Analysis of externally loaded bolted joints : analytical, computational and experimental study

The behaviour of a simple single-bolted-joint under tensile separating loads is analysed using conventional analytical methods, a finite element approach and experimental techniques. The variation in bolt force with external load predicted by the finite element analysis conforms well to the experimental results. It is demonstrated that certain detailed features such thread interaction do not need to be modelled to ensure useful results. Behaviour during the pre-loading phase of use agrees with previous long-standing studies. However, the pre-loading analysis does not carry over to the stage when external loading is applied, as is normally assumed and it is shown that the current, conventional analytical methods substantially over-predict the proportion of the external load carried by the bolt. The basic reason for this is shown to be related to the non-linear variation in contact conditions between the clamped members during the external loading stage

A short proof of the tree-packing theorem

We give a short elementary proof of Tutte and Nash-Williams' characterization of graphs with k edge-disjoint spanning trees

Simple constructions for balanced incomplete block designs with block size three

AbstractLet S be a finite set with v elements. It is known that there exists a sequence of three-element subsets of S such that each two-element subset of S is contained in exactly λ terms of the sequence if and only if λ(v − 1)2 and λv(v − 1)6 are integers. The known proof is somewhat complicated when v ≡ 2 (mod 6), and this paper provides a simpler proof for this case. Proofs are also given for all other values of v by reviewing known constructions or providing new ones

Computer-based assessment: from objective tests to automated essay grading. Now for automated essay writing?

Assessment of student learning is an important task undertaken by educators. However it can be time consuming and costly for humans to grade student work. Technology has been available to assist teachers in grading objective tests for several decades; however these true-false and multiple choice tests do not capture the deeper aspects of student learning. Essay writing can be used to assess this deeper learning, which includes a student's ability to synthesize his/her thoughts, and argue for propositions. Automated essay grading systems are now starting to be used in the educational sector with some success. They can reduce the cost of grading, and they also eliminate the inconsistencies that are found amongst human graders when marking the same essay. The next development in essay processing technology is automated essay writing. This development will present a new set of challenges for educators. The detection of automatically generated essays may be difficult, and students may be given credit for writing which does not reflect their true ability. An understanding ofhow these systems would work, and the characteristics of the generated essays, is thus needed in order to detect them. This paper describes the components we believe an automated essay generator would need to have, and the results of building a prototype of the first of these components, the Gatherer

Wiretapping a hidden network

We consider the problem of maximizing the probability of hitting a strategically chosen hidden virtual network by placing a wiretap on a single link of a communication network. This can be seen as a two-player win-lose (zero-sum) game that we call the wiretap game. The value of this game is the greatest probability that the wiretapper can secure for hitting the virtual network. The value is shown to equal the reciprocal of the strength of the underlying graph. We efficiently compute a unique partition of the edges of the graph, called the prime-partition, and find the set of pure strategies of the hider that are best responses against every maxmin strategy of the wiretapper. Using these special pure strategies of the hider, which we call omni-connected-spanning-subgraphs, we define a partial order on the elements of the prime-partition. From the partial order, we obtain a linear number of simple two-variable inequalities that define the maxmin-polytope, and a characterization of its extreme points. Our definition of the partial order allows us to find all equilibrium strategies of the wiretapper that minimize the number of pure best responses of the hider. Among these strategies, we efficiently compute the unique strategy that maximizes the least punishment that the hider incurs for playing a pure strategy that is not a best response. Finally, we show that this unique strategy is the nucleolus of the recently studied simple cooperative spanning connectivity game

Fully Dynamic Matching in Bipartite Graphs

Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for dynamic matching (in general graphs) seem to fall into two groups: there are fast (mostly randomized) algorithms that do not achieve a better than 2-approximation, and there slow algorithms with \O(\sqrt{m}) update time that achieve a better-than-2 approximation. Thus the obvious question is whether we can design an algorithm -- deterministic or randomized -- that achieves a tradeoff between these two: a $o(\sqrt{m})$ approximation and a better-than-2 approximation simultaneously. We answer this question in the affirmative for bipartite graphs. Our main result is a fully dynamic algorithm that maintains a 3/2 + \eps approximation in worst-case update time O(m^{1/4}\eps^{/2.5}). We also give stronger results for graphs whose arboricity is at most \al, achieving a (1+ \eps) approximation in worst-case time O(\al (\al + \log n)) for constant \eps. When the arboricity is constant, this bound is $O(\log n)$ and when the arboricity is polylogarithmic the update time is also polylogarithmic. The most important technical developement is the use of an intermediate graph we call an edge degree constrained subgraph (EDCS). This graph places constraints on the sum of the degrees of the endpoints of each edge: upper bounds for matched edges and lower bounds for unmatched edges. The main technical content of our paper involves showing both how to maintain an EDCS dynamically and that and EDCS always contains a sufficiently large matching. We also make use of graph orientations to help bound the amount of work done during each update.Comment: Longer version of paper that appears in ICALP 201

Size reconstructibility of graphs

The deck of a graph $G$ is given by the multiset of (unlabelled) subgraphs $\{G-v:v\in V(G)\}$. The subgraphs $G-v$ are referred to as the cards of $G$. Brown and Fenner recently showed that, for $n\geq29$, the number of edges of a graph $G$ can be computed from any deck missing 2 cards. We show that, for sufficiently large $n$, the number of edges can be computed from any deck missing at most $\frac1{20}\sqrt{n}$ cards.Comment: 15 page

Inverting Supervised Representations with Autoregressive Neural Density Models

We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features conditioned on intermediate model representations. Insights into the invariances learned by supervised models can be gained by viewing samples from these inversion models. In addition, we can use these inversion models to estimate the mutual information between a model's inputs and its intermediate representations, thus quantifying the amount of information preserved by the network at different stages. Using this method we examine the types of information preserved at different layers of convolutional neural networks, and explore the invariances induced by different architectural choices. Finally we show that the mutual information between inputs and network layers decreases over the course of training, supporting recent work by Shwartz-Ziv and Tishby (2017) on the information bottleneck theory of deep learning.Comment: Accepted for publication by AISTATS 201

Hamilton decompositions of regular expanders: applications

In a recent paper, we showed that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge-disjoint Hamilton cycles. The main consequence of this theorem is that every regular tournament on n vertices can be decomposed into (n-1)/2 edge-disjoint Hamilton cycles, whenever n is sufficiently large. This verified a conjecture of Kelly from 1968. In this paper, we derive a number of further consequences of our result on robust outexpanders, the main ones are the following: (i) an undirected analogue of our result on robust outexpanders; (ii) best possible bounds on the size of an optimal packing of edge-disjoint Hamilton cycles in a graph of minimum degree d for a large range of values for d. (iii) a similar result for digraphs of given minimum semidegree; (iv) an approximate version of a conjecture of Nash-Williams on Hamilton decompositions of dense regular graphs; (v) the observation that dense quasi-random graphs are robust outexpanders; (vi) a verification of the `very dense' case of a conjecture of Frieze and Krivelevich on packing edge-disjoint Hamilton cycles in random graphs; (vii) a proof of a conjecture of Erdos on the size of an optimal packing of edge-disjoint Hamilton cycles in a random tournament.Comment: final version, to appear in J. Combinatorial Theory