Converting between quadrilateral and standard solution sets in normal surface theory

The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds up this operation by using a much smaller space (quadrilateral coordinates), at the cost of a reduced solution set that might not always be sufficient for our needs. In this paper we present algorithms for converting between solution sets in quadrilateral and standard coordinates. As a consequence we obtain a new algorithm for enumerating all standard vertex normal surfaces, yielding both the speed of quadrilateral coordinates and the wider applicability of standard coordinates. Experimentation with the software package Regina shows this new algorithm to be extremely fast in practice, improving speed for large cases by factors from thousands up to millions.Comment: 55 pages, 10 figures; v2: minor fixes only, plus a reformat for the journal styl

Linear LL-positive sets and their polar subspaces

In this paper, we define a Banach SNL space to be a Banach space with a certain kind of linear map from it into its dual, and we develop the theory of linear $L$-positive subsets of Banach SNL spaces with Banach SNL dual spaces. We use this theory to give simplified proofs of some recent results of Bauschke, Borwein, Wang and Yao, and also of the classical Brezis-Browder theorem.Comment: 11 pages. Notational changes since version

Necessary and sufficient condition on global optimality without convexity and second order differentiability

The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function and its bidual (the latter is known from convex analysis)

Quantum Sign Permutation Polytopes

Convex polytopes are convex hulls of point sets in the $n$-dimensional space \E^n that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in \E^n called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness

Excited States of Proton-bound DNA/RNA Base Homo-dimers: Pyrimidines

We are presenting the electronic photo fragment spectra of the protonated pyrimidine DNA bases homo-dimers. Only the thymine dimer exhibits a well structured vibrational progression, while protonated monomer shows broad vibrational bands. This shows that proton bonding can block some non radiative processes present in the monomer.Comment: We acknowledge the use of the computing facility cluster GMPCS of the LUMAT federation (FR LUMAT 2764

Action spectroscopy of the isolated red Kaede fluorescent protein chromophore

Incorporation of fluorescent proteins into biochemical systems has revolutionized the field of bioimaging. In a bottom-up approach, understanding the photophysics of fluorescent proteins requires detailed investigations of the light-absorbing chromophore, which can be achieved by studying the chromophore in isolation. This paper reports a photodissociation action spectroscopy study on the deprotonated anion of the red Kaede fluorescent protein chromophore, demonstrating that at least three isomers–assigned to deprotomers–are generated in the gas phase. Deprotomer-selected action spectra are recorded over the S1 ← S0 band using an instrument with differential mobility spectrometry coupled with photodissociation spectroscopy. The spectrum for the principal phenoxide deprotomer spans the 480–660 nm range with a maximum response at ≈610 nm. The imidazolate deprotomer has a blue-shifted action spectrum with a maximum response at ≈545 nm. The action spectra are consistent with excited state coupled-cluster calculations of excitation wavelengths for the deprotomers. A third gas-phase species with a distinct action spectrum is tentatively assigned to an imidazole tautomer of the principal phenoxide deprotomer. This study highlights the need for isomer-selective methods when studying the photophysics of biochromophores possessing several deprotonation sites

The regeneration capacity of the flatworm Macrostomum lignano—on repeated regeneration, rejuvenation, and the minimal size needed for regeneration

The lion’s share of studies on regeneration in Plathelminthes (flatworms) has been so far carried out on a derived taxon of rhabditophorans, the freshwater planarians (Tricladida), and has shown this group’s outstanding regeneration capabilities in detail. Sharing a likely totipotent stem cell system, many other flatworm taxa are capable of regeneration as well. In this paper, we present the regeneration capacity of Macrostomum lignano, a representative of the Macrostomorpha, the basal-most taxon of rhabditophoran flatworms and one of the most basal extant bilaterian protostomes. Amputated or incised transversally, obliquely, and longitudinally at various cutting levels, M. lignano is able to regenerate the anterior-most body part (the rostrum) and any part posterior of the pharynx, but cannot regenerate a head. Repeated regeneration was observed for 29 successive amputations over a period of almost 12 months. Besides adults, also first-day hatchlings and older juveniles were shown to regenerate after transversal cutting. The minimum number of cells required for regeneration in adults (with a total of 25,000 cells) is 4,000, including 160 neoblasts. In hatchlings only 1,500 cells, including 50 neoblasts, are needed for regeneration. The life span of untreated M. lignano was determined to be about 10 months

A characterization of Smyth complete quasi-metric spaces via Caristi's fixed point theorem

We obtain a quasi-metric generalization of Caristi's fixed point theorem for a kind of complete quasi-metric spaces. With the help of a suitable modification of its proof, we deduce a characterization of Smyth complete quasi-metric spaces which provides a quasi-metric generalization of the well-known characterization of metric completeness due to Kirk. Some illustrative examples are also given. As an application, we deduce a procedure which allows to easily show the existence of solution for the recurrence equation of certain algorithms.The authors are grateful to the reviewers for several suggestions which have allowed to improve the first version of the paper. This research is supported by the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.Romaguera Bonilla, S.; Tirado Peláez, P. (2015). A characterization of Smyth complete quasi-metric spaces via Caristi's fixed point theorem. Fixed Point Theory and Applications. 2015:183. https://doi.org/10.1186/s13663-015-0431-1S2015:183Cobzaş, S: Functional Analysis in Asymmetric Normed Spaces. Springer, Basel (2013)Künzi, HPA: Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology. In: Aull, CE, Lowen, R (eds.) Handbook of the History of General Topology, vol. 3, pp. 853-968. Kluwer Academic, Dordrecht (2001)Reilly, IL, Subrhamanyam, PV, Vamanamurthy, MK: Cauchy sequences in quasi-pseudo-metric spaces. Monatshefte Math. 93, 127-140 (1982)Künzi, HPA, Schellekens, MP: On the Yoneda completion of a quasi-metric spaces. Theor. Comput. Sci. 278, 159-194 (2002)Romaguera, S, Valero, O: Domain theoretic characterisations of quasi-metric completeness in terms of formal balls. Math. Struct. Comput. Sci. 20, 453-472 (2010)Künzi, HPA: Nonsymmetric topology. In: Proc. Szekszárd Conf. Bolyai Society of Math. Studies, vol. 4, pp. 303-338 (1993)García-Raffi, LM, Romaguera, S, Schellekens, MP: Applications of the complexity space to the general probabilistic divide and conquer algorithms. J. Math. Anal. Appl. 348, 346-355 (2008)Stoltenberg, RA: Some properties of quasi-uniform spaces. Proc. Lond. Math. Soc. 17, 226-240 (1967)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976)Abdeljawad, T, Karapınar, E: Quasi-cone metric spaces and generalizations of Caristi Kirk’s theorem. Fixed Point Theory Appl. 2009, Article ID 574387 (2009)Acar, O, Altun, I: Some generalizations of Caristi type fixed point theorem on partial metric spaces. Filomat 26(4), 833-837 (2012)Acar, O, Altun, I, Romaguera, S: Caristi’s type mappings on complete partial metric spaces. Fixed Point Theory 14, 3-10 (2013)Aydi, H, Karapınar, E, Kumam, P: A note on ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210’. J. Inequal. Appl. 2013, 355 (2013)Cobzaş, S: Completeness in quasi-metric spaces and Ekeland variational principle. Topol. Appl. 158, 1073-1084 (2011)Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001)Karapınar, E: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011, 4 (2011)Romaguera, S: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. 2010, Article ID 493298 (2010)Park, S: On generalizations of the Ekeland-type variational principles. Nonlinear Anal. TMA 39, 881-889 (2000)Du, W-S, Karapınar, E: A note on Caristi type cyclic maps: related results and applications. Fixed Point Theory Appl. 2013, 344 (2013)Ali-Akbari, M, Honari, B, Pourmahdian, M, Rezaii, MM: The space of formal balls and models of quasi-metric spaces. Math. Struct. Comput. Sci. 19, 337-355 (2009)Romaguera, S, Schellekens, M: Quasi-metric properties of complexity spaces. Topol. Appl. 98, 311-322 (1999)Brøndsted, A: On a lemma of Bishop and Phelps. Pac. J. Math. 55, 335-341 (1974)Brøndsted, A: Fixed points and partial order. Proc. Am. Math. Soc. 60, 365-366 (1976)Smyth, MB: Quasi-uniformities: reconciling domains with metric spaces. In: Main, M, Melton, A, Mislove, M, Schmidt, D (eds.) Mathematical Foundations of Programming Language Semantics, 3rd Workshop, Tulane, 1987. Lecture Notes in Computer Science, vol. 298, pp. 236-253. Springer, Berlin (1988)Cull, P, Flahive, M, Robson, R: Difference Equations: From Rabbits to Chaos. Springer, New York (2005)Schellekens, M: The Smyth completion: a common foundation for denotational semantics and complexity analysis. Electron. Notes Theor. Comput. Sci. 1, 535-556 (1995)García-Raffi, LM, Romaguera, S, Sánchez-Pérez, EA: Sequence spaces and asymmetric norms in the theory of computational complexity. Math. Comput. Model. 49, 1852-1868 (2009)Rodríguez-López, J, Schellekens, MP, Valero, O: An extension of the dual complexity space and an application to computer science. Topol. Appl. 156, 3052-3061 (2009)Romaguera, S, Schellekens, MP, Valero, O: The complexity space of partial functions: a connection between complexity analysis and denotational semantics. Int. J. Comput. Math. 88, 1819-1829 (2011