On real analytic functions of unbounded type

In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space. RESUMEN. Los autores demuestran varios resultados de existencia de funciones analíticas en espacios de Banach reales de dimensión infinita que están acotadas en un colección de subconjuntos abiertos y no acotadas en los conjuntos de otra colección. Además, se demuestra la densidad de ciertos subconjuntos de funciones analíticas para varias topologías localmente convexas.

Inference and optimization of real edges on sparse graphs:A statistical physics perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory. © 2007 The American Physical Society.

Lessons learned from INTAMAP, an interoperable web service for the real-time interpolation of environmental variables

Interpolated data are an important part of the environmental information exchange as many variables can only be measured at situate discrete sampling locations. Spatial interpolation is a complex operation that has traditionally required expert treatment, making automation a serious challenge. This paper presents a few lessons learnt from INTAMAP, a project that is developing an interoperable web processing service (WPS) for the automatic interpolation of environmental data using advanced geostatistics, adopting a Service Oriented Architecture (SOA). The “rainbow box” approach we followed provides access to the functionality at a whole range of different levels. We show here how the integration of open standards, open source and powerful statistical processing capabilities allows us to automate a complex process while offering users a level of access and control that best suits their requirements. This facilitates benchmarking exercises as well as the regular reporting of environmental information without requiring remote users to have specialized skills in geostatistics.

On Averaging Null Sequences of Real-Valued Functions

If ξ is a countable ordinal and (fk) a sequence of real-valued functions we define the repeated averages of order ξ of (fk). By using a partition theorem of Nash-Williams for families of finite subsets of positive integers it is proved that if ξ is a countable ordinal then every sequence (fk) of real-valued functions has a subsequence (f'k) such that either every sequence of repeated averages of order ξ of (f'k) converges uniformly to zero or no sequence of repeated averages of order ξ of (f'k) converges uniformly to zero. By the aid of this result we obtain some results stronger than Mazur’s theorem.

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Application of Fuzzy Variables for Systems of Management Decision Support

The following article describes an approach covering the variety of opinions and uncertainties of estimates within the chosen technique of decision support. Mathematical operations used for assessment of options are traced to operations of working with functions that are used for assessment of possible options of decision-making. Approach proposed could be used within any technique of decision support based on elementary mathematical operations. In this article the above-mentioned approach is described under analytical hierarchy process.

A Panel Data Investigation of Real Exchange Rate Misalignment and Growth

The paper investigates the role of real exchange rate misalignment on long-run growth for a set of ninety countries using time series data from 1980 to 2004. We first estimate a panel data model (using fixed and random effects) for the real exchange rate, with different model specifications, in order to produce estimates of the equilibrium real exchange rate and this is then used to construct measures of real exchange rate misalignment. We also provide an alternative set of estimates of real exchange rate misalignment using panel cointegration methods. The variables used in our real exchange rate models are: real per capita GDP; net foreign assets; terms of trade and government consumption. The results for the two-step System GMM panel growth models indicate that the coefficients for real exchange rate misalignment are positive for different model specification and samples, which means that a more depreciated (appreciated) real exchange rate helps (harms) long-run growth. The estimated coefficients are higher for developing and emerging countries.

Further evidence on the statistical properties of real GNP

The well-known lack of power of unit root tests has often been attributed to the shortlength of macroeconomic variables and also to DGP s that depart from the I(1)-I(0)alternatives. This paper shows that by using long spans of annual real GNP and GNPper capita (133 years) high power can be achieved, leading to the rejection of both theunit root and the trend-stationary hypothesis. This suggests that possibly neither modelprovides a good characterization of these data. Next, more flexible representations areconsidered, namely, processes containing structural breaks (SB) and fractional ordersof integration (FI). Economic justification for the presence of these features in GNP isprovided. It is shown that the latter models (FI and SB) are in general preferred to theARIMA (I(1) or I(0)) ones. As a novelty in this literature, new techniques are appliedto discriminate between FI and SB models. It turns out that the FI specification ispreferred, implying that GNP and GNP per capita are non-stationary, highly persistentbut mean-reverting series. Finally, it is shown that the results are robust when breaksin the deterministic component are allowed for in the FI model. Some macroeconomicimplications of these findings are also discussed.

On the configuration of Herman rings of meromorphic functions

We prove some results concerning the possible configuration s of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period a nd give a sufficient condition for a configuration to be realizable.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

A nonparametric method for the measurement of size diversity with emphasis on data standardization

The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposedas the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where kis the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

Thermal and air conditions inside animal facilities change during the day due to the influence of the external environment. For statistical and geostatistical analyses to be representative, a large number of points spatially distributed in the facility area must be monitored. This work suggests that the time variation of environmental variables of interest for animal production, monitored within animal facility, can be modeled accurately from discrete-time records. The aim of this study was to develop a numerical method to correct the temporal variations of these environmental variables, transforming the data so that such observations are independent of the time spent during the measurement. The proposed method approached values recorded with time delays to those expected at the exact moment of interest, if the data were measured simultaneously at the moment at all points distributed spatially. The correction model for numerical environmental variables was validated for environmental air temperature parameter, and the values corrected by the method did not differ by Tukey's test at 5% significance of real values recorded by data loggers.

Novel Functions of ErbB4 and NRG-1 in Development and Cancer

Cells communicate, or signal, with each other constantly to ensure proper functioning of tissues and organs. Cell signaling is often performed by interplay of receptors and ligands that bind these receptors. ErbB receptors (epidermal growth factor receptors, EGFR, HER) bind extracellular growth factors and transduce these signals inside of cells. ErbB dysfunction promotes carcinogenesis, and also results in numerous defects during normal development. This study focused on the functions of one member of the ErbB receptor family, ErbB4, and growth factor, neuregulin-1 (NRG-1), that can bind and activate ErbB4. This study aimed to find novel functions of ErbB4 and NRG-1. Hypoxia, or deficiency of oxygen, is common in cancer and ischemic conditions. One of the key findings of the work was the identification and characterization of a cross-talk between ErbB4 and Hypoxia-inducible factor 1α (HIF-1α), the central mediator of hypoxia signaling. ErbB4 activation by NRG-1 was found to increase HIF-1α activity. Interestingly, this regulation occurred in reciprocal manner as HIF-1α was also able to increase protein levels of NRG-1 and ErbB4. Moreover, expression of NRG-1 and ErbB4 was associated with HIF activity in vivo in human clinical samples and in mice. Reduction of functional ErbB4 in developing zebrafish embryos resulted in defects in development of the skeletal muscles. To study ErbB4 functions in pathological situation in humans, clinical samples of serous ovarian carcinoma were analyzed using tissue microarrays and real-time RT-PCR. A specific isoform of ErbB4, CYT-1, was associated with poor survival in serous ovarian cancer and increased anchorage independent growth of ovarian cancer cells in vitro. These observations demonstrate that ErbB4 and NRG-1 are essential regulators of cellular response to hypoxia, of development, and of ovarian carcinogenesis.

Silencing HIF-1α reduces the adhesion and secretion functions of acute leukemia hBMSCs

Hypoxia inducible factor-1α (HIF-1α) is an important transcription factor, which plays a critical role in the formation of solid tumor and its microenviroment. The objective of the present study was to evaluate the expression and function of HIF-1α in human leukemia bone marrow stromal cells (BMSCs) and to identify the downstream targets of HIF-1α. HIF-1α expression was detected at both the RNA and protein levels using real-time PCR and immunohistochemistry, respectively. Vascular endothelial growth factor (VEGF) and stromal cell-derived factor-1α (SDF-1α) were detected in stromal cells by enzyme-linked immunosorbent assay. HIF-1α was blocked by constructing the lentiviral RNAi vector system and infecting the BMSCs. The Jurkat cell/BMSC co-cultured system was constructed by putting the two cells into the same suitable cultured media and conditions. Cell adhesion and secretion functions of stromal cells were evaluated after transfection with the lentiviral RNAi vector of HIF-1α. Increased HIF-1α mRNA and protein was detected in the nucleus of the acute myeloblastic and acute lymphoblastic leukemia compared with normal BMSCs. The lentiviral RANi vector for HIF-1α was successfully constructed and was applied to block the expression of HIF-1α. When HIF-1α of BMSCs was blocked, the expression of VEGF and SDF-1 secreted by stromal cells were decreased. When HIF-1α was blocked, the co-cultured Jurkat cell’s adhesion and migration functions were also decreased. Taken together, these results suggest that HIF-1α acts as an important transcription factor and can significantly affect the secretion and adhesion functions of leukemia BMSCs.