A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.

Accurate WKB Approximation for a 1D Problem with Low Regularity

2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

Special compositions in affinely connected spaces without a torsion

2000 Mathematics Subject Classification: 53B05, 53B99.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

Applicazione ai gruppi di Lie della prolungabilità per Equazioni Differenziali Ordinarie

Lo scopo di questa tesi è studiare in dettaglio l'articolo "A Completeness Result for Time-Dependent Vector Fields and Applications" di Stefano Biagi e Andrea Bonfiglioli, dove si ottiene una condizione sufficiente per la completezza di un campo vettoriale (dipendente dal tempo) in RN, che generalizza la ben nota condizione di invarianza a sinistra per i gruppi di Lie.

Truncation identities for the small polaron fusion hierarchy

We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions; the latter case includes the presence of Grassmann valued non-diagonal boundary fields breaking the bulk U(1) symmetry of the model. Starting from the embedding of this model into a graded Yang-Baxter algebra, an infinite hierarchy of commuting transfer matrices is constructed by means of a fusion procedure. For certain values of the coupling constant related to anisotropies of the underlying vertex model taken at roots of unity, this hierarchy is shown to truncate giving a finite set of functional equations for the spectrum of the transfer matrices. For generic coupling constants, the spectral problem is formulated in terms of a functional (or TQ-)equation which can be solved by Bethe ansatz methods for periodic and diagonal open boundary conditions. Possible approaches for the solution of the model with generic non-diagonal boundary fields are discussed.

Finite time extinction for nonlinear fractional evolution equations and related properties

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Finite time extinction for nonlinear fractional evolution equations and related properties.

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Desenvolvimento de nanosistemas farmacêuticos para terapia gênica

Gene therapy is one of the major challenges of the post-genomic research and it is based on the transfer of genetic material into a cell, tissue or organ in order to cure or improve the patient s clinical status. In general, gene therapy consists in the insertion of functional genes aiming substitute, complement or inhibit defective genes. The achievement of a foreigner DNA expression into a population of cells requires its transfer to the target. Therefore, a key issue is to create systems, vectors, able to transfer and protect the DNA until it reaches the target. The disadvantages related to the use of viral vectors have encouraged efforts to develop emulsions as non-viral vectors. In fact, they are easy to produce, present suitable stability and enable transfection. The aim of this work was to evaluate two different non-viral vectors, cationic liposomes and nanoemulsions, and the possibility of their use in gene therapy. For the two systems, cationic lipids and helper lipids were used. Nanoemulsions were prepared using sonication method and were composed of Captex® 355; Tween® 80; Spam® 80; cationic lipid, Stearylamine (SA) or 1,2-dioleoyl-3-trimethylammoniumpropane (DOTAP) and water (Milli-Q®). These systems were characterized by average droplet size, Polidispersion Index (PI) and Zeta Potential. The stability of the systems; as well as the DNA compaction capacity; their cytotoxicity and the cytotoxicity of the isolated components; and their transfection capacity; were also evaluated. Liposomes were made by hydration film method and were composed of DOTAP; 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE), containing or not Rhodaminephosphatidylethanolamine (PE- Rhodamine) and the conjugate Hyaluronic Acid DOPE (HA-DOPE). These systems were also characterized as nanoemulsions. Stability of the systems and the influence of time, size of plasmid and presence or absence of endotoxin in the formation of lipoplexes were also analyzed. Besides, the ophthalmic biodistribution of PE-Rhodamine containing liposomes was studied after intravitreal injection. The obtained results show that these systems are promising non-viral vector for further utilization in gene therapy and that this field seems to be very important in the clinical practice in this century. However, from the possibility to the practice, there is still a long way

Life-history traits of Spodoptera frugiperda populations exposed to low-dose Bt maize.

Exposure to Bacillus thuringiensis (Bt) toxins in low- and moderate-dose transgenic crops may induce sublethal effects and increase the rate of Bt resistance evolution, potentially compromising control efficacy against target pests. We tested this hypothesis using the fall armyworm Spodoptera frugiperda, a major polyphagous lepidopteran pest relatively tolerant to Bt notorious for evolving field-relevant resistance to single-gene Bt maize. Late-instar larvae were collected from Bt Cry1Ab and non-Bt maize fields in five locations in Brazil, and their offspring was compared for survival, development, and population growth in rearing environment without and with Cry1Ab throughout larval development. Larval survival on Cry1Ab maize leaves varied from 20 to 80% among the populations. Larvae reared on Cry1Ab maize had seven-day delay in development time in relation to control larvae, and such delay was shorter in offspring of armyworms from Cry1Ab maize. Population growth rates were 50?70% lower for insects continuously exposed to Cry1Ab maize relative to controls, showing the population-level effect of Cry1Ab, which varied among the populations and prior exposure to Cry1Ab maize in the field. In three out of five populations, armyworms derived from Bt maize reared on Cry1Ab maize showed higher larval weight, faster larval development and better reproductive performance than the armyworms derived from non-Bt maize, and one of these populations showed better performance on both Cry1Ab and control diets, indicating no fitness cost of the resistance trait. Altogether, these results indicate that offspring of armyworms that developed on field-grown, single-gene Bt Cry1Ab maize had reduced performance on Cry1Ab maize foliage in two populations studied, but in other three populations, these offspring had better overall performance on the Bt maize foliage than that of the armyworms from non-Bt maize fields, possibly because of Cry1Ab resistance alleles in these populations. Implications of these findings for resistance management of S. frugiperda in Bt crops are discussed.

Lie symmetries in cortical inspired CNNs

Our scope in this thesis is to propose architectures of CNNs in such a way to model the early visual pathway, including the Lateral Geniculate Nucleus and the Horizontal Connectivity of the primary visual cortex. Moreover, we will show how cortically inspired architectures allow to perform contrast perceptual invariance as well as grouping and the emergence of visual percepts. Particularly, the LGN is modeled with a first layer l0 containing a single filter Ψ0 that pre-filters the image I. Since the RPs of the LGN cells can be modeled as a LoG, we expect to obtain a radially symmetric filter with a similar shape; to this end, we prove the rotational invariance of Ψ0 and we study the influence of this filter to the subsequent layer. Indeed, we compare the statistic distribution of the filters in the second layer l1 of our architecture with the statistic distribution of the RPs of V1 cells of a macaque. Then, we model the horizontal connectivity of V1 implementing a transition kernel K1 to the layer l1. In this setting, we study the vector fields and the association fields induced by the connectivity kernel K1. To this end, we first approximate the filters bank in l1 with a Gabor function and use the parameters just found to re-parameterize the kernel. Thanks to this step, the kernel is now re-parameterized into a sub-Riemmanian space R2 × S1. Now we are able to compare the vector and association fields induced by K1 with the models of the horizontal connectivity.

Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance. © 2010.

Gene transfer and expression of a non-viral polycation-based vector in CD4(+) cells

CD4-selective targeting of an antibody-polycation-DNA complex was investigated The complex was synthesized with the anti-CD4 monoclonal antibody B-F5, polylysine(268) (pLL) and either the pGL3 control vector containing the luciferase reporter gene or the pGeneGrip vector containing the green fluorescent protein (GFP) gene. B-F5-pLL-DNA complexes inhibited the binding of I-125-B-F5 to CD4(+) Jurkat cells, while complexes synthesised either without B-F5 or using a non-specific mouse IgG1 antibody had little or no effect Expression of the luciferase reporter gene was achieved in Jurkat cells using the B-F5-pLL-pGL3 complex and was enhanced in the presence of PMA. Negligible luciferase activity was defected with the non-specific antibody complex in Jurkat cells or with the B-F5-pLL-pGL3 complex in the CD4(-) K-562 cells. Using complexes synthesised with the pGeneGrip vector, the transfection efficiency in Jurkat and K-562 cells was examined using confocal microscopy. More than 95% of Jurkat cells expressed GFP and the level of this expression was markedly enhanced by PMA. Negligible GFP expression was seen in K-562 cells or when B-F5 was replaced by a nonspecific antibody. Using flow cytometry, fluorescein-labelled complex showed specific targeting to CD4(+) cells in a mixed cell population from human peripheral blood. These studies demonstrate the selective transfection of CD4(+) T-lymphoid cells using a polycation-based gene delivery system. The complex may provide a means of delivering anti-HIV gene therapies to CD4(+) cells in vivo.