Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

MöBIUS-α commutative functions and partially coincident functions

The M¨obius transform of Boolean functions is often involved in cryptographic design and analysis. As studied previously, a Boolean function f is said to be coincident if it is identical with its M¨obius transform fμ, i.e., f = fμ...

Validation of ACE-FTS satellite data in the upper troposphere/lower stratosphere (UTLS) using non-coincident measurements

CO, O3, and H2O data in the upper troposphere/lower stratosphere (UTLS) measured by the Atmospheric Chemistry Experiment Fourier Transform Spectrometer(ACE-FTS) on Canada’s SCISAT-1 satellite are validated using aircraft and ozonesonde measurements. In the UTLS, validation of chemical trace gas measurements is a challenging task due to small-scale variability in the tracer fields, strong gradients of the tracers across the tropopause, and scarcity of measurements suitable for validation purposes. Validation based on coincidences therefore suffers from geophysical noise. Two alternative methods for the validation of satellite data are introduced, which avoid the usual need for coincident measurements: tracer-tracer correlations, and vertical tracer profiles relative to tropopause height. Both are increasingly being used for model validation as they strongly suppress geophysical variability and thereby provide an “instantaneous climatology”. This allows comparison of measurements between non-coincident data sets which yields information about the precision and a statistically meaningful error-assessment of the ACE-FTS satellite data in the UTLS. By defining a trade-off factor, we show that the measurement errors can be reduced by including more measurements obtained over a wider longitude range into the comparison, despite the increased geophysical variability. Applying the methods then yields the following upper bounds to the relative differences in the mean found between the ACE-FTS and SPURT aircraft measurements in the upper troposphere (UT) and lower stratosphere (LS), respectively: for CO ±9% and ±12%, for H2O ±30% and ±18%, and for O3 ±25% and ±19%. The relative differences for O3 can be narrowed down by using a larger dataset obtained from ozonesondes, yielding a high bias in the ACEFTS measurements of 18% in the UT and relative differences of ±8% for measurements in the LS. When taking into account the smearing effect of the vertically limited spacing between measurements of the ACE-FTS instrument, the relative differences decrease by 5–15% around the tropopause, suggesting a vertical resolution of the ACE-FTS in the UTLS of around 1 km. The ACE-FTS hence offers unprecedented precision and vertical resolution for a satellite instrument, which will allow a new global perspective on UTLS tracer distributions.

Regulating the expression of eEF1A to decipher its non canonical functions in eukaryotic cells

The canonical function of eEF1A is delivery of the aminoacylated tRNA to the A site of the ribosome during protein translation, however, it is also known to be an actin binding protein. As well as this actin binding function, eEF1A has been shown to be involved in other cellular processes such as cell proliferation and apoptosis. It has long been thought that the actin cytoskeleton and protein synthesis are linked and eEF1A has been suggested to be a candidate protein to form this link, though very little is understood about the relationship between its two functions. Overexpression of eEF1A has also been shown to be implicated in many different types of cancers, especially cancers that are metastatic, therefore it is important to further understand how eEF1A can affect both translation and the organisation of the actin cytoskeleton. To this end, we aimed to determine the effects of reduced expression of eEF1A on both translation and its non canonical functions in CHO cells. We have shown that reduced expression of eEF1A in this cell system results in no change in protein synthesis, however results in an increased number of actin stress fibres and other proteins associated with these fibres such as myosin IIA, paxillin and vinculin. Cell motility and attachment are also affected by this reduction in eEF1A protein expression. The organisational and motility phenotypes were found to be specific to eEF1A by transforming the cells with plasmids containing either human eEF1A1 or eEF1A2. Though the mechanisms by which these effects are regulated have not yet been established, this data provides evidence to show that the translation and actin binding functions of eEF1A are independent of each other as well as being suggestive of a role for eEF1A in cell motility as supported by the observation that overexpression of eEF1A protein tends to be associated with the cancer cells that are metastatic.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Professional non-neutrality: criticising the third party in psychotherapy

Using audio-recorded data from cognitive-constructivist psychotherapy, the article shows a particular institutional context in which successful professional action does not adhere to the pattern of affective neutrality which Parsons saw as an inherent component of medicine and psychotherapy. In our data, the professional’s non-neutrality functions as a tool for achieving institutional goals. The analysis focuses on the psychotherapist’s actions that convey a critical stance towards a third party with whom the patient has experienced problems. The data analysis revealed two practices of this kind of critique: (1) the therapist can confirm the critique that the patient has expressed or (2) return to the critique from which the patient has focused away. These actions are shown to build grounds for the therapist’s further actions that challenge the patient’s dysfunctional beliefs. The article suggests that in the case of psychotherapy, actions that as such might be seen as apparent lapses from the neutral professional role can in their specific context perform the task of the institution at hand.

Expanding the Toolkit for Synthetic Biology: Frameworks for Native-like Non-natural Gene Circuits

Synthetic biology combines biological parts from different sources in order to engineer non-native, functional systems. While there is a lot of potential for synthetic biology to revolutionize processes, such as the production of pharmaceuticals, engineering synthetic systems has been challenging. It is oftentimes necessary to explore a large design space to balance the levels of interacting components in the circuit. There are also times where it is desirable to incorporate enzymes that have non-biological functions into a synthetic circuit. Tuning the levels of different components, however, is often restricted to a fixed operating point, and this makes synthetic systems sensitive to changes in the environment. Natural systems are able to respond dynamically to a changing environment by obtaining information relevant to the function of the circuit. This work addresses these problems by establishing frameworks and mechanisms that allow synthetic circuits to communicate with the environment, maintain fixed ratios between components, and potentially add new parts that are outside the realm of current biological function. These frameworks provide a way for synthetic circuits to behave more like natural circuits by enabling a dynamic response, and provide a systematic and rational way to search design space to an experimentally tractable size where likely solutions exist. We hope that the contributions described below will aid in allowing synthetic biology to realize its potential.

A generalized Hausdorff dimension for functions and sets

Let E be a compact subset of the n-dimensional unit cube, 1_n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number

d_C(E) = sup(β:H_{β, C}(E) > 0),

where H_{β, C} is the outer measure

inf(Ʃm(C_i)^β:UC_i Ↄ E, C_i ϵ C) .

Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’_n, of 1_n, whose closure intersects 1_n - 1’_n. For n = 2, the outer measure H_{β, C} is adopted in place of the usual:

Inf(Ʃ(diam. (C_i))^β: UC_i Ↄ E, C_i ϵ C),

for the purpose of studying the influence of the shape of the covering sets on the dimension d_C(E).

If E is a closed set in 1₁, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),

d_C(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)

where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that

d_C(E) = sup (d_C(μ):μ ϵ M(E)).

This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of d_C(E) as a function of the covering class C is reduced to the study of d_C(f) where f ϵ Ӻ. Specifically, the set of points in 1₁,

(*) {d_B(F), d_C(f)): f ϵ Ӻ}

is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 1₂, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.

In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 1₂ with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula

d_C(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C

where

∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).

A characterization of the equivalence d_C1(f) = d_C2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ C_i (I = 1, 2).

On the functions of products

Understanding the performance and manner of functioning of existing products is at the base of new product development activities. In engineering design the term function is generally used to refer to the technical actions performed by a product. However, products accomplish a wider range of goals. This research explores the opportunity to describe and model, through the concept of function, product actions across four dimensions including technical, aesthetic, social and economic. The research demonstrates that non-technical functions can be represented through active verbs and nouns and modelled using a method known as the Function Analysis Diagram (FAD). The research argues that when technical, aesthetic, social and economic perspectives on product development are considered as different types of function, stakeholders have a common language to communicate which can benefit design collaboration.

Early impairment of cognitive functions in Parkinson's disease

Background: Impairment in non-motor functions such as disturbances of some executive functions are also common events in Parkinson's disease patients. Objective: To verify the performance of Parkinson's disease patients in activities requiring visuoconstructive and visuospatial skills. Method: Thirty elderly patients with mild or moderate stages of Parkinson's disease were studied. The assessment of the clinical condition was based on the unified Parkinson's disease rating scale (56.28; SD=33.48), Hoehn and Yahr (2.2; SD=0.83), Schwab and England (78.93%), clock drawing test (7.36; SD=2.51), and mini-mental state examination (26.48; SD=10.11). Pearson's correlation and stepwise multiple regression were used for statistical analyses. Results: The patients presented deterioration in visuospatial and visuoconstructive skills. Conclusion: The clock drawing test proved to be a useful predictive tool for identifying early cognitive impairment in these individuals.

FANCM AND FAAP24 MAINTAIN GENOMIC STABILITY THROUGH COOPERATIVE AND UNIQUE FUNCTIONS

Fanconi anemia (FA) is a rare recessive genetic disease with an array of clinical manifestations including multiple congenital abnormalities, progressive bone marrow failure and profound cancer susceptibility. A hallmark of cells derived from FA patients is hypersensitivity to DNA interstrand crosslinking agents such as mitomycin C (MMC) and cisplatin, suggesting that FA- and FA-associated proteins play important roles in protecting cells from DNA interstrand crosslink (ICL) damage. Two genes involved in the FA pathway, FANCM and FAAP24, are of particular interest because they contain DNA interacting domains. However, there are no definitive patient mutations for these two genes, and the resulting lack of human genetic model system renders their functional studies difficult. In this study, I established isogenic human FANCM- and FAAP24-null mutants through homologous replacement-mediated gene targeting in HCT-116 cells, and systematically investigated the functions of FANCM and FAAP24 inchromosome stability, FA pathway activation, DNA damage checkpoint signaling, and ICL repair. I found that the FANCM-/-/FAAP24-/- double mutant was much more sensitive to DNA crosslinking agents than FANCM-/- and FAAP24-/- single mutants, suggesting that FANCM and FAAP24 possess epistatic as well as unique functions in response to ICL damage. I demonstrated that FANCM and FAAP24 coordinately support the activation of FA pathway by promoting chromatin localization of FA core complex and FANCD2 monoubiqutination. They also cooperatively function to suppress sister chromatid exchange and radial chromosome formation, likely by limiting crossovers in recombination repair. In addition, I defined novel non-overlapping functions of FANCM and FAAP24 in response to ICL damage. FAAP24 plays a major role in activating ICL-induced ATR-dependent checkpoint, which is independent of its interaction with FANCM. On the other hand, FANCM promotes recombination-independent ICL repair independently of FAAP24. Mechanistically, FANCM facilitates recruitment of nucleotide excision repair machinery and lesion bypass factors to ICL damage sites through its translocase activity. Collectively, my studies provide mechanistic insights into how genome integrity is both coordinately and independently protected by FANCM and FAAP24.

CaV channels and cancer: canonical functions indicate benefits of repurposed drugs as cancer therapeutics

The importance of ion channels in the hallmarks of many cancers is increasingly recognised. This article reviews current knowledge of the expression of members of the voltage-gated calcium channel family (CaV) in cancer at the gene and protein level and discusses their potential functional roles. The ten members of the CaV channel family are classified according to expression of their pore-forming α-subunit; moreover, co-expression of accessory α2δ, β and γ confers a spectrum of biophysical characteristics including voltage dependence of activation and inactivation, current amplitude and activation/inactivation kinetics. CaV channels have traditionally been studied in excitable cells including neurones, smooth muscle, skeletal muscle and cardiac cells, and drugs targeting the channels are used in the treatment of hypertension and epilepsy. There is emerging evidence that several CaV channels are differentially expressed in cancer cells compared to their normal counterparts. Interestingly, a number of CaV channels also have non-canonical functions and are involved in transcriptional regulation of the expression of other proteins including potassium channels. Pharmacological studies show that CaV canonical function contributes to the fundamental biology of proliferation, cell-cycle progression and apoptosis. This raises the intriguing possibility that calcium channel blockers, approved for the treatment of other conditions, could be repurposed to treat particular cancers. Further research will reveal the full extent of both the canonical and non-canonical functions of CaV channels in cancer and whether calcium channel blockers are beneficial in cancer treatment.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Neuropsychological development in children with early and continuously treated phenylketonuria : association with biochemical markers

PKU is a genetically inherited inborn error of metabolism caused by a deficiency of the enzyme phenylalanine hydroxylase. The failure of this enzyme causes incomplete metabolism of protein ingested in the diet, specifically the conversion of one amino acid, phenylalanine, to tyrosine, which is a precursor to the neurotransmitter dopamine. Rising levels of phenylalanine is toxic to the developing brain, disrupting the formation of white matter tracts. The impact of tyrosine deficiency is not as well understood, but is hypothesized to lead to a low dopamine environment for the developing brain. Detection in the newborn period and continuous treatment (a low protein phe-restricted diet supplemented with phenylalanine-free protein formulas) has resulted in children with early and continuously treated PKU now developing normal I.Q. However, deficits in executive function (EF) are common, leading to a rate of Attention Deficit Hyperactivity Disorder (ADHD) up to five times the norm. EF worsens with exposure to higher phenylalanine levels, however recent research has demonstrated that a high phenylalanine to tyrosine ratio (phenylalanine:tyrosine ratio), which is hypothesised to lead to poorer dopamine function, has a more negative impact on EF than phenylalanine levels alone. Research and treatment of PKU is currently phenylalanine-focused, with little investigation of the impact of tyrosine on neuropsychological development. There is no current consensus as to the veracity of tyrosine monitoring or treatment in this population. Further, the research agenda in this population has demonstrated a primary focus on EF impairment alone, even though there may be additional neuropsychological skills compromised (e.g., mood, visuospatial deficits). The aim of this PhD research was to identify residual neuropsychological deficits in a cohort of children with early and continuously treated phenylketonuria, at two time points in development (early childhood and early adolescence), separated by eight years. In addition, this research sought to determine which biochemical markers were associated with neuropsychological impairments. A clinical practice survey was also undertaken to ascertain the current level of monitoring/treatment of tyrosine in this population. Thirteen children with early and continuously treated PKU were tested at mean age 5.9 years and again at mean age 13.95 years on several neuropsychological measures. Four children with hyperphenylalaninemia (a milder version of PKU) were also tested at both time points and provide a comparison group in analyses. Associations between neuropsychological function and biochemical markers were analysed. A between groups analysis in adolescence was also conducted (children with PKU compared to their siblings) on parent report measures of EF and mood. Minor EF impairments were evident in the PKU group by age 6 years and these persisted into adolescence. Life-long exposure to high phenylalanine:tyrosine ratio and/or low tyrosine independent of phenylalanine were significantly associated with EF impairments at both time points. Over half the children with PKU showed severe impairment on a visuospatial task, and this was associated only with concurrent levels of tyrosine in adolescence. Children with PKU also showed a statistically significant decline in a language comprehension task from 6 years to adolescence (going from normal to subnormal), this deficit was associated with lifetime levels of phenylalanine. In comparison, the four children with hyperphenylalaninemia demonstrated normal function at both time points, across all measures. No statistically significant differences were detected between children with PKU and their siblings on the parent report of EF and mood. However, depressive symptoms were significantly correlated with: EF; long term high phe:tyr exposure; and low tyrosine levels independent of phenylalanine. The practice survey of metabolic clinics from 12 countries indicated a high level of variability in terms of monitoring/treatment of tyrosine in this population. Whilst over 80% of clinics surveyed routinely monitored tyrosine levels in their child patients, 25% reported treatment strategies to increase tyrosine (and thereby lower the phenylalanine:tyrosine ratio) under a variety of patient presentation conditions. Overall, these studies have shown that EF impairments associated with PKU provide support for the dopamine-deficiency model. A language comprehension task showed a different trajectory, serving a timely reminder that non-EF functions also remain vulnerable in this population; and that normal function in childhood does not guarantee normal function by adolescence. Mood impairments were associated with EF impairments as well as long term measures of phenylalanine:tyrosine and/or tyrosine. The implications of this research for enhanced clinical guidelines are discussed given varied current practice.

Spatio-temporal modelling of ultrafine particle number concentration

This thesis developed semi-parametric regression models for estimating the spatio-temporal distribution of outdoor airborne ultrafine particle number concentration (PNC). The models developed incorporate multivariate penalised splines and random walks and autoregressive errors in order to estimate non-linear functions of space, time and other covariates. The models were applied to data from the "Ultrafine Particles from Traffic Emissions and Child" project in Brisbane, Australia, and to longitudinal measurements of air quality in Helsinki, Finland. The spline and random walk aspects of the models reveal how the daily trend in PNC changes over the year in Helsinki and the similarities and differences in the daily and weekly trends across multiple primary schools in Brisbane. Midday peaks in PNC in Brisbane locations are attributed to new particle formation events at the Port of Brisbane and Brisbane Airport.