Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Functional Characterization of a Novel Frameshift Mutation in the C-terminus of the Nav1.5 Channel Underlying a Brugada Syndrome with Variable Expression in a Spanish Family.

INTRODUCTION We functionally analyzed a frameshift mutation in the SCN5A gene encoding cardiac Na(+) channels (Nav1.5) found in a proband with repeated episodes of ventricular fibrillation who presented bradycardia and paroxysmal atrial fibrillation. Seven relatives also carry the mutation and showed a Brugada syndrome with an incomplete and variable expression. The mutation (p.D1816VfsX7) resulted in a severe truncation (201 residues) of the Nav1.5 C-terminus. METHODS AND RESULTS Wild-type (WT) and mutated Nav1.5 channels together with hNavβ1 were expressed in CHO cells and currents were recorded at room temperature using the whole-cell patch-clamp. Expression of p.D1816VfsX7 alone resulted in a marked reduction (≈90%) in peak Na(+) current density compared with WT channels. Peak current density generated by p.D1816VfsX7+WT was ≈50% of that generated by WT channels. p.D1816VfsX7 positively shifted activation and inactivation curves, leading to a significant reduction of the window current. The mutation accelerated current activation and reactivation kinetics and increased the fraction of channels developing slow inactivation with prolonged depolarizations. However, late INa was not modified by the mutation. p.D1816VfsX7 produced a marked reduction of channel trafficking toward the membrane that was not restored by decreasing incubation temperature during cell culture or by incubation with 300 μM mexiletine and 5 mM 4-phenylbutirate. CONCLUSION Despite a severe truncation of the C-terminus, the resulting mutated channels generate currents, albeit with reduced amplitude and altered biophysical properties, confirming the key role of the C-terminal domain in the expression and function of the cardiac Na(+) channel.

Recombinant hepatitis C virus-envelope protein 2 interactions with low-density lipoprotein/CD81 receptors

Hepatitis C virus (HCV) envelope protein 2 (E2) is involved in viral binding to host cells. The aim of this work was to produce recombinant E2B and E2Y HCV proteins in Escherichia coli and Pichia pastoris, respectively, and to study their interactions with low-density lipoprotein receptor (LDLr) and CD81 in human umbilical vein endothelial cells (HUVEC) and the ECV304 bladder carcinoma cell line. To investigate the effects of human LDL and differences in protein structure (glycosylated or not) on binding efficiency, the recombinant proteins were either associated or not associated with lipoproteins before being assayed. The immunoreactivity of the recombinant proteins was analysed using pooled serum samples that were either positive or negative for hepatitis C. The cells were immunophenotyped by LDLr and CD81 using flow cytometry. Binding and binding inhibition assays were performed in the presence of LDL, foetal bovine serum (FCS) and specific antibodies. The results revealed that binding was reduced in the absence of FCS, but that the addition of human LDL rescued and increased binding capacity. In HUVEC cells, the use of antibodies to block LDLr led to a significant reduction in the binding of E2B and E2Y. CD81 antibodies did not affect E2B and E2Y binding. In ECV304 cells, blocking LDLr and CD81 produced similar effects, but they were not as marked as those that were observed in HUVEC cells. In conclusion, recombinant HCV E2 is dependent on LDL for its ability to bind to LDLr in HUVEC and ECV304 cells. These findings are relevant because E2 acts to anchor HCV to host cells; therefore, high blood levels of LDL could enhance viral infectivity in chronic hepatitis C patients.

Low postseroconversion CD4 count and rapid decrease of CD4 density identify HIV+ fast progressors.

CD4 expression in HIV replication is paradoxical: HIV entry requires high cell-surface CD4 densities, but replication requires CD4 down-modulation. However, is CD4 density in HIV+ patients affected over time? Do changes in CD4 density correlate with disease progression? Here, we examined the role of CD4 density for HIV disease progression by longitudinally quantifying CD4 densities on CD4+ T cells and monocytes of ART-naive HIV+ patients with different disease progression rates. This was a retrospective study. We defined three groups of HIV+ patients by their rate of CD4+ T cell loss, calculated by the time between infection and reaching a CD4 level of 200 cells/microl: fast (<7.5 years), intermediate (7.5-12 years), and slow progressors (>12 years). Mathematical modeling permitted us to determine the maximum CD4+ T cell count after HIV seroconversion (defined as "postseroconversion CD4 count") and longitudinal profiles of CD4 count and density. CD4 densities were quantified on CD4+ T cells and monocytes from these patients and from healthy individuals by flow cytometry. Fast progressors had significantly lower postseroconversion CD4 counts than other progressors. CD4 density on T cells was lower in HIV+ patients than in healthy individuals and decreased more rapidly in fast than in slow progressors. Antiretroviral therapy (ART) did not normalize CD4 density. Thus, postseroconversion CD4 counts define individual HIV disease progression rates that may help to identify patients who might benefit most from early ART. Early discrimination of slow and fast progressors suggests that critical events during primary infection define long-term outcome. A more rapid CD4 density decrease in fast progressors might contribute to progressive functional impairments of the immune response in advanced HIV infection. The lack of an effect of ART on CD4 density implies a persistent dysfunctional immune response by uncontrolled HIV infection.

Telomere length dynamics in human lymphocyte subpopulations measured by flow cytometry.

To measure the average length of telomere repeats at chromosome ends in individual cells we developed a flow cytometry method using fluorescence in situ hybridization (flow FISH) with labeled peptide nucleic acid (PNA) probes. Results of flow FISH measurements correlated with results of conventional telomere length measurements by Southern blot analysis (R = 0.9). Consistent differences in telomere length in CD8+ T-cell subsets were identified. Naive and memory CD4+ T lymphocytes in normal adults differed by around 2.5 kb in telomere length, in agreement with known replicative shortening of telomeres in lymphocytes in vivo. T-cell clones grown in vitro showed stabilization of telomere length after an initial decline and rare clones capable of growing beyond 100 population doublings showed variable telomere length. These results show that flow FISH can be used to measure specific nucleotide repeat sequences in single cells and indicate that the very large replicative potential of lymphocytes is only indirectly related to telomere length.

Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale

The development of susceptibility maps for debris flows is of primary importance due to population pressure in hazardous zones. However, hazard assessment by processbased modelling at a regional scale is difficult due to the complex nature of the phenomenon, the variability of local controlling factors, and the uncertainty in modelling parameters. A regional assessment must consider a simplified approach that is not highly parameter dependant and that can provide zonation with minimum data requirements. A distributed empirical model has thus been developed for regional susceptibility assessments using essentially a digital elevation model (DEM). The model is called Flow-R for Flow path assessment of gravitational hazards at a Regional scale (available free of charge under www.flow-r.org) and has been successfully applied to different case studies in various countries with variable data quality. It provides a substantial basis for a preliminary susceptibility assessment at a regional scale. The model was also found relevant to assess other natural hazards such as rockfall, snow avalanches and floods. The model allows for automatic source area delineation, given user criteria, and for the assessment of the propagation extent based on various spreading algorithms and simple frictional laws.We developed a new spreading algorithm, an improved version of Holmgren's direction algorithm, that is less sensitive to small variations of the DEM and that is avoiding over-channelization, and so produces more realistic extents. The choices of the datasets and the algorithms are open to the user, which makes it compliant for various applications and dataset availability. Amongst the possible datasets, the DEM is the only one that is really needed for both the source area delineation and the propagation assessment; its quality is of major importance for the results accuracy. We consider a 10m DEM resolution as a good compromise between processing time and quality of results. However, valuable results have still been obtained on the basis of lower quality DEMs with 25m resolution.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus (Diptera, Culicidae) by Bacillus thuringiensis var israelensis, related with temperature, density and concentration of insecticide

The dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus, (Diptera, Culicidae) by Bacillus thuringiensis var israelensis has been related with the temperature, density and concentration of the insecticide. A mathematical model for biological control of Aedes aegypti with Bacillus thuringiensis var israelensis (Bti) was constructed by using data from the literature regarding the biology of the vector. The life cycle was described by differential equations. Lethal concentrations (LC50 and LC95) of Bti were determined in the laboratory under different experimental conditions. Temperature, colony, larvae density and bioinsecticide concentration presented marked differences in the analysis of the whole set of variables; although when analyzed individually, only the temperature and concentration showed changes. The simulations indicated an inverse relationship between temperature and mosquito population, nonetheless, faster growth of populations is reached at higher temperatures. As conclusion, the model suggests the use of integrated control strategies for immature and adult mosquitoes in order to achieve a reduction of Aedes aegypti.

Are there vascular density gradients along myocardial laser channels?

BACKGROUND: Clinical studies suggest that transmyocardial laser revascularization may improve regional blood flow of the subendocardial layer. The vascular growth pattern of laser channels was analyzed. METHODS: Twenty pigs were randomized to undergo ligation of left marginal arteries (n = 5), to undergo transmyocardial laser revascularization of the left lateral wall (n = 5), to undergo both procedures (n = 5) or to a control group (n = 5). All the animals were sacrificed after 1 month. Computed morphometric analysis of vascular density of the involved area was expressed as number of vascular structures per square millimeter (+/-1 standard deviation). RESULTS: The vascular density of the scar tissue of the laser channel was significantly increased in comparison with myocardial infarction alone: 49.6+/-12.8/mm2 versus 25.5+/-8.6/mm2 (p < 0.0001). The vascular densities of subendocardial and subepicardial channel areas were similar: 52.9+/-16.8/mm2 versus 46.3+/-13.6/mm2 (p = 0.41). The area immediately adjacent to the channels showed a vascular density similar to that of normal tissue: 6.02+/-1.7/mm2 versus 5.2+/-1.9/mm2 (p = 0.08). In the infarction + transmyocardial laser revascularization group, the channels were indistinguishable from infarction scar. CONCLUSIONS: Scars of transmyocardial laser revascularization channels exhibit an increased vascular density in comparison with scar tissue of myocardial infarction, which does not extend into their immediate vicinity. There was no vascular density gradient along the longitudinal axis of the channels.

Variable phenotypic expressivity in a Swiss family with autosomal dominant retinitis pigmentosa due to a T494M mutation in the PRPF3 gene.

PURPOSE: To characterize the clinical, psychophysical, and electrophysiological phenotypes in a five-generation Swiss family with dominantly inherited retinitis pigmentosa caused by a T494M mutation in the Precursor mRNA-Processing factor 3 (PRPF3) gene, and to relate the phenotype to the underlying genetic mutation. METHODS: Eleven affected patients were ascertained for phenotypic and genotypic characterization. Ophthalmologic evaluations included color vision testing, Goldmann perimetry, and digital fundus photography. Some patients had autofluorescence imaging, Optical Coherence Tomography, and ISCEV-standard full-field electroretinography. All affected patients had genetic testing. RESULTS: The age of onset of night blindness and the severity of the progression of the disease varied between members of the family. Some patients reported early onset of night blindness at age three, with subsequent severe deterioration of visual acuity, which was 0.4 in the best eye after their fifties. The second group of patients had a later onset of night blindness, in the mid-twenties, with a milder disease progression and a visual acuity of 0.8 at age 70. Fundus autofluorescence imaging and electrophysiological and visual field abnormalities also showed some degree of varying phenotypes. The autofluorescence imaging showed a large high-density ring bilaterally. Myopia (range: -0.75 to -8) was found in 10/11 affected subjects. Fundus findings showed areas of atrophy along the arcades. A T494M change was found in exon 11 of the PRPF3 gene. The change segregates with the disease in the family. CONCLUSIONS: A mutation in the PRPF3 gene is rare compared to other genes causing autosomal dominant retinitis pigmentosa (ADRP). Although a T494M change has been reported, the family in our study is the first with variable expressivity. Mutations in the PRPF3 gene can cause a variable ADRP phenotype, unlike in the previously described Danish, English, and Japanese families. Our report, based on one of the largest affected pedigree, provides a better understanding as to the phenotype/genotype description of ADRP caused by a PRPF3 mutation.

Radio detections towards unidentified variable EGRET sources

A considerable fraction of the -ray sources discovered with the Energetic Gamma-Ray Experiment Telescope (EGRET) remain unidentified. The EGRET sources that have been properly identified are either pulsars or variable sources at both radio and gamma-ray wavelengths. Most of the variable sources are strong radio blazars. However, some low galactic-latitude EGRET sources, with highly variable -ray emission, lack any evident counterpart according to the radio data available until now. Aims. The primary goal of this paper is to identify and characterise the potential radio counterparts of four highly variable -ray sources in the galactic plane through mapping the radio surroundings of the EGRET confidence contours and determining the variable radio sources in the field whenever possible. Methods. We have carried out a radio exploration of the fields of the selected EGRET sources using the Giant Metrewave Radio Telescope (GMRT) interferometer at 21 cm wavelength, with pointings being separated by months. Results. We detected a total of 151 radio sources. Among them, we identified a few radio sources whose flux density has apparently changed on timescales of months. Despite the limitations of our search, their possible variability makes these objects a top-priority target for multiwavelength studies of the potential counterparts of highly variable, unidentified gamma-ray sources.

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).

Density modes in spherical 4He shells

We compute the density-fluctuation spectrum of spherical 4HeN shells adsorbed on the outer surface of Cn fullerenes. The excitation spectrum is obtained within the random-phase approximation, with particle-hole elementary excitations and effective interaction extracted from a density-functional description of the shell structure. The presence of one or two solid helium layers adjacent to the adsorbing fullerene is phenomenologically accounted for. We illustrate our results for a selection of numbers of adsorbed atoms on C20, C60, and C120. The hydrodynamical model that has proven successful to describe helium excitations in the bulk and in restricted geometries permits to perform a rather exhaustive analysis of various fluid spherical systems, namely, spheres, cavities, free bubbles, and bound shells of variable size.

Preserved capillary density of dorsal finger skin in treated hypertensive patients with or without type 2 diabetes.

OBJECTIVES: Capillary rarefaction is a hallmark of untreated hypertension. Recent data indicate that rarefaction may be reversed by antihypertensive treatment in nondiabetic hypertensive patients. Despite the frequent association of diabetes with hypertension, nothing is known on the capillary density of treated diabetic patients with hypertension. METHODS: We enrolled 21 normotensive healthy, 25 hypertensive only, and 21 diabetic (type 2) hypertensive subjects. All hypertensive patients were treated with a blocker of the renin-angiotensin system, and a majority had a home blood pressure ≤135/85 mmHg. Capillary density was assessed with videomicroscopy on dorsal finger skin and with laser Doppler imaging on forearm skin (maximal vasodilation elicited by local heating). RESULTS: There was no difference between any of the study groups in either dorsal finger skin capillary density (controls 101 ± 11 capillaries/mm(2) , nondiabetic hypertensive 99 ± 16, diabetic hypertensive 96 ± 18, p > 0.5) or maximal blood flow in forearm skin (controls 666 ± 114 perfusion units, nondiabetic hypertensive 612 ± 126, diabetic hypertensive 620 ± 103, p > 0.5). CONCLUSIONS: Irrespective of the presence or not of type 2 diabetes, capillary density is normal in hypertensive patients with reasonable control of blood pressure achieved with a blocker of the renin-angiotensin system.

Properties of debris flow deposits and source materials compared: implications for debris flow characterization

In the Alps, debris flow deposits generally contain < 5% clay-size particles, and the role of the surface-charged < 2 mu m particles is often neglected, although these particles may have a significant impact on the rheological properties of the interstitial fluid. The objective of this study was to compare debris flow deposits and parent materials from two neighbouring catchments of the Swiss Alps, with special emphasis on the colloidal constituents. The catchments are small in area (4 km(2)), 2.5 km long, similar in morphology, but different in geology. The average slopes are 35-40%. The catchments were monitored for debris flow events and mapped for surface aspect and erosion activity. Debris flow deposits and parent materials were sampled, the clay and silt fractions extracted and the bulk density, < 2 mm fraction bulk density, particle size distribution, chemical composition, cation exchange capacity (CEC) and mineralogy analysed. The results show that the deposits are similar to the parent screes in terms of chemical composition, but differ in terms of: (i) particle size distribution; and (ii) mineralogy, reactivity and density of the < 2 mm fraction. In this fraction, compared with the parent materials the deposits show dense materials enriched in coarse monocrystalline particles, of which the smallest and more reactive particles were leached. The results suggest that deposit samples should not be considered as representative of source or flow materials, particularly with respect to their physical properties.