Looking into the Eye with REAP

Keratoprosthesis is an artificial cornea that is surgically implanted in the eye to replace damaged cornea, correcting corneal blindness. Keratoprosthesis offers a unique solution that eliminates the possible rejection of donor cornea, a common problem with keratoplasty. The design used currently for this procedure is Boston Keratoprosthesis (KPro), but it has some flaws. Boston KPro needs donor cornea for its design, which is in high demand and short supply. The design is also open to the environment, creating a pathway for bacteria to enter the eye and cause permanent damage. My research through the Research Experience and Apprenticeship Program (REAP) at the University of New Hampshire involved creating a new artificial cornea that fixes both of these issues. I started fabricating a cornea out of silk fibroin and gelatin, called a hydrogel, to replace the need for donor cornea. These hydrogels were tested using a rheometer and a scanning electron microscope for the stiffness, mechanical strength, and porousness of the structure, as these qualities have to be similar to a real cornea. It was a success. We created hydrogels that replicated the characteristics of a human cornea and fixed the issues Boston KPro has. REAP was a great opportunity to explore my interests in bioengineering while potentially changing peoples’ lives

Categorification of Seidel's representation

Two natural symplectic constructions, the Lagrangian suspension and Seidel's quantum representation of the fundamental group of the group of Hamiltonian diffeomorphisms, Ham(M), with (M,\omega) a monotone symplectic manifold, admit categorifications as actions of the fundamental groupoid \Pi(Ham(M)) on a cobordism category recently introduced in \cite{Bi-Co:cob2} and, respectively, on a monotone variant of the derived Fukaya category. We show that the functor constructed in \cite{Bi-Co:cob2} that maps the cobordism category to the derived Fukaya category is equivariant with respect to these actions.Comment: 32 pages, 4 figures. Updated to agree with the published version. To appear in Israel Journal of Mathematic

MOTIVATION AND RECRUITMENT OF PUBLIC SERVANTS - THE ETHOS OR THE MANAGERIAL MODEL?

The need to continue the reduction of the state bureaucracy and the orientation towards the managerial models from the private sector, the usage of financial incentive systems, generally in the form of merit base promotion and financial rewards, have introduced in the public system the incentives of the market, aiming to lead towards the efficiency and the effectiveness of the private organizations. Those practices considered that the labor force in the public and private systems is substantially the same, avoiding the essential differences between the public and private employees. The public servant does not answer only to financial incentives; a variety of nonfinancial motives affect the behavior: trust, sense of duty, altruism or community reputation. Public managers need to carefully balance the incidence and consistency of financial motivation in time with the impact on the organizational performance as well to avoid treating the public organization as a private company because such a measure does not identify the specific motives of public service and the way a bureaucracy works.Motivation, recruitment, employees, public administration, private companies

Rigidity and gluing for Morse and Novikov complexes

We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold $(M,\omega)$ with $c_{1}|_{\pi_{2}(M)}=[\omega]|_{\pi_{2}(M)}=0$. The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently $C^{0}$ close generic function/hamiltonian. The gluing result is a type of Mayer-Vietoris formula for the Morse complex. It is used to express algebraically the Novikov complex up to isomorphism in terms of the Morse complex of a fundamental domain. Morse cobordisms are used to compare various Morse-type complexes without the need of bifurcation theory.Comment: 46 pages, LATEX file with XYPIC diagrams, and one .EPS file. Final version, accepted for publication by the Journal of the European Mathematical Societ

Glycosaminoglycans in the human cornea: age-related changes

Abstract AIM: To investigate possible age-related changes in glycosaminoglycans (GAGs) in the human cornea. The substances today called GAGs were previously referred to as mucopolysaccharides. METHODS: Samples of human cornea were taken from 12 younger (age 21 ± 1.2) and 12 older (age 72 ± 1.6) male subjects. Samples were weighed, homogenized, and used for biochemical and molecular analyses. All the quantitative results were statistically analyzed. RESULTS: The human cornea appears to undergo age-related changes, as evidenced by our biochemical and molecular results. The total GAG and hyaluronic acid counts were significantly higher in the younger subjects than in the older subjects. The sulfated heavy GAGs, such as chondroitin, dermatan, keratan, and heparan sulfate, were lower in the younger subjects than in the older subjects. DISCUSSION: GAGs of the human cornea undergo numerous age-related changes. Their quantity is significantly altered in the elderly in comparison with younger subjects. GAGs play an important role in age-related diseases of the human cornea

Effect of corneal light scatter on vision: a review of the literature

The cornea is the transparent connective tissue window at the front of the eye. The physiological role of the cornea is to conduct external light into the eye, focus it, together with the lens, onto the retina, and to provide rigidity to the entire eyeball. Therefore, good vision requires maintenance of the transparency and proper refractive shape of the cornea. The surface structures irregularities can be associated with wavefront aberrations and scattering errors. Light scattering in the human cornea causes a reduction of visual quality. In fact, the cornea must be transparent and maintain a smooth and stable curvature since it contributes to the major part of the focusing power of the eye. In most cases, a simple examination of visual acuity cannot demonstrate the reduction of visual quality secondary light scattering. In fact, clinical techniques for examining the human cornea in vivo have greatly expanded over the last few decades. The measurement of corneal back scattering qualifies the degree of corneal transparency. The measurement of corneal forward-scattering quantifies the amount of visual impairment that is produced by the alteration of transparency. The aim of this study was to review scattering in the human cornea and methods of measuring it

A parametric bootstrap for heavytailed distributions

It is known that Efron's resampling bootstrap of the mean of random variables with common distribution in the domain of attraction of the stable laws with infinite variance is not consistent, in the sense that the limiting distribution of the bootstrap mean is not the same as the limiting distribution of the mean from the real sample. Moreover, the limiting distribution of the bootstrap mean is random and unknown. The conventional remedy for this problem, at least asymptotically, is either the m out of n bootstrap or subsampling. However, we show that both these procedures can be quite unreliable in other than very large samples. A parametric bootstrap is derived by considering the distribution of the bootstrap P value instead of that of the bootstrap statistic. The quality of inference based on the parametric bootstrap is examined in a simulation study, and is found to be satisfactory with heavy-tailed distributions unless the tail index is close to 1 and the distribution is heavily skewed.bootstrap inconsistency, stable distribution, domain of attraction, infinite variance