The identification of teaching interactions used in one-to-one teaching of number in the early years of schooling

This research paper reports on phase one of an investigation of video recorded intensive one-to-one teaching interactions with 6–7-year-old students who were in their second year of schooling in Australia and identified by the their teacher as low attaining in early number. The two-phased study from which this paper emerges was originally conducted in 1998 as part of my Bachelor of Teaching Honours (Research) program at Southern Cross University Lismore, New South Wales. That study identified teaching interactions particularly suited to one-to-one teaching in the Maths Recovery Program, a program designed for these students who were at risk of failure in early number. Since that time a great deal has not changed with limited literature available that comprehensively reports on teaching interactions in intensive one-to-one settings. Revisiting the original study is considered timely given the increasing number of withdrawal and intensive programs now funded and adopted by schools and yet, rarely reported on in terms of the effectiveness of the teaching interactions that occur in such settings. This paper then presents a discussion of a preliminary series of teaching interactions that either positively and or negatively influence an intensive one-to-one teaching and learning setting

Circulating concentrations of leptin, ovarian follicle number, and oocyte lipid content and active mitochondria, in Zebu crossbred cows maintained on standard or improved nutrition

Zebu (Bos indicus) crossbred beef cows (Droughtmaster) were maintained long-term (16 months) on standard nutrition (SN) or improved nutrition (IN). Cows on IN had better body condition and greater (P<0.05) circulating concentrations of leptin than cows on SN (0.7±0.1n/ml and 1.7±0.1n/ml, respectively). There were no outstanding differences between SN and IN cows in basal number of ovarian follicles (≤4mm, 5-8mm, and≥9mm) and there were also no differences in number of oocytes recovered by oocyte pick-up. Cows on IN had a greater (P<0.05) number of total follicles after stimulation with FSH than cows on SN. Oocytes from cows on IN had greater (P<0.05) lipid content than cows on SN (-0.23±0.16 and 0.20±0.18 arbitrary units, respectively) and oocytes of the former cows also tended to have more active mitochondria, although this was not significant. Cows on IN showed a positive relationship (R2=0.31, P<0.05) between plasma leptin and oocyte lipid content. Lipids are utilized by oocytes during high energy consumptive processes including fertilization and early cleavage. The greater lipid content of oocytes from IN cows could therefore confer a reproductive advantage. The present study has shown relationships between nutrition, body condition, circulating leptin, and oocyte lipid content, but a clear cause-and-effect requires further investigation in the cow. © 2013 Elsevier B.V.

Hadwiger Number and the Cartesian Product of Graphs

The Hadwiger number eta(G) of a graph G is the largest integer n for which the complete graph K-n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, eta(G) >= chi(G), where chi(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G square H of graphs. As the main result of this paper, we prove that eta(G(1) square G(2)) >= h root 1 (1 - o(1)) for any two graphs G(1) and G(2) with eta(G(1)) = h and eta(G(2)) = l. We show that the above lower bound is asymptotically best possible when h >= l. This asymptotically settles a question of Z. Miller (1978). As consequences of our main result, we show the following: 1. Let G be a connected graph. Let G = G(1) square G(2) square ... square G(k) be the ( unique) prime factorization of G. Then G satisfies Hadwiger's conjecture if k >= 2 log log chi(G) + c', where c' is a constant. This improves the 2 log chi(G) + 3 bound in [2] 2. Let G(1) and G(2) be two graphs such that chi(G1) >= chi(G2) >= clog(1.5)(chi(G(1))), where c is a constant. Then G1 square G2 satisfies Hadwiger's conjecture. 3. Hadwiger's conjecture is true for G(d) (Cartesian product of G taken d times) for every graph G and every d >= 2. This settles a question by Chandran and Sivadasan [2]. ( They had shown that the Hadiwger's conjecture is true for G(d) if d >= 3).

MECHANISMS AND EFFECTS OF MITOCHONDRIAL DNA INSTABILITY AND COPY NUMBER MANIPULATION

Defects in mitochondrial DNA (mtDNA) maintenance cause a range of human diseases, including autosomal dominant progressive external ophthalmoplegia (adPEO). This study aimed to clarify the molecular background of adPEO. We discovered that deoxynucleoside triphosphate (dNTP) metabolism plays a crucial in mtDNA maintenance and were thus prompted to search for therapeutic strategies based on the modulation of cellular dNTP pools or mtDNA copy number. Human mtDNA is a 16.6 kb circular molecule present in hundreds to thousands of copies per cell. mtDNA is compacted into nucleoprotein clusters called nucleoids. mtDNA maintenance diseases result from defects in nuclear encoded proteins that maintain the mtDNA. These syndromes typically afflict highly differentiated, post-mitotic tissues such as muscle and nerve, but virtually any organ can be affected. adPEO is a disease where mtDNA molecules with large-scale deletions accumulate in patients tissues, particularly in skeletal muscle. Mutations in five nuclear genes, encoding the proteins ANT1, Twinkle, POLG, POLG2 and OPA1, have previously been shown to cause adPEO. Here, we studied a large North American pedigree with adPEO, and identified a novel heterozygous mutation in the gene RRM2B, which encodes the p53R2 subunit of the enzyme ribonucleotide reductase (RNR). RNR is the rate-limiting enzyme in dNTP biosynthesis, and is required both for nuclear and mitochondrial DNA replication. The mutation results in the expression of a truncated form of p53R2, which is likely to compete with the wild-type allele. A change in enzyme function leads to defective mtDNA replication due to altered dNTP pools. Therefore, RRM2B is a novel adPEO disease gene. The importance of adequate dNTP pools and RNR function for mtDNA maintenance has been established in many organisms. In yeast, induction of RNR has previously been shown to increase mtDNA copy number, and to rescue the phenotype caused by mutations in the yeast mtDNA polymerase. To further study the role of RNR in mammalian mtDNA maintenance, we used mice that broadly overexpress the RNR subunits Rrm1, Rrm2 or p53R2. Active RNR is a heterotetramer consisting of two large subunits (Rrm1) and two small subunits (either Rrm2 or p53R2). We also created bitransgenic mice that overexpress Rrm1 together with either Rrm2 or p53R2. In contrast to the previous findings in yeast, bitransgenic RNR overexpression led to mtDNA depletion in mouse skeletal muscle, without mtDNA deletions or point mutations. The mtDNA depletion was associated with imbalanced dNTP pools. Furthermore, the mRNA expression levels of Rrm1 and p53R2 were found to correlate with mtDNA copy number in two independent mouse models, suggesting nuclear-mitochondrial cross talk with regard to mtDNA copy number. We conclude that tight regulation of RNR is needed to prevent harmful alterations in the dNTP pool balance, which can lead to disordered mtDNA maintenance. Increasing the copy number of wild-type mtDNA has been suggested as a strategy for treating PEO and other mitochondrial diseases. Only two proteins are known to cause a robust increase in mtDNA copy number when overexpressed in mice; the mitochondrial transcription factor A (TFAM), and the mitochondrial replicative helicase Twinkle. We studied the mechanisms by which Twinkle and TFAM elevate mtDNA levels, and showed that Twinkle specifically implements mtDNA synthesis. Furthermore, both Twinkle and TFAM were found to increase mtDNA content per nucleoid. Increased mtDNA content in mouse tissues correlated with an age-related accumulation of mtDNA deletions, depletion of mitochondrial transcripts, and progressive respiratory dysfunction. Simultaneous overexpression of Twinkle and TFAM led to a further increase in the mtDNA content of nucleoids, and aggravated the respiratory deficiency. These results suggested that high mtDNA levels have detrimental long-term effects in mice. These data have to be considered when developing and evaluating treatment strategies for elevating mtDNA copy number.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Studies on the effects of test gas on the flow field around large angle blunt cone flying at hypersonic Mach number

The effect of the test gas on the flow field around a 120degrees apex angle blunt cone has been investigated in a shock tunnel at a nominal Mach number of 5.75. The shock standoff distance around the blunt cone was measured by an electrical discharge technique using both carbon dioxide and air as test gases. The forebody laminar convective heat transfer to the blunt cone was measured with platinum thin-film sensors in both air and carbon dioxide environments. An increase of 10 to 15% in the measured heat transfer values was observed with carbon dioxide as the test gas in comparison to air. The measured thickness of the shock layer along the stagnation streamline was 3.57 +/- 0.17 mm in air and 3.29 +/- 0.26 mm in carbon dioxide. The computed thickness of the shock layer for air and carbon dioxide were 3.98 mm and 3.02 mm, respectively. The observed increase in the measured heat transfer rates in carbon dioxide compared to air was due to the higher density ratio across the bow shock wave and the reduced shock layer thickness.

Measurement of Heat Transfer Rate on Backward-Facing Steps at Hypersonic Mach Number

Two backward-facing models with step heights of 2 and 3 mm are used to measure the convective surface heat transfer rates by using platinum thin-film gauges, deposited on Macor inserts. Heat transfer rates have been theoretically calculated along the flat plate portion of a model using the Eckert reference temperature method. The experimentally determined surface heat transfer rate distributions are compared with theoretical and numerical estimations. Experimental heat flux distribution over a flat plate model showed good agreement with the reference temperature method at stagnation enthalpy range of 0.8-2 MJ/kg. Theoretical analysis has been used for downstream of a backward-facing step using Gai's nondimensional analysis. It has been found from the present study that approximately 10 and 8 step heights are required for the flow to reattach for 2 and 3 mm step height backward-facing step models, respectively, at a nominal Mach number of 7.6.

Active Vibration Suppression of One-dimensional Nonlinear Structures Using Optimal Dynamic Inversion

A flexible robot arm can be modeled as an Euler-Bernoulli beam which are infinite degrees of freedom (DOF) system. Proper control is needed to track the desired motion of a robotic arm. The infinite number of DOF of beams are reduced to finite number for controller implementation, which brings in error (due to their distributed nature). Therefore, to represent reality better distributed parameter systems (DPS) should be controlled using the systems partial differential equation (PDE) directly. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a controller to suppress nonlinear vibration of a beam. The method used in this paper determines control forces directly from the PDE model of the system. The formulation has better practical significance, because it leads to a closed form solution of the controller (hence avoids computational issues).

Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

Effect of myonuclear number and mitochondrial fusion on Drosophila indirect flight muscle organization and size

Mechanisms involved in establishing the organization and numbers of fibres in a muscle are not completely understood. During Drosophila indirect flight muscle (IFM) formation, muscle growth is achieved by both incorporating hundreds of nuclei, and hypertrophy. As a result, IFMs provide a good model with which to understand the mechanisms that govern overall muscle organization and growth. We present a detailed analysis of the organization of dorsal longitudinal muscles (DLMs), a subset of the IFMs. We show that each DLM is similar to a vertebrate fascicle and consists of multiple muscle fibres. However, increased fascicle size does not necessarily change the number of constituent fibres, but does increase the number of myofibrils packed within the fibres. We also find that altering the number of myoblasts available for fusion changes DLM fascicle size and fibres are loosely packed with myofibrils. Additionally, we show that knock down of genes required for mitochondrial fusion causes a severe reduction in the size of DLM fascicles and fibres. Our results establish the organization levels of DLMs and highlight the importance of the appropriate number of nuclei and mitochondrial fusion in determining the overall organization, growth and size of DLMs. (C) 2013 Elsevier Inc. All rights reserved.

Impact dynamics of high Weber number drops on chemically modified metallic surfaces

Hydrophobic/superhydrophobic metallic surfaces prepared via chemical treatment are encountered in many industrial scenarios involving the impingement of spray droplets. The effectiveness of such surfaces is understood through the analysis of droplet impact experiments. In the present study, three target surfaces with aluminum (Al-6061) as base material-acid-etched, Octadecyl Trichloro Silane (OTS) coated, and acid-etched plus OTS-coated-were prepared. Experiments on the impact of inertia dominated water drops on these chemically modified aluminum surfaces were carried out with the objective to highlight the effect of chemical treatment on the target surfaces on key sub-processes occurring in drop impact phenomenon. High speed videos of the entire drop impact dynamics were captured at three Weber number (We) conditions representative of high We (We > 200) regime. During the early stages of drop spreading, the drop impact resulted in ejection of secondary droplets from spreading drop front on the etched surfaces resembling prompt splash on rough surfaces whereas no such splashing was observable on untreated aluminum surface. Prominent development of undulations (fingers) were observed at the rim of drop spreading on the etched surfaces; between the etched surfaces the OTS-coated surface showed a subdued development of fingers than the uncoated surface. The impacted drops showed intense receding on OTS-coated surfaces whereas on the etched surface a highly irregular receding, with drop liquid sticking to the surface, was observed. Quantitative analyses were performed to reveal the effect of target surface characteristics on drop impact parameters such as temporal variation of spread factor of drop lamella, temporal variation of average finger length during spreading phase, maximum drop spreading, time taken to attain maximum spreading, sensitivity of maximum spreading to We, number of fingers at maximum spreading, and average receding velocity of drop lamella. Existing models for maximum drop spreading showed reasonably good agreement with the experimental measurements on the target surfaces except the acid-etched surface. (C) 2014 Elsevier B.V. All rights reserved.

On Additive Combinatorics of Permutations of Z(n)

Let Z(n) denote the ring of integers modulo n. A permutation of Z(n) is a sequence of n distinct elements of Z(n). Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Z(n), namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s (n) and t (n) respectively. The case when n is even is trivial in both the cases, with s (n) = 1 and t (n) = n!. For n odd, we prove (n phi(n))/2(k) <= s(n) <= n!.2(-)(n-1)/2/((n-1)/2)! and 2 (n-1)/2 . (n-1/2)! <= t (n) <= 2(k) . (n-1)!/phi(n), where k is the number of distinct prime divisors of n and phi is the Euler's totient function.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Hydrothermal Instability Of Thermocapillary Convection In Large-Prandtl-Number Liquid Bridges Under Microgravity

Linear stability analysis was performed to study the mechanism of transition of thermocapillary convection in liquid bridges with liquid volume ratios ranging from 0.4 to 1.2, aspect ratio of 0.75 and Prandtl number of 100. 2-D governing equations were solved to obtain the steady axi-symmetric basic flow and temperature distributions. 3-D perturbation equations were discretized at the collocation grid points using the Chebyshev-collocation method. Eigenvalues and eigenfunctions were obtained by using the Q-R. method. The predicted critical Marangoni numbers and critical frequencies were compared with data from space experiments. The disturbance of the temperature distribution on the free surface causes the onset of oscillatory convection. It is shown that the origin of instability is related to the hydrothermal origin for convections in large-Prandtl-number liquid bridges. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.