A methodology for automatic classification of breast cancer immunohistochemical data using semi-supervised Fuzzy c-means

Previously, a semi-manual method was used to identify six novel and clinically useful classes in the Nottingham Tenovus Breast Cancer dataset. 663 out of 1,076 patients were classified. The objectives of our work is three folds. Firstly, our primary objective is to use one single automatic method (post-initialisation) to reproduce the six classes for the 663 patients and to classify the remaining 413 patients. Secondly, we explore using semi-supervised fuzzy c-means with various distance metrics and initialisation techniques to achieve this. Thirdly, the clinical characteristics of the 413 patients are examined by comparing with the 663 patients. Our experiments use various amount of labelled data and 10-fold cross validation to reproduce and evaluate the classification. ssFCM with Euclidean distance and initialisation technique by Katsavounidis et al. produced the best results. It is then used to classify the 413 patients. Visual evaluation of the 413 patients’ classifications revealed common characteristics as those previously reported. Examination of clinical characteristics indicates significant associations between classification and clinical parameters. More importantly, association between classification and survival based on the survival curves is shown.     

Auxetic metamaterials exhibiting giant negative Poisson's ratios

Auxetic metamaterials have generated a great deal of interest in recent years. In this letter, a novel approach which can be used to produce such auxetic metamaterials is presented. This method involves the introduction of patterned slit perforations within a sheet/block of material in order to create systems which resemble a large variety of auxetic systems ranging from rotating units to chiral honeycombs. These perforated systems have also been shown to have the potential to exhibit giant negative Poisson's ratios. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Colouring of generalized signed triangle-free planar graphs

We view an undirected graph $G$ as a symmetric digraph, where each edge $xy$ is replaced by two opposite arcs $e=(x,y)$ and $e^{?1}=(y,x)$. Assume $S$ is an inverse closed subset of permutations of positive integers. We say $G$ is $S$-$k$-colourable if for any mapping $\sigma :E\left(G\right)\to S$ with $\sigma (x,y)={\left(\sigma (y,x)\right)}^{?1}$, there is a mapping $f:V\left(G\right)\to \left[k\right]=\{1,2,\dots ,k\}$ such that ${\sigma }_e\left(f\left(x\right)\right)\ne f\left(y\right)$ for each arc $e=(x,y)$. The concept of $S$-$k$-colourable is a common generalization of several other colouring concepts. This paper is focused on finding the sets $S$ such that every triangle-free planar graph is $S$-3-colourable. Such a set $S$ is called TFP-good. Grötzsch’s theorem is equivalent to say that $S=\left\{id\right\}$ is TFP-good. We prove that for any inverse closed subset $S$ of $S_3$ which is not isomorphic to $\{id,\left(12\right)\}$, $S$ is TFP-good if and only if either $S=\left\{id\right\}$ or there exists $a\in \left[3\right]$ such that for each $\pi \in S$, $\pi \left(a\right)\ne a$. It remains an open question to determine whether or not $S=\{id,\left(12\right)\}$ is TFP-good.     

Multivariate analysis for the assessment of factors affecting industrial competitiveness: The case of Greek food and beverage industries

Principal component analysis is integrated with canonical analysis to examine aspects of the competitiveness of two different sectors of the Greek manufacturing, i.e. the food and the beverage industries. Different measures of labour productivity, vertical integration, technological innovation and size of the firms which are considered as critical factors of industrial competitiveness are used in the application of the principal component analysis. Canonical analysis is then applied to correlate the variables of labour productivity with the other variables. In the case of the food and beverage integrated sector, the results of the principal component analysis pinpoint that there are two main principal components: (a) labour productivity and vertical integration, and (b) technological innovation and size. The first factor depicts the internal organizational, structural and production processes changes realized so that the competitiveness of the sector firms improves, whereas the second factor reflects the response of the sector to technological and growth trends. The two variables of labour productivity are affected by the degree of vertical integration and, at a lesser degree, by a common factor of the size of the firm and the level of investment for technological innovation. Copyright © 2000 John Wiley & Sons, Ltd.     

Intensity patterns of pionic X-rays emitted from simple molecules

Intensity patterns in the Balmer series of pionic X-rays emitted from carbon and oxygen in simple molecules are reported and analysed using a cascade code. It is shown that modifications are needed in the angular momentum distribution at the beginning of the cascade calculation in order to fit the data.     

Theories of alpha-decay

The derivation of the width for α-decay is examined with particular emphasis on methods which do not involve arbitrary channel radii. A new method of treating the initial decaying states is introduced and the use of ambiguous phenomenological potentials is avoided. This method yields consistent and acceptable quantitative results for the g.s. to g.s. (ground state) transitions in even polonium isotopes and for the branching ratio for the decay of the isomeric state ^212mPo.     

Distance graphs with missing multiples in the distance sets

Given positive integers m, k, and s with m > ks, let D_m,k,s represent the set {1, 2, …, m} − {k, 2k, …, sk}. The distance graph G(Z, D_m,k,s) has as vertex set all integers Z and edges connecting i and j whenever |i − j| ∈ D_m,k,s. The chromatic number and the fractional chromatic number of G(Z, D_m,k,s) are denoted by χ(Z, D_m,k,s) and χf(Z, D_m,k,s), respectively. For s = 1, χ(Z, D_m,k,1) was studied by Eggleton, Erdős, and Skilton [6], Kemnitz and Kolberg [12], and Liu [13], and was solved lately by Chang, Liu, and Zhu [2] who also determined χf(Z, D_m,k,1) for any m and k. This article extends the study of χ(Z, D_m,k,s) and χf(Z, D_m,k,s) to general values of s. We prove χf(Z, D_m,k,s) = χ(Z, D_m,k,s) = k if m < (s + 1)k; and χf(Z, D_m,k,s) = (m + sk + 1)/(s + 1) otherwise. The latter result provides a good lower bound for χ(Z, D_m,k,s). A general upper bound for χ(Z, D_m,k,s) is obtained. We prove the upper bound can be improved to ⌈(m + sk + 1)/(s + 1)⌉ + 1 for some values of m, k, and s. In particular, when s + 1 is prime, χ(Z, D_m,k,s) is either ⌈(m + sk + 1)/(s + 1)⌉ or ⌈(m + sk + 1)/(s + 1)⌉ + 1. By using a special coloring method called the precoloring method, many distance graphs G(Z, D_m,k,s) are classified into these two possible values of χ(Z, D_m,k,s). Moreover, complete solutions of χ(Z, D_m,k,s) for several families are determined including the case s = 1 (solved in [2]), the case s = 2, the case (k, s + 1) = 1, and the case that k is a power of a prime. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 245–259, 1999     

(8‐Dimethylamino‐1‐naphthyl)dimethylammonium 3‐carboxy‐1,4,5,‐6,7,7‐hexachlorobicyclo[2.2.1]hept‐5‐ene‐2‐carboxylate hydrate

The structure of the title compound, C₁₄H₁₉N₂⁺·C₉H₃Cl₆O₄^?·H₂O, consists of singly ionized 1,4,5,6,7,7‐hexachlorobicyclo[2.2.1]hept‐5‐ene‐2,3‐dicarboxylic acid anions and protonated 1,8‐bis(dimethylamino)naphthalene cations. In the (8‐dimethylamino‐1‐napthyl)dimethylammonium cat­ion, a strong disordered intramolecular hydrogen bond is formed with N?N = 2.589 (3) Å. The geometry and occupancy obtained in the final restrained refinement suggest that the disordered hydrogen bond may be asymmetric. Water mol­ecules link the anion dimers into infinite chains via hydrogen bonding.     

The Crystal Structure of Non‐Modified and Bipyridine‐Modified PNA Duplexes

Peptide nucleic acid (PNA) is a synthetic analogue of DNA that commonly has an N‐aminoethyl glycine backbone. The crystal structures of two PNA duplexes, one containing eight standard nucleobase pairs (GGCATGCC)₂, and the other containing the same nucleobase pairs and a central pair of bipyridine ligands, have been solved with a resolution of 1.22 and 1.10 Å, respectively. The non‐modified PNA duplex adopts a P‐type helical structure similar to that of previously characterized PNAs. The atomic‐level resolution of the structures allowed us to observe for the first time specific modes of interaction between the terminal lysines of the PNA and the backbone and the nucleobases situated in the vicinity of the lysines, which are considered an important factor in the induction of a preferred handedness in PNA duplexes. Our results support the notion that whereas PNA typically adopts a P‐type helical structure, its flexibility is relatively high. For example, the base‐pair rise in the bipyridine‐containing PNA is the largest measured to date in a PNA homoduplex. The two bipyridines bulge out of the duplex and are aligned parallel to the major groove of the PNA. In addition, two bipyridines from adjacent PNA duplexes form a π‐stacked pair that relates the duplexes within the crystal. The bulging out of the bipyridines causes bending of the PNA duplex, which is in contrast to the structure previously reported for biphenyl‐modified DNA duplexes in solution, where the biphenyls are π stacked with adjacent nucleobase pairs and adopt an intrahelical geometry. This difference shows that relatively small perturbations can significantly impact the relative position of nucleobase analogues in nucleic acid duplexes.     

Two‐Dimensional Ketone‐Driven Metal–Organic Coordination on Cu(111)

Two‐dimensional metal–organic nanostructures based on the binding of ketone groups and metal atoms were fabricated by depositing pyrene‐4,5,9,10‐tetraone (PTO) molecules on a Cu(111) surface. The strongly electronegative ketone moieties bind to either copper adatoms from the substrate or codeposited iron atoms. In the former case, scanning tunnelling microscopy images reveal the development of an extended metal–organic supramolecular structure. Each copper adatom coordinates to two ketone ligands of two neighbouring PTO molecules, forming chains that are linked together into large islands through secondary van der Waals interactions. Deposition of iron atoms leads to a transformation of this assembly resulting from the substitution of the metal centres. Density functional theory calculations reveal that the driving force for the metal substitution is primarily determined by the strength of the ketone–metal bond, which is higher for Fe than for Cu. This second class of nanostructures displays a structural dependence on the rate of iron deposition.