Algorithms for Stable Matching and Clustering in a Grid

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so that each cluster center is apportioned a set of points of equal area. We show that, for a discretization of the problem to an $n\times n$ grid of pixels with $k$ centers, the problem can be solved in time $O(n^2 \log^5 n)$, and we experiment with two slower but more practical algorithms and a hybrid method that switches from one of these algorithms to the other to gain greater efficiency than either algorithm alone. We also show how to combine geometric stable matchings with a $k$-means clustering algorithm, so as to provide a geometric political-districting algorithm that views distance in economic terms, and we experiment with weighted versions of stable $k$-means in order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th International Workshop on Combinatorial Image Analysis, June 19-21, 2017, Plovdiv, Bulgari

Differential pain response at local and remote muscle sites following aerobic cycling exercise at mild and moderate intensity

Physical exercise has been shown to inhibit experimental pain response in the post-exercise period. Modulation of the pain system may be differentiated between muscle sites engaging in contractile activity. The purpose of this study was to assess the pain response at remote and local muscle sites following aerobic exercise at different work intensities. Participants included 10 healthy and physically active males (mean age ± SD, 21.2 ± 3.4). Somatic pressure pain threshold (PPT) at the rectus femoris (local) and brachioradialis (remote) muscle site was measured at before (Pre), 5 min after (Post1), and 15 min after (Post2) aerobic cycling exercise at 70 and 30 % of peak oxygen uptake (VO(2peak)) performed on different occasions in a counterbalanced order, separated by minimum of 3 days interval. Repeated measures ANOVA for PPT reveals significant main effect for time (f = 3.581, p = 0.049, observed power = 0.588) and muscle site (f = 17.931, p = 0.002, observed power = 0.963). There was a significant interaction shown for exercise intensity by time (f = 11.390, p = 0.012, observed power = 0.790). PPT at rectus femoris following cycling exercise at 70 % of VO(2peak) reveals a significant increase between Pre-Post1 (p = 0.040). PPT for rectus femoris following cycling exercise at 30 % of VO(2peak) revealed a significant decrease between Pre-Post1 (p = 0.026) and Pre-Post2 (p = 0.008). The PPT for brachioradialis following cycling exercise at 30 % of VO(2peak) revealed a significant decrease between Pre-Post1 (p = 0.011) and Pre-Post2 (p = 0.005). These results show that aerobic exercise increases PPT locally at the exercise muscle site following exercise at 70 % of VO(2peak) but reduces PPT following exercise at 30 % of VO(2peak)

Increasing confidence and changing behaviors in primary care providers engaged in genetic counselling.

BackgroundScreening and counseling for genetic conditions is an increasingly important part of primary care practice, particularly given the paucity of genetic counselors in the United States. However, primary care physicians (PCPs) often have an inadequate understanding of evidence-based screening; communication approaches that encourage shared decision-making; ethical, legal, and social implication (ELSI) issues related to screening for genetic mutations; and the basics of clinical genetics. This study explored whether an interactive, web-based genetics curriculum directed at PCPs in non-academic primary care settings was superior at changing practice knowledge, attitudes, and behaviors when compared to a traditional educational approach, particularly when discussing common genetic conditions.MethodsOne hundred twenty one PCPs in California and Pennsylvania physician practices were randomized to either an Intervention Group (IG) or Control Group (CG). IG physicians completed a 6 h interactive web-based curriculum covering communication skills, basics of genetic testing, risk assessment, ELSI issues and practice behaviors. CG physicians were provided with a traditional approach to Continuing Medical Education (CME) (clinical review articles) offering equivalent information.ResultsPCPs in the Intervention Group showed greater increases in knowledge compared to the Control Group. Intervention PCPs were also more satisfied with the educational materials, and more confident in their genetics knowledge and skills compared to those receiving traditional CME materials. Intervention PCPs felt that the web-based curriculum covered medical management, genetics, and ELSI issues significantly better than did the Control Group, and in comparison with traditional curricula. The Intervention Group felt the online tools offered several advantages, and engaged in better shared decision making with standardized patients, however, there was no difference in behavior change between groups with regard to increases in ELSI discussions between PCPs and patients.ConclusionWhile our intervention was deemed more enjoyable, demonstrated significant factual learning and retention, and increased shared decision making practices, there were few differences in behavior changes around ELSI discussions. Unfortunately, barriers to implementing behavior change in clinical genetics is not unique to our intervention. Perhaps the missing element is that busy physicians need systems-level support to engage in meaningful discussions around genetics issues. The next step in promoting active engagement between doctors and patients may be to put into place the tools needed for PCPs to easily access the materials they need at the point-of-care to engage in joint discussions around clinical genetics

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Weighted Banach spaces of harmonic functions

“The final publication is available at Springer via http://dx.doi.org/10.1007/s13398-012-0109-z."We study Banach spaces of harmonic functions on open sets of or endowed with weighted supremum norms. We investigate the harmonic associated weight defined naturally as the analogue of the holomorphic associated weight introduced by Bierstedt, Bonet, and Taskinen and we compare them. We study composition operators with holomorphic symbol between weighted Banach spaces of pluriharmonic functions characterizing the continuity, the compactness and the essential norm of composition operators among these spaces in terms of associated weights.The research of the first author was partially supported by MEC and FEDER Project MTM2010-15200 and by GV project ACOMP/2012/090.Jorda Mora, E.; Zarco García, AM. (2014). Weighted Banach spaces of harmonic functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 108(2):405-418. https://doi.org/10.1007/s13398-012-0109-zS4054181082Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory, 2nd edn. Springer, Berlin (2001)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on balanced domains. Mich. Math. J. 40(2), 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127(2), 137–168 (1998)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 54(1), 70–79 (1993)Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42(2), 139–148 (1999)Bonet, J., Domański, P., Lindström, M.: Weakly compact composition operators on weighted vector-valued Banach spaces of analytic mappings. Ann. Acad. Sci. Fenn. Math. Ser. A I 26, 233–248 (2001)Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 64, 101–118 (1998)Bonet, J., Friz, M., Jordá, E.: Composition operators between weighted inductive limits of spaces of holomorphic functions. Publ. Math. Debr. Ser. A 67, 333–348 (2005)Boyd, C., Rueda, P.: The v-boundary of weighted spaces of holomorphic functions. Ann. Acad. Sci. Fenn. Math. 30, 337–352 (2005)Boyd, C., Rueda, P.: Complete weights and v-peak points of spaces of weighted holomorphic functions. Isr. J. Math. 155, 57–80 (2006)Boyd, C., Rueda, P.: Isometries of weighted spaces of harmonic functions. Potential Anal. 29(1), 37–48 (2008)Carando, D., Sevilla-Peris, P.: Spectra of weighted algebras of holomorphic functions. Math. Z. 263, 887–902 (2009)Contreras, M.D., Hernández-Díaz, G.: Weighted composition operators in weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 69(1), 41–60 (2000)García, D., Maestre, M., Rueda, P.: Weighted spaces of holomorphic functions on Banach spaces. Stud. Math. 138(1), 1–24 (2000)García, D., Maestre, M., Sevilla-Peris, P.: Composition operators between weighted spaces of holomorphic functions on Banach spaces. Ann. Acad. Sci. Fenn. Math. 29, 81–98 (2004)Gunning, R., Rossi, H.: Analytic Functions of Several Complex Variables. AMS Chelsea Publishing, Providence (2009)Hoffman, K.: Banach Spaces of Analytic Functions. Prentice-Hall, Englewood Cliffs (1962)Krantz, S.G.: Function Theory of Several Complex Variables. AMS, Providence (2001)Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309–320 (1995)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175(1), 19–45 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, Oxford (1997)Montes-Rodríguez, A.: Weight composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(2), 872–884 (2000)Ng, K.F.: On a theorem of Diximier. Math. Scand. 29, 279–280 (1972)Rudin, W.: Real and Complex Analysis. MacGraw-Hill, NY (1970)Rudin, W.: Functional analysis. In: International series in pure and applied mathematics, 2nd edn. McGraw-Hill, Inc., New York (1991)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of harmonic functions. J. Reine Angew. Math. 299(300), 256–279 (1978)Shields, A.L., Williams, D.L.: Bounded projections and the growth of harmonic conjugates in the unit disc. Mich. Math. J. 29, 3–25 (1982)Zheng, L.: The essential norms and spectra of composition operators on $$H^\infty$$ . Pac. J. Math. 203(2), 503–510 (2002

Trend-TDT – a transmission/disequilibrium based association test on functional mini/microsatellites

<p>Abstract</p> <p>Background</p> <p>Minisatellites and microsatellites are associated with human disease, not only as markers of risk but also involved directly in disease pathogenesis. They may play significant roles in replication, repair and mutation of DNA, regulation of gene transcription and protein structure alteration. Phenotypes can thus be affected by mini/microsatellites in a manner proportional to the length of the allele. Here we propose a new method to assess the linear trend toward transmission of shorter or longer alleles from heterozygote parents to affected child.</p> <p>Results</p> <p>This test (trend-TDT) performs better than other TDT (Transmission/Disequilibrium Test) type tests, such as TDT_maxand TDT_L/S, under most marker-disease association models.</p> <p>Conclusion</p> <p>The trend-TDT test is a more powerful association test when there is a biological basis to suspect a relationship between allele length and disease risk.</p

WW domain interactions regulate the Hippo tumor suppressor pathway

The Hippo kinase pathway is emerging as a conserved signaling pathway that is essential for organ growth and tumorigenesis in Drosophila and mammalians. Although the signaling of the core kinases is relatively well understood, less is known about the upstream inputs, downstream outputs and regulation of the whole cascade. Enrichment of the Hippo pathway components with WW domains and their cognate proline-rich interacting motifs provides a versatile platform for further understanding the mechanisms that regulate organ growth and tumorigenesis. Here, we review recently discovered mechanisms of WW domain-mediated interactions that contribute to the regulation of the Hippo signaling pathway in tumorigenesis. We further discuss new insights and future directions on the emerging role of such regulation

A Community Study of Factors Related to Poorly Controlled Asthma among Brazilian Urban Children

BACKGROUND: Asthma constitutes a serious public health problem in many regions of the world, including the city of Salvador, State of Bahia-Brazil. The purpose of this study was to analyse the factors associated with poor asthma control. METHODOLOGY/PRINCIPAL FINDINGS: Two definitions were used for asthma: 1) wheezing in the last 12 months; 2) wheezing in the last 12 months plus other asthma symptoms or asthma diagnosis ever. The definition of poorly controlled asthma was: at least one reported hospitalisation due to asthma and/or high frequency of symptoms, in the last year. Children with poorly controlled asthma (N = 187/374) were compared with wheezing children with controlled asthma regarding age, gender, atopy, parental asthma, rhinitis, eczema, exposure to second hand tobacco smoke, presence of moulds, pets and pests in the house, helminth infections and body mass index. Crude and logistic regression adjusted odds ratios were used as measures of association. There was a higher proportion of poorly controlled asthma among children with eczema (OR = 1.55; 95% CI 1.02; 2.37). The strength of the association was greater among children with eczema and rhinitis (42.6%, 53.4% and 57.7%, respectively, in children who had no rhinitis nor eczema, had only one of those, and had both (p = 0.02 for trend test). The presence of mould in the houses was inversely associated with poorly controlled asthma (OR = 0.54; 95% CI 0.34; 0.87). CONCLUSIONS/SIGNIFICANCE: Our results indicate an association between eczema and poor asthma control in this environment, but emphasize the role of various other individual and environmental factors as determinants of poor control