Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics.

Generation of a tightly regulated all-cis beta cell-specific tetracycline-inducible vector.

Ability to induce protein expression at will in a cell is a powerful strategy used by scientists to better understand the function of a protein of interest. Various inducible systems have been designed in eukaryotic cells to achieve this goal. Most of them rely on two distinct vectors, one encoding a protein that can regulate transcription by binding a compound X, and one hosting the cDNA encoding the protein of interest placed downstream of promoter sequences that can bind the protein regulated by compound X (e.g., tetracycline, ecdysone). The commercially available systems are not designed to allow cell- or tissue-specific regulated expression. Additionally, although these systems can be used to generate stable clones that can be induced to express a given protein, extensive screening is often required to eliminate the clones that display poor induction or high basal levels. In the present report, we aimed to design a pancreatic beta cell-specific tetracycline-inducible system. Since the classical two-vector based tetracycline-inducible system proved to be unsatisfactory in our hands, a single vector was eventually designed that allowed tight beta cell-specific tetracycline induction in unselected cell populations.

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

Real interpolation for families of Banach spaces (II)

In this paper, we study the dual space and reiteration theorems for the real method of interpolation for infinite families of Banach spaces introduced in [2]. We also give examples of interpolation spaces constructed with this method.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Monitoring network optimisation for spatial data classification using support vector machines

The paper presents a novel method for monitoring network optimisation, based on a recent machine learning technique known as support vector machine. It is problem-oriented in the sense that it directly answers the question of whether the advised spatial location is important for the classification model. The method can be used to increase the accuracy of classification models by taking a small number of additional measurements. Traditionally, network optimisation is performed by means of the analysis of the kriging variances. The comparison of the method with the traditional approach is presented on a real case study with climate data.

Individual prediction of cognitive decline in mild cognitive impairment using support vector machine-based analysis of diffusion tensor imaging data.

Although cross-sectional diffusion tensor imaging (DTI) studies revealed significant white matter changes in mild cognitive impairment (MCI), the utility of this technique in predicting further cognitive decline is debated. Thirty-five healthy controls (HC) and 67 MCI subjects with DTI baseline data were neuropsychologically assessed at one year. Among them, there were 40 stable (sMCI; 9 single domain amnestic, 7 single domain frontal, 24 multiple domain) and 27 were progressive (pMCI; 7 single domain amnestic, 4 single domain frontal, 16 multiple domain). Fractional anisotropy (FA) and longitudinal, radial, and mean diffusivity were measured using Tract-Based Spatial Statistics. Statistics included group comparisons and individual classification of MCI cases using support vector machines (SVM). FA was significantly higher in HC compared to MCI in a distributed network including the ventral part of the corpus callosum, right temporal and frontal pathways. There were no significant group-level differences between sMCI versus pMCI or between MCI subtypes after correction for multiple comparisons. However, SVM analysis allowed for an individual classification with accuracies up to 91.4% (HC versus MCI) and 98.4% (sMCI versus pMCI). When considering the MCI subgroups separately, the minimum SVM classification accuracy for stable versus progressive cognitive decline was 97.5% in the multiple domain MCI group. SVM analysis of DTI data provided highly accurate individual classification of stable versus progressive MCI regardless of MCI subtype, indicating that this method may become an easily applicable tool for early individual detection of MCI subjects evolving to dementia.

Optimal priming of poxvirus vector (NYVAC)-based HIV vaccine regimens requires 3 DNA injections. Results of the EV03/ANRS Vac20 Phase I/II Trial

Background: Two or three DNA primes have been used in previous smaller clinical trials, but the number required for optimal priming of viral vectors has never been assessed in adequately powered clinical trials. The EV03/ANRS Vac20 phase I/II trial investigated this issue using the DNA prime/poxvirus NYVAC boost combination, both expressing a common HIV-1 clade C immunogen consisting of Env and Gag-Pol-Nef polypeptide. Methods: 147 healthy volunteers were randomly allocated through 8 European centres to either 3xDNA plus 1xNYVAC (weeks 0, 4, 8 plus 24; n¼74) or to 2xDNA plus 2xNYVAC (weeks 0, 4 plus 20, 24; n¼73), stratified by geographical region and sex. T cell responses were quantified using the interferon g Elispot assay and 8 peptide pools; samples from weeks 0, 26 and 28 (time points for primary immunogenicity endpoint), 48 and 72 were considered for this analysis. Results: 140 of 147 participants were evaluable at weeks 26 and/ or 28. 64/70 (91%) in the 3xDNA arm compared to 56/70 (80%) in the 2xDNA arm developed a T cell response (P¼0.053). 26 (37%) participants of the 3xDNA arm developed a broader T cell response (Env plus at least to one of the Gag, Pol, Nef peptide pools) versus 15 (22%) in the 2xDNA arm (P¼0.047). At week 26, the overall magnitude of responses was also higher in the 3xDNA than in the 2xDNA arm (similar at week 28), with a median of 545 versus 328 SFUs/106 cells at week 26 (P<0.001). Preliminary overall evaluation showed that participants still developed T-cell response at weeks 48 (78%, n¼67) and 72 (70%, n¼66). Conclusion: This large clinical trial demonstrates that optimal priming of poxvirus-based vaccine regimens requires 3 DNA regimens and further confirms that the DNA/NYVAC prime boost vaccine combination is highly immunogenic and induced durable T-cell responses.

Chemodiversity and molecular plasticity: recognition processes as explored by property spaces.

In the last few years, a need to account for molecular flexibility in drug-design methodologies has emerged, even if the dynamic behavior of molecular properties is seldom made explicit. For a flexible molecule, it is indeed possible to compute different values for a given conformation-dependent property and the ensemble of such values defines a property space that can be used to describe its molecular variability; a most representative case is the lipophilicity space. In this review, a number of applications of lipophilicity space and other property spaces are presented, showing that this concept can be fruitfully exploited: to investigate the constraints exerted by media of different levels of structural organization, to examine processes of molecular recognition and binding at an atomic level, to derive informative descriptors to be included in quantitative structure--activity relationships and to analyze protein simulations extracting the relevant information. Much molecular information is neglected in the descriptors used by medicinal chemists, while the concept of property space can fill this gap by accounting for the often-disregarded dynamic behavior of both small ligands and biomacromolecules. Property space also introduces some innovative concepts such as molecular sensitivity and plasticity, which appear best suited to explore the ability of a molecule to adapt itself to the environment variously modulating its property and conformational profiles. Globally, such concepts can enhance our understanding of biological phenomena providing fruitful descriptors in drug-design and pharmaceutical sciences.