A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

“Unintended effects”: A theorem for complex systems

Unintended effects are well known to economists and sociologists and their consequences may be devastating. The main objective of this article is to formulate a mathematical theorem, based on Gödel's famous incompleteness theorem, in which it is shown, that from the moment deontical modalities (prohibition, obligation, permission, and faculty) are introduced into the social system, responses are allowed by the system that are not produced, however, prohibited responses or unintended effects may occur.

Thermoregulatory response in hair sheep and shorn wool sheep

This study’s main goal was to evaluate the thermoregulatory responses velocity through the variation of rectal temperature (RT), related to the thermolytic pathways, respiratory rate (RR) and sweating rate (SR) among different sheep breeds. Ninety female sheep, eighteen of each breed: Santa Ines and Morada Nova (Brazilian hair breeds), Texel, Suffolk and Ile de France (wool breeds) were challenged during three non-consecutive summer days (22◦42′S, 47◦18′W, and 570m of altitude, maximum air temperature of 33.5◦C, average relative humidity of 52±6.9%). The physiological variables were registered at 0800h (T1), 1300 h (T2: after 2 h of shade rest), 1400 h (T3) (after one hour of sun exposure) and in the shade at 1415 h (T4), 1430 h (T5), 1445 h (T6) and 1500 h (T7) and a thermotolerance index (TCI) was calculated as (10-(T7 to T4)-T1). The statistical analysis was performed by a mathematical model including the fixed effects of breeds and time frames, and the interaction between these effects, besides random effects such as animal and day. The Santa Ines breed presented the lowest RT after sun exposure (39.3 ± 0.12 ◦ C; P < 0.05) and it was the only one to recover morning RT 60 min after heat stress (38.7 and 38.9 for 1300 h and 1500 h; P > 0.05). Hair breeds presented RR lower (P < 0.05) than wool breeds. Although thick wool or hair thickness differs among and within hair and wool breeds (P < 0.05), SR did not differ among breeds and time (227.7 ± 16.44 g m−2 h−1 ; P > 0.05). The thermotolerance index did not differ among breeds, but it showed similar response (P > 0.05) 45 min or 1 h of shade after sun exposure. One week post shearing is not enough to wool breeds present to show thermotolerance similar to hair breeds.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Antifungal activity of Pseudomonas frederiksbergensis CMAA 1323 isolated from the Antarctic hair grass Deschampsia antarctica.

Abstract: Aims: Epiphytic bacteria, isolated from Deschampsia antarctica, were screened for their potential to inhibit the plant pathogen Botrytis cinerea, the causal agent of gray mold disease of strawberry pseudofruits. This phytopathogenic fungus is more active and the disease is more serious in temperate climate where the temperatures are lower.

Membrane associated transporter protein gene (SLC45A2) and the genetic basis of normal human pigmentation variation

This work is concerned with the genetic basis of normal human pigmentation variation. Specifically, the role of polymorphisms within the solute carrier family 45 member 2 (SLC45A2 or membrane associated transporter protein; MATP) gene were investigated with respect to variation in hair, skin and eye colour ― both between and within populations. SLC45A2 is an important regulator of melanin production and mutations in the gene underly the most recently identified form of oculocutaneous albinism. There is evidence to suggest that non-synonymous polymorphisms in SLC45A2 are associated with normal pigmentation variation between populations. Therefore, the underlying hypothesis of this thesis is that polymorphisms in SLC45A2 will alter the function or regulation of the protein, thereby altering the important role it plays in melanogenesis and providing a mechanism for normal pigmentation variation. In order to investigate the role that SLC45A2 polymorphisms play in human pigmentation variation, a DNA database was established which collected pigmentation phenotypic information and blood samples of more than 700 individuals. This database was used as the foundation for two association studies outlined in this thesis, the first of which involved genotyping two previously-described non-synonymous polymorphisms, p.Glu272Lys and p.Phe374Leu, in four different population groups. For both polymorphisms, allele frequencies were significantly different between population groups and the 272Lys and 374Leu alleles were strongly associated with black hair, brown eyes and olive skin colour in Caucasians. This was the first report to show that SLC45A2 polymorphisms were associated with normal human intra-population pigmentation variation. The second association study involved genotyping several SLC45A2 promoter polymorphisms to determine if they also played a role in pigmentation variation. Firstly, the transcription start site (TSS), and hence putative proximal promoter region, was identified using 5' RNA ligase mediated rapid amplification of cDNA ends (RLM-RACE). Two alternate TSSs were identified and the putative promoter region was screened for novel polymorphisms using denaturing high performance liquid chromatography (dHPLC). A novel duplication (c.–1176_–1174dupAAT) was identified along with other previously described single nucleotide polymorphisms (c.–1721C>G and c.–1169G>A). Strong linkage disequilibrium ensured that all three polymorphisms were associated with skin colour such that the –1721G, +dup and –1169A alleles were associated with olive skin in Caucasians. No linkage disequilibrium was observed between the promoter and coding region polymorphisms, suggesting independent effects. The association analyses were complemented with functional data, showing that the –1721G, +dup and –1169A alleles significantly decreased SLC45A2 transcriptional activity. Based on in silico bioinformatic analysis that showed these alleles remove a microphthalmia-associated transcription factor (MITF) binding site, and that MITF is a known regulator of SLC45A2 (Baxter and Pavan, 2002; Du and Fisher, 2002), it was postulated that SLC45A2 promoter polymorphisms could contribute to the regulation of pigmentation by altering MITF binding affinity. Further characterisation of the SLC45A2 promoter was carried out using luciferase reporter assays to determine the transcriptional activity of different regions of the promoter. Five constructs were designed of increasing length and their promoter activity evaluated. Constitutive promoter activity was observed within the first ~200 bp and promoter activity increased as the construct size increased. The functional impact of the –1721G, +dup and –1169A alleles, which removed a MITF consensus binding site, were assessed using electrophoretic mobility shift assays (EMSA) and expression analysis of genotyped melanoblast and melanocyte cell lines. EMSA results confirmed that the promoter polymorphisms affected DNA-protein binding. Interestingly, however, the protein/s involved were not MITF, or at least MITF was not the protein directly binding to the DNA. In an effort to more thoroughly characterise the functional consequences of SLC45A2 promoter polymorphisms, the mRNA expression levels of SLC45A2 and MITF were determined in melanocyte/melanoblast cell lines. Based on SLC45A2’s role in processing and trafficking TYRP1 from the trans-Golgi network to stage 2 melanosmes, the mRNA expression of TYRP1 was also investigated. Expression results suggested a coordinated expression of pigmentation genes. This thesis has substantially contributed to the field of pigmentation by showing that SLC45A2 polymorphisms not only show allele frequency differences between population groups, but also contribute to normal pigmentation variation within a Caucasian population. In addition, promoter polymorphisms have been shown to have functional consequences for SLC45A2 transcription and the expression of other pigmentation genes. Combined, the data presented in this work supports the notion that SLC45A2 is an important contributor to normal pigmentation variation and should be the target of further research to elucidate its role in determining pigmentation phenotypes. Understanding SLC45A2’s function may lead to the development of therapeutic interventions for oculocutaneous albinism and other disorders of pigmentation. It may also help in our understanding of skin cancer susceptibility and evolutionary adaptation to different UV environments, and contribute to the forensic application of pigmentation phenotype prediction.

Does a high UV environment ensure adequate vitamin D status?

This study assesses the Vitamin D status of 126 healthy free-living adults aged 18–87 years, in southeast Queensland, Australia (27°S) at the end of the 2006 winter. Participants provided blood samples for analysis of 25(OH)D (the measure of an individual’s Vitamin D status), PTH, Calcium, Phosphate, and Albumin, completed a questionnaire on sun-protective/sun-exposure behaviours, and were assessed for phenotypic characteristics such as skin/hair/eye colour and BMI. We found that 10.2% of the participants had serum 25(OH)D levels below 25 nmol/l (considered deficient) and a further 32.3% had levels between 25 nmol/l and 50 nmol/l (considered insufficient). Our results show that low levels of 25(OH)D can occur in a substantial proportion of the population at the end of winter, even in a sunny climate. 25(OH)D levels were higher amongst those who spent more time in the sun and lower among obese participants (BMI > 30) than those who were not obese (BMI < 30). 25(OH)D levels were also lower in participants who had black hair, dark/olive skin, or brown eyes, when compared with participants who had brown or fair hair, fair skin, or blue/green eyes. No associations were found between 25(OH)D status and age, gender, smoking status, or the use of sunscreen.

Millwork

An exhibition of drawing and sculpture that extends the artist's process of self-portraiture, applying the historical form of the portrait roundel to the crown of the head as an exclusive subject matter.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

Soft-biometrics : unconstrained authentication in a surveillance environment

Soft biometrics are characteristics that can be used to describe, but not uniquely identify an individual. These include traits such as height, weight, gender, hair, skin and clothing colour. Unlike traditional biometrics (i.e. face, voice) which require cooperation from the subject, soft biometrics can be acquired by surveillance cameras at range without any user cooperation. Whilst these traits cannot provide robust authentication, they can be used to provide coarse authentication or identification at long range, locate a subject who has been previously seen or who matches a description, as well as aid in object tracking. In this paper we propose three part (head, torso, legs) height and colour soft biometric models, and demonstrate their verification performance on a subset of the PETS 2006 database. We show that these models, whilst not as accurate as traditional biometrics, can still achieve acceptable rates of accuracy in situations where traditional biometrics cannot be applied.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Workers’ UV exposure and the subsequent impact on skin

Introduction: Excessive exposure to ultraviolet (UV) radiation from sunlight is a causative factor in the development of skin damage and skin cancer. Little research has been undertaken into assessing the sun exposure linking to skin damage inside buildings or behind window glass. This project directly addressed this issue by aiming to assess the role that UV exposure has on skin damage for indoor workers and drivers. Methods: Measurements of personal UV exposure using UV sensitive polymer dosimeters were undertaken of 41 indoor workers and 3 professional drivers. Physical measurements of skin characteristics including skin pigmentation and UV induced skin photoaging were also determined. In addition, demographic information along with phenotypic characteristics, sun exposure and sun protection practice history, and history of skin damage were assessed through a questionnaire. Results: Indoor workers typically received low doses of UV radiation. However, one driver received a high dose (13J/cm2 UVA and 4.99 MED UVB on the arm). Age and years residing in Australia had a positive correlation with UV induced skin pigmentation. The number of major sunburns before 18 years was a risk factor for skin damage in adults. Those participants with fair skin, non-black hair and blue/green /blue-grey eye were more likely to have skin damage related to sun exposure. Conclusions: A person’s age, years residing in Australia, numbers of major sunburn, skin colour, hair colour and eye colour are important factors associated with the development of sun-related skin damage in workers. ‘Real World’ implications: 1. The number of major sunburns before 18 years was a risk factor for skin damage in adults. This clearly confirms the importance of early prevention. To protect the skin from extensive sun exposure for your generation should have significance for further prevention of skin damage. 2. It is unsurprising that age and years residing in Australia were associated with skin damage related UV radiation. Therefore, the general public should reinforce their sun protective measures and check skin regularly. 3. Drivers should take sun protective measures during their working hours between sunrise and sunset.

Melanocyte homeostasis in vivo tolerates Rb1 loss in a developmentally independent fashion

There has been uncertainty regarding the precise role that the pocket protein Rb1 plays in murine melanocyte homeostasis. It has been reported that the TAT-Cre mediated loss of exon 19 from a floxed Rb1 allele causes melanocyte apoptosis in vivo and in vitro. This is at variance with other findings showing, either directly or indirectly, that Rb1 loss in melanocytes has no noticeable effect in vivo, but in vitro leads to a semi-transformed phenotype. In this study, we show that Rb1-null melanocytes lacking exon 19 do not undergo apoptosis and survive both in vitro and in vivo, irrespective of the developmental stage at which Cre-mediated ablation of the exon occurs. Further, Rb1 loss has no serious long-term ramifications on melanocyte homeostasis in vivo, with Rb1-null melanocytes being detected in the skin after numerous hair cycles, inferring that the melanocyte stem cell population carrying the Cre-mediated deletion is maintained. Consequently, whilst Rb1 loss in the melanocyte is able to alter cellular behaviour in vitro, it appears inconsequential with respect to melanocyte homeostasis in the mouse skin.