Computational Complexity of Fixed Points and Intersection Points

AbstractWe study the computational complexity of Brouwer′s fixed point theorem and the intersection point theorem in the two-dimensional case. Papadimitriou (1990, in "Proceedings, 31st IEEE Sympos. Found. Comput. Sci.," pp. 794-801) defined a complexity class PDLF to characterize the complexity of the fixed point theorem in the three-dimensional case. We define a subclass PMLF of PDLF and show that the fixed points and the intersection points of polynomial-time computable functions are not polynomial-time computable if PMLF contains a function on unary inputs that is not polynomial-time computable

Solving analytic differential equations in polynomial time over unbounded domains

In this paper we consider the computational complexity of solving initial-value problems de ned with analytic ordinary diferential equations (ODEs) over unbounded domains of Rn and Cn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of de nition, provided it satis es a very generous bound on its growth, and that the function admits an analytic extension to the complex plane

Computing domains of attraction for planar dynamics

In this note we investigate the problem of computing the domain of attraction of a ow on R2 for a given attractor. We consider an operator that takes two inputs, the description of the ow and a cover of the attractors, and outputs the domain of attraction for the given attractor. We show that: (i) if we consider only (structurally) stable systems, the operator is (strictly semi-)computable; (ii) if we allow all systems de ned by C1-functions, the operator is not (semi-)computable. We also address the problem of computing limit cycles on these systems

Search for the radiative decay η→π0γγ\eta \to \pi^0 \gamma \gamma in the SND experiment at VEPP-2M

The $\eta \to \pi^0 \gamma \gamma$ decay was investigated by the SND detector at VEPP-2M $e^+e^-$ collider in the reaction $e^+e^-\to\phi\to \eta\gamma$. Here we present the results and some details of this study. We report an upper limit (90% c.l.) $Br(\eta \to \pi^0 \gamma \gamma)<8.4\times 10^{-4}$ as our final result. Our upper limit does not contradict the earlier measurement by GAMS spectrometer. To facilitate future studies a rather detailed review of the problem is also given.Comment: 24 pages, 6 figures, LaTex. To be published in Nucl. Phys.

Matching action to need: an analysis of Global Burden of Disease 2017 and population health data to focus adolescent health policy and actions in Myanmar

Background: Myanmar is a country undergoing rapid transitions in health. Its national strategic policy for young people's health is being revised but there is a paucity of population data to inform local priorities and needs. Objective: In this paper we describe a comprehensive profile of adolescent health in Myanmar to focus policy and health actions. Methods: We used available primary data, and modelled estimates from the GBD 2017, to describe health outcomes (mortality and morbidity), health risks and determinants for adolescents in Myanmar between 1990-2017. A governance group of key stakeholders guided the framing of the study, interpretation of findings, and recommendations. Results: Overall health has improved for adolescents in Myanmar since 1990, however adolescent mortality remains high, particularly so for older adolescent males; all-cause mortality rate for 10-24 years was 70 per 100,000 for females and 149 per 100,000 for males (16,095 adolescent deaths in 2017). Overall, the dominant health problems were injuries for males and non-communicable disease for females in a context of ongoing burden of communicable and nutritional diseases for both sexes, and reproductive health needs for females. Health risks relating to undernutrition (thinness and anaemia) remain prevalent, with other health risks (overweight, binge alcohol use, and substance use) relatively low by global and regional standards but increasing. Gains have been made in social determinants such as adolescent fertility and modern contraception use; however, advances have been more limited in secondary education completion and engagement in employment and post education training. Conclusions: These results highlight the need to focus current efforts on addressing disease and mortality experienced by adolescents in Myanmar, with a specific focus on injury, mental health and non-communicable disease.Karly I. Cini, Phone Myint Win, Zay Yar Swe, Kyu Kyu Than, Thin Mar Win ... Peter S. Azzopardi ... et al

Designing a broad-spectrum integrative approach for cancer prevention and treatment

Targeted therapies and the consequent adoption of "personalized" oncology have achieved notablesuccesses in some cancers; however, significant problems remain with this approach. Many targetedtherapies are highly toxic, costs are extremely high, and most patients experience relapse after a fewdisease-free months. Relapses arise from genetic heterogeneity in tumors, which harbor therapy-resistantimmortalized cells that have adopted alternate and compensatory pathways (i.e., pathways that are notreliant upon the same mechanisms as those which have been targeted). To address these limitations, aninternational task force of 180 scientists was assembled to explore the concept of a low-toxicity "broad-spectrum" therapeutic approach that could simultaneously target many key pathways and mechanisms. Using cancer hallmark phenotypes and the tumor microenvironment to account for the various aspectsof relevant cancer biology, interdisciplinary teams reviewed each hallmark area and nominated a widerange of high-priority targets (74 in total) that could be modified to improve patient outcomes. For thesetargets, corresponding low-toxicity therapeutic approaches were then suggested, many of which werephytochemicals. Proposed actions on each target and all of the approaches were further reviewed forknown effects on other hallmark areas and the tumor microenvironment. Potential contrary or procar-cinogenic effects were found for 3.9% of the relationships between targets and hallmarks, and mixedevidence of complementary and contrary relationships was found for 7.1%. Approximately 67% of therelationships revealed potentially complementary effects, and the remainder had no known relationship. Among the approaches, 1.1% had contrary, 2.8% had mixed and 62.1% had complementary relationships. These results suggest that a broad-spectrum approach should be feasible from a safety standpoint. Thisnovel approach has potential to be relatively inexpensive, it should help us address stages and types ofcancer that lack conventional treatment, and it may reduce relapse risks. A proposed agenda for futureresearch is offered

Fine-Scale Mapping of the 4q24 Locus Identifies Two Independent Loci Associated with Breast Cancer Risk

Background: A recent association study identified a common variant (rs9790517) at 4q24 to be associated with breast cancer risk. Independent association signals and potential functional variants in this locus have not been explored. Methods: We conducted a fine-mapping analysis in 55,540 breast cancer cases and 51,168 controls from the Breast Cancer Association Consortium. Results: Conditional analyses identified two independent association signals among women of European ancestry, represented by rs9790517 [conditional P = 2.51 × 10−4; OR, 1.04; 95% confidence interval (CI), 1.02–1.07] and rs77928427 (P = 1.86 × 10−4; OR, 1.04; 95% CI, 1.02–1.07). Functional annotation using data from the Encyclopedia of DNA Elements (ENCODE) project revealed two putative functional variants, rs62331150 and rs73838678 in linkage disequilibrium (LD) with rs9790517 (r2 ≥ 0.90) residing in the active promoter or enhancer, respectively, of the nearest gene, TET2. Both variants are located in DNase I hypersensitivity and transcription factor–binding sites. Using data from both The Cancer Genome Atlas (TCGA) and Molecular Taxonomy of Breast Cancer International Consortium (METABRIC), we showed that rs62331150 was associated with level of expression of TET2 in breast normal and tumor tissue. Conclusion: Our study identified two independent association signals at 4q24 in relation to breast cancer risk and suggested that observed association in this locus may be mediated through the regulation of TET2. Impact: Fine-mapping study with large sample size warranted for identification of independent loci for breast cancer risk

Interpretation of stream programs: characterizing type 2 polynomial time complexity

We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These characterizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over the reals, a particular case of type 2 functions, and we provide a characterization of polynomial time complexity in Recursive Analysis