Correspondence between the one-loop three-point vertex and the Y and Delta electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Two alpha subunits and one beta subunit of meprin zinc-endopeptidases are differentially expressed in the zebrafish Danio rerio

Meprins are members of the astacin family of metalloproteases expressed in epithelial tissues, intestinal leukocytes and certain cancer cells. In mammals, there are two homologous subunits, which form complex glycosylated disulfide-bonded homo- and heterooligomers. Both human meprin alpha and meprin beta cleave several basement membrane components, suggesting a role in epithelial differentiation and cell migration. There is also evidence that meprin beta is involved in immune defence owing to its capability of activating interleukin-1beta and the diminished mobility of intestinal leukocytes in meprin beta-knockout mice. Here we show for the first time by reverse transcription PCR, immunoblotting and immunofluorescence analyses that meprins are expressed not only in mammals, but also in the zebrafish Danio rerio. In contrast to the human, mouse and rat enzymes, zebrafish meprins are encoded by three genes, corresponding to two homologous alpha subunits and one beta subunit. Observations at both the mRNA and protein level indicate a broad distribution of meprins in zebrafish. However, there are strikingly different expression patterns of the three subunits, which is consistent with meprin expression in mammals. Hence, D. rerio appears to be a suitable model to gain insight into the basic physiological functions of meprin metalloproteases.

Results of the Technical Validation of an Accessible Contact Manager for Mobile Devices

The apparition of new mobile phones operating systems often leads to a flood of mobile applications rushing into the market without taking into account needs of the most vulnerable users groups: the people with disabilities. The need of accessible applications for mobile is very important especially when it comes to access basic mobile functions such as making calls through a contact manager. This paper presents the technical validation process and results of an Accessible Contact Manager for mobile phones as a part of the evaluation of accessible applications for mobile phones for people with disabilities.

Selectively enhanced contextual fear conditioning in mice lacking the transcriptional regulator CCAAT/enhancer binding protein δ

CCAAT/enhancer binding protein δ (C/EBPδ) is a transcriptional regulator implicated in the hepatic acute phase response and in adipogenic and myeloid cell differentiation. We found that C/EBPδ is widely expressed in the peripheral and central nervous systems, including neurons of the hippocampal formation, indicating a role in neural functions. To examine the role of C/EBPδ in vivo, we generated mice with a targeted deletion of the C/EBPδ gene. This mutation does not interfere with normal embryonic and postnatal development. Performance in a battery of behavioral tests indicates that basic neurological functions are normal. Furthermore, performance in a Morris water maze task suggests that C/EBPδ mutant mice have normal spatial learning. However, in the contextual and auditory-cue-conditioned fear task, C/EBPδ null mice displayed significantly more conditioned freezing to the test context than did wild-type controls, but equivalent conditioning to the auditory cue. These data demonstrate a selectively enhanced contextual fear response in mice carrying a targeted genomic mutation and implicate C/EBPδ in the regulation of a specific type of learning and memory.

Targeted disruption of the Rad51 gene leads to lethality in embryonic mice.

The mouse Rad51 gene is a mammalian homologue of the Escherichia coli recA and yeast RAD51 genes, both of which are involved in homologous recombination and DNA repair. To elucidate the physiological role of RAD51 protein, the gene was targeted in embryonic stem (ES) cells. Mice heterozygous for the Rad51 null mutation were intercrossed and their offspring were genotyped. There were no homozygous (Rad51-/-) pups among 148 neonates examined but a few Rad51-/- embryos were identified when examined during the early stages of embryonic development. Doubly knocked-out ES cells were not detected under conditions of selective growth. These results are interpreted to mean that RAD51 protein plays an essential role in the proliferation of cell. The homozygous Rad51 null mutation can be categorized in cell-autonomous defects. Pre-implantational lethal mutations that disrupt basic molecular functions will thus interfere with cell viability.

Identificação de sistemas para o estudo de controle motor.

Qualquer tarefa motora ativa se dá pela ativação de uma população de unidades motoras. Porém, devido a diversas dificuldades, tanto técnicas quanto éticas, não é possível medir a entrada sináptica dos motoneurônios em humanos. Por essas razões, o uso de modelos computacionais realistas de um núcleo de motoneurônios e as suas respectivas fibras musculares tem um importante papel no estudo do controle humano dos músculos. Entretanto, tais modelos são complexos e uma análise matemática é difícil. Neste texto é apresentada uma abordagem baseada em identificação de sistemas de um modelo realista de um núcleo de unidades motoras, com o objetivo de obter um modelo mais simples capaz de representar a transdução das entradas do núcleo de unidades motoras na força do músculo associado ao núcleo. A identificação de sistemas foi baseada em um algoritmo de mínimos quadrados ortogonal para achar um modelo NARMAX, sendo que a entrada considerada foi a condutância sináptica excitatória dendrítica total dos motoneurônios e a saída foi a força dos músculos produzida pelo núcleo de unidades motoras. O modelo identificado reproduziu o comportamento médio da saída do modelo computacional realista, mesmo para pares de sinal de entrada-saída não usados durante o processo de identificação do modelo, como sinais de força muscular modulados senoidalmente. Funções de resposta em frequência generalizada do núcleo de motoneurônios foram obtidas do modelo NARMAX, e levaram a que se inferisse que oscilações corticais na banda-beta (20 Hz) podem influenciar no controle da geração de força pela medula espinhal, comportamento do núcleo de motoneurônios até então desconhecido.

Molecular introduction to head and neck cancer (HNSCC) carcinogenesis

Of all human cancers, HNSCC is the most distressing affecting pain, disfigurement, speech and the basic survival functions of breathing and swallowing. Mortality rates have not significantly changed in the last 40 years despite advances in radiotherapy and surgical treatment. Molecular markers are currently being identified that can determine prognosis preoperatively by routine tumour biopsy Leading to improved management of HNSCC patients. The approach could help decide which early stage patient should have adjuvant neck dissection and radiotherapy, and whether Later stage patients with operable lesions would benefit from resection and reconstructive surgery or adopt a conservative approach to patients with poor prognosis regardless of treatment. In the future, understanding these basic genetic changes in HNSCC would be important for the management of HNSCC. (C) 2004 The British Association of Plastic Surgeons. Published by Elsevier Ltd. All rights reserved.

Novel markers for poor prognosis in head and neck cancer

Head and neck cancer (HNSCC) is one of the most distressing human cancers, causing pain and affecting the basic survival functions of breathing and swallowing. Mortality rates have not changed despite recent advances in radiotherapy and surgical treatment. We have compared the expression of over 13,000 unique genes in 7 cases of matched HNSCC and normal oral mucosa. Of the 1,260 genes that showed statistically significant differences in expression between normal and tumor tissue at the mRNA level, the three top ranking of the top 5% were selected for further analysis by immunohistochemistry on paraffin sections,. along with the tumor suppressor genes p16 and p53, in a total of 62 patients including 55 for whom >4-year clinical data was available. Using univariate and multivariate survival analysis, we identified SPARC/osteonectin as a powerful independent prognostic marker for short disease-free interval (DFI) (p < 0.002) and poor overall survival (OS) (p = 0.018) of HNSCC patients. In combination with other ECM proteins found in our analysis, PAI-1 and uPA, the association with DFI and OS became even more significant (p < 0.001). Our study represents the first instance of SPARC as an independent prognostic marker in HNSCC.

Mining-associated Seismicity in Kolar Gold Mines: Some Case Studies using Multi-fractals

The occurrence of rockbursts was quite common during active mining periods in the Champion reef mines of Kolar gold fields, India. Among the major rockbursts, the ‘area-rockbursts’ were unique both in regard to their spatio-temporal distribution and the extent of damage caused to the mine workings. A detailed study of the spatial clustering of 3 major area-rockbursts (ARB) was carried out using a multi-fractal technique involving generalized correlation integral functions. The spatial distribution analysis of all 3 area-rockbursts showed that they are heterogeneous. The degree of heterogeneity (D2 – D∞) in the cases of ARB-I, II and III were found to be 0.52, 0.37 and 0.41 respectively. These differences in fractal structure indicate that the ARBs of the present study were fully controlled by different heterogeneous stress fields associated with different mining and geological conditions. The present study clearly showed the advantages of the application of multi-fractals to seismic data and to characterise, analyse and examine the area-rockbursts and their causative factors in the Kolar gold mines.

Further Generalization of Kobayashi's Gamma Function

In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)

Reliability for Beta Models

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper we consider some of these distributions and derive the corresponding forms for the reliability R. The calculations involve the use of various special functions.

Temperature-averaged and total free-free Gaunt factors for κ and Maxwellian distributions of electrons

Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by κ-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than 10−10 in units of z2Ry. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the κ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing κ. Tables of these Gaunt factors are provided.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.