On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

Local distinguishability of quantum states in infinite dimensional systems

We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states

Characterization of structural and immunological properties of a fusion protein between flagellin from Salmonella and lumazine synthase from Brucella

Aiming to combine the flexibility of Brucella lumazine synthase (BLS) to adapt different protein domains in a decameric structure and the capacity of BLS and flagellin to enhance the immunogenicity of peptides that are linked to their structure, we generated a chimeric protein (BLS-FliC131) by fusing flagellin from Salmonella in the N-termini of BLS. The obtained protein was recognized by anti-flagellin and anti-BLS antibodies, keeping the oligomerization capacity of BLS, without affecting the folding of the monomeric protein components determined by circular dichroism. Furthermore, the thermal stability of each fusion partner is conserved, indicating that the interactions that participate in its folding are not affected by the genetic fusion. Besides, either in vitro or in vivo using TLR5-deficient animals we could determine that BLS-FliC131 retains the capacity of triggering TLR5. The humoral response against BLS elicited by BLS-FliC131 was stronger than the one elicited by equimolar amounts of BLS + FliC. Since BLS scaffold allows the generation of hetero-decameric structures, we expect that flagellin oligomerization on this protein scaffold will generate a new vaccine platform with enhanced capacity to activate immune responsesFil: Hiriart, Yanina. Inmunova S.A; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Estudios Inmunológicos y Fisiopatológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Estudios Inmunológicos y Fisiopatológicos; ArgentinaFil: Rossi, Andrés Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Biedma, Marina Elizabeth. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Estudios Inmunológicos y Fisiopatológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Estudios Inmunológicos y Fisiopatológicos; ArgentinaFil: Errea, Agustina Juliana. Universidad Nacional de La Plata; Argentina. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Estudios Inmunológicos y Fisiopatológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Estudios Inmunológicos y Fisiopatológicos; ArgentinaFil: Moreno, Griselda Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Estudios Inmunológicos y Fisiopatológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Estudios Inmunológicos y Fisiopatológicos; ArgentinaFil: Cayet, D.. Universidad Nacional de La Plata; ArgentinaFil: Rinaldi, Jimena Julieta. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Blancá, Bruno Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Estudios Inmunológicos y Fisiopatológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Estudios Inmunológicos y Fisiopatológicos; ArgentinaFil: Sirard, J.C.. Centre National de la Recherche Scientifique; FranciaFil: Goldbaum, Fernando Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Berguer, Paula Mercedes. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Rumbo, Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Estudios Inmunológicos y Fisiopatológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Estudios Inmunológicos y Fisiopatológicos; Argentin

A study of the photometric variability of the peculiar magnetic white dwarf WD1953-011

We present and interpret simultaneous new photometric and spectroscopic observations of the peculiar magnetic white dwarf WD1953-011. The flux in the V-band filter and intensity of the Balmer spectral lines demonstrate variability with the rotation period of about 1.45 days. According to previous studies, this variability can be explained by the presence of a dark spot having a magnetic nature, analogous to a sunspot. Motivated by this idea, we examine possible physical relationships between the suggested dark spot and the strong-field magnetic structure (magnetic "spot", or "tube") recently identified on the surface of this star. Comparing the rotationally-modulated flux with the variable spectral observables related to the magnetic "spot" we establish their correlation, and therefore their physical relationship. Modeling the variable photometric flux assuming that it is associated with temperature variations in the stellar photosphere, we argue that the strong-field area and dark, low-temperature spot are comparable in size and located at the same latitudes, essentially overlapping each other with a possible slight longitudinal shift. In this paper we also present a new, improved value of the star's rotational period and constrain the characteristics of the thermal inhomogeneity over the degenerate's surface.Comment: accepted to the Ap

The SuperMACHO Microlensing Survey

We present the first results from our next-generation microlensing survey, the SuperMACHO project. We are using the CTIO 4m Blanco telescope and the MOSAIC imager to carry out a search for microlensing toward the Large Magellanic Cloud (LMC). We plan to ascertain the nature of the population responsible for the excess microlensing rate seen by the MACHO project. Our observing strategy is optimized to measure the differential microlensing rate across the face of the LMC. We find this derivative to be relatively insensitive to the details of the LMC's internal structure but a strong discriminant between Galactic halo and LMC self lensing. In December 2003 we completed our third year of survey operations. 2003 also marked the first year of real-time microlensing alerts and photometric and spectroscopic followup. We have extracted several dozen microlensing candidates, and we present some preliminary light curves and related information. Similar to the MACHO project, we find SNe behind the LMC to be a significant contaminant - this background has not been completely removed from our current single-color candidate sample. Our follow-up strategy is optimized to discriminate between SNe and true microlensing.Comment: To appear in Proceedings of IAU Symposium 225: Impact of Gravitational Lensing on Cosmology, 6 page

Multifrequency Photo-polarimetric WEBT Observation Campaign on the Blazar S5 0716+714: Source Microvariability and Search for Characteristic Timescales

Here we report on the results of the WEBT photo-polarimetric campaign targeting the blazar S5~0716+71, organized in March 2014 to monitor the source simultaneously in BVRI and near IR filters. The campaign resulted in an unprecedented dataset spanning $\sim 110$\,h of nearly continuous, multi-band observations, including two sets of densely sampled polarimetric data mainly in R filter. During the campaign, the source displayed pronounced variability with peak-to-peak variations of about $30\%$ and "bluer-when-brighter" spectral evolution, consisting of a day-timescale modulation with superimposed hourlong microflares characterized by $\sim 0.1$\,mag flux changes. We performed an in-depth search for quasi-periodicities in the source light curve; hints for the presence of oscillations on timescales of $\sim 3$\,h and $\sim 5$\,h do not represent highly significant departures from a pure red-noise power spectrum. We observed that, at a certain configuration of the optical polarization angle relative to the positional angle of the innermost radio jet in the source, changes in the polarization degree led the total flux variability by about 2\,h; meanwhile, when the relative configuration of the polarization and jet angles altered, no such lag could be noted. The microflaring events, when analyzed as separate pulse emission components, were found to be characterized by a very high polarization degree ($> 30\%$) and polarization angles which differed substantially from the polarization angle of the underlying background component, or from the radio jet positional angle. We discuss the results in the general context of blazar emission and energy dissipation models.Comment: 16 pages, 17 Figures; ApJ accepte

The Necessary and Sufficient Conditions for Representing Lipschitz Bivariate Functions as a Difference of Two Convex Functions

In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this algorithm is a sequence of pairs of convex functions that converge uniformly to a pair of convex functions if the conditions of the formulated theorems are satisfied. A geometric interpretation is also given