Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space

This thesis mainly treats two developments of the classical theory of hypersurfaces inside pseudo-Riemannian space forms. The former - a joint work with Francesco Bonsante - consists in the study of immersions of smooth manifolds into holomorphic Riemannian space forms of constant curvature -1 (including SL(2,C) with a multiple of its Killing form): this leads to a Gauss-Codazzi theorem, it suggests an approach to holomorphic transitioning of immersions into pseudo-Riemannian space forms, a trick to construct holomorphic maps into the PSL(2,C)-character variety, and leads to a restatement of Bers theorem. The latter - a joint work with Andrea Seppi - consists in the study of immersions of n-manifolds inside the space of geodesics of the hyperbolic (n+1)-space. We give a characterization, in terms of the para-Sasaki structure of this space of geodesics, of the Riemannian immersions which turn out to be Gauss maps of equivariant immersions into the hyperbolic space.Comment: PhD thesis. Partially joint with Francesco Bonsante and Andrea Seppi. 210 pages, 12 figure

A metric uniformizing model for the Quasi-Fuchsian space

We introduce and study a novel uniformization metric model for the quasi-Fuchsian space QF(S) of a closed oriented surface S, defined through a class of C-valued bilinear forms on S, called Bers metrics, which coincide with hyperbolic Riemannian metrics along the Fuchsian locus. By employing this approach, we present a new model of the holomorphic tangent bundle of QF(S) that extends the metric model for Teichm\"uller space defined by Berger and Ebin, and give an integral representation of the Goldman symplectic form and of the holomorphic extension of the Weil-Petersson metric to QF(S), with a new proof of its existence and non-degeneracy. We also determine new bounds for the Schwarzian of Bers projective structures extending Kraus estimate. Lastly, we use this formalism to give alternative proofs to several classic results in quasi-Fuchsian theory

Methods for the de-identification of electronic health records for genomic research

Electronic health records are increasingly being linked to DNA repositories and used as a source of clinical information for genomic research. Privacy legislation in many jurisdictions, and most research ethics boards, require that either personal health information is de-identified or that patient consent or authorization is sought before the data are disclosed for secondary purposes. Here, I discuss how de-identification has been applied in current genomic research projects. Recent metrics and methods that can be used to ensure that the risk of re-identification is low and that disclosures are compliant with privacy legislation and regulations (such as the Health Insurance Portability and Accountability Act Privacy Rule) are reviewed. Although these methods can protect against the known approaches for re-identification, residual risks and specific challenges for genomic research are also discussed

On the Gauss map of equivariant immersions in hyperbolic space

Given an oriented immersed hypersurface in hyperbolic space $\mathbb{H}^{n+1}$, its Gauss map is defined with values in the space of oriented geodesics of $\mathbb{H}^{n+1}$, which is endowed with a natural para-K\"ahler structure. In this paper we address the question of whether an immersion $G$ of the universal cover of an $n$-manifold $M$, equivariant for some group representation of $\pi_1(M)$ in $\mathrm{Isom}(\mathbb{H}^{n+1})$, is the Gauss map of an equivariant immersion in $\mathbb{H}^{n+1}$. We fully answer this question for immersions with principal curvatures in $(-1,1)$: while the only local obstructions are the conditions that $G$ is Lagrangian and Riemannian, the global obstruction is more subtle, and we provide two characterizations, the first in terms of the Maslov class, and the second (for $M$ compact) in terms of the action of the group of compactly supported Hamiltonian symplectomorphisms.Comment: 55 pages, 12 figure

MODIFIED MULTI-LEVEL STEGANOGRAPHY TO ENHANCE DATA SECURITY

Data-hiding using steganography algorithm becomes an important technique to prevent unauthorized users to have access to a secret data.  In this paper, steganography algorithm has been constructed to hide a secret data in a gray and a color images, this algorithm is named deep hiding/extraction algorithm (DHEA) to modify multi-level steganography (MLS). The suggested hiding algorithm is based on modified least significant bit (MDLSB) to scatter data in a cover-image and it utilizes a number of levels; where each level perform hiding data on a gray image except the last level that applies a color image to keep secret data. Furthermore, proper randomization approach with two layers is implemented; the first layer uses random pixels selection for hiding a secret data at each level, while the second layer implements at the last level to move randomly from segment to the others. In addition, the proposed hiding algorithm implements an effective lossless image compression using DEFLATE algorithm to make it possible to hide data into a next level. Dynamic encryption algorithm based on Advanced Encryption Standard (AES) is applied at each level by changing cipher keys (Ck) from level to the next, this approach has been applied to increase the security and working against attackers. Soft computing using a meta-heuristic approach based on artificial bee colony (ABC) algorithm has been introduced to achieve smoothing on pixels of stego-image, this approach is effective to reduce the noise caused by a hidden large amount of data and to increase a stego-image quality on the last level. The experimental result demonstrates the effectiveness of the proposed algorithm with bee colony DHA-ABC to show high-performing to hide a large amount of data up to four bits per pixel (bpp) with high security in terms of hard extraction of a secret message and noise reduction of the stego-image. Moreover, using deep hiding with unlimited levels is promising to confuse attackers and to compress a deep sequence of images into one image

Analysis, assessment and optimization of integrated solar energy systems for multigeneration

The extensive usage of fossil fuel in most of human activities has led to the undesirable effects on the environment starting from global warming and greenhouse effects to the climate changes, acid rain and others. Renewable energy is at the core of most of recent research activities to overcome these environmental challenges. Being an integral part of other renewable resources, solar energy utilization aims to occupy more portion of the world energy framework. Integrated energy systems for multigeneration produces several useful products using the same energy input. Electrical power generation, fresh water, space heating and cooling and domestic hot water are the major commodities that furnish our life activities. Hydrogen is another useful product taken into consideration. The proposed systems in this work cover all these products as a step for achieving a sustainable and environmentally benign community. These systems pose great potential for global warming mitigation. In the work presented, different multigeneration energy systems based on solar energy are introduced. Comprehensive thermodynamic, environmental and economic analyses for the proposed multigeneration energy systems are the main goals of this thesis study. Thermodynamic analyses are based on energy and exergy, associated with the efficiencies of overall and system components performances. For a better understanding of the systems performances and the potential of more improvement in their performances, exergoeconomic and environmental analyses and system optimization are performed. Solar dish based integrated system considering biomass-SOFC as alternative for solar unavailability is the first studied system. The system performance is assessed during solar availability and considering the performance of a 24-hours operation. The second system is based on solar parabolic trough providing concentrated heat to an organic Rankine cycle. The system is integrated with electrolyzer for hydrogen production, a reverse osmosis water desalination unit and absorption chiller system and providing domestic hot water. The third main system is based on heliostat solar system integrated with steam turbine for multigeneration purposes. The system produces cooling, heating, fresh water and hydrogen through electrolysis

On PSL(2, C) and on the space of geodesics of H^3 as holomorphic Riemannian manifolds

editorial reviewe

Ethyl 4-{[3-(adamantan-1-yl)-4-phenyl-5-sulfanyl­idene-4,5-dihydro-1H-1,2,4-triazol-1-yl]meth­yl}piperazine-1-carboxyl­ate

The title mol­ecule, C26H35N5O2S, displays a chair-shaped piperazine ring, as well as a planar triazole ring whose phenyl substituent is perpendicular to the mean plane of the five-membered ring [dihedral angle = 90.00 (13)°]. The methyl­ene substituent on the piperazine ring occupies an equatorial site. Weak inter­molecular C—H⋯O hydrogen bonding is present in the crystal structure. The crystal studied was a non-merohedral twin, with a 33.9 (3)% minor component