future management strategies. Here, we use an ancient DNA dataset to test more directly postglacial histories of the water vole (Arvicola amphibius, formerly A terrestris), a species that is both a conservation priority and a pest in different parts of its range. We specifically examine colonization of Britain, where a complex genetic structure can be observed today. Although we focus on population history at the limits of the species' range, the inclusion of additional European samples allows insights into European postglacial colonization events and provides a molecular perspective on water vole taxonomy

Clinical assessment of hand oedema: A systematic review

Introduction: Assessment of oedema after trauma or surgery is important to determine whether treatment is effective and to detect change over time. Volumetry is referred to as the ‘gold standard’ method of measuring volume. However, this has practical limitations and other methods are available. The aim of this systematic review was to evaluate the psychometric properties of alternative methods used to assess hand oedema. Methods: A search of electronic bibliographic databases was undertaken for any studies published in English reporting the psychometric evaluation of a method for measuring hand oedema, in an adult population with hand swelling from surgery, trauma or stroke. The Consensus‐based Standards for the Selection of health Measurement Instruments (COSMIN) checklist was used to evaluate the methodological quality. Results: Six studies met the inclusion criteria. Three methods were identified assessing hand oedema: perometry, visual inspection and the figure-of-eight tape measure, all were compared to volumetry. Four different psychometric properties were assessed. Studies scored fair or poor on COSMIN criteria. There is low-quality evidence supporting the use of the figure-of-eight tape measure to assess hand volume. The perometer systematically overestimated volume and visual estimation had poor sensitivity and specificity. Discussion: The figure-of-eight tape measure is the best alternative to volumetry for hand oedema. Benefits include reduced cost and time while having comparable reliability to the ‘gold standard’. Further research is needed to compare methods in patients with greater variability of conditions and with isolated digit oedema. Visual estimation of hand oedema is not recommended

Chemo-enzymatic saccharification strategy of microalgae chlorella sorokiniana

Biofuel production using microalgae attracted much attention because it can be cultured using CO2 and sunlight. With high carbohydrate content, microalgae have the potential to be used as a fermentation feedstock for bioethanol production. In present work, chemo-enzymatic saccharification of Chlorella sorokiniana microalgae were investigated. Chemical hydrolysis of the biomass followed by enzymatic hydrolysis and was also evaluated the effect of combining the two enzymes and the sequential addition. The effect of α-amylase concentrations was analyzed in ranged between 50 and 8000 U/g of biomass and for amyloglucosidase between 90 and 600 U/g of biomass. The higher concentrations showed the highest conversion of reducing sugars. The α-amylase concentration 8000 U/g of biomass presented a conversion of 43.06 ± 2.92% (w/w), while amyloglucosidase with 600 U/g of biomass obtained 76.57 ± 6.42% (w/w). The combination of two enzymes simultaneously was more efficient than the sequential addition for low enzyme concentrations (α-amylase 50 U/g and amyloglucosidase 90 U/g) with a total reducing sugar of 22.78 ± 3.06 and 16.92 ± 2.06% (w/w), respectively. On the other hand, using the higher enzymes concentrations, no difference was observed between the two addition strategies, 58.9 ± 3.55 and 57.05 ± 2.33% (w/w) for the sequential and simultaneous, respectively. Both strategies didn’t present advantage, since the amyloglucosidase enzyme alone produced slightly higher results. Even thought, the obtained results showed successfully performed saccharification of microalgal biomass and clearly point to microalgae use for saccharification and subsequent bioethanol production.Part of this work has been supported by European governments (INTERREG VA-POCTEP- 2014-2020; 0055_ALGARED_PLUS_5_E) and the Portuguese Science Foundation (FCT) through the grant UID/MAR/00350/2013 to the CIMA of the University of Algarve.info:eu-repo/semantics/publishedVersio

Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

Vitamin D status in chronic fatigue syndrome/myalgic encephalomyelitis: a cohort study from the North-West of England

Objective Severe vitamin D deficiency is a recognised cause of skeletal muscle fatigue and myopathy. The aim of this study was to examine whether chronic fatigue syndrome/myalgic encephalomyelitis (CFS/ME) is associated with altered circulating vitamin D metabolites. Design Cohort study. Setting UK university hospital, recruiting from April 2014 to April 2015. Participants Ninety-two patients with CFS/ME and 94 age-matched healthy controls (HCs). Main outcome measures The presence of a significant association between CFS/ME, fatigue and vitamin D measures. Results No evidence of a deficiency in serum total 25(OH) vitamin D (25(OH)D2 and 25(OH)D3 metabolites) was evident in individuals with CFS/ME. Liquid chromatography tandem mass spectrometry (LC–MS/MS) analysis revealed that total 25(OH)D was significantly higher (p=0.001) in serum of patients with CFS/ME compared with HCs (60.2 and 47.3 nmol/L, respectively). Analysis of food/ supplement diaries with WinDiets revealed that the higher total 25(OH) vitamin D concentrations observed in the CFS/ ME group were associated with increased vitamin D intake through use of supplements compared with the control group. Analysis of Chalder Fatigue Questionnaire data revealed no association between perceived fatigue and vitamin D levels. Conclusions Low serum concentrations of total 25(OH) D do not appear to b

First-order flows and stabilisation equations for non-BPS extremal black holes

We derive a generalised form of flow equations for extremal static and rotating non-BPS black holes in four-dimensional ungauged N = 2 supergravity coupled to vector multiplets. For particular charge vectors, we give stabilisation equations for the scalars, analogous to the BPS case, describing full known solutions. Based on this, we propose a generic ansatz for the stabilisation equations, which surprisingly includes ratios of harmonic functions.Comment: 27 pages; v2: presentation improved and references added as in the published versio

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ~6 x 10^{-9} Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.Comment: 165 pages, 40 figures, 16 tables; accepted for publication in Living Reviews in Relativit