Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

Effect of egg turning and incubation time on carbonic anhydrase gene expression in the blastoderm of the Japanese quail (Coturnix c. japonica)

(1) The gene expression of carbonic anhydrase, a key enzyme for the production sub-embryonic fluid (SEF), was assessed in turned and unturned eggs of the Japanese quail. The plasma membrane-associated isoforms CA IV, CAIX, CA XII, CA XIV, and the cytoplasmic isoform CA II, were investigated in the extra-embryonic tissue of the blastoderm and in embryonic blood. (2) Eggs were incubated at 37.6C, c. 60% R.H., and turned hourly (90 ) or left unturned. From 48 to 96 hours of incubation mRNA was extracted from blastoderm tissue, reverse-transcribed to cDNA and quantified by real-time qPCR using gene-specific primers. Blood collected at 96h was processed identically. (3) Blastoderm CAIV gene expression increased with the period of incubation only in turned eggs, with maxima at 84 and 96h of incubation. Only very low levels were found in blood. (4) Blastoderm CA II gene expression was greatest at 48 and 54h of incubation, subsequently declining to much lower levels and una ected by turning. Blood CA II gene expression was about 25-fold greater than that in the blastoderm. (5) The expression of CA IX in the blastoderm was the highest of all isoforms, yet unaffected by turning. CA XII did not amplify and CA XIV was present at unquantifiable low levels. (6) It is concluded that solely gene expression for CA IV is sensitive to egg turning, and that increased CA IV gene expression could account for the additional SEF mass found at 84-96h of incubation. in embryos of turned eggs

Standardized volumetric 3D-analysis of SPECT/CT imaging in orthopaedics: overcoming the limitations of qualitative 2D analysis

<p>Abstract</p> <p>Background</p> <p>SPECT/CT combines high resolution anatomical 3D computerized tomography (CT) and single photon emission computerized tomography (SPECT) as functional imaging, which provides 3D information about biological processes into a single imaging modality. The clinical utility of SPECT/CT imaging has been recognized in a variety of medical fields and most recently in orthopaedics; however, clinical adoption has been limited due to shortcomings of analytical tools available. Specifically, SPECT analyses are mainly qualitative due to variation in overall metabolic uptake among patients. Furthermore, most analyses are done in 2D, although rich 3D data are available. Consequently, it is difficult to quantitatively compare the position, size, and intensity of SPECT uptake regions among patients, and therefore difficult to draw meaningful clinical conclusions.</p> <p>Methods</p> <p>We propose a method for normalizing orthopaedic SPECT/CT data that enables standardised 3D volumetric quantitative measurements and comparison among patients. Our method is based on 3D localisation using clinically relevant anatomical landmarks and frames of reference, along with intensity value normalisation using clinically relevant reference regions. Using the normalised data, we describe a thresholding technique to distinguish clinically relevant hot spots from background activity.</p> <p>Results</p> <p>Using an exemplar comparison of two patients, we demonstrate how the normalised, 3D-rendered data can provide a richer source of clinical information and allow quantitative comparison of SPECT/CT measurements across patients. Specifically, we demonstrate how non-normalized SPECT/CT analysis can lead to different clinical conclusions than the normalized SPECT/CT analysis, and that normalized quantitative analysis can be a more accurate indicator of pathology.</p> <p>Conclusions</p> <p>Conventional orthopaedic frames of reference, 3D volumetric data analysis and thresholding are used to distinguish clinically relevant hot spots from background activity. Our goal is to facilitate a standardised approach to quantitative data collection and comparison of clinical studies using SPECT/CT, enabling more widespread clinical use of this powerful imaging tool.</p

A single sub-km Kuiper Belt object from a stellar Occultation in archival data

The Kuiper belt is a remnant of the primordial Solar System. Measurements of its size distribution constrain its accretion and collisional history, and the importance of material strength of Kuiper belt objects (KBOs). Small, sub-km sized, KBOs elude direct detection, but the signature of their occultations of background stars should be detectable. Observations at both optical and X-ray wavelengths claim to have detected such occultations, but their implied KBO abundances are inconsistent with each other and far exceed theoretical expectations. Here, we report an analysis of archival data that reveals an occultation by a body with a 500 m radius at a distance of 45 AU. The probability of this event to occur due to random statistical fluctuations within our data set is about 2%. Our survey yields a surface density of KBOs with radii larger than 250 m of 2.1^{+4.8}_{-1.7} x 10^7 deg^{-2}, ruling out inferred surface densities from previous claimed detections by more than 5 sigma. The fact that we detected only one event, firmly shows a deficit of sub-km sized KBOs compared to a population extrapolated from objects with r>50 km. This implies that sub-km sized KBOs are undergoing collisional erosion, just like debris disks observed around other stars.Comment: To appear in Nature on December 17, 2009. Under press embargo until 1800 hours London time on 16 December. 19 pages; 7 figure

Design principles for riboswitch function

Scientific and technological advances that enable the tuning of integrated regulatory components to match network and system requirements are critical to reliably control the function of biological systems. RNA provides a promising building block for the construction of tunable regulatory components based on its rich regulatory capacity and our current understanding of the sequence–function relationship. One prominent example of RNA-based regulatory components is riboswitches, genetic elements that mediate ligand control of gene expression through diverse regulatory mechanisms. While characterization of natural and synthetic riboswitches has revealed that riboswitch function can be modulated through sequence alteration, no quantitative frameworks exist to investigate or guide riboswitch tuning. Here, we combined mathematical modeling and experimental approaches to investigate the relationship between riboswitch function and performance. Model results demonstrated that the competition between reversible and irreversible rate constants dictates performance for different regulatory mechanisms. We also found that practical system restrictions, such as an upper limit on ligand concentration, can significantly alter the requirements for riboswitch performance, necessitating alternative tuning strategies. Previous experimental data for natural and synthetic riboswitches as well as experiments conducted in this work support model predictions. From our results, we developed a set of general design principles for synthetic riboswitches. Our results also provide a foundation from which to investigate how natural riboswitches are tuned to meet systems-level regulatory demands

Constraints on the opacity of spiral disks from near-infrared observations

In this paper I review how near-infrared (NIR) observations can constrain the opacity of spiral disks. Basic considerations show that NIR photometry provides a powerful probe of the optical depths in spiral galaxy disks in the regime of interest, where the optical depth in the V-band is near unity. I review the existing opacity constraints from the analysis of dust lanes in edge-on and face-on galaxies. The ``internal extinction correction" in the NIR-Tully-Fisher relation deserves particular attention as the most powerful constraint on the impact of dust on the total luminosity of spiral galaxies. All observations for luminous spirals point towards an effective, face-on optical depth of tau_V=0.5-1

Unchanged incidence and increased survival in children with neuroblastoma in Denmark 1981–2000: a population-based study

Treatment results for neuroblastoma in Denmark have been poorer than in other Nordic countries, so we investigated whether a change in incidence, stage distribution and survival had occurred between 1981 and 2000. Clinical data were retrieved from the medical charts of 160 children <15 years of age with extra-cranial neuroblastoma (n=139) or ganglioneuroblastoma (n=21) diagnosed in Denmark between 1981 and 2000. The minimal follow-up time was 52 months. Statistical analyses were performed in STATA. The incidence was 8.55 per million children below 15 years of age (world standard 9.6) and 42.6 per million children below 12 months of age, and it has remained unchanged since 1970. The median age at diagnosis was 27 months. In all, 32% of the children were aged below 12 months at diagnosis, 53% had metastatic disease and in 12% the diagnosis was made incidentally. Prognostic factors such as age, stage and site of primary tumour were the same as in other studies and did not change. During the study period, the mortality rate decreased steadily, and the 5-year survival rate increased from 38% in 1981–1985 to 59% in 1996–2000, corresponding to the level found in other Western countries. Increased survival was also seen in children with metastatic disease. Participation in international studies, better supportive care and possibly postoperative autologous stem cell transplantation may have contributed to the increased survival

Genome-Scale Validation of Deep-Sequencing Libraries

Chromatin immunoprecipitation followed by high-throughput (HTP) sequencing (ChIP-seq) is a powerful tool to establish protein-DNA interactions genome-wide. The primary limitation of its broad application at present is the often-limited access to sequencers. Here we report a protocol, Mab-seq, that generates genome-scale quality evaluations for nucleic acid libraries intended for deep-sequencing. We show how commercially available genomic microarrays can be used to maximize the efficiency of library creation and quickly generate reliable preliminary data on a chromosomal scale in advance of deep sequencing. We also exploit this technique to compare enriched regions identified using microarrays with those identified by sequencing, demonstrating that they agree on a core set of clearly identified enriched regions, while characterizing the additional enriched regions identifiable using HTP sequencing

Ultraviolet Irradiation Induces the Accumulation of Chondroitin Sulfate, but Not Other Glycosaminoglycans, in Human Skin

Ultraviolet (UV) light alters cutaneous structure and function. Prior work has shown loss of dermal hyaluronan after UV-irradiation of human skin, yet UV exposure increases total glycosaminoglycan (GAG) content in mouse models. To more fully describe UV-induced alterations to cutaneous GAG content, we subjected human volunteers to intermediate-term (5 doses/week for 4 weeks) or single-dose UV exposure. Total dermal uronyl-containing GAGs increased substantially with each of these regimens. We found that UV exposure substantially increased dermal content of chondroitin sulfate (CS), but not hyaluronan, heparan sulfate, or dermatan sulfate. UV induced the accumulation of both the 4-sulfated (C4S) and 6-sulfated (C6S) isoforms of CS, but in distinct distributions. Next, we examined several CS proteoglycan core proteins and found a significant accumulation of dermal and endothelial serglycin, but not of decorin or versican, after UV exposure. To examine regulation in vitro, we found that UVB in combination with IL-1α, a cytokine upregulated by UV radiation, induced serglycin mRNA in cultured dermal fibroblasts, but did not induce the chondroitin sulfate synthases. Overall, our data indicate that intermediate-term and single-dose UVB exposure induces specific GAGs and proteoglycan core proteins in human skin in vivo. These molecules have important biologic functions and contribute to the cutaneous response to UV