Some remarks on the hyperelliptic moduli of genus 3

In 1967, Shioda \cite{Shi1} determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in \cite{Shi1} are incorrect. In this paper, we compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed field $k$, $\ch k \neq 2, 3, 5, 7$. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants.Comment: arXiv admin note: text overlap with arXiv:1209.044

Elliptic Curve Cryptography and Coding Theory

From the earliest days of history, the requirement for methods of secret communication and protection of information had been present. Cryptography is such an important field of science developed to facilitate secret communication and safeguard information. Cryptography is based on mathematics. It is an application of different disciplines such as Algebra, Number Theory, Graph Theory etc. Private key cryptography and Public key cryptography are the two main types of cryptography. Public key cryptosystems offer more security and convenience for the users. The main objective of this study is to explore thepossibilities of further improvement of Elliptic Curve Cryptography (ECC) by studying the mathematical aspects behind the “Elliptic curve cryptosystem” which is one of the latest of this kind and develop a computer program to generate the cyclic subgroup of a given elliptic curve defined over a finite field ℤ, where p is a prime, which is the major requirement to perform ECC and then use the same to illustrate how data security is achieved from this. For an elliptic curve defined over a field, the points on an elliptic curve naturally form an abelian group. Elliptic curve arithmetic can be employed to develop a variety of Elliptic curve cryptographic schemes such as key exchange, encryption, digital signatures and specific construction of a keyed-Hash Message Authentication Code (HMAC) which are illustrated through this study. Moreover this study proposes an improvement for the encryption of a message through utilization of a concept in “Coding Theory” of Abstract algebra which offers an additional shield for the transmitted message. KEYWORDS: Abelian group, cyclic subgroup, ECDH, ECDSA, AE

Magnetic order in the two-dimensional metal-organic framework manganese pyrazinecarboxylate with Mn-Mn dimers

The magnetic properties of [Mn(pyrazinecarboxylate)2]n (Mn-pyrazine), empirical formula C10H6MnN4O4, are investigated through susceptibility, heat capacity and neutron scattering measurements. The structure of Mn-pyrazine consists of Mn-Mn dimers linked on a distorted 2D hexagonal structure. The weak out of plane interactions create a quasi-2D magnetic material within the larger three dimensional metal organic framework (MOF) structure. We show that this material undergoes a two stage magnetic transition, related to the low dimensionality of the Mn lattice. First at 5 K, which is assigned to the initial development of short range order in the 2D layers. This is followed by long range order at 3.3 K. Applied field measurements reveal the potential to induce magnetic transitions in moderately small fields of 2 T. Neutron powder diffraction enabled the determination of a unique magnetic space group P21'/c (#14.77) at 1.5 K. This magnetic structure consists of antiferromagnetically coupled Mn-Mn dimers with spins principally along the out of plane a-axis

Diabetic retinopathy: a complex pathophysiology requiring novel therapeutic strategies.

INTRODUCTION: Diabetic retinopathy (DR) is the leading cause of vision loss in the working age population of the developed world. DR encompasses a complex pathology, and one that is reflected in the variety of currently available treatments, which include laser photocoagulation, glucocorticoids, vitrectomy and agents which neutralize vascular endothelial growth factor (VEGF). Whilst these options demonstrate modest clinical benefits, none is yet to fully attenuate clinical progression or reverse damage to the retina. This has led to an interest in developing novel therapies for the condition, such as mediators of angiopoietin signaling axes, immunosuppressants, nonsteroidal anti-inflammatory drugs (NSAIDs), oxidative stress inhibitors and vitriol viscosity inhibitors. Further, preclinical research suggests that gene therapy treatment for DR could provide significant benefits over existing treatments options. AREAS COVERED: Here we review the pathophysiology of DR and provide an overview of currently available treatments. We then outline recent advances made towards improved patient outcomes and highlight the potential of the gene therapy paradigm to revolutionize DR management. EXPERT OPINION: Whilst significant progress has been made towards our understanding of DR, further research is required to enable the development of a detailed spatiotemporal model of the disease. In addition, we hope that improvements in our knowledge of the condition facilitate therapeutic innovations that continue to address unmet medical need and improve patient outcomes, with a focus on the development of targeted medicines.Cambridge Eye Trust Research Councils UK - Medical Research Council the Wellcome Trus

EQ-5D-3L Derived Population Norms for Health Related Quality of Life in Sri Lanka

Background Health Related Quality of Life (HRQoL) is an important outcome measure in health economic evaluation that guides health resource allocations. Population norms for HRQoL are an essential ingredient in health economics and in the evaluation of population health. The aim of this study was to produce EQ-5D-3L-derived population norms for Sri Lanka. Method A population sample (n =  780) was selected from four districts of Sri Lanka. A stratified cluster sampling approach with probability proportionate to size was employed. Twenty six clusters of 30 participants each were selected; each participant completed the EQ-5D-3L in a face-to-face interview. Utility weights for their EQ-5D-3L health states were assigned using the Sri Lankan EQ-5D-3L algorithm. The population norms are reported by age and socio-economic variables. Results The EQ-5D-3L was completed by 736 people, representing a 94% response rate. Sixty per cent of the sample reported being in full health. The percentage of people responding to any problems in the five EQ-5D-3L dimensions increased with age. The mean EQ-5D-3L weight was 0.85 (SD 0.008; 95%CI 0.84-0.87). The mean EQ-5D-3L weight was significantly associated with age, housing type, disease experience and religiosity. People above 70 years of age were 7.5 times more likely to report mobility problems and 3.7 times more likely to report pain/discomfort than those aged 18-29 years. Those with a tertiary education were five times less likely to report any HRQoL problems than those without a tertiary education. A person living in a shanty was 4.3 more likely to have problems in usual activities than a person living in a single house. Conclusion The population norms in Sri Lanka vary with socio-demographic characteristics. The socioeconomically disadvantaged have a lower HRQoL. The trends of population norms observed in this lower middle income country were generally similar to those previously reported in high income countries