Along the Traces of the Conic Sections

Based on a geometry problem by Ivan Salabashev we demonstrate an exploratory process leading to conic sections as a locus of points. We work for the purpose with the GeoGebra dynamic software making use of different objects’ representations for explorations related with conic sections.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Eye shape and retinal shape, and their relation to peripheral refraction

Purpose: We provide an account of the relationships between eye shape, retinal shape and peripheral refraction. Recent findings: We discuss how eye and retinal shapes may be described as conicoids, and we describe an axis and section reference system for determining shapes. Explanations are given of how patterns of retinal expansion during the development of myopia may contribute to changing patterns of peripheral refraction, and how pre-existing retinal shape might contribute to the development of myopia. Direct and indirect techniques for determining eye and retinal shape are described, and results are discussed. There is reasonable consistency in the literature of eye length increasing at a greater rate than height and width as the degree of myopia increases, so that eyes may be described as changing from oblate/spherical shapes to prolate shapes. However, one study indicates that the retina itself, while showing the same trend, remains oblate in shape for most eyes (discounting high myopia). Eye shape and retinal shape are not the same and merely describing an eye shape as being prolate or oblate is insufficient without some understanding of the parameters contributing to this; in myopia a prolate eye shape is likely to involve both a steepening retina near the posterior pole combined with a flattening (or a reduction in steepening compared with an emmetrope) away from the pole.

Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo

Purpose. The purpose of this article was to present methods capable of estimating the size and shape of the human eye lens without resorting to phakometry or magnetic resonance imaging (MRI). Methods. Previously published biometry and phakometry data of 66 emmetropic eyes of 66 subjects (age range [18, 63] years, spherical equivalent range [−0.75, +0.75] D) were used to define multiple linear regressions for the radii of curvature and thickness of the lens, from which the lens refractive index could be derived. MRI biometry was also available for a subset of 30 subjects, from which regressions could be determined for the vertex radii of curvature, conic constants, equatorial diameter, volume, and surface area. All regressions were compared with the phakometry and MRI data; the radii of curvature regressions were also compared with a method proposed by Bennett and Royston et al. Results. The regressions were in good agreement with the original measurements. This was especially the case for the regressions of lens thickness, volume, and surface area, which each had an R2 > 0.6. The regression for the posterior radius of curvature had an R2 < 0.2, making this regression unreliable. For all other regressions we found 0.25 < R2 < 0.6. The Bennett-Royston method also produced a good estimation of the radii of curvature, provided its parameters were adjusted appropriately. Conclusions. The regressions presented in this article offer a valuable alternative in case no measured lens biometry values are available; however care must be taken for possible outliers.

On the security of TLS renegotiation

The Transport Layer Security (TLS) protocol is the most widely used security protocol on the Internet. It supports negotiation of a wide variety of cryptographic primitives through different cipher suites, various modes of client authentication, and additional features such as renegotiation. Despite its widespread use, only recently has the full TLS protocol been proven secure, and only the core cryptographic protocol with no additional features. These additional features have been the cause of several practical attacks on TLS. In 2009, Ray and Dispensa demonstrated how TLS renegotiation allows an attacker to splice together its own session with that of a victim, resulting in a man-in-the-middle attack on TLS-reliant applications such as HTTP. TLS was subsequently patched with two defence mechanisms for protection against this attack. We present the first formal treatment of renegotiation in secure channel establishment protocols. We add optional renegotiation to the authenticated and confidential channel establishment model of Jager et al., an adaptation of the Bellare--Rogaway authenticated key exchange model. We describe the attack of Ray and Dispensa on TLS within our model. We show generically that the proposed fixes for TLS offer good protection against renegotiation attacks, and give a simple new countermeasure that provides renegotiation security for TLS even in the face of stronger adversaries.

Molecular cytogenetic analysis of basal cell carcinoma DNA using comparative genomic hybridization

In an attempt to define genomic copy number changes associated with the development of basal cell carcinoma, we investigated 15 sporadic tumors by comparative genomic hybridization. With the incorporation of tissue microdissection and degenerate oligonucleotide primed-polymerase chain reaction we were able to isolate, and then universally amplify, DNA from the tumor type. This combined approach allows the investigation of chromosomal imbalances within a histologically distinct region of tissue. Using comparative genomic hybridization we have observed novel and recurrent chromosomal gains at 6p (47%), 6q (20%), 9p (20%), 7 (13%), and X (13%). In addition comparative genomic hybridization revealed regional loss on 9q in 33% of tested tumors encompassing 9q22.3 to which the putative tumor suppressor gene, Patched, has been mapped. The deletion of Patched has been indicated in the development of hereditary and sporadic basal cell carcinomas. The identification of these recurrent genetic aberrations suggests that basal cell carcinomas may not be as genetically stable as previously thought. Further investigation of these regions may lead to the identification of other genes responsible for basal cell carcinoma formation.

Cryptanalysis of LASH

We show that the LASH-x hash function is vulnerable to attacks that trade time for memory, including collision attacks as fast as 2(4x/11) and preimage attacks as fast as 2(4x/7). Moreover, we briefly mention heuristic lattice based collision attacks that use small memory but require very long messages that are expected to find collisions much faster than 2 x/2. All of these attacks exploit the designers’ choice of an all zero IV. We then consider whether LASH can be patched simply by changing the IV. In this case, we show that LASH is vulnerable to a 2(7x/8) preimage attack. We also show that LASH is trivially not a PRF when any subset of input bytes is used as a secret key. None of our attacks depend upon the particular contents of the LASH matrix – we only assume that the distribution of elements is more or less uniform.

Is retinal shape different in Asians and Caucasians? Estimation from peripheral refraction and peripheral eye length methods

Purpose:Race appears to be associated with myopiogenesis, with East Asians showing high myopia prevalence. Considering structural variations in the eye, it is possible that retinal shapes are different between races. The purpose of this study was to quantify and compare retinal shapes between racial groups using peripheral refraction (PR) and peripheral eye lengths (PEL). Methods:A Shin-Nippon SRW5000 autorefractor and a Haag-Streit Lenstar LS900 biometer measured PR and PEL, respectively, along horizontal (H) and vertical (V) fields out to ±35° in 5° steps in 29 Caucasian (CA), 16 South Asian (SA) and 23 East Asian (EA) young adults (spherical equivalent range +0.75D to –5.00D in all groups). Retinal vertex curvature Rv and asphericity Q were determined from two methods: a) PR (Dunne): The Gullstrand-Emsley eye was modified according to participant’s intraocular lengths and anterior cornea curvature. Ray-tracing was performed at each angle through the stop, altering cornea asphericity until peripheral astigmatism matched experimental measurements. Retinal curvature and hence retinal co-ordinate intersection with the chief ray were altered until sagittal refraction matched its measurement. b) PEL: Ray-tracing was performed at each angle through the anterior corneal centre of curvature of the Gullstrand-Emsley eye. Ignoring lens refraction, retinal co-ordinates relative to the fovea were determined from PEL and trigonometry. From sets of retinal co-ordinates, conic retinal shapes were fitted in terms of Rv and Q. Repeated-measures ANOVA were conducted on Rv and Q, and post hoc t-tests with Bonferroni correction were used to compare races. Results:In all racial groups both methods showed greater Rv for the horizontal than for the vertical meridian and greater Rv for myopes than emmetropes. Rv was greater in EA than in CA (P=0.02), with Rv for SA being intermediate and not significantly different from CA and EA. The PEL method provided larger Rv than the PR method: PEL: EA vs CA 87±13 vs 83±11 m-1 (H), 79±13 vs 72±14 m-1 (V); PR: EA vs CA 79±10 vs 67±10 m-1 (H), 71±17 vs 66±12 m-1 (V). Q did not vary significantly with race. Conclusions:Estimates of Rv, but not of Q, varied significantly with race. The greater Rv found in EA than in CA and the comparatively high prevalence rate of myopia in many Asian countries may be related.

The Mechanisms of Hedgehog Signal Transduction

Studies in both vertebrates and invertebrates have identified proteins of the Hedgehog (Hh) family of secreted signaling molecules as key organizers of tissue patterning. Initially discovered in Drosophila in 1992, Hh family members have been discovered in animals with body plans as diverse as those of mammals, insects and echinoderms. In humans three related Hh genes have been identified: Sonic, Indian and Desert hedgehog (Shh, Ihh and Dhh). Transduction of the Hh signal to the cytoplasm utilizes an unusual mechanism involving consecutive repressive interactions between Hh and its receptor components, Patched (Ptc) and Smoothened (Smo). Several cytoplasmic proteins involved in Hh signal transduction are known in Drosophila, but mammalian homologs are known only for the Cubitus interruptus (Ci) transcription factor (GLI(1-3)) and for the Ci/GLI-associated protein, Suppressor of Fused (Su(fu)). In this study I analyzed the mechanisms of how the Hh receptor Ptc regulates the signal transducer Smo, and how Smo relays the Shh signal from the cell surface to the cytoplasm ultimately leading to the activation of GLI transcription factors. In Drosophila, the kinesin-like protein Costal2 (Cos2) is required for suppression of Hh target gene expression in the absence of ligand, and loss of Cos2 causes embryonic lethality. Cos2 acts by bridging Smo to the Ci. Another protein, Su(Fu) exerts a weak suppressive influence on Ci activity and loss of Su(Fu) causes subtle changes in Drosophila wing pattern. This study revealed that domains in Smo that are critical for Cos2 binding in Drosophila are dispensable for mammalian Smo function. Furthermore, by analyzing the function of Su(Fu) and the closest mouse homologs of Cos2 by protein overexpression and RNA interference I found that inhibition of the Hh response pathway in the absence of ligand does not require Cos2 activity, but instead critically depends on the activity of Su(Fu). These results indicate that a major change in the mechanism of action of a conserved signaling pathway occurred during evolution, probably through phenotypic drift made possible by the existence in some species of two parallel pathways acting between the Hh receptor and the Ci/GLI transcription factors. In a second approach to unravel Hh signaling we cloned > 90% of all human full-length protein kinase cDNAs and constructed the corresponding kinase-activity deficient mutants. Using this kinome resource as a screening tool, two kinases, MAP3K10 and DYRK2 were found to regulate Shh signaling. DYRK2 directly phosphorylated and induced the proteasome dependent degradation of the key Hh-pathway regulated transcription factor, GLI2. MAP3K10, in turn, affected GLI2 indirectly by modulating the activity of DYRK2.

Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

Precoder Designs for MIMO Broadcast Channels with Imperfect CSI

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Expression of Sonic Hedgehog During Cell Proliferation in the Human Cerebellum

The regulation of cell proliferation in the external granular layer (EGL) of the developing cerebellum is important for its normal patterning. An important signal that regulates EGL cell proliferation is Sonic hedgehog (Shh). Shh is secreted by the Purkinje cells (PC) and has a mitogenic effect on the granule cell precursors of the EGL. Deregulation of Shh signaling has been associated with abnormal development, and been implicated in medulloblastomas, which are tumors that arise from the cerebellum. Given the importance of the Shh pathway in cerebellum development and disease, there has been no systematic study of its expression pattern during human cerebellum development. In this study, we describe the expression pattern of Shh, its receptor patched, smoothened, and its effectors that belong to the Gli family of transcription factors, during normal human cerebellum development from 10 weeks of gestational age, and in medulloblastomas that represents a case of abnormal cell proliferation in the cerebellum. This expression pattern is compared to equivalent stages in the normal development of cerebellum in mouse, as well as in tumors. Important differences between human and mouse that reflect differences in the normal developmental program between the 2 species are observed. First, in humans there appears to be a stage of Shh signaling within the EGL, when the PC are not yet the source of Shh. Second, unlike in the postnatal mouse cerebellum, expression of Shh in the PC in the postnatal human cerebellum is downregulated. Finally, medulloblastomas in the human but not in patched heterozygote mouse express Shh. These results highlight cross-species differences in the regulation of the Shh signaling pathway.

Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

Crystal growth and nonlinear optical properties of sodium D-isoascorbate monohydrate

Optical quality single crystals of sodium D-isoascorbate monohydrate were grown by a slow cooling technique. The crystal possesses a bulky prismatic morphology. Thermal analyses indicate that the crystals are stable up to 125 degrees C. The optical transmission window ranges from 307 nm to 1450 nm. The principal refractive indices have been measured employing Brewster's angle method. The crystallographic and the principal dielectric axes coincide with each other such that a lies along Z, b along X and c along Y. The optic axis is oriented 58 degrees (at 532 nm) to the crystallographic a axis in the XZ plane and the crystal is negative biaxial. Type 1 and type 2 phase matching curves are generated and experimentally verified. No polarization dependence of the light absorption was observed confirming the validity of Kleinman's symmetry conjecture, leading to a single nonvanishing nonlinear tensor component. According to Hobden's classification the crystal belongs to class 3. The crystal also exhibits second order noncollinear conic sections. The single shot and multiple shot surface laser damage thresholds are determined to be 32.7 GW cm(-2) and 6.5 GW cm(-2) respectively for 1064 nm radiation.