Applications of the complexity space to the General Probabilistic Divide and Conquer Algorithms

AbstractSchellekens [M. Schellekens, The Smyth completion: A common foundation for denotational semantics and complexity analysis, in: Proc. MFPS 11, in: Electron. Notes Theor. Comput. Sci., vol. 1, 1995, pp. 535–556], and Romaguera and Schellekens [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311–322] introduced a topological foundation to obtain complexity results through the application of Semantic techniques to Divide and Conquer Algorithms. This involved the fact that the complexity (quasi-metric) space is Smyth complete and the use of a version of the Banach fixed point theorem and improver functionals. To further bridge the gap between Semantics and Complexity, we show here that these techniques of analysis, based on the theory of complexity spaces, extend to General Probabilistic Divide and Conquer schema discussed by Flajolet [P. Flajolet, Analytic analysis of algorithms, in: W. Kuich (Ed.), 19th Internat. Colloq. ICALP'92, Vienna, July 1992; Automata, Languages and Programming, in: Lecture Notes in Comput. Sci., vol. 623, 1992, pp. 186–210]. In particular, we obtain a general method which is useful to show that for several recurrence equations based on the recursive structure of General Probabilistic Divide and Conquer Algorithms, the associated functionals have a unique fixed point which is the solution for the corresponding recurrence equation

Duality and quasi-normability for complexity spaces

[EN] The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,) ω. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provides a suitable setting to carry out an analysis of the dual complexity space. We show that if (E,) is a biBanach space (i.e., a quasi-normed space whose induced quasi-metric is bicomplete), then the function space (B*E, B* ) is biBanach, where B*E = {f : E Σ∞n=0 2-n( V ) } and B* = Σ∞n=0 2-n We deduce that the dual complexity space admits a structure of quasinormed semlinear space such that the induced quasi-metric space is order-convex, upper weightable and Smyth complete, not only in the case that this dual is a subspace of [0,)ω but also in the general case that it is a subspace of Fω where F is any biBanach normweightable space. We also prove that for a large class of dual complexity (sub)spaces, lower boundedness implies total boundedness. Finally, we investigate completeness of the quasi-metric of uniform convergence and of the Hausdorff quasi-pseudo-metric for the dual complexity space, in the context of function spaces and hyperspaces, respectively.The first-listed author ackowledges the support of the Spanish Ministry of Science and Technology, grant BFM2000-1111Romaguera, S.; Schellekens, M. (2002). Duality and quasi-normability for complexity spaces. Applied General Topology. 3(1):91-112. https://doi.org/10.4995/agt.2002.2116SWORD911123

Локальные элиминационные алгоритмы обработки запросов в базах данных

Рассмотрено использование локальных элиминационных алгоритмов (ЛЭА) для обработки запросов в реляционных базах данных. Обсуждаются особенности реализации локального алгоритма, использующего лишь прямую часть.Розглянуто використання локальних елімінаційних алгоритмів (ЛЕА) для обробки запитів в реляційних базах даних. Обговорюються особливості реалізації локального алгоритму, що використовує лише пряму частину.The applying local elimination algorithms (LEA) for processing queries in relational databases is considered. The special features of realization of local algorithm using only a forward part are discussed

High-pressure CO electroreduction at silver produces ethanol and propanol

Reducing CO2 to long-chain carbon products is attractive considering such products are typically more valuable than shorter ones. However, the best electrocatalyst for making such products from CO2, copper, lacks selectivity. By studying alternate C2+ producing catalysts we can increase our mechanistic understanding, which is beneficial for improving catalyst performance. Therefore, we investigate CO reduction on silver, as density functional theory (DFT) results predict it to be good at forming ethanol. To address the current disagreement between DFT and experimental results (ethanol vs. no ethanol), we investigated CO reduction at higher surface coverage (by increasing pressure) to ascertain if desorption effects can explain the discrepancy. In terms of product trends, our results agree with the DFT-proposed acetaldehyde-like intermediate, yielding ethanol and propanol as C2+ products-making the CO2 electrochemistry of silver very similar to that of copper at sufficiently high coverage.Catalysis and Surface Chemistr

Complexity spaces as quantitative domains of computation

We study domain theoretic properties of complexity spaces. Although the so-called complexity space is not a domain for the usual pointwise order, we show that, however, each pointed complexity space is an ¿-continuous domain for which the complexity quasi-metric induces the Scott topology, and the supremum metric induces the Lawson topology. Hence, each pointed complexity space is both a quantifiable domain in the sense of M. Schellekens and a quantitative domain in the sense of P. Waszkiewicz, via the partial metric induced by the complexity quasi-metric. © 2011 Elsevier B.V.Romaguera Bonilla, S.; Schellekens, M.; Valero Sierra, O. (2011). Complexity spaces as quantitative domains of computation. Topology and its Applications. 158:853-860. doi:10.1016/j.topol.2011.01.005S85386015

Fixed point results for generalized cyclic contraction mappings in partial metric spaces

Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. P˘acurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic φ-contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak φ- contraction mappings and studied well-posedness problem for such mappings. On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.S. Romaguera acknowledges the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Abbas, M.; Nazir, T.; Romaguera Bonilla, S. (2012). Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 106(2):287-297. https://doi.org/10.1007/s13398-011-0051-5S2872971062Abdeljawad T., Karapinar E., Tas K.: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24(11), 1894–1899 (2011). doi: 10.1016/j.aml.2011.5.014Altun, I., Erduran A.: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. article ID 508730 (2011). doi: 10.1155/2011/508730Altun I., Sadarangani K.: Corrigendum to “Generalized contractions on partial metric spaces” [Topology Appl. 157 (2010), 2778–2785]. Topol. Appl. 158, 1738–1740 (2011)Altun I., Simsek H.: Some fixed point theorems on dualistic partial metric spaces. J. Adv. Math. Stud. 1, 1–8 (2008)Altun I., Sola F., Simsek H.: Generalized contractions on partial metric spaces. Topol. Appl. 157, 2778–2785 (2010)Aydi, H.: Some fixed point results in ordered partial metric spaces. arxiv:1103.3680v1 [math.GN](2011)Boyd D.W., Wong J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)Bukatin M., Kopperman R., Matthews S., Pajoohesh H.: Partial metric spaces. Am. Math. Monthly 116, 708–718 (2009)Bukatin M.A., Shorina S.Yu. et al.: Partial metrics and co-continuous valuations. In: Nivat, M. (eds) Foundations of software science and computation structure Lecture notes in computer science vol 1378., pp. 125–139. Springer, Berlin (1998)Derafshpour M., Rezapour S., Shahzad N.: On the existence of best proximity points of cyclic contractions. Adv. Dyn. Syst. Appl. 6, 33–40 (2011)Heckmann R.: Approximation of metric spaces by partial metric spaces. Appl. Cat. Struct. 7, 71–83 (1999)Karapinar E.: Fixed point theory for cyclic weak $${\phi}$$ -contraction. App. Math. Lett. 24, 822–825 (2011)Karapinar, E.: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011,4 (2011). doi: 10.1186/1687-1812-2011-4Karapinar E.: Weak $${\varphi}$$ -contraction on partial metric spaces and existence of fixed points in partially ordered sets. Math. Aeterna. 1(4), 237–244 (2011)Karapinar E., Erhan I.M.: Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24, 1894–1899 (2011)Karpagam S., Agrawal S.: Best proximity point theorems for cyclic orbital Meir–Keeler contraction maps. Nonlinear Anal. 74, 1040–1046 (2011)Kirk W.A., Srinavasan P.S., Veeramani P.: Fixed points for mapping satisfying cylical contractive conditions. Fixed Point Theory. 4, 79–89 (2003)Kosuru, G.S.R., Veeramani, P.: Cyclic contractions and best proximity pair theorems). arXiv:1012.1434v2 [math.FA] 29 May (2011)Matthews S.G.: Partial metric topology. in: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 728, 183–197 (1994)Neammanee K., Kaewkhao A.: Fixed points and best proximity points for multi-valued mapping satisfying cyclical condition. Int. J. Math. Sci. Appl. 1, 9 (2011)Oltra S., Valero O.: Banach’s fixed theorem for partial metric spaces. Rend. Istit. Mat. Univ. Trieste. 36, 17–26 (2004)Păcurar M., Rus I.A.: Fixed point theory for cyclic $${\phi}$$ -contractions. Nonlinear Anal. 72, 1181–1187 (2010)Petric M.A.: Best proximity point theorems for weak cyclic Kannan contractions. Filomat. 25, 145–154 (2011)Romaguera, S.: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. (2010, article ID 493298, 6 pages).Romaguera, S.: Fixed point theorems for generalized contractions on partial metric spaces. Topol. Appl. (2011). doi: 10.1016/j.topol.2011.08.026Romaguera S., Valero O.: A quantitative computational model for complete partial metric spaces via formal balls. Math. Struct. Comput. Sci. 19, 541–563 (2009)Rus, I.A.: Cyclic representations and fixed points. Annals of the Tiberiu Popoviciu Seminar of Functional equations. Approx. Convexity 3, 171–178 (2005), ISSN 1584-4536Schellekens M.P.: The correspondence between partial metrics and semivaluations. Theoret. Comput. Sci. 315, 135–149 (2004)Valero O.: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Top. 6, 229–240 (2005)Waszkiewicz P.: Quantitative continuous domains. Appl. Cat. Struct. 11, 41–67 (2003

Seeing through the String Landscape - a String Hunter's Companion in Particle Physics and Cosmology

In this article we will overview several aspects of the string landscape, namely intersecting D-brane models and their statistics, possible model independent LHC signatures of intersecting brane models, flux compactification, moduli stabilization in type II compactifications, domain wall solutions and brane inflation.Comment: 94 pages, Review paper invited and accepted for publication by JHEP, revised version contains several new references and other minor modification

How institutional logics hamper innovation : The case of animal testing

For radical innovation to become successful the substitution of established practices are essential. Nevertheless, in the innovation literature novelty is often at the center and only little attention is paid to the influence of established technologies and underlying routines. This paper aims to contribute to this gap by increasing the understanding about the effect of persistence of established practices on the innovation process. We do this by using a framework that combines the Technological Innovation System approach with an analysis of the institutional logics reinforcing the established practice. The studied case concerns the innovation process to animal-free medicine development. Despite the fact that the substitution of animal tests is called for since the 1980s and animal-free methods are available, animal tests are still being used in medicine development. This study shows that adding institutional logics to the innovation systems analysis creates a much better understanding of the speed and direction of radical innovation

Implementation of in vitro replacement technologies in regulatory drug testing - An innovation systems perspective

The replacement of in vivo methods by in vitro methods in regulatory drug testing is rare. The aim of this research is to identify barriers and drivers of the replacement of in vivo methods by in vitro methods in Europe. We studied two cases. The first case is the Draize eye test. Since 2009, the in vivo test is partly replaced by in vitro methods. The second case concerns EPO potency testing. Since the eighties, financial and scientific efforts have been made to replace the in vivo EPO potency test with in vitro methods; however the efforts failed to deliver expected outcomes. The innovation systems approach is used to identify the drivers and barriers regarding replacement of in vivo methods by in vitro methods in regulatory drug testing in Europe, such as the presence or absence of legislative pressure, legitimacy, and funding. Combining and comparing the outcomes resulted in an overview of potential barriers and drivers, and an indication of which of these factors are critical for replacement of in vivo methods by in vitro methods in regulatory drug testing. Policy makers could use these results to formulate policies that enable the replacement of in vivo methods by in vitro methods in regulatory drug testing