Generalised Mersenne Numbers Revisited

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property --- and hence the same efficiency ratio --- holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio

The flavour of warped extra dimensions

Models with warped extra dimensions offer a promising solution to the hierarchy problem. However, it is known that flavour changing neutral currents arise at tree level in models with warped extra dimensions, which can lead to fatally large corrections to rare processes in the standard model. Since the introduction of the warped mechanism in 1999 by Randall and Sundrum, modifications of the original AdS5 geometries have been considered, having different phenomenologies. In particular, it has been previously shown that CP-violation in the K-K mixing system can be suppressed in what is known as the soft-wall model, in which the extra dimension is effectively compactified via a background scalar dilation field. Prior to the work presented in this thesis, however, this study had been limited to a background geometry with a specific form. A detailed study of bosonic propagators in soft-wall models has been conducted as part of this research, yielding some novel results, which permit the study of particle interactions throughout an extended family of warped 5D backgrounds in a practicable way. This methodology has then been applied, via the development of numerical routines, to an investigation of K and B meson phenomenology in a range of geometries in this family. The relevant and necessary technical prerequisites are reviewed and discussed, including (but not limited to) some of the general properties of warped extra dimensions, the application of Kaluza-Klein theory in warped 5D, topics in flavour physics and quark mixing and the application of effective field theory methods in perturbative calculations of flavour observables. It is found that there is indeed a significant interplay between the structure of the extra dimension and flavour phenomenology at a scale of 1-10 TeV. Although it turns out that the previously studied construction was already quite well-optimised with regard to flavour constraints, it is demonstrated that one can do more to ameliorate these via deformations to the background geometry and modifications to the power law dependence of the fermion masses on the extra dimension

Changes of oxygen isotope values of soil P pools associated with changes in soil pH

Field data about the effect of soil pH on phosphorus (P) cycling is limited. A promising tool to study P cycling under field conditions is the 18O:16O ratio of phosphate (δ18OP). In this study we investigate whether the δ18OP can be used to elucidate the effect of soil pH on P cycling in grasslands. Soils and plants were sampled from different fertilisation and lime treatments of the Park Grass long term experiment at Rothamsted Research, UK. The soils were sequentially extracted to isolate different soil P pools, including available P and corresponding δ18OP values were determined. We did not observe changes in plant δ18OP value, but soil P δ18OP values changed, and lower δ18OP values were associated with higher soil pH values. At sites where P was not limiting, available P δ18OP increased by up to 3‰ when lime was applied. We show that the δ18OP method is a useful tool to investigate the effect of pH on soil P cycling under field conditions as it highlights that different soil processes must govern P availability as pH shifts. The next challenge is now to identify these underlying processes, enabling better management of soil P at different pH

Experience of the JPL Exploratory Data Analysis Team at validating HIRS2/MSU cloud parameters

Validation of the HIRS2/MSU cloud parameters began with the cloud/climate feedback problem. The derived effective cloud amount is less sensitive to surface temperature for higher clouds. This occurs because as the cloud elevation increases, the difference between surface temperature and cloud temperature increases, so only a small change in cloud amount is needed to effect a large change in radiance at the detector. By validating the cloud parameters it is meant 'developing a quantitative sense for the physical meaning of the measured parameters', by: (1) identifying the assumptions involved in deriving parameters from the measured radiances, (2) testing the input data and derived parameters for statistical error, sensitivity, and internal consistency, and (3) comparing with similar parameters obtained from other sources using other techniques

Validating a large geophysical data set: Experiences with satellite-derived cloud parameters

We are validating the global cloud parameters derived from the satellite-borne HIRS2 and MSU atmospheric sounding instrument measurements, and are using the analysis of these data as one prototype for studying large geophysical data sets in general. The HIRS2/MSU data set contains a total of 40 physical parameters, filling 25 MB/day; raw HIRS2/MSU data are available for a period exceeding 10 years. Validation involves developing a quantitative sense for the physical meaning of the derived parameters over the range of environmental conditions sampled. This is accomplished by comparing the spatial and temporal distributions of the derived quantities with similar measurements made using other techniques, and with model results. The data handling needed for this work is possible only with the help of a suite of interactive graphical and numerical analysis tools. Level 3 (gridded) data is the common form in which large data sets of this type are distributed for scientific analysis. We find that Level 3 data is inadequate for the data comparisons required for validation. Level 2 data (individual measurements in geophysical units) is needed. A sampling problem arises when individual measurements, which are not uniformly distributed in space or time, are used for the comparisons. Standard 'interpolation' methods involve fitting the measurements for each data set to surfaces, which are then compared. We are experimenting with formal criteria for selecting geographical regions, based upon the spatial frequency and variability of measurements, that allow us to quantify the uncertainty due to sampling. As part of this project, we are also dealing with ways to keep track of constraints placed on the output by assumptions made in the computer code. The need to work with Level 2 data introduces a number of other data handling issues, such as accessing data files across machine types, meeting large data storage requirements, accessing other validated data sets, processing speed and throughput for interactive graphical work, and problems relating to graphical interfaces

A comparison of aphasia therapy outcomes before and after a Very Early Rehabilitation programme following stroke

Background Very early aphasia rehabilitation studies have shown mixed results. Differences in therapy intensity and therapy type contribute significantly to the equivocal results. Aims To compare a standardized, prescribed very early aphasia therapy regimen with a historical usual care control group at therapy completion (4-5 weeks post-stroke) and again at follow-up (6 months). Methods & Procedures This study compared two cohorts from successive studies conducted in four Australian acute/sub-acute hospitals. The studies had near identical recruitment, blinded assessment and data-collection protocols. The Very Early Rehabilitation (VER) cohort (N = 20) had mild-severe aphasia and received up to 20 1-h sessions of impairment-based aphasia therapy, up to 5 weeks. The control cohort (n = 27) also had mild-severe aphasia and received usual care (UC) therapy for up to 4 weeks post-stroke. The primary outcome measure was the Aphasia Quotient (AQ) and a measure of communicative efficiency (DA) at therapy completion. Outcomes were measured at baseline, therapy completion and 6 months post-stroke and were compared using Generalised Estimating Equations (GEE) models. Outcomes & Results After controlling for initial aphasia and stroke disability, the GEE models demonstrated that at the primary end-point participants receiving VER achieved 18% greater recovery on the AQ and 1.5% higher DA scores than those in the control cohort. At 6 months, the VER participants maintained a 16% advantage in recovery on the AQ and 0.6% more on DA scores over the control cohort participants. Conclusions & Implications A prescribed, impairment-based aphasia therapy regimen, provided daily in very early post-stroke recovery, resulted in significantly greater communication gains in people with mild-severe aphasia at completion of therapy and at 6 months, when compared with a historical control cohort. Further research is required to demonstrate large-scale and long-term efficacy

A comparison of aphasia therapy outcomes before and after a Very Early Rehabilitation programme following stroke

Background Very early aphasia rehabilitation studies have shown mixed results. Differences in therapy intensity and therapy type contribute significantly to the equivocal results. Aims To compare a standardized, prescribed very early aphasia therapy regimen with a historical usual care control group at therapy completion (4-5 weeks post-stroke) and again at follow-up (6 months). Methods & Procedures This study compared two cohorts from successive studies conducted in four Australian acute/sub-acute hospitals. The studies had near identical recruitment, blinded assessment and data-collection protocols. The Very Early Rehabilitation (VER) cohort (N = 20) had mild-severe aphasia and received up to 20 1-h sessions of impairment-based aphasia therapy, up to 5 weeks. The control cohort (n = 27) also had mild-severe aphasia and received usual care (UC) therapy for up to 4 weeks post-stroke. The primary outcome measure was the Aphasia Quotient (AQ) and a measure of communicative efficiency (DA) at therapy completion. Outcomes were measured at baseline, therapy completion and 6 months post-stroke and were compared using Generalised Estimating Equations (GEE) models. Outcomes & Results After controlling for initial aphasia and stroke disability, the GEE models demonstrated that at the primary end-point participants receiving VER achieved 18% greater recovery on the AQ and 1.5% higher DA scores than those in the control cohort. At 6 months, the VER participants maintained a 16% advantage in recovery on the AQ and 0.6% more on DA scores over the control cohort participants. Conclusions & Implications A prescribed, impairment-based aphasia therapy regimen, provided daily in very early post-stroke recovery, resulted in significantly greater communication gains in people with mild-severe aphasia at completion of therapy and at 6 months, when compared with a historical control cohort. Further research is required to demonstrate large-scale and long-term efficacy

Factors associated with recovery from paraplegia in dogs with loss of pain perception in the pelvic limbs following intervertebral disk herniation

Abstract OBJECTIVE To investigate associations between recovery of locomotion and putative prognostic factors in dogs with loss of deep pain perception in the pelvic limbs caused by intervertebral disk herniation (IVDH). DESIGN Prospective cohort study. ANIMALS 78 client-owned dogs evaluated for IVDH that underwent spinal decompression surgery. PROCEDURES Dogs with complete loss of deep pain perception in the pelvic limbs and tail underwent routine examinations, advanced imaging, and spinal decompression surgery in accordance with standards of practice and owner consent. For each dog, information was prospectively collected on duration of clinical signs prior to onset of paraplegia; delay between onset of paraplegia and initial referral evaluation; date of recovery of locomotion, death, or euthanasia (3-month follow-up period); and whether dogs had received corticosteroid drugs before surgery. Severity of spinal cord compression at the lesion epicenter was measured via CT or MRI. RESULTS 45 of 78 (58%) of dogs recovered the ability to ambulate independently within 3 months after spinal decompression surgery. No evidence of prognostic value was identified for any of the investigated factors; importantly, a greater delay between onset of paraplegia and referral evaluation was not associated with a poorer prognosis. CONCLUSIONS AND CLINICAL RELEVANCE In this group of dogs with IVDH, immediacy of surgical treatment had no apparent association with outcome. The prognosis for recovery may instead be strongly influenced by the precise nature of the initiating injury.</jats:p