New results on the mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces

Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211-232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in 1995. The applicability of this theory to the asymptotic complexity analysis of divide and conquer algorithms was also illustrated by Schellekens in the same paper. In particular, he gave a new formal proof, based on the use of the Banach fixed-point theorem, of the well-known fact that the asymptotic upper bound of the average running time of computing of Mergesort belongs to the asymptotic complexity class of n log(2) n. Recently, Schellekens' method has been shown to be useful in yielding asymptotic upper bounds for a class of algorithms whose running time of computing leads to recurrence equations different from the divide and conquer ones reported in Cerda-Uguet et al. [The Baire partial quasi-metric space: A mathematical tool for the asymptotic complexity analysis in Computer Science, Theory Comput. Syst. 50 (2012), pp. 387-399.]. However, the variety of algorithms whose complexity can be analysed with this approach is not much larger than that of algorithms that can be analysed with the original Schellekens method. In this paper, on the one hand, we extend Schellekens' method in order to yield asymptotic upper bounds for a certain class of recursive algorithms whose running time of computing cannot be discussed following the techniques given by Cerda-Uguet et al. and, on the other hand, we improve the original Schellekens method by introducing a new fixed-point technique for providing, contrary to the case of the method introduced by Cerda-Uguet et al., lower asymptotic bounds of the running time of computing of the aforementioned algorithms and those studied by Cerda-Uguet et al. We illustrate and validate the developed method by applying our results to provide the asymptotic complexity class (asymptotic upper and lower bounds) of the celebrated algorithms Quicksort, Largetwo and Hanoi.The authors are thankful for the support from the Spanish Ministry of Science and Innovation, grant MTM2009-12872-C02-01.Romaguera Bonilla, S.; Tirado Peláez, P.; Valero Sierra, Ó. (2012). New results on the mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces. International Journal of Computer Mathematics. 89(13-14):1728-1741. https://doi.org/10.1080/00207160.2012.659246S172817418913-14Cerdà-Uguet, M. A., Schellekens, M. P., & Valero, O. (2011). The Baire Partial Quasi-Metric Space: A Mathematical Tool for Asymptotic Complexity Analysis in Computer Science. Theory of Computing Systems, 50(2), 387-399. doi:10.1007/s00224-010-9310-7Cull, P., & Ecklund, E. F. (1985). Towers of Hanoi and Analysis of Algorithms. The American Mathematical Monthly, 92(6), 407. doi:10.2307/2322448García-Raffi, L. M., Romaguera, S., & Sánchez-Pérez, E. A. (2002). Sequence spaces and asymmetric norms in the theory of computational complexity. Mathematical and Computer Modelling, 36(1-2), 1-11. doi:10.1016/s0895-7177(02)00100-0García-Raffi, L. M., Romaguera, S., & Schellekens, M. P. (2008). Applications of the complexity space to the General Probabilistic Divide and Conquer Algorithms. Journal of Mathematical Analysis and Applications, 348(1), 346-355. doi:10.1016/j.jmaa.2008.07.026Künzi, H.-P. A. (2001). Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymmetric Topology. History of Topology, 853-968. doi:10.1007/978-94-017-0470-0_3Rodríguez-López, J., Romaguera, S., & Valero, O. (2008). Denotational semantics for programming languages, balanced quasi-metrics and fixed points. International Journal of Computer Mathematics, 85(3-4), 623-630. doi:10.1080/00207160701210653Rodríguez-López, J., Schellekens, M. P., & Valero, O. (2009). An extension of the dual complexity space and an application to Computer Science. Topology and its Applications, 156(18), 3052-3061. doi:10.1016/j.topol.2009.02.009Romaguera, S., & Schellekens, M. (1999). Quasi-metric properties of complexity spaces. Topology and its Applications, 98(1-3), 311-322. doi:10.1016/s0166-8641(98)00102-3Romaguera, S., & Valero, O. (2008). On the structure of the space of complexity partial functions. International Journal of Computer Mathematics, 85(3-4), 631-640. doi:10.1080/00207160701210117Romaguera, S., Schellekens, M. P., & Valero, O. (2011). The complexity space of partial functions: a connection between complexity analysis and denotational semantics. International Journal of Computer Mathematics, 88(9), 1819-1829. doi:10.1080/00207161003631885Schellekens, M. (1995). The Smyth Completion. Electronic Notes in Theoretical Computer Science, 1, 535-556. doi:10.1016/s1571-0661(04)00029-5Scott, D. S. 1970. Outline of a mathematical theory of computation. Proceedings of the 4th Annual Princeton Conference on Information Sciences and Systems. March26–271970, Princeton, NJ. pp.169–176

Dietary determinants of changes in waist circumference adjusted for body mass index - a proxy measure of visceral adiposity

Background Given the recognized health effects of visceral fat, the understanding of how diet can modulate changes in the phenotype “waist circumference for a given body mass index (WCBMI)”, a proxy measure of visceral adiposity, is deemed necessary. Hence, the objective of the present study was to assess the association between dietary factors and prospective changes in visceral adiposity as measured by changes in the phenotype WCBMI. Methods and Findings We analyzed data from 48,631 men and women from 5 countries participating in the European Prospective Investigation into Cancer and Nutrition (EPIC) study. Anthropometric measurements were obtained at baseline and after a median follow-up time of 5.5 years. WCBMI was defined as the residuals of waist circumference regressed on body mass index, and annual change in WCBMI (¿WCBMI, cm/y) was defined as the difference between residuals at follow-up and baseline, divided by follow-up time. The association between energy, energy density (ED), macronutrients, alcohol, glycemic index (GI), glycemic load (GL), fibre and ¿WCBMI was modelled using centre-specific adjusted linear regression, and random-effects meta-analyses to obtain pooled estimates. Men and women with higher ED and GI diets showed significant increases in their WCBMI, compared to those with lower ED and GI [1 kcal/g greater ED predicted a ¿WCBMI of 0.09 cm (95% CI 0.05 to 0.13) in men and 0.15 cm (95% CI 0.09 to 0.21) in women; 10 units greater GI predicted a ¿WCBMI of 0.07 cm (95% CI 0.03 to 0.12) in men and 0.06 cm (95% CI 0.03 to 0.10) in women]. Among women, lower fibre intake, higher GL, and higher alcohol consumption also predicted a higher ¿WCBMI. Conclusions Results of this study suggest that a diet with low GI and ED may prevent visceral adiposity, defined as the prospective changes in WCBMI. Additional effects may be obtained among women of low alcohol, low GL, and high fibre intake

Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres

A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.Comment: Submitted to special issue of Prammna-Journal of Physics devoted to the Vortex State Studie

Origin of discrepancy between electrical and mechanical anomalies in lead-free (K,Na)NbO3 -based ceramics

[EN] Ferroelectric polymorphic phase coexistence, associated with either the presence of a morphotropic phase boundary or a temperature-driven polymorphic phase transition, is currently acknowledged as the key to high piezoelectric activity and is searched when new perovskite materials are developed, like lead-free alternatives to state-of-the-art Pb(Zr,Ti)O3. This requires characterization tools that allow phase coexistence and transitions to be readily identified, among which measurements of the temperature dependences of Young's modulus and mechanical losses by dynamical mechanical analysis stand out as a powerful technique to complement standard electrical characterizations. We report here the application of this technique to (K1-xNax)NbO3-based materials, which are under extensive investigation as environmentally friendly high sensitivity piezoelectrics. The elastic anomalies associated with the different phase transitions are identified and are shown to be distinctively shifted in relation to the dielectric ones. The origin of this discrepancy is discussed with the help of temperature-dependent Raman spectroscopy and is proposed to be a characteristic of diffuse phase transitions.The authors would like to thank CAPES and the Sâo Paulo Research Foundation (FAPESP), Grants No. 2012/08457-7 and No. 2013/00134-7, for the financial support. M.A. also acknowledges funding from MINECO through the MAT2014-58816-R Project.Peer Reviewe

Adherence to predefined dietary patterns and incident type 2 diabetes in European populations: EPIC-InterAct Study

Aims/hypothesis - Few studies have investigated the relationship between predefined dietary patterns and type 2 diabetes incidence; little is known about the generalisability of these associations. We aimed to assess the association between predefined dietary patterns and type 2 diabetes risk in European populations. Methods - From among a case-cohort of 12,403 incident diabetes cases and 16,154 subcohort members nested within the prospective European Prospective Investigation into Cancer and Nutrition study, we used data on 9,682 cases and 12,595 subcohort participants from seven countries. Habitual dietary intake was assessed at baseline with country-specific dietary questionnaires. Two diet-quality scores (alternative Healthy Eating Index [aHEI], Dietary Approaches to Stop Hypertension [DASH] score) and three reduced rank regression (RRR)-derived dietary-pattern scores were constructed. Country-specific HRs were calculated and combined using a random-effects meta-analysis. Results - After multivariable adjustment, including body size, the aHEI and DASH scores were not significantly associated with diabetes, although for the aHEI there was a tendency towards an inverse association in countries with higher mean age. We observed inverse associations of the three RRR-derived dietary-pattern scores with diabetes: HRs (95% CIs) for a 1-SD difference were 0.91 (0.86, 0.96), 0.92 (0.84, 1.01) and 0.87 (0.82, 0.92). Random-effects meta-analyses revealed heterogeneity between countries that was explainable by differences in the age of participants or the distribution of dietary intake. Conclusions/interpretation - Adherence to specific RRR-derived dietary patterns, commonly characterised by high intake of fruits or vegetables and low intake of processed meat, sugar-sweetened beverages and refined grains, may lower type 2 diabetes risk

Obesidad sarcopénica y disfuncionalidad en población con síndrome metabólico

The sarcopenic obesity (SO) is a new category of obesity, specially related with the elderly population, characterized by high fat mass and low muscle mass. It is intended to analyze the relation between SO and disability, in a population older than 55 years with overweight or obesity and metabolic syndrome.  For the body composition analyzes we used DXA in 303 patients, and for the assessment of disability we used 5 physical validated test in a subsample of 53 patients. We constructed a global physical capacity score and we studied the association with SO phenotypes, defined using the skeletal muscle mass and the total body fat.  It has not been found significant associations between SO and disability in our sample. Studies with a large sample are needed. La obesidad sarcopénica (OS) es una nueva categoría de obesidad, especialmente asociada a población envejecida, caracterizada por una elevada masa grasa y baja masa muscular. Se pretende analizar la relación entre la OS y la disfuncionalidad en una población mayor de 55 años con sobrepeso u obesidad y síndrome metabólico.Para el análisis de la composición corporal se ha utilizado la absorciometria dual de rayos X (DXA) en un total de 303 participantes, y para la valoración de la disfuncionalidad se han realizado 5 test físicos validados en una submuestra de 53 participantes. Se ha realizado una puntuación global de capacidad física y se ha mirado su asociación con los fenotipos de OS, definidos en función de la masa muscular esquelética y la grasa corporal total. No se observó una asociación significativa entre la OS y la disfuncionalidad en esta muestra. Son necesarios estudios con mayor tamaño muestral

A systematic review and meta-analysis of the 2007 WCRF/AICR score in relation to cancer-related health outcomes

Background: We conducted a systematic literature review and meta-analysis of observational studies investigating adherence to the 2007 World Cancer Research Fund/American Institute for Cancer Research (WCRF/AICR) lifestyle recommendations for cancer prevention and health outcomes. Patients and methods: We searched PubMed and the in-house database of the WCRF Continuous Update Project for publications up to June 2019. Cross-sectional studies were only narratively reviewed given their heterogeneity while findings of cohort/case-control studies were synthesized in umbrella reviews and meta-analyses. Summary relative risks (RRs) and 95% confidence intervals (CI) were estimated using a random-effects model when at least two studies reported results on a specific outcome. Results: Thirty-eight articles (17 prospective, 8 case-control, and 13 cross-sectional studies) were included. The summary RR per each point increment in the 2007 WCRF/AICR score was 0.90 (95% CI: 0.87e0.93, n 1⁄4 11) for breast cancer, regardless of hormone receptor and menopausal status, 0.86 (95% CI: 0.82e0.89, n 1⁄4 10) for colorectal cancer, and 0.93 (95% CI: 0.89e0.96, n 1⁄4 2) for lung cancer risk. No statistically significant associations were reported for prostate (n 1⁄4 6) and pancreatic cancers (n 1⁄4 2). Adherence to the recommendations was associated with lower overall mortality (RR 1⁄4 0.90, 95% CI 0.84e0.96, n 1⁄4 3) and cancer-specific mortality (RR 1⁄4 0.91, 95% CI 0.89e0.92; n 1⁄4 3) in healthy populations, as well as with higher survival in cancer patients (n 1⁄4 2). In cross-sectional studies, a healthier plasma marker profile and lower cancer risk factors in the general population and a better health status and quality of life in cancer patients/survivors were reported. Conclusions: Adhering to the 2007 WCRF/AICR recommendations is associated with lower risks of cancer incidence, namely breast and colorectal cancers, and mortality. Primary prevention of cancer should emphasize modification of multiple lifestyle factors. Upcoming studies examining the recently updated 2018 guidelines will further clarify such associations