How many independent bets are there?

The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of in- dependent bets available to an investor. Conventionally applications us- ing breadth frequently assume only the number of separate bets. There may be a large discrepancy between these two interpretations. We uti- lize a simple singular-value decomposition (SVD) and the Keiser-Gutman stopping criterion to select the integer-valued effective dimensionality of the correlation matrix of returns. In an emerging market such as South African we document an estimated breadth that is considerably lower than anticipated. This lack of diversification may be because of market concentration, exposure to the global commodity cycle and local currency volatility. We discuss some practical extensions to a more statistically correct interpretation of market breadth, and its theoretical implications for both global and domestic investors.Comment: Less technical rewrite. 12 Pages, 6 Figures (.eps

Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example

We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differetial equation for the resource concentration). As many results for such systems are available, we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman-Metz Daphnia model and a model introduced by Gurney-Nisbet and Jones et al., and next obtain various ecological insights by analytical or numerical studies of special cases

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables

[EN] Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A completely multiplicative sequence (b(n)) of complex numbers is said to be an l(1)-multiplier for H-infinity whenever Sigma(n vertical bar)a(n)b(n vertical bar) < infinity for every D is an element of H-infinity. We study the problem of describing such sequences (b(n)) in terms of the asymptotic decay of the subsequence (b(pj)), where p(j) denotes the j th prime number. Given a completely multiplicative sequence b = (b(n)) we prove (among other results): b is an l(1)-multiplier for H-infinity provided vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) < 1, and conversely, if b is an l(1)-multiplier for H-infinity, then vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) <= 1 (here b* stands for the decreasing rearrangement of b). Following an ingenious idea of Harald Bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk D-infinity (the open unit ball of l(infinity)) for which every bounded and holomorphic function f on D-infinity has an absolutely convergent monomial series expansion Sigma(alpha) partial derivative alpha f (0)/alpha! z alpha. Moreover, we study analogous problems in Hardy spaces of Dirichlet series and Hardy spaces of functions on the infinite dimensional polytorus T-infinity.The second, fourth and fifth authors were supported by MINECO and FEDER Project MTM2014-57838-C2-2-P. The fourth author was also supported by PrometeoII/2013/013. The fifth author was also supported by project SP-UPV20120700.Bayart, F.; Defant, A.; Frerick, L.; Maestre, M.; Sevilla Peris, P. (2017). Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables. Mathematische Annalen. 368(1-2):837-876. https://doi.org/10.1007/s00208-016-1511-1S8378763681-2Aleman, A., Olsen, J.-F., Saksman, E.: Fatou and brother Riesz theorems in the infinite-dimensional polydisc. arXiv:1512.01509Balasubramanian, R., Calado, B., Queffélec, H.: The Bohr inequality for ordinary Dirichlet series. Studia Math. 175(3), 285–304 (2006)Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Monatsh. Math. 136(3), 203–236 (2002)Bayart, F., Pellegrino, D., Seoane-Sepúlveda, J.B.: The Bohr radius of the $$n$$ n -dimensional polydisk is equivalent to $$\sqrt{(\log n)/n}$$ ( log n ) / n . Adv. Math. 264:726–746 (2014)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann. Math. 32(3), 600–622 (1931)Bohr, H.: Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichlet–schen Reihen $$\sum \,\frac{a_n}{n^s}$$ ∑ a n n s . Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl. 441–488 (1913)Bohr, H.: Über die gleichmäßige Konvergenz Dirichletscher Reihen. J. Reine Angew. Math. 143, 203–211 (1913)Cole, B.J., Gamelin., T.W.: Representing measures and Hardy spaces for the infinite polydisk algebra. Proc. Lond. Math. Soc. 53(1), 112–142 (1986)Davie, A.M., Gamelin, T.W.: A theorem on polynomial-star approximation. Proc. Am. Math. Soc. 106(2), 351–356 (1989)de la Bretèche, R.: Sur l’ordre de grandeur des polynômes de Dirichlet. Acta Arith. 134(2), 141–148 (2008)Defant, A., Frerick, L., Ortega-Cerdà, J., Ounaïes, M., Seip, K.: The Bohnenblust–Hille inequality for homogeneous polynomials is hypercontractive. Ann. Math. 174(1), 485–497 (2011)Defant, A., García, D., Maestre, M.: New strips of convergence for Dirichlet series. Publ. Mat. 54(2), 369–388 (2010)Defant, A., García, D., Maestre, M., Pérez-García, D.: Bohr’s strip for vector valued Dirichlet series. Math. Ann. 342(3), 533–555 (2008)Defant, A., Maestre, M., Prengel, C.: Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables. J. Reine Angew. Math. 634, 13–49 (2009)Dineen, S.: Complex Analysis on Infinite-dimensional Spaces. Springer Monographs in Mathematics. Springer-Verlag London Ltd, London (1999)Floret, K.: Natural norms on symmetric tensor products of normed spaces. Note Mat. 17(153–188), 1997 (1999)Harris, L. A.: Bounds on the derivatives of holomorphic functions of vectors. In: Analyse fonctionnelle et applications (Comptes Rendus Colloq. Analyse, Inst. Mat., Univ. Federal Rio de Janeiro, Rio de Janeiro, 1972), pp. 145–163. Actualités Aci. Indust., No. 1367. Hermann, Paris (1975)Hedenmalm, H., Lindqvist, P., Seip, K.: A Hilbert space of Dirichlet series and systems of dilated functions in $$L^2(0,1)$$ L 2 ( 0 , 1 ) . Duke Math. J. 86(1), 1–37 (1997)Helson, H., Lowdenslager, D.: Prediction theory and Fourier series in several variables. Acta Math. 99, 165–202 (1958)Hibert, D.: Gesammelte Abhandlungen (Band 3). Verlag von Julius Springer, Berlin (1935)Hilbert, D.: Wesen und Ziele einer Analysis der unendlichvielen unabhängigen Variablen. Rend. del Circolo Mat. di Palermo 27, 59–74 (1909)Kahane, J.-P.: Some Random Series of Functions, Volume 5 of Cambridge Studies in Advanced Mathematics, second edn. Cambridge University Press, Cambridge (1985)Konyagin, S.V., Queffélec, H.: The translation $$\frac{1}{2}$$ 1 2 in the theory of Dirichlet series. Real Anal. Exchange 27(1):155–175 (2001/2002)Maurizi, B., Queffélec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16(5), 676–692 (2010)Queffélec, H.: H. Bohr’s vision of ordinary Dirichlet series; old and new results. J. Anal. 3, 43–60 (1995)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet Series. HRI Lecture Notes Series, New Delhi (2013)Rudin, W.: Function Theory in Polydisks. W. A. Benjamin Inc, New York (1969)Toeplitz, O.: Über eine bei den Dirichletschen Reihen auftretende Aufgabe aus der Theorie der Potenzreihen von unendlichvielen Veränderlichen. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 417–432 (1913)Weissler, F.B.: Logarithmic Sobolev inequalities and hypercontractive estimates on the circle. J. Funct. Anal. 37(2), 218–234 (1980)Wojtaszczyk, P.: Banach Spaces for Analysts, Volume 25 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1991

The feasibility of gene therapy in the treatment of head and neck cancer

Standard approach to the treatment of head and neck cancer include surgery, chemotherapy, and radiation. More recently, dramatic increases in our knowledge of the molecular and genetic basis of cancer combined with advances in technology have resulted in novel molecular therapies for this disease. In particular, gene therapy, which involves the transfer of genetic material to cells to produce a therapeutic effect, has become a promising approach. Clinical trials concerning gene therapy strategies in head and neck cancer as well as combination of these strategies with chemotherapy and radiation therapy will be discussed

Height and timing of growth spurt during puberty in young people living with vertically acquired HIV in Europe and Thailand.

OBJECTIVE: The aim of this study was to describe growth during puberty in young people with vertically acquired HIV. DESIGN: Pooled data from 12 paediatric HIV cohorts in Europe and Thailand. METHODS: One thousand and ninety-four children initiating a nonnucleoside reverse transcriptase inhibitor or boosted protease inhibitor based regimen aged 1-10 years were included. Super Imposition by Translation And Rotation (SITAR) models described growth from age 8 years using three parameters (average height, timing and shape of the growth spurt), dependent on age and height-for-age z-score (HAZ) (WHO references) at antiretroviral therapy (ART) initiation. Multivariate regression explored characteristics associated with these three parameters. RESULTS: At ART initiation, median age and HAZ was 6.4 [interquartile range (IQR): 2.8, 9.0] years and -1.2 (IQR: -2.3 to -0.2), respectively. Median follow-up was 9.1 (IQR: 6.9, 11.4) years. In girls, older age and lower HAZ at ART initiation were independently associated with a growth spurt which occurred 0.41 (95% confidence interval 0.20-0.62) years later in children starting ART age 6 to 10 years compared with 1 to 2 years and 1.50 (1.21-1.78) years later in those starting with HAZ less than -3 compared with HAZ at least -1. Later growth spurts in girls resulted in continued height growth into later adolescence. In boys starting ART with HAZ less than -1, growth spurts were later in children starting ART in the oldest age group, but for HAZ at least -1, there was no association with age. Girls and boys who initiated ART with HAZ at least -1 maintained a similar height to the WHO reference mean. CONCLUSION: Stunting at ART initiation was associated with later growth spurts in girls. Children with HAZ at least -1 at ART initiation grew in height at the level expected in HIV negative children of a comparable age

Breast imaging technology: Recent advances in imaging endogenous or transferred gene expression utilizing radionuclide technologies in living subjects - applications to breast cancer

A variety of imaging technologies is being investigated as tools for studying gene expression in living subjects. Two technologies that use radiolabeled isotopes are single photon emission computed tomography (SPECT) and positron emission tomography (PET). A relatively high sensitivity, a full quantitative tomographic capability, and the ability to extend small animal imaging assays directly into human applications characterize radionuclide approaches. Various radiolabeled probes (tracers) can be synthesized to target specific molecules present in breast cancer cells. These include antibodies or ligands to target cell surface receptors, substrates for intracellular enzymes, antisense oligodeoxynucleotide probes for targeting mRNA, probes for targeting intracellular receptors, and probes for genes transferred into the cell. We briefly discuss each of these imaging approaches and focus in detail on imaging reporter genes. In a PET reporter gene system for in vivo reporter gene imaging, the protein products of the reporter genes sequester positron emitting reporter probes. PET subsequently measures the PET reporter gene dependent sequestration of the PET reporter probe in living animals. We describe and review reporter gene approaches using the herpes simplex type 1 virus thymidine kinase and the dopamine type 2 receptor genes. Application of the reporter gene approach to animal models for breast cancer is discussed. Prospects for future applications of the transgene imaging technology in human gene therapy are also discussed. Both SPECT and PET provide unique opportunities to study animal models of breast cancer with direct application to human imaging. Continued development of new technology, probes and assays should help in the better understanding of basic breast cancer biology and in the improved management of breast cancer patients

Bcl-2 and β1-integrin predict survival in a tissue microarray of small cell lung cancer.

INTRODUCTION: Survival in small cell lung cancer (SCLC) is limited by the development of chemoresistance. Factors associated with chemoresistance in vitro have been difficult to validate in vivo. Both Bcl-2 and β(1)-integrin have been identified as in vitro chemoresistance factors in SCLC but their importance in patients remains uncertain. Tissue microarrays (TMAs) are useful to validate biomarkers but no large TMA exists for SCLC. We designed an SCLC TMA to study potential biomarkers of prognosis and then used it to clarify the role of both Bcl-2 and β(1)-integrin in SCLC. METHODS: A TMA was constructed consisting of 184 cases of SCLC and stained for expression of Bcl-2 and β(1)-integrin. The slides were scored and the role of the proteins in survival was determined using Cox regression analysis. A meta-analysis of the role of Bcl-2 expression in SCLC prognosis was performed based on published results. RESULTS: Both proteins were expressed at high levels in the SCLC cases. For Bcl-2 (n=140), the hazard ratio for death if the staining was weak in intensity was 0.55 (0.33-0.94, P=0.03) and for β(1)-integrin (n=151) was 0.60 (0.39-0.92, P=0.02). The meta-analysis showed an overall hazard ratio for low expression of Bcl-2 of 0.91(0.74-1.09). CONCLUSIONS: Both Bcl-2 and β(1)-integrin are independent prognostic factors in SCLC in this cohort although further validation is required to confirm their importance. A TMA of SCLC cases is feasible but challenging and an important tool for biomarker validation