Image processing via level set curvature flow.

We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach.

A constant radius of curvature model for the organization of DNA in toroidal condensates.

Toroidal DNA condensates have received considerable attention for their possible relationship to the packaging of DNA in viruses and in general as a model of ordered DNA condensation. A spool-like model has primarily been supported for DNA organization within toroids. However, our observations suggest that the actual organization may be considerably different. We present an alternate model in which DNA for a given toroid is organized within a series of equally sized contiguous loops that precess about the toroid axis. A related model for the toroid formation process is also presented. This kinetic model predicts a distribution of toroid sizes for DNA condensed from solution that is in good agreement with experimental data.

The elements of the differential calculus, comprehending the general theory of curve surfaces, and of curves of double curvature. Intended for the use of mathematical students in schools and universities.

Available on demand as hard copy or computer file from Cornell University Library.

A treatise on analytical geometry of three dimensions : containing the theory of curve surfaces and of curves of double curvature /

Mode of access: Internet.

Overexpression of sonic hedgehog suppresses embryonic hair follicle morphogenesis

The Sonic Hedgehog (Shh) signalling pathway plays a central role in the development of the skin and hair follicle and is a major determinant of skin tumorigenesis, most notably of basal cell carcinoma (BCC). Various mouse models involving either ablation or overexpression of key members of the Shh signalling pathway display a range of skin tumours. To further examine the role of Shh in skin development. we have overexpressed Shh in a subset of interfollicular basal cells from 12.5 dpc under the control of the human keratin 1 (HK1) promoter. The HK1-Shh transgenic mice display a range of skin anomalies, including highly pigmented inguinal lesions and regions of alopecia. The most striking hair follicle phenotype is a suppression in embryonic follicle development between 14.0 and 19.0 dpc, resulting in a complete absence of guard, awl, and auchene hair fibres. These data indicate that alternative signals are responsible for the development of different hair follicles and point to a major role of Shh signalling in the morphogenesis of guard, awl, and auchene hair fibres. Through a comparison with other mouse models, the characteristics of the HK1-Shh transgenic mice suggest that the precise timing and site of Shh expression are key in dictating the resultant skin and tumour phenotype. 2003 Elsevier Inc. All rights reserved.

Pore size characterization of mesoporous materials by a thermodynamic approach: A curvature-dependent solid-fluid potential

A thermodynamic analysis of nitrogen adsorption in cylindrical pores of MCM-41 and SBA-15 samples at 77 K is presented within the framework of the Broekhoff and de Boer (BdB) theory. We accounted for the effect of the solid surface curvature on the potential exerted by the pore walls. The developed model is in quantitative agreement with the non-local density functional theory (NLDFT) for pores larger than 2 tun. This modified BdB theory accounting for the Curvature Dependent Potential (CDP-BdB) was applied to determine the pore size distribution (PSD) of a number of MCM-41 and SBA-15 samples on the basis of matching the equilibrium theoretical isotherm against the adsorption branch of the experimental isotherm. In all cases investigated the PSDs determined with the new approach are very similar to those determined with the non-local density functional theory also using the same basis of matching of theoretical isotherm against the experimental adsorption branch. The developed continuum theory is very simple in its utilization, suggesting that CDP-BdB could be used as an alternative tool to obtain PSD for mesoporous solids from the analysis of adsorption branch of adsorption isotherms of any sub-critical fluids.

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models-a fixed effects model and a random effects model-are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed. (c) 2004 Elsevier B.V. All rights reserved.

CXCR4/SDF1 interaction inhibits the primordial to primary follicle transition in the neonatal mouse ovary

The molecular mechanisms behind the entry of the primordial follicle into the growing follicle pool remain poorly understood. To investigate this process further, a microarray-based comparison was undertaken between 2-day postpartum mouse ovaries consisting of primordial follicles/naked oocytes only and those with both primordial follicles and newly activated follicles (7-day postpartum). Gene candidates identified included the chemoattractive cytokine stromal derived factor-1 (SDF1) and its receptor CXCR4. SDF1 and CXCR4 have been implicated in a variety of physiological processes including the migration of embryonic germ cells to the gonads. SDF1-alpha expression increased with the developmental stage of the follicle. Embryonic expression was found to be dichotomous post-genii cell migration, with low expression in the female. Immunohistochemical studies nonetheless indicate that the autocrine pattern of expression ligand and receptor begins during embryonic life. Addition of recombinant SDF1-alpha to neonatal mouse ovaries in vitro resulted in significantly higher follicle densities than for control ovaries. TUNEL analysis indicated no detectable difference in populations of apoptotic cells of treated or control ovaries. Treated ovaries also contained a significantly lower percentage of activated follicles as determined by measurement of oocyte diameter and morphological analysis. Treatment of cultured ovaries with an inhibitor of SDF1-alpha, AMD3100, ablated the effect of SDF1-alpha. By retaining follicles in an unactivated state, SDF1/CXCR4 signaling may play an important role in maintaining the size and longevity of the primordial follicle pool. (c) 2006 Elsevier Inc. All rights reserved.

Remodeling of extracellular matrix at ovulation of the bovine ovarian follicle

Using immunohistochemistry and RNA analyses we examined the fate of components of a newly identified matrix that develops between granulosa cells (focimatrix, abbreviated from focal intraepithelial matrix) and of the follicular basal lamina in ovulating bovine ovarian follicles. Pre- and postovulatory follicles were generated by treatment with estradiol (Day 1), progesterone (Days 1-10), and prostaglandin analogue (Day 9) with either no further treatment (Group 1, n = 6) and or with 25 mg porcine LH (Day 11, Group 2, n = 8 or Day 10, Group 3, n = 8) and ovariectomy on Day 12 (12-14 hr post LH in Group 2, 38-40.5 hr in Group 3). In the time frame examined no loss of follicular basal lamina laminin chains beta 2 and gamma 1 or nidogen 1 was observed. In the follicular basal lamina collagen type IV alpha 1 and perlecan were present prior to ovulation; after ovulation collagen type IV alpha 1 was discontinuously distributed and perlecan was absent. Versican in the theca interna adjacent to the follicular basal lamina in preovulatory follicles was not observed post ovulation, however, the granulosa cells then showed strong cytoplasmic staining for versican. Expression of versican isoforms V0, V1, and V3 was detected at all stages. Focimatrix was observed in preovulatory follicles. It contained collagen type IV alpha 1, laminins beta 2 and gamma 1, nidogen 1 and perlecan and underwent changes in composition similar to that of the follicular basal lamina. In conclusion focimatrix and the follicular basal lamina are degraded at ovulation. Individual components are lost at different times.

Curvature-driven smoothing: a learning algorithm for feed-forward networks

The performance of feed-forward neural networks in real applications can be often be improved significantly if use is made of a-priori information. For interpolation problems this prior knowledge frequently includes smoothness requirements on the network mapping, and can be imposed by the addition to the error function of suitable regularization terms. The new error function, however, now depends on the derivatives of the network mapping, and so the standard back-propagation algorithm cannot be applied. In this paper, we derive a computationally efficient learning algorithm, for a feed-forward network of arbitrary topology, which can be used to minimize the new error function. Networks having a single hidden layer, for which the learning algorithm simplifies, are treated as a special case.

Incorporating curvature information into on-line learning

We analyse the dynamics of a number of second order on-line learning algorithms training multi-layer neural networks, using the methods of statistical mechanics. We first consider on-line Newton's method, which is known to provide optimal asymptotic performance. We determine the asymptotic generalization error decay for a soft committee machine, which is shown to compare favourably with the result for standard gradient descent. Matrix momentum provides a practical approximation to this method by allowing an efficient inversion of the Hessian. We consider an idealized matrix momentum algorithm which requires access to the Hessian and find close correspondence with the dynamics of on-line Newton's method. In practice, the Hessian will not be known on-line and we therefore consider matrix momentum using a single example approximation to the Hessian. In this case good asymptotic performance may still be achieved, but the algorithm is now sensitive to parameter choice because of noise in the Hessian estimate. On-line Newton's method is not appropriate during the transient learning phase, since a suboptimal unstable fixed point of the gradient descent dynamics becomes stable for this algorithm. A principled alternative is to use Amari's natural gradient learning algorithm and we show how this method provides a significant reduction in learning time when compared to gradient descent, while retaining the asymptotic performance of on-line Newton's method.

Phakometric measurement of ocular surface radii of curvature, axial separations and alignment in relaxed and accommodated human eyes

Measurements (autokeratometry, A-scan ultrasonography and video ophthalmophakometry) of ocular surface radii, axial separations and alignment were made in the horizontal meridian of nine emmetropes (aged 20-38 years) with relaxed (cycloplegia) and active accommodation (mean ± 95% confidence interval: 3.7 ± 1.1 D). The anterior chamber depth (-1.5 ± 0.3 D) and both crystalline lens surfaces (front 3.1 ± 0.8 D; rear 2.1 ± 0.6 D) contributed to dioptric vergence changes that accompany accommodation. Accommodation did not alter ocular surface alignment. Ocular misalignment in relaxed eyes is mainly because of eye rotation (5.7 ± 1.6° temporally) with small amounts of lens tilt (0.2 ± 0.8° temporally) and decentration (0.1 ± 0.1 mm nasally) but these results must be viewed with caution as we did not account for corneal asymmetry. Comparison of calculated and empirically derived coefficients (upon which ocular surface alignment calculations depend) revealed that negligible inherent errors arose from neglect of ocular surface asphericity, lens gradient refractive index properties, surface astigmatism, effects of pupil size and centration, assumed eye rotation axis position and use of linear equations for analysing Purkinje image shifts. © 2004 The College of Optometrists.