Monotone graph limits and quasimonotone graphs

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasi-monotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1-W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.Comment: 38 page

Development of a digital electronic rebalance loop for a dry tuned-rotor two degree-of-freedom gyroscope

Digital electronic rebalance loops were designed and implemented in brassboard form to capture both X and Y axes of the Kearfott Gyroflex. The loops were width-modulated binary types using a 614.4 kHz keying signal and a 2.4 kHz sample frequency. The loops were designed for a torquing rate of 2 deg/sec (70.6 mA torquing current) and a data resolution of 23.4 milli-arc-sec per data pulse. Design considerations, implementation details, and preliminary experimental results are presented

Online containers for hypergraphs, with applications to linear equations

A set of containers for a hypergraph G is a collection CC of vertex subsets, such that for every independent (or, indeed, merely sparse) set I of G there is some C∈CC∈C with I⊂CI⊂C, no member of CC is large, and the collection CC is relatively small. Containers with useful properties have been exhibited by Balogh, Morris and Samotij [6] and by the authors [39]; [40] ; [41], along with several applications. Our purpose here is to give a simpler algorithm than the one used in [40], which nevertheless yields containers with all the properties needed for the main container theorem of [40] and its consequences. Moreover this algorithm produces containers having the so-called online property, allowing the colouring results of [40] to be extended to all, not just simple, hypergraphs. Most of the proof of the container theorem remains the same if this new algorithm is used, and we do not repeat all the details here, but describe only the changes that need to be made. However, for illustrative purposes, we do include a complete proof of a slightly weaker but simpler version of the theorem, which for many (perhaps most) applications is plenty. We also present applications to the number of solution-free sets of linear equations, including the number of Sidon sets, that were announced in [40]

Auditing the PCAOB: A Test to the Accountability of the Uniquely Structured Regulator of Accountants

After a slew of highly publicized corporate accounting scandals during the early 2000s at prominent companies-including Enron, WorldCom, Adelphia, and Tyco-public confidence in the integrity of financial reporting by public companies was undoubtedly shaken. Several major financial reporting frauds demonstrated serious weaknesses with the then self-regulated accounting profession, including the failure of auditors to detect those companies that were cooking their books. The collapse of several prominent companies not only affected top executives, who often were subjected to civil and criminal charges, but also produced harsh consequences for several other constituencies who relied on the integrity of the accounting firms to detect these discrepancies in financial reporting. As one scholar phrased it: The growing number of accounting and corporate governance scandals had sounded an alarm, which was made all the more deafening by the staggering sums of money lost by shareholders, employees, and retirees of the companies involved. Reacting swiftly to the public concern, Congress passed landmark legislation in 2002. Congress designed the Sarbanes-Oxley Act ( SOX ) to regulate the conduct of public accounting firms and to revive investors\u27 confidence in the integrity of public companies\u27 financial reporting and disclosures. After signing SOX into law, President George W. Bush declared that SOX included some of the most far-reaching reforms of American business practices since the time of Franklin Delano Roosevelt. SOX represented a radical departure from the previously self- regulated accounting profession. As a central part of SOX, Congress created the Public Company Accounting Oversight Board ( PCAOB ) and provided it with extensive authority to ensure that SOX\u27s lofty objectives were met. Among the PCAOB\u27s significant powers and responsibilities is the authority to promulgate rules and regulations governing the standards and issuance of audit reports, to conduct inspections and investigations of registered public accounting firms, and to impose monetary sanctions on registered firms for noncompliance with its standards

Faster Separators for Shallow Minor-Free Graphs via Dynamic Approximate Distance Oracles

Plotkin, Rao, and Smith (SODA'97) showed that any graph with $m$ edges and $n$ vertices that excludes $K_h$ as a depth $O(\ell\log n)$-minor has a separator of size $O(n/\ell + \ell h^2\log n)$ and that such a separator can be found in $O(mn/\ell)$ time. A time bound of $O(m + n^{2+\epsilon}/\ell)$ for any constant $\epsilon > 0$ was later given (W., FOCS'11) which is an improvement for non-sparse graphs. We give three new algorithms. The first has the same separator size and running time O(\mbox{poly}(h)\ell m^{1+\epsilon}). This is a significant improvement for small $h$ and $\ell$. If $\ell = \Omega(n^{\epsilon'})$ for an arbitrarily small chosen constant $\epsilon' > 0$, we get a time bound of O(\mbox{poly}(h)\ell n^{1+\epsilon}). The second algorithm achieves the same separator size (with a slightly larger polynomial dependency on $h$) and running time O(\mbox{poly}(h)(\sqrt\ell n^{1+\epsilon} + n^{2+\epsilon}/\ell^{3/2})) when $\ell = \Omega(n^{\epsilon'})$. Our third algorithm has running time O(\mbox{poly}(h)\sqrt\ell n^{1+\epsilon}) when $\ell = \Omega(n^{\epsilon'})$. It finds a separator of size O(n/\ell) + \tilde O(\mbox{poly}(h)\ell\sqrt n) which is no worse than previous bounds when $h$ is fixed and $\ell = \tilde O(n^{1/4})$. A main tool in obtaining our results is a novel application of a decremental approximate distance oracle of Roditty and Zwick.Comment: 16 pages. Full version of the paper that appeared at ICALP'14. Minor fixes regarding the time bounds such that these bounds hold also for non-sparse graph

The effect of alkalisation on the mechanical properties of natural fibres

A study on the effect of alkalisaton using 3% NaOH solution was carried out on Flax, Kenaf, Abaca and Sisal to observe the impact that the common pre-treatment process has on fibre mechanical properties. The result of the investigation indicated that over-treatment of natural fibres using NaOH could have a negative effect on the base fibre properties. It is concluded that a treatment time of less than 10 minutes is sufficient to remove hemicelluloses and to give the optimum effect

Mechanical testing of natural fibre reinforced polyester resin composites and Mode 1 fracture toughness testing of resin blocks

Recent European Parliament directive requires companies to achieve materials recycling greater than 80% in particular in the automotive sector [1]. The research on natural fibre based composite materials fits well into this ecological image. The advantages of natural fibres over synthetic materials include, low density, relative cheapness, availability and biodegradability. In this paper we explore the fabrication and mechanical testing of natural fibre composites and this is part of an on going study at Strathclyde University and describes the fabrication of composites using natural fibre and styrene polyester resin. The properties of the synthetic resin can be varied by changing the catalysts concentration and flexural (three point bending) and single-edged notched bending (SENB) properties are reported at different concentrations of the catalyst

Vacuum infusion of natural fibre composites for structural applications

Numerous methods of manufacturing natural fibre composites have been reported in the literature, including compression moudling, often in conjunction with a hot press. Other forms of composite manufacture include 'Vacuum Assisted Resin Transfer Moulding' (VATRM) and the 'Seemann Composite Resin Infusion Moulding Process' (SCRIMP). These methods have been reported to produce natural fibre composies with reasonable mechanical properties [1-2]. In this paper, a vacuum infusion rig is described that has been developed to produce consistent quality composite plates for studies into optimising natural fibre composites. The process aims to harness the benefits of vacuum infusion and compression moulding, where vacuum infusion encourages the removal of trapped air in the system and hence avoid reduction, and additional compression moulding can help to achieve high volume fractions that are otherwise difficult in other processes

Are Women'S Parenting‐Specific Beliefs Associated With Depressive Symptoms In The Perinatal Period? Development Of The Rigidity Of Maternal Beliefs Scale

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/110632/1/da22280.pd

A Paley-like graph in characteristic two

The Paley graph is a well-known self-complementary pseudo-random graph, defined over a finite field of odd order. We describe an attempt at an analogous construction using fields of even order. Some properties of the graph are noted, such as the existence of a Hamiltonian decomposition