On large bipartite graphs of diameter 3

We consider the bipartite version of the {\it degree/diameter problem}, namely, given natural numbers $d\ge2$ and $D\ge2$, find the maximum number $\N^b(d,D)$ of vertices in a bipartite graph of maximum degree $d$ and diameter $D$. In this context, the bipartite Moore bound \M^b(d,D) represents a general upper bound for $\N^b(d,D)$. Bipartite graphs of order \M^b(d,D) are very rare, and determining $\N^b(d,D)$ still remains an open problem for most $(d,D)$ pairs. This paper is a follow-up to our earlier paper \cite{FPV12}, where a study on bipartite $(d,D,-4)$-graphs (that is, bipartite graphs of order \M^b(d,D)-4) was carried out. Here we first present some structural properties of bipartite $(d,3,-4)$-graphs, and later prove there are no bipartite $(7,3,-4)$-graphs. This result implies that the known bipartite $(7,3,-6)$-graph is optimal, and therefore $\N^b(7,3)=80$. Our approach also bears a proof of the uniqueness of the known bipartite $(5,3,-4)$-graph, and the non-existence of bipartite $(6,3,-4)$-graphs. In addition, we discover three new largest known bipartite (and also vertex-transitive) graphs of degree 11, diameter 3 and order 190, result which improves by 4 vertices the previous lower bound for $\N^b(11,3)$

Robust artificial neural networks and outlier detection. Technical report

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks to contaminated data using least trimmed squares criterion. We introduce a penalized least trimmed squares criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression

Image-Dependent Spatial Shape-Error Concealment

Existing spatial shape-error concealment techniques are broadly based upon either parametric curves that exploit geometric information concerning a shape's contour or object shape statistics using a combination of Markov random fields and maximum a posteriori estimation. Both categories are to some extent, able to mask errors caused by information loss, provided the shape is considered independently of the image/video. They palpably however, do not afford the best solution in applications where shape is used as metadata to describe image and video content. This paper presents a novel image-dependent spatial shape-error concealment (ISEC) algorithm that uses both image and shape information by employing the established rubber-band contour detecting function, with the novel enhancement of automatically determining the optimal width of the band to achieve superior error concealment. Experimental results corroborate both qualitatively and numerically, the enhanced performance of the new ISEC strategy compared with established techniques

The degree-diameter problem for sparse graph classes

The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree $\Delta$ and diameter $k$. For fixed $k$, the answer is $\Theta(\Delta^k)$. We consider the degree-diameter problem for particular classes of sparse graphs, and establish the following results. For graphs of bounded average degree the answer is $\Theta(\Delta^{k-1})$, and for graphs of bounded arboricity the answer is \Theta(\Delta^{\floor{k/2}}), in both cases for fixed $k$. For graphs of given treewidth, we determine the the maximum number of vertices up to a constant factor. More precise bounds are given for graphs of given treewidth, graphs embeddable on a given surface, and apex-minor-free graphs

Introduced birds in urban remnant vegetation : does remnant size really matter?

Introduced birds are a pervasive and dominant element of urban ecosystems. We examined the richness and relative abundance of introduced bird species in small (1&ndash;5 ha) medium (6&ndash;15 ha) and large (&gt;15 ha) remnants of native vegetation within an urban matrix. Transects were surveyed during breeding and non-breeding seasons. There was a significant relationship between introduced species richness and remnant size with larger remnants supporting more introduced species. There was no significant difference in relative abundance of introduced species in remnants of different sizes. Introduced species, as a proportion of the relative abundance of the total avifauna (native and introduced species), did not vary significantly between remnants of differing sizes. There were significant differences in the composition of introduced bird species between the different remnant sizes, with large remnants supporting significantly different assemblages than medium and small remnants. Other variables also have substantial effects on the abundance of introduced bird species. The lack of significant differences in abundance between remnant sizes suggests they were all equally susceptible to invasion. No patches in the urban matrix are likely to be unaffected by introduced species. The effective long-term control of introduced bird species is difficult and resources may be better spent managing habitat in a way which renders it less suitable for introduced species (e.g. reducing areas of disturbed ground and weed dominated areas).<br /

The psychological contract in apprenticeships and traineeships : differing perceptions

As with any contract of employment, the mutual expectations of the employer and the apprentice/trainee are very important. Apprenticeships and traineeships have greater expectations than other employment contracts of employment because of the training component of the contract. This paper reports on some of the findings of a major NCVER-funded national project examining mutual expectations in apprenticeships and traineeships through the concept of the psychological contract. The paper focuses on the differences between employers and apprentices/trainees, in the expectations each party has of the other and in the extent to which the expectations are perceived to have been met.<br /

Molecular Dynamics Studies on 3D Structures of the Hydrophobic Region PrP(109-136)

Prion diseases caused by the conversion from a soluble normal cellular prion protein into insoluble abnormally folded infectious prions, are invariably fatal and highly infectious degenerative diseases that affect a wide variety of mammalian species. The palindrome and the Glycine-rich conserved segment in the hydrophobic region 109-136 control the conversion from normal prion protein to form into diseased prions. This paper gives detailed reviews on the 109-136 region and presents the studies of its 3D structures and structural dynamics.Comment: This paper was accepted on 18-02-2013 by the journal Acta Biochimica et Biophysica Sinica, in press in Vol 45 No 4, Apr 201

Fitting Voronoi Diagrams to Planar Tesselations

Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of $G$, assuming that the smallest angle in $G$ is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop on Combinatorial Algorithms), Rouen, France, July 201

An examination of writing pauses in the handwriting of children with Developmental Coordination Disorder.

This article has been made available through the Brunel Open Access Publishing Fund.Difficulties with handwriting are reported as one of the main reasons for the referral of children with Developmental Coordination Disorder (DCD) to healthcare professionals. In a recent study we found that children with DCD produced less text than their typically developing (TD) peers and paused for 60% of a free-writing task. However, little is known about the nature of the pausing; whether they are long pauses possibly due to higher level processes of text generation or fatigue, or shorter pauses related to the movements between letters. This gap in the knowledge-base creates barriers to understanding the handwriting difficulties in children with DCD. The aim of this study was to characterise the pauses observed in the handwriting of English children with and without DCD. Twenty-eight 8-14 year-old children with a diagnosis of DCD participated in the study, with 28 TD age and gender matched controls. Participants completed the 10 min free-writing task from the Detailed Assessment of Speed of Handwriting (DASH) on a digitising writing tablet. The total overall percentage of pausing during the task was categorised into four pause time-frames, each derived from the literature on writing (250 ms to 2 s; 2-4 s; 4-10 s and >10 s). In addition, the location of the pauses was coded (within word/between word) to examine where the breakdown in the writing process occurred. The results indicated that the main group difference was driven by more pauses above 10 s in the DCD group. In addition, the DCD group paused more within words compared to TD peers, indicating a lack of automaticity in their handwriting. These findings may support the provision of additional time for children with DCD in written examinations. More importantly, they emphasise the need for intervention in children with DCD to promote the acquisition of efficient handwriting skill

Corners-based composite descriptor for shapes

In this paper, a composite descriptor for shape retrieval is proposed. The composite descriptor is obtained based upon corner-points and shape region. In an earlier paper, we proposed a composite descriptor based on shape region and shape contour, however, the descriptor was not effective for all perspective and geometric transformations. Hence, we modify the composite descriptor by replacing contour features with corner-points features. The proposed descriptor is obtained from Generic FourierDescriptors (GFD) of the shape region and the GFD ofthe corner-points. We study the performance of the proposed composite descriptor. The proposed method is evaluated using Item S8 within the MPEG-7 Still Images Content Set. Experimental results show that the proposed descriptor is effective.<br /