On Hausdorff dimension of the set of closed orbits for a cylindrical transformation

We deal with Besicovitch's problem of existence of discrete orbits for transitive cylindrical transformations $T_\varphi:(x,t)\mapsto(x+\alpha,t+\varphi(x))$ where $Tx=x+\alpha$ is an irrational rotation on the circle \T and \varphi:\T\to\R is continuous, i.e.\ we try to estimate how big can be the set D(\alpha,\varphi):=\{x\in\T:|\varphi^{(n)}(x)|\to+\infty\text{as}|n|\to+\infty\}. We show that for almost every $\alpha$ there exists $\varphi$ such that the Hausdorff dimension of $D(\alpha,\varphi)$ is at least $1/2$. We also provide a Diophantine condition on $\alpha$ that guarantees the existence of $\varphi$ such that the dimension of $D(\alpha,\varphi)$ is positive. Finally, for some multidimensional rotations $T$ on \T^d, $d\geq3$, we construct smooth $\varphi$ so that the Hausdorff dimension of $D(\alpha,\varphi)$ is positive.Comment: 32 pages, 1 figur

Artificial Neural Networks for Classification in Metabolomic Studies of Whole Cells Using 1H Nuclear Magnetic Resonance

We report the successful classification, by artificial neural networks (ANNs), of 1H NMR spectroscopic data recorded on whole-cell culture samples of four different lung carcinoma cell lines, which display different drug resistance patterns. The robustness of the approach was demonstrated by its ability to classify the cell line correctly in 100% of cases, despite the demonstrated presence of operator-induced sources of variation, and irrespective of which spectra are used for training and for validation. The study demonstrates the potential of ANN for lung carcinoma classification in realistic situations

Territorial Tactics: The Socio-spatial Significance of Private Policing Strategies in Cape Town

This paper analyses the policing strategies of private security companies operating in urban space. An existing literature has considered the variety of ways that territory becomes of fundamental importance in the work of public police forces. However, this paper examines territory in the context of private security companies. Drawing on empirical research in Cape Town, it examines how demarcated territories become key subjects in private policing. Private security companies are responsible for a relatively small section of the city, while in contrast the public police ultimately have to see city space as a whole. Hence, private policing strategy becomes one of displacement, especially of so-called undesirables yielding a patchworked public space associated with private enclaves of consumption. The conclusions signal the historical resonances and comparative implications of these political-legal-security dynamics. © 2013 Urban Studies Journal Limited

Scheme and Scale Dependence of Charm Production in Neutrino Scattering

We discuss some theoretical uncertainties in the calculation of the cross section for charm production in charged current deep inelastic neutrino scattering related to ambiguities in the treatment of terms which are singular in the limit of a vanishing charm mass. In particular we compare the so-called variable flavour scheme where these terms are absorbed in the parton distribution functions containing the charm as an active flavour, with the so-called fixed flavour scheme with no charm mass subtraction where the charm appears only in the final state of fixed-order scattering matrix elements. Using available parametrizations of parton distribution functions we find that the two schemes lead to largely differing results for separate structure functions whereas the differences cancel to a large extent in the total cross section in that kinematical region which has been measured so far.Comment: 20pages, uuencoded postscript, figures include

Heavy Quark Initiated Contributions to Deep Inelastic Structure Functions

We present O(alpha_s^1) corrections to deep inelastic scattering amplitudes on massive quarks obtained within the scheme of Aivazis, Collins, Olness and Tung (ACOT). After identifying the correct subtraction term the convergence of these contributions towards the analogous coefficient functions for massless quarks, obtained within the modified minimal subtraction scheme (MSbar), is demonstrated. Furthermore, the quantitative relevance of the contributions to neutral current (NC) and charged current (CC) structure functions is investigated for several choices of the factorization scale.Comment: 29 pages, 6 figures; uses epsfig.sty, amssymb.sty, axodraw.sty; minor changes for publication in Phys. Rev.

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie