JLMC: A clustering method based on Jordan-Form of Laplacian-Matrix

Among the current clustering algorithms of complex networks, Laplacian-based spectral clustering algorithms have the advantage of rigorous mathematical basis and high accuracy. However, their applications are limited due to their dependence on prior knowledge, such as the number of clusters. For most of application scenarios, it is hard to obtain the number of clusters beforehand. To address this problem, we propose a novel clustering algorithm - Jordan-Form of Laplacian-Matrix based Clustering algorithm (JLMC). In JLMC, we propose a model to calculate the number (n) of clusters in a complex network based on the Jordan-Form of its corresponding Laplacian matrix. JLMC clusters the network into n clusters by using our proposed modularity density function (P function). We conduct extensive experiments over real and synthetic data, and the experimental results reveal that JLMC can accurately obtain the number of clusters in a complex network, and outperforms Fast-Newman algorithm and Girvan-Newman algorithm in terms of clustering accuracy and time complexity.

Mitigation of symmetry condition in positive realness for adaptive control

Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state-space realization (A, B, C) is apparently limited by the standard strictly positive realness conditions that imply that the product CB must be positive definite symmetric. This paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric CB is only required to have a diagonal Jordan form and positive eigenvalues. The paper also shows that under the new condition any minimum-phase systems can be made strictly positive real via constant output feedback. The paper illustrates the usefulness of these extended properties with an adaptive control example. (C) 2006 Elsevier Ltd. All rights reserved.

The Jordan canonical form for a class of weighted directed graphs

Recently, Cardon and Tuckfield (2011) [1] have described the Jordan canonical form for a class of zero-one matrices, in terms of its associated directed graph. In this paper, we generalize this result to describe the Jordan canonical form of a weighted adjacency matrix A in terms of its weighted directed graph.

Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

The establishment of an ISO compliant cancer biobank for Jordan and its neighboring countries through knowledge transfer and training

Research studies aimed at advancing cancer prevention, diagnosis, and treatment depend on a number of key resources, including a ready supply of high-quality annotated biospecimens from diverse ethnic populations that can be used to test new drugs, assess the validity of prognostic biomarkers, and develop tailor-made therapies. In November 2011, KHCCBIO was established at the King Hussein Cancer Center (KHCC) with the support of Seventh Framework Programme (FP7) funding from the European Union (khccbio.khcc.jo). KHCCBIO was developed for the purpose of achieving an ISO accredited cancer biobank through the collection, processing, and preservation of high-quality, clinically annotated biospecimens from consenting cancer patients, making it the first cancer biobank of its kind in Jordan. The establishment of a state-of-the-art, standardized biospecimen repository of matched normal and lung tumor tissue, in addition to blood components such as serum, plasma, and white blood cells, was achieved through the support and experience of its European partners, Trinity College Dublin, Biostor Ireland, and accelopment AG. To date, KHCCBIO along with its partners, have worked closely in establishing an ISO Quality Management System (QMS) under which the biobank will operate. A Quality Policy Manual, Validation, and Training plan have been developed in addition to the development of standard operating procedures (SOPs) for consenting policies on ethical issues, data privacy, confidentiality, and biobanking bylaws. SOPs have also been drafted according to best international practices and implemented for the donation, procurement, processing, testing, preservation, storage, and distribution of tissues and blood samples from lung cancer patients, which will form the basis for the procurement of other cancer types. KHCCBIO will be the first ISO accredited cancer biobank from a diverse ethnic Middle Eastern and North African population. It will provide a unique and valuable resource of high-quality human biospecimens and anonymized clinicopathological data to the cancer research communities world-wide.

Spot form of net blotch resistance in barley is under complex genetic control

Key message: Evaluation of resistance toPyrenophora teresf.maculatain barley breeding populations via association mapping revealed a complex genetic architecture comprising a mixture of major and minor effect genes. Abstract: In the search for stable resistance to spot form of net blotch (Pyrenophora teres f. maculata, SFNB), association mapping was conducted on four independent barley (Hordeum vulgare L.) breeding populations comprising a total of 898 unique elite breeding lines from the Northern Region Barley Breeding Program in Australia for discovery of quantitative trait loci (QTL) influencing resistance at seedling and adult plant growth stages. A total of 29 significant QTL were validated across multiple breeding populations, with 22 conferring resistance at both seedling and adult plant growth stages. The remaining 7 QTL conferred resistance at either seedling (2 QTL) or adult plant (5 QTL) growth stages only. These 29 QTL represented 24 unique genomic regions, of which five were found to co-locate with previously identified QTL for SFNB. The results indicated that SFNB resistance is controlled by a large number of QTL varying in effect size with large effects QTL on chromosome 7H. A large proportion of the QTL acted in the same direction for both seedling and adult responses, suggesting that phenotypic selection for SFNB resistance performed at either growth stage could achieve adequate levels of resistance. However, the accumulation of specific resistance alleles on several chromosomes must be considered in molecular breeding selection strategies.

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the conservation form of equations of a weakly nonlinear ray theory. The proposed set of equations forms a weakly hyperbolic system of seven conservation laws with an additional vector constraint, each of whose components is a divergence-free condition. This constraint is an involution for the system of conservation laws, and it is termed a geometric solenoidal constraint. The analysis of a Cauchy problem for the linearized system shows that when this constraint is satisfied initially, the solution does not exhibit any Jordan mode. For the numerical simulation of the conservation laws we employ a high resolution central scheme. The second order accuracy of the scheme is achieved by using MUSCL-type reconstructions and Runge-Kutta time discretizations. A constrained transport-type technique is used to enforce the geometric solenoidal constraint. The results of several numerical experiments are presented, which confirm the efficiency and robustness of the proposed numerical method and the control of the Jordan mode.

Length-weight relationship of fishes from coral reefs along the coastline of Jordan (Gulf of Aqaba)

The parameters a and b of the length-weight relationship of the form W = a.Lb were estimated for 15 fish species caught along the coastline of Jordan in the Gulf of Aqaba. The sampling was carried out between July 1999 and January 2001. Data from 1 000 fish individuals (identified to eight families and 15 species) were used for this purpose.

The heavy metal content of skeletons from an ancient metalliferous polluted area in southern Jordan with particular reerence to bioaccumulation and human health

Pyatt, F.B., Pyatt, A.J., Walker, C., Sheen, T., Grattan, J.P, The heavy metal content of skeletons from an ancient metalliferous polluted area in southern Jordan with particular reerence to bioaccumulation and human health, Ecotoxicology & Environmental Safety 60, 13th August 2003, 295-300

Experimental crop growing in Jordan to develop methodology for the identification of ancient crop irrigation

Crop irrigation has long been recognized as having been important for the evolution of social complexity in several parts of the world. Structural evidence for water management, as in the form of wells, ditches and dams, is often difficult to interpret and may be a poor indicator of past irrigation that may have had no need for such constructions. It would be of considerable value, therefore, to be able to infer past irrigation directly from archaeo-botanical remains, and especially the type of archaeo-botanical remains that are relatively abundant in the archaeological record, such as phytoliths. Building on the pioneering work of Rosen and Wiener (1994), this paper describes a crop-growing experiment designed to explore the impact of irrigation on the formation of phytoliths within cereals. If it can be shown that a systemic and consistent relationship exists between phytolith size, structure and the intensity of irrigation, and if various taphonomic and palaeoenvironmental processes can be controlled for, then the presence of past irrigation can feasibly be inferred from the phytoliths recovered from the archaeological record.

A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.