A generic variant of NIST’s KAS2 key agreement protocol

We propose a generic three-pass key agreement protocol that is based on a certain kind of trapdoor one-way function family. When specialized to the RSA setting, the generic protocol yields the so-called KAS2 scheme that has recently been standardized by NIST. On the other hand, when specialized to the discrete log setting, we obtain a new protocol which we call DH2. An interesting feature of DH2 is that parties can use different groups (e.g., different elliptic curves). The generic protocol also has a hybrid implementation, where one party has an RSA key pair and the other party has a discrete log key pair. The security of KAS2 and DH2 is analyzed in an appropriate modification of the extended Canetti-Krawczyk security model.

Generic identity of Camptorrhiza indica (Colchicaceae) based on cytogenetics and molecular phylogenetics

The tribe Iphigenieae (Colchicaceace, Liliales) includes two genera, viz. Camptorrhiza and Iphigenia, which are distributed in Africa, India, and Australasia. Iphigenia is represented by 12 species, of which six occur in India while Camptorrhiza comprises one species each in Africa (C. strumosa) and India (C. indica). The genus Camptorrhiza possesses a knee-shaped tuber attached to the corms, filaments with a thick bulge in the middle and styles with single stigma. Iphigenia on the other hand lacks knee-shaped tuber, bears linear filaments and has styles with three stigmas. Camptorrhiza indica possesses ovoid corms, linear filaments and styles with a single stigma. These characters are intermediate between Iphigenia and Camptorrhiza and hence we studied the cytogenetics and phylogenetic placement of this species to ascertain its generic identity. Somatic chromosome count (2n = 22) and karyotypic features of C. indica are very similar to that of Iphigenia species. Molecular phylogenetic studies based on atpB-rbcL, rps16, trnL, and trnL-F regions showed that C. indica is nested within a lineage of Indian Iphigenia species. Thus, C. indica was reduced to a species of Iphigenia, i.e., I. ratnagirica. Camptorrhiza is now a monotypic genus restricted only to southern Africa. A key to the Indian Iphigenia species is provided. In addition, a new combination Wurmbea novae-zelandiae is proposed for Iphigenia novae-zelandiae.

Generic differentiability of convex functions and monotone operators

The aim of this paper is to investigate to what extent the known theory of subdifferentiability and generic differentiability of convex functions defined on open sets can be carried out in the context of convex functions defined on not necessarily open sets. Among the main results obtained I would like to mention a Kenderov type theorem (the subdifferential at a generic point is contained in a sphere), a generic Gâteaux differentiability result in Banach spaces of class S and a generic Fréchet differentiability result in Asplund spaces. At least two methods can be used to prove these results: first, a direct one, and second, a more general one, based on the theory of monotone operators. Since this last theory was previously developed essentially for monotone operators defined on open sets, it was necessary to extend it to the context of monotone operators defined on a larger class of sets, our "quasi open" sets. This is done in Chapter III. As a matter of fact, most of these results have an even more general nature and have roots in the theory of minimal usco maps, as shown in Chapter II.

Innovations of wide-field optical-sectioning fluorescence microscopy : toward high-speed volumetric bio-imaging with simplicity

Optical microscopy has become an indispensable tool for biological researches since its invention, mostly owing to its sub-cellular spatial resolutions, non-invasiveness, instrumental simplicity, and the intuitive observations it provides. Nonetheless, obtaining reliable, quantitative spatial information from conventional wide-field optical microscopy is not always intuitive as it appears to be. This is because in the acquired images of optical microscopy the information about out-of-focus regions is spatially blurred and mixed with in-focus information. In other words, conventional wide-field optical microscopy transforms the three-dimensional spatial information, or volumetric information about the objects into a two-dimensional form in each acquired image, and therefore distorts the spatial information about the object. Several fluorescence holography-based methods have demonstrated the ability to obtain three-dimensional information about the objects, but these methods generally rely on decomposing stereoscopic visualizations to extract volumetric information and are unable to resolve complex 3-dimensional structures such as a multi-layer sphere.

The concept of optical-sectioning techniques, on the other hand, is to detect only two-dimensional information about an object at each acquisition. Specifically, each image obtained by optical-sectioning techniques contains mainly the information about an optically thin layer inside the object, as if only a thin histological section is being observed at a time. Using such a methodology, obtaining undistorted volumetric information about the object simply requires taking images of the object at sequential depths.

Among existing methods of obtaining volumetric information, the practicability of optical sectioning has made it the most commonly used and most powerful one in biological science. However, when applied to imaging living biological systems, conventional single-point-scanning optical-sectioning techniques often result in certain degrees of photo-damages because of the high focal intensity at the scanning point. In order to overcome such an issue, several wide-field optical-sectioning techniques have been proposed and demonstrated, although not without introducing new limitations and compromises such as low signal-to-background ratios and reduced axial resolutions. As a result, single-point-scanning optical-sectioning techniques remain the most widely used instrumentations for volumetric imaging of living biological systems to date.

In order to develop wide-field optical-sectioning techniques that has equivalent optical performance as single-point-scanning ones, this thesis first introduces the mechanisms and limitations of existing wide-field optical-sectioning techniques, and then brings in our innovations that aim to overcome these limitations. We demonstrate, theoretically and experimentally, that our proposed wide-field optical-sectioning techniques can achieve diffraction-limited optical sectioning, low out-of-focus excitation and high-frame-rate imaging in living biological systems. In addition to such imaging capabilities, our proposed techniques can be instrumentally simple and economic, and are straightforward for implementation on conventional wide-field microscopes. These advantages together show the potential of our innovations to be widely used for high-speed, volumetric fluorescence imaging of living biological systems.