text:
- Research article
- Open Access
Understanding network concepts in modules
- Jun Dong1 and
- Steve Horvath1Email author
© Dong and Horvath; licensee BioMed Central Ltd. 2007
- Received: 22 January 2007
- Accepted: 04 June 2007
- Published: 04 June 2007
Network concepts are increasingly used in biology and genetics. For example, the clustering coefficient has been used to understand network architecture; the connectivity (also known as degree) has been used to screen for cancer targets; and the topological overlap matrix has been used to define modules and to annotate genes. Dozens of potentially useful network concepts are known from graph theory.
Here we study network concepts in special types of networks, which we refer to as approximately factorizable networks. In these networks, the pairwise connection strength (adjacency) between 2 network nodes can be factored into node specific contributions, named node 'conformity'. The node conformity turns out to be highly related to the connectivity. To provide a formalism for relating network concepts to each other, we define three types of network concepts: fundamental-, conformity-based-, and approximate conformity-based concepts. Fundamental concepts include the standard definitions of connectivity, density, centralization, heterogeneity, clustering coefficient, and topological overlap. The approximate conformity-based analogs of fundamental network concepts have several theoretical advantages. First, they allow one to derive simple relationships between seemingly disparate networks concepts. For example, we derive simple relationships between the clustering coefficient, the heterogeneity, the density, the centralization, and the topological overlap. The second advantage of approximate conformity-based network concepts is that they allow one to show that fundamental network concepts can be approximated by simple functions of the connectivity in module networks.
Using protein-protein interaction, gene co-expression, and simulated data, we show that a) many networks comprised of module nodes are approximately factorizable and b) in these types of networks, simple relationships exist between seemingly disparate network concepts. Our results are implemented in freely available R software code, which can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/ModuleConformity/ModuleNetworks
- Adjacency Matrix
- Cluster Coefficient
- Module Network
- Module Size
- Network Concept
Network terminology is used to study important questions in systems biology. For example, networks are used to study functional enrichment [1], to analyze the structure of cellular networks [2], to model biological signalling or regulatory networks [1, 3], to reconstruct metabolic networks [4], and to study the dynamic behavior of gene regulatory networks [5].
Here we study the meaning of network concepts in relatively simple networks, e.g. gene co-expression networks and protein-protein interaction (PPI) networks. Specifically, we consider undirected networks that can be represented by a symmetric adjacency matrix A = [a ij ], where the pairwise adjacency (connection strength) a ij takes values in the unit interval, i.e., 0 ≤ a ij ≤ 1. For an unweighted network, the adjacency a ij = 1 if nodes i and j are connected and 0 otherwise. For a weighted network, 0 ≤ a ij ≤ 1. For notational convenience, we set the diagonal elements to 1.
Fundamental network concepts
Other authors refer to network concepts as network statistics or network indices. Network concepts include connectivity, mean connectivity, density, variance of the connectivity (related to the heterogeneity) etc. Network concepts can be used as descriptive statistics for networks. While some network concepts (e.g. connectivity) have found important uses in biology and genetics, other network concepts (e.g. network centralization) appear less interesting to biologists. Before attempting to understand why some concepts are more interesting than others, it is important to understand how network concepts relate to each other in biologically interesting networks. As a step toward this goal, we explore the meaning of network concepts in module networks, which are defined below.
In the following, we review fundamental network concepts. Further details on the definitions and notations can be found in the Methods section.
In unweighted networks, the connectivity k i of node i equals the number of directly linked neighbors. In weighted networks, the connectivity equals the sum of connection weights with all other nodes. Highly connected 'hub' genes are thought to play an important role in organizing the behavior of biological networks [6–9]. Connectivity has been found to be an important complementary gene screening variable for finding biologically significant genes in cancer [10, 11] and primate brain development [12].
where the function S p (·) is defined for a vector v as S p (v) = ∑ i = (v p ) τ 1.
A frequent question of social network analysis concerns the causes and consequences of centralization in network structure, i.e. the extent to which certain nodes are far more central than others within the network in question. The centralization index has been used to describe structural differences of metabolic networks [15].
This heterogeneity measure is scale invariant with respect to multiplying the connectivity by a scalar. Biological networks tend to be very heterogeneous: while some 'hub' nodes are highly connected, the majority of nodes tend to have very few connections. Describing the heterogeneity (inhomogeneity) of the connectivity (degree) distribution has been the focus of considerable research in recent years [6, 16–18].
In unweighted networks, n i equals twice the number of direct connections among the nodes connected to node i, and π i equals twice the maximum possible number of direct connections among the nodes connected to node i. Consequently, ClusterCoef i equals 1 if and only if all neighbors of i are also connected to each other. For general weighted networks with 0 ≤ a ij ≤ 1, one can prove 0 ≤ ClusterCoef i ≤ 1 [21]. The relationship between the clustering coefficient and modular structure has been investigated by several authors [20, 22–24].
where l ij = ∑u≠i,ja iu a uj . In an unweighted network, l ij equals the number of nodes to which both i and j are connected. In this case, TopOverlap ij = 1 if the node with fewer connections satisfies two conditions: (a) all of its neighbors are also neighbors of the other node, and (b) it is connected to the other node. In contrast, TopOverlap ij = 0 if i and j are un-connected and the two nodes do not share any neighbors. By convention, TopOverlap ii = 1. One can prove that 0 ≤ a ij ≤ 1 implies 0 ≤ TopOverlap ij ≤ 1 [21].
The Topological Overlap Matrix Can Be Considered as Adjacency Matrix
Since the matrix TopOverlap = [TopOverlap ij ] is symmetric and its entries lie in [0, 1], it satisfies our assumptions on an adjacency matrix. Roughly speaking, the topological overlap matrix can be considered as a 'smoothed out' version of the adjacency matrix. The elements of TopOverlap provide an alternative measure of connection strength based on shared neighbors. There is evidence that replacing A by TopOverlap may counter the adverse effects of spurious or missing adjacencies [25, 26]. Since the adjacency matrices of the PPI networks in our applications were very sparse, we replaced them by the corresponding topological overlap matrices. In contrast, we used the original adjacency matrix when analyzing gene co-expression networks since high specificity is desirable for measuring interconnectedness in co-expression networks.
The topological overlap matrix can be used for module definition
Our main interest lies in (sub-)networks comprised of nodes that form a module inside a larger network. Since a particular module network may encode a pathway or a protein complex, these special types of networks have great practical importance. Similar to the term 'cluster', no consensus on the meaning of the term 'module' seems to exist in the literature. In our applications, we use a clustering procedure to identify modules (clusters) of nodes with high topological overlap. We follow the suggestion of [20] to turn the topological overlap matrix TopOverlap into a dis similarity measure by subtracting it from 1, i.e. dissTopOverlap ij = 1 - TopOverlap ij .
Conformity and factorizable networks
We define an adjacency matrix A to be exactly factorizable if, and only if, there exists a vector CF with non-negative elements such that
a ij = CF i CF j for all i ≠ j (7)
If the non-negative solution of equation (7) is unique, it is referred to as conformity vector CF and CF i is the conformity of node i. One can easily show that the vector CF is not unique if the network contains only n = 2 nodes. However, for n > 2 it is unique for a weighted network, see our derivations surrounding equation (20).
We also define the concept of conformity for a general, non-factorizable network. The idea is to find an exactly factorizable adjacency matrix A CF = CF CF τ - diag(CF2) + I that best approximates A. Note that the diagonal elements of A CF and A equal 1.
In the appendix, we define the conformity as a maximizer of the factorizability function . Alternative methods of decomposing an adjacency matrix are briefly discussed below.
The factorizability F(A) is normalized to take on values in the unit interval [0, 1]. The higher F(A), the better A CF - I approximates A - I.
Modules can be approximately factorizable
Summary of fundamental network concepts in real network applications.
Fly Protein
Yeast Protein
Yeast (Weighted)
Yeast (Unweighted)
.82 (.086)
.85 (.100)
.73 (.084)
.62 (.130)
.21 (.074)
.28 (.120)
.08 (.056)
.40 (.150)
.18 (.091)
.20 (.055)
.10 (.026)
.41 (.110)
.35 (.130)
.36 (.140)
.56 (.066)
.51 (.097)
Mean Cluster Coef.
.28 (.110)
.36 (.120)
.13 (.072)
.72 (.087)
Mean Conformity
.45 (.076)
.51 (.120)
.26 (.084)
.63 (.100)
Our empirical results support the following
Observation 1 For many modules defined with a clustering procedure, the subnetwork comprised of the module nodes is approximately factorizable.
This observation motivates us to study network concepts in approximately factorizable networks.
Conformity-based network concepts
Brief overview of different types of network concepts.
Input Matrix
Type of Concept
Example: Connectivity
Connectivity i (A - I) = ∑j≠ia ij
A CF - I = CF CF τ - diag(CF2)
Connectivity i (A CF - I) = CF i ∑j≠iCF j
ACF,app= CF CF τ
approximate CF-based
Connectivity i (A CF , app ) = CF i ∑ j CF j
ACF,app= CF CF τ = [CF i CF j ].
Note that the i-th diagonal element of ACF,appequals . When ACF,appis used as input of a network concept function, one arrives at an approximate CF-based concept (see Definition 7 in the Methods section).
We will demonstrate that approximate CF-based concepts satisfy simple relationships. Below, we show that these simple relationships carry over to fundamental network concepts in approximately factorizable networks.
where S p (CF) = ∑ i (CF i ) p . Note that the approximate CF-based clustering coefficient does not depend on the i-index. This is why we sometimes omit this index and simply write ClusterCoefCF,app.
Approximate CF-based network concepts satisfy simple relationships
In the following subsection, we outline the conditions when equations (9) and (10) hold approximately for fundamental network concepts in approximately factorizable module networks.
Relating fundamental- to approximate CF-based concepts
In the Methods section, we provide a heuristic argument for the following
Observation 2 In approximately factorizable networks, fundamental network concepts are approximately equal to their approximate CF-based analogs,
FundamentalNetworkConcept ≈ NetworkConceptCF,app.
Observation 3 In approximately factorizable networks, the following relationships hold among fundamental network concepts
mean(ClusterCoef) ≈ (1 + Heterogeneity2)2 × Density, (11)
As an aside, we briefly mention that TopOverlap[1]jhas a simple interpretation in terms of the hierarchical clustering dendrogram that results from using dissTopOverlap ij = 1 -TopOverlap ij as input. In this case, TopOverlap[1]jis related to the longest branch length in the dendrogram.
In the following, we relate TopOverlap[1]jto the fundamental network concept Centralization. According to equation (3), ≈ Centralization + Density. Substituting this expression in equation (13) implies
TopOverlap[1]j≈ (Centralization + Density)(1 + Heterogeneity2). (14)
In factorizable networks, fundamental network concepts are simple functions of the connectivity
This equation shows that conformity can be interpreted as a scaled connectivity in approximately factorizable networks. Since approximate CF-based network concepts are simple functions of the conformity, substituting for CF implies that approximate CF-based concepts can be approximated by simple functions of the connectivity. For example, we find the following simple expressions for the cluster coefficient and the topological overlap.
where the last approximation assumes and
Protein-protein interaction and gene co-expression network applications
Drosophila and yeast protein-protein network
To illustrate our results, we computed network concepts in module networks based on Drosophila and yeast protein-protein interaction (PPI) networks downloaded from BioGrid [31]. As described before, we defined the modules as branches of the hierarchical clustering dendrogram, see Figure 1.
Of the 1371 proteins in the Drosophila PPI network, 862 were clustered into 28 modules, and the remaining proteins grouped into an improper (grey) module. The module sizes of the proper modules range from 10 to 96, mean 30.79, median 23, and interquartile range 24.
Of the 2292 proteins in the yeast PPI network, 2050 were clustered into 44 proper modules, and the remaining proteins grouped into an improper module. The module sizes of the proper modules range from 10 to 219, mean 46.59, median 24, and interquartile range 38.8.
Yeast gene co-expression networks
We now illustrate our theoretical results using gene co-expression networks that have been used by many authors, e.g. [11, 21, 32]. Gene co-expression networks are constructed on the basis of microarray data from the transcriptional response of cells to changing conditions. There is evidence that genes with similar expression profiles are more likely to encode interacting proteins [33, 34].
In gene co-expression networks, nodes correspond to gene expression profiles. The corresponding adjacency matrix is determined from a measure of co-expression between the genes. In the examples below, we will use the absolute value of the Pearson correlation coefficient between the gene expression profiles to measure co-expression between gene pairs. As detailed at the end of the Methods section, one can transform the Pearson correlation matrix into an adjacency matrix by hard thresholding or soft thresholding. Hard thresholding results in an unweighted network and soft thresholding results in a weighted network [21]. We applied our methods to a yeast cell cycle microarray data comprised of 44 microarrays and 2001 genes. This dataset recorded gene expression levels during different stages of cell cycles in yeasts and has been widely used before to illustrate clustering methods [35].
Of the 2001 genes (microarray probesets) in the weighted yeast gene co-expression network, 1081 were clustered into 8 proper modules. The module sizes of the proper modules range from 53 to 308, mean 135.1, median 101.5, and interquartile range 69.3. To facilitate a comparison between the weighted and the unweighted gene co-expression networks, we used the module assignment of the weighted network for the unweighted network as well. It turns out that the module assignment is highly preserved between the weighted and the unweighted gene co-expression networks, see Figures 1C) and 1D).
Functional annotation of modules
Since the scope of this paper is a mathematical and topological analysis of module networks, we defined modules without regard to external gene ontology information. Also we do not provide an in-depth analysis of the biological meaning of the network modules. But we briefly mention that there is indirect evidence that most of the resulting modules are biologically meaningful. We used the functional gene annotation tools from the Database for Annotation, Visualization and Integrated Discovery (DAVID) [36] to test for both enriched biochemical pathways and subcellular compartmentalization. We find that most modules are significantly enriched with known gene ontologies. A functional enrichment analysis for each network application is provided. For the Drosophila PPI network, [see Additional file 3]; for the yeast PPI network, [see Additional file 4]; for the weighted and unweighted yeast gene co-expression networks, [see Additional file 5].
Empirical relationships in 4 different networks
In accordance with Observation 2, we find a close relationship (R2 ≥ 0.6) between the fundamental network concepts and their approximate CF-based analogs. Specifically, we relate the network density, centralization, heterogeneity and clustering coefficients to their approximate CF-based analogs in Figures 2 (Drosophila PPI network), Figure 3 (yeast PPI network), and Figure 4 (weighted and unweighted yeast gene co-expression networks).
In accordance with Observation 3, we find a close relationship (R2 ≥ 0.6) between the mean clustering coefficient mean (ClusterCoef) and (1 + Heterogeneity2)2 × Density. Further, we find a close relationship between TopOverlap[1]jand (Centralization + Density)(1 + Heterogeneity2), see Figures 5 (Drosophila PPI network), Figure 6 (yeast PPI network), and Figure 7 (weighted and unweighted yeast gene co-expression networks).
We find that our theoretical observations fit better in the weighted- than in the unweighted yeast gene co-expression network.
Network concepts and module size
Since the number of genes inside a module (module size) varies greatly among the modules, it is natural to wonder whether the reported relationships between network concepts are due to the underlying module sizes. We find that the relationship between fundamental network concepts and their approximate CF-based analogs remains highly significant even after correcting for module sizes [see Additional file 2]. The same holds for the relationships between network concepts. Thus, none of the reported relationships is trivially due to module sizes. But we find that many network concepts depend on the underlying module size. We find that large modules are less factorizable than small modules: there is a strong negative correlation between module factorizability F(A) and module size. We also find that fundamental network concepts (e.g. density) depend on module size in our applications. For the factorizability, density, centralization, heterogeneity and mean clustering coefficient, the correlation coefficients with module size are -0.84, -0.46, -0.17, 0.26, and -0.36 in Drosophila PPI module networks; they are -0.55, -0.52, 0.05, 0.5, and -0.44 in yeast PPI module networks; they are -0.93, -0.52, -0.82, 0.27, and -0.55 in weighted yeast gene co-expression module networks; they are -0.86, -0.77, -0.56, 0.87, and -0.85 in unweighted yeast gene co-expression module networks. A more detailed analysis is presented in the Additional files [see Additional file 2].
A simple exactly factorizable network example: constant network
A simple, exactly factorizable network is given by an adjacency matrix A with constant adjacencies (a ij = b, b ∈ (0, 1]). The adjacency matrix is exactly factorizable since a ij = CF i CF j where CF i = . This network can be interpreted as the expected adjacency matrix of an Erdös-Rényi network [37]. One can easily derive the following expressions for the fundamental network concepts: Connectivity i = (n - 1)b, Density = b, Centralization = 0, Heterogeneity = 0, ClusterCoef i = b and TopOverlap ij = b.
Network concepts in the constant Erdös-Rényi network.
Network Concepts
Approximate CF-based
Connectivity i
(n - 1)b
TopOverlap ij
ClusterCoef i
Example: block diagonal adjacency matrix
We assume that the first and second blocks have dimensions n1 × n1 and n2 × n2, respectively. Such a block diagonal matrix can be interpreted as a network with two distinct modules. Setting n2 = 0 results in the simple constant adjacency matrix, which we considered before.
In particular, if n1 ≈ n2 and b1 = b2, i.e. if the adjacency matrix is comprised of two nearly identical blocks, the factorizability is F(A) ≈ 1/2. Similarly, one can show that if the matrix A is comprised of B identical blocks, then F(A) ≈ 1/B.
Network concepts in the simulated block-diagonal network.
Approx CF-based
Connectivity i
TopOverlap ij
ClusterCoef i
For reasonably large values of n1 (say n1 > 20), these limits illustrate Observation 2. Similarly, one can easily verify Observation 3 and equation (16) in the case when the factorizability F(A) is close to 1 and n1 is reasonably large.
This paper does not describe a new software or method for constructing networks. Instead, it presents theoretical results which clarify the mathematical relationship between network concepts in module networks. A deeper understanding of network concepts may guide the data analyst on how to construct and use networks in practice. Our results will pertain to any network that is approximately factorizable irrespective of its construction method. While the term 'factorizable' network is new, numerous examples of these types of networks can be found in the literature, e.g. [38]. A recent physical model for experimentally determined protein-protein interactions is exactly factorizable [39]. In that model, the 'affinity' a ij between proteins i and j is the product of the corresponding conformities. The conformities are approximately given by CF i = exp(-K i ) where K i is the number of hydrophobic residues in the i-th protein. Another related example is an exactly factorizable random network model for which the edges between pairs of nodes are drawn according to a linking probability function [40, 41].
We find that in many applications, the conformity is highly related to the first eigenvector of the adjacency matrix. The idea of using a variant of the singular value decomposition for decomposing an adjacency matrix has been proposed by several authors [42–45]. However, we prefer to define the conformity as a maximizer of the factorizability function for the following reasons: First, the factorizability satisfies that F A (CF) = 1 if, and only if, A is exactly factorizable network with a ij = CF i CF j . Second, we prefer to define the conformity without reference to the diagonal elements a ii of the adjacency matrix. Third, the definition naturally fits within the framework of least squares factor analysis where conformity can be interpreted as the first factor [46]. An algorithm for computing the conformity in general networks is presented in the appendix. While network analysis focuses on the adjacency matrix, factor analysis takes as input a correlation or covariance matrix. In module networks, the first factor (conformity) corresponds to a normalized connectivity measure, see equation (16). Future research could explore the network interpretation of higher order factors.
The topological structure of complex networks has been the focus of numerous studies, e.g. [7, 8, 16–18, 20, 38, 47]. Here we explore the structure of special types of networks, which we refer to as module networks.
To derive results for factorizable module networks, we define several novel terms including a measure of network factorizability F(A), conformity, CF-based network concepts, approximate CF-based network concepts.
The first result (Observation 1) uses both PPI and gene co-expression network data to show empirically that subnetworks comprised of module nodes are often approximately factorizable. This insight could be interesting to researchers who develop module detection methods. Approximate factorizability is a very stringent structural assumption that is not satisfied in general networks. While modules in gene co-expression networks tend to be approximately factorizable if the corresponding expression profiles are highly correlated, the situation is more complicated for modules in PPI networks: only after replacing the original adjacency matrix by a 'smoothed out' version (the topological overlap matrix), do we find that the resulting modules are approximately factorizable.
The second result (Observation 2) shows that fundamental network concepts are approximately equal to their approximate CF-based analogs in approximately factorizable networks (e.g. modules). While fundamental network concepts are defined with respect to the adjacency matrix, approximate CF-based network concepts are defined with respect to the conformity vector. The close relationship between fundamental and approximate CF-based concepts in module networks can be used to provide an intuitive interpretation of network concepts in modules. We demonstrate that these high correlations between module concepts remain significant even after adjusting the analysis for differences in module size [see Additional file 2].
The third result (Observation 3) shows that the mean clustering coefficient is determined by the density and the network heterogeneity in approximately factorizable networks. Further, the topological overlap between two nodes is determined by the maximum of their respective connectivities and the heterogeneity. Thus, seemingly disparate network concepts satisfy simple and intuitive relationships in these special but biologically important types of networks.
The fourth result (Observation 4) is that in approximately factorizable networks, fundamental network concepts can be expressed as simple functions of the connectivity. Under mild assumptions, we argue that the clustering coefficient and the topological overlap matrix can be approximated by simple functions of the connectivity.
Our empirical data also highlight how network concepts differ between subnetworks of 'proper' modules and the subnetwork comprised of improper (grey) module nodes, see Table 1. For all applications, we find that proper modules have high factorizability, high density, high mean conformity. Based on our theoretical derivations, it comes as no surprise that proper modules also have a high average clustering coefficient and a high centralization when compared to the improper module. But we find no difference in heterogeneity between proper and improper module networks.
As a consequence of approximate factorizability, network concepts with disparate meanings in social network theory are closely related in module networks. Our results shed some light on the relationship between network concepts traditionally used by social scientists (e.g. centralization, heterogeneity) and concepts used by systems biologists (e.g. topological overlap). For example, equation (13) shows that in module networks, the topological overlap between a hub gene and other module genes is related to the centralization.
Using several protein-protein interaction and gene co-expression networks, we provide empirical evidence that subnetworks comprised of module nodes often satisfy an important structural property, which we call 'approximate factorizability'. In these types of networks, simple relationships exist between seemingly disparate network concepts. Several network concepts with very different meanings in general networks turn out to be highly correlated across modules. These results are pertinent for systems biology since a biological pathways may correspond to an approximately factorizable module network.
The adjacency matrix and notation
We study the properties of an adjacency matrix (network) A that satisfies the following three conditions:
(A.1) A is symmetric and has dimension n × n.
(A.2) The entries of A are bounded within [0, 1], that is, 0 ≤ a ij ≤ 1 for all 1 ≤ i,j ≤ n.
(A.3) The diagonal elements of A are all 1, that is, a ii = 1 for all 1 ≤ i ≤ n.
Matrix and vector notation
We will make use of the following notations. We denote by e i the unit vector whose i-th entry equals 1 and by 1 the 'one' vector whose components all equal 1. The Frobenius matrix norm is denoted by . The transpose of a matrix or vector is denoted by the superscript τ . For any real number p, we use the notation M p and v p to denote the element-wise power of a matrix M and a vector v respectively. We define the function S p (·) for a vector v as S p (v) = ∑ i = (v p ) τ 1. Further denote by I the identity matrix and by diag(v2) a diagonal matrix with its i-th diagonal component given by ,i = 1, ...,n. We define the maximum function max(M) as the maximum entry of matrix M and max(v) as the maximum entry of the vector v. Similarly we define the minimum function min(·). Also, we define mean(v) = S1(v)/n and variance(v) = S2(v)/n - (S1(v)/n)2.
Uniqueness of the conformity for an exactly factorizable network
One can easily show that the vector CF is not unique if an exactly factorizable network contains only n = 2 nodes. However, for n > 2 the conformity is uniquely defined when dealing with a weighted network where a ij > 0.
where denotes the 'product connectivity' of the i-th node.
Network concept functions and fundamental network concepts
In general, we define a network concept function to be a tensor valued function (e.g. the connectivity vector) that takes a square matrix (e.g. the network adjacency matrix) as input.
where the components of matrix B M in the denominator of the clustering coefficient function are given by b ij = 1 if i ≠ j and b ii = Ind(m ii > 0). Here the indicator function Ind(·) takes on the value 1 if the condition is satisfied and 0 otherwise.
For the sake of brevity, we study only a limited selection of network concept functions and do not claim that these are more important than others studied in the literature. Our general formalism for relating fundamental network concepts to their approximate CF-based analogs should allow the reader to adapt our derivations to alternative concepts as well.
Now we are ready to define the fundamental network concepts that are studied in this article.
Definition 5 (Fundamental Network Concept) The fundamental network concepts of a network A are defined by evaluating the network functions (equation (21)) on A - I, i.e.
FundamentalNetworkConcept = NetworkConcept(A - I).
For notational convenience, we sometimes omit the reference to the adjacency matrix and simply write Density to denote the fundamental network concepts.
Note that Heterogeneity(b * M) = Heterogeneity(M) for a scalar b ≠ 0.
where l ij = ∑u≠i,ja iu a uj .
Network concepts in exactly factorizable networks
In the following, we will present explicit formulas for the fundamental network concepts in Definition 5 when the adjacency matrix A is exactly factorizable, i.e. if a ij = CF i CF j . We define the CF-based adjacency matrix as follows
A CF := CF CF τ - diag(CF2) + I, (27)
Approximate CF-based network concepts in general networks
When A CF - I is used as input of a network concept function, it gives rise to a CF-based network concept as detailed in the following
Definition 6 (CF-based Network Concepts) Assume that the conformity vector CF can be defined for a general adjacency matrix A. Then the CF-based network concepts are defined by evaluating the network concept functions on A CF - I = CF CF τ - diag(CF2), i.e.
NetworkConcept CF := NetworkConcept(A CF - I).
By definition, fundamental network concepts are equal to their CF-based analogs if A is exactly factorizable.
In the following, we define approximate CF-based analogs of the fundamental network concepts. The theoretical advantage of these approximate CF-based concepts is that they satisfy simple relationships. Define the approximate CF-based adjacency matrix as follows
ACF,app= CF CF τ .
Note that only the diagonal elements differ between ACF,appand A CF . We define the approximate CF-based network concepts by using ACF,appas input of the network concept functions as detailed in the following
Definition 7 (Approximate CF-based Network Concepts) The approximate CF-based network concepts of a network A with conformity CF are defined by evaluating the network functions (equations (21)) on ACF,app= CF CF τ , i.e.
NetworkConceptCF,app:= NetworkConcept(ACF,app).
In approximately factorizable networks, fundamental network concepts are approximately equal to their approximate CF-based analogs
Here we will provide a heuristic derivation of Observation 2. Since the components of CF are positive, one can easily show that S4(CF) ≤ S2(CF)2. For many large, exactly factorizable networks, the ratio S4(CF)/S2(CF)2 is close to 0. Since S4(CF)/S2(CF)2 = , this implies that A CF - I ≈ ACF,app. Since the network concept functions are continuous functions, this implies NetworkConcept(A CF - I) ≈ NetworkConcept(ACF,app). These derivations are summarized in the following
Observation 8 (Approximate Formulas for CF-based Concepts) If S4(CF)/S2(CF)2 ≈ 0, then
NetworkConcept(A CF - I) ≈ NetworkConcept(ACF,app). (31)
In particular, for exactly factorizable networks (i.e. A - I = A CF - I), this means that the fundamental network concepts can be approximated by their approximate CF-based analogs.
In our real data applications, we show empirically that equation (31) holds even in networks that satisfy the assumptions of Observation 8 only approximately.
Thus, in approximately factorizable networks (i.e. F(A) close to 1), A - I can be approximated by A CF - I. For a continuous network functions, this implies
NetworkConcept(A -I) ≈ NetworkConcept(A CF - I),
i.e. the fundamental network concepts are approximately equal to their CF-based analogs in approximately factorizable networks. Observation 8 states that NetworkConcept(A CF -I) ≈ NetworkConcept(ACF,app).
Combining the last two equations leads to NetworkConcept(A - I) ≈ NetworkConcept(ACF,app). These derivations are summarized as follows.
In approximately factorizable networks, the fundamental network concepts are approximately equal to their approximate CF-based analogs, i.e.
FundamentalNetworkConcept ≈ NetworkConceptCF,app.
Construction of gene co-expression networks
Gene co-expression networks are constructed from microarray data that measures the transcriptional response of cells to changing conditions. We consider the case of n genes with gene expression profiles across m microarray samples. Thus, the gene expression profiles are given by an n × m matrix
X= [x ij ] = (x1 x2 ... x n ) τ , i = 1, ..., n; j = 1, ..., m, (33)
where the i-th row is the transcriptional responses of the i-th gene.
Recently, several groups have suggested thresholding the pairwise Pearson correlation coefficient cor(x i , x j ) in order to arrive at gene co-expression networks, which are sometimes referred to as 'relevance' networks [11, 32]. In these networks, a node corresponds to the gene expression profile of a given gene. The corresponding adjacency matrix is determined from a measure of co-expression between the genes. In the examples below, we will use the absolute value of the Pearson correlation coefficient between the gene expression profiles to measure co-expression.
To transform the co-expression measure into an adjacency, one can make use of an adjacency function. The choice of the adjacency function determines whether the resulting network will be weighted (soft-thresholding) or unweighted (hard-thresholding). The adjacency function is a monotonically increasing function that maps the interval [0, 1] into [0, 1]. A widely used adjacency function is the signum function which implements 'hard' thresholding involving the threshold parameter τ. Specifically,
a ij = Signum(|cor(x i , x j )|, τ) = Ind(|cor(x i , x j )| ≥ τ), (34)
where the indicator function Ind(·) takes on the value 1 if the condition is satisfied and 0 otherwise. Hard thresholding using the signum function leads to intuitive network concepts (e.g., the node connectivity equals the number of direct neighbors), but it may lead to a loss of information: if τ has been set to 0.8, there will be no connection between two nodes if their similarity equals 0.79.
To avoid the disadvantages of hard thresholding, we proposed a 'soft' thresholding approach that raises the absolute value of the correlation to the power β ≥ 1 [21], i.e.
a ij = Power(|cor(x i , x j )|, β) = |cor(x i , x j )| β .
In our yeast cell cycle gene co-expression network analysis, we followed the analysis steps described in [21]. Briefly, we used the 2001 most varying and connected genes. Next, we used the power adjacency function with β = 7 (equation (35)) to construct a weighted gene co-expression network and the signum adjacency function with τ = 0.65 (equation (34)) to construct an unweighted network.
Using our R software tutorial, the reader can easily verify that our conclusions are highly robust with respect to a) different ways of constructing co-expression networks and b) different ways of constructing modules.
Availability and requirements
An R implementation and the data can be obtained from the internet: http://www.genetics.ucla.edu/labs/horvath/ModuleConformity/ModuleNetworks
Appendix: node conformity and factorizability of a general network
Equation (20) provides an explicit formula for the conformity of a weighted, exactly factorizable network. For a general, non-factorizable network, we describe here how to compute the conformity by optimizing an objective function. In the following, we assume a general n × n adjacency matrix A where n > 2. Let v= (v1,v2, ...,v n ) τ be a vector of length n. We could define the conformity as a vector v* that minimizes the following objective function f(v) = ∑ i ∑j≠i(a ij - v i v j )2. But instead, we find the following equivalent formulation as a maximization problem more useful since it naturally gives rise to a measure of factorizability.
It is clear that F A (CF) = 1 for an exactly factorizable network with a ij = CF i CF j for i ≠ j. Note that F A (v) ≤ 1 and F A (0) = 0. One can easily show that if v* maximizes F A (v), then -v* also maximizes F A (v). Further, all components of v* must have the same sign since otherwise, flipping the sign of the negative components leads to a higher value of F A (v). This leads us to the following
Definition 9 (Conformity, Factorizability) We define the conformity CF as the vector with non-negative entries that maximizes F A (v). If there is more than one such maximizer, then a maximizer closest to k/is chosen. Further, we define the factorizability F(A) as the corresponding maximum value F A (CF).
Our definition of the conformity is a generalization of Definition 7 since F(A) = 1 if, and only if, A is exactly factorizable with a ij = CF i CF j for i ≠ j. The advantages of this Definition are briefly described in the discussion section.
Proof Since , it will be sufficient to show that . From the definition of the Frobenius norm of a matrix B, one can show that where the trace of a matrix is the sum of its diagonal elements. Thus, . Using equation (38), we find that trace((A - I)(A CF - I)) = tr((A - I)CF CF τ ) - tr((A - I)diag(CF2)) = CF τ (A - I)CF= . Thus, The remainder of the proof is straightforward.
:= A - I + diag(CF2).
An algorithm for computing the conformity is based on the following
Lemma 11 If A denotes a symmetric real matrix with eigenvalues d1, ..., d n sorted according to their absolute values, i.e., |d1| ≥ |d2| ≥ ... ≥ |d n |, and the corresponding orthonormal eigenvectors are denoted by u1, ..., u n , then is minimized at v*= u1.
The proof can be found in Horn and Johnson [49].
(i - 1) = A - I + diag(CF(i - 1)2).
Thus, we arrive at the following
F A (CF(i)) ≥ F A (CF(i - 1)), (42)
which suggests a monotonic algorithm for computing CF. Equation (16) suggests to choose k/ as a starting value of the algorithm. These comments give rise to the following
Note that the conformity satisfies equation (38) by definition of convergence. One can easily show that 0 ≤ F(A) ≤ 1. Further, one can easily show that F(A) = 1 if, and only if, A is exactly factorizable with a ij = CF i CF j , i.e. A - I = A CF - I.
The algorithm described by equations (40) and (41) is monotonic (equation (42)). It is a special case of an algorithm described in [46] for fitting a least squares factor analysis model with one factor. Theoretical properties of the algorithm are discussed in [46] and [48].
We find that for most real networks, the conformity is highly related to the first eigenvector of the adjacency matrix, i.e. the conformity vector CF is roughly equal to u1 where d1 is the largest eigenvalue of A and u1 is the corresponding unit length eigenvector with positive components.
We would like to acknowledge the grant support from Program Project Grant 1U19AI063603-01 and NINDS/NIMH 1U24NS043562-01. We are grateful for discussions with Andy Yip, Lora Bagryanova, Dan Geschwind, Johanna Hardin, Ken Lange, Peter Langfelder, Ai Li, Jake Lusis, Paul Mischel, Stan Nelson, Nan Zhang and Wei Zhao.
Authors' Affiliations
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I request people to list some moderately and/or very famous open problems which high school students,perhaps with enough contest math background, can understand, classified by categories as on arxiv.org. Please include statement of the theorems,if possible, and if there are specific terms, please state what they mean.
Thank you.I am quite inquisitive to know about them and I asked this question after seeing how Andrew J.Wiles was fascinated by Fermat's last theorem back in high school.

subset: commoncrawl


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I'm a 4.0 level and can be a 3,5 level from time to time, and also can achieve 3.0 when I least expect it.
What I'm looking for is a hitting partner (Male or Female ) that would like to rally, drill and develop skills.
I hit at Fort Greene, Prospect Park and other Brooklyn locations.
If you are interested and available , please let me know.
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Replies to This Discussion
Hi Rob, I am probably a 3.25 but an athlete, how about a match in Van Voorhees Park Cobble Hill, Sunday AM?
Thanks for your reply. as it turns out I have a match set up for Sunday already. You may want to check out Brooklyn Manhattan Tennis Meet Up.
Hi Rob,
I previously posted a write-up that is very similar to yours. (See below.) Are you available weekday mornings for Prospect Park? I could hit as early as tomorrow (Thursday) at 7am. Also available later this week and weekend. I can be reached directly at email@example.com.
I am a 38-yr old, female 3.5 player looking to rally and build skills (rather than play sets) at Ave L or Prospect Park Tennis Center. I am available weekday mornings (some), afternoons, early evenings, as well as some weekends. I am looking to build up a mini network of hitting partners for the spring and summer and am comfortable playing with men or women. Great if you have the tennis permit and can play regularly at Prospect Park or Friends Field (Ave L). Reply or send me your email if your interested.
Hi Rob,
My yahoo account is temporarily down. Can you let me know here if you can play tomorrow?
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CCSD59 Celebrates Staff Excellence With ISBE Award
Every year, the Illinois State Board of Education (ISBE) recognizes a variety of educational staff and community members for their outstanding contributions to Illinois schools. The program, called Those Who Excel, annually recognizes and honors educators who have made outstanding contributions to elementary and secondary education. There are seven different categories and three levels of awards that are issued each year.
Nomination letters and letters of recommendation meeting strict criteria must be sent in support of each candidate. A committee then determines the winners and the level of recognition, including: Award of Excellence, Award of Meritorious Service, and Award of Special Recognition.
CCSD59 is proud to announce that all of its nominees will receive an award at the ISBE's Those Who Excel Awards Banquet on October 28, 2017, at the Bloomington-Normal Marriott Conference Center.
CCSD59 had five staff members recognized this year for their outstanding contributions to education.
The CCSD59 award recipients are:
Linda Johnson – Language Arts Teacher, Grove Jr. High
"It's impossible to overstate the positive impact that Linda has on her teaching colleagues and administration. In our district, she is a teacher-leader, department chairperson, mentor, curriculum designer, and confidant." – John Harrington, Grove Principal
Ryan Schroeder – PE Teacher & Brenda Wojcik – LRC Director
Byrd Elementary (Specials Team)
"Their non-traditional thinking and willingness to try innovative ideas to spark student engagement has transformed how our specials team operates. This has had a great impact not only in creating a successful environment for all our students, but one the students truly enjoy going to. The specials team truly has ignited a love for learning in all their students, and it's why they are so deserving of this award."
– Mary Ellen Esser, Byrd Principal
Anna Szczesik – Psychologist, Clearmont Elementary
"Anna's willingness to give of her time and of herself, as someone who is always putting the needs of every student first, is what truly sets her apart as the incredible team player she is. We feel extremely fortunate that Anna is on our team."
– Rachel Solomon, Clearmont Principal
Paul Wutz – Head Custodian, ELC and Holmes Jr. High
"Paul demonstrates his care by the way he interacts with students. He is kind. He takes time to talk with our students. They are typically very interested in what he
is doing and have many questions and Paul answers each and every one. He shows interests in what our students and staff are doing and they really know he cares."
– Michele Ramsey, ELC Principal
The award recipients are very quick to share their recognition with both fellow staff members and the district. Award recipient Linda Johnson said, "I have been with District 59 my entire teaching life. It is my second home, and it has always encouraged me and expected me to excel."
Ryan Schroeder and Brenda Wojcik, who received their award for the Byrd specials team, said it this way: "There are so many well-deserving staff members in this district that we felt very humbled to receive this recognition."
Congratulations to all the recipients for representing CCSD59 so well.


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Yankton Commissioners Say Study Needed on Housing
YANKTON - City commissioners in Yankton want to study what they believe is a housing shortage.
The commission on Monday approved a motion to create a committee to explore a housing survey and how to pay for it.
Commissioner David Knoff says he's been told the city is lacking in apartments and houses in the $125,000 to $175,000 range, yet nobody is building.
Knoff says it may be that infrastructure costs are too high.
The Yankton Press and Dakotan reports that the city of Mitchell recently completed a housing study for a cost of about $28,000.
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.


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I'm committed to my career in higher ed and after a long, far too long time, I'm leaving my current job at a local public university to take a nice position at another local university, smaller and private. I couldn't be more excited. It certainly is something to celebrate.
Let's be clear - bubbles are not just for celebrations. It's a shame that Champagne and the world of sparkling wines are so often saved only to celebrate. Those of us who know better know that bubbles go tremendously well with all kinds of food, and honestly, short of some nasty cheap, sweet "champagne" out there, is there a wine category with more to offer at the lower end than sparkling wine?
Sparkling wines at reasonable prices from Italy, Spain, France, California, Oregon, even the state of New Mexico (Gruet!), abound on shelves across the US. I honestly don't know why I don't drink more of them myself.
Perhaps I too am guilty, and with the new job, what did I do? I went out and bought a bottle of sparkling wine to celebrate. Nothing wrong with that, I suppose.
I didn't spend a ton, paying about $23, but it's true I didn't exactly cheap out. Still, the NV Clotilde Davenne Cremant de Bourgogne Brut Extra is astonishingly good bubbly worthy of celebration and even a simple dinner at home. It's excellent wine for some money but hardly too much.
This producer is located in the Chablis region, where the chalky soils suggest the unique terroirs of nearby Champagne. I knew nothing of the wine when I bought it. I just trusted a favorite retailer - Division Wines in SE Portland - and it's what they had in the cold box. I didn't expect it to be bad, I just had no idea how good this would be.
Pale in color with a lovely texture of bubbles and bright acidity, the middle palate was the key. A burst of energy in the mouth took this from pleasant sparkler to near Champagne in quality, and I don't say that lightly. The finish was pretty long and graceful, and the bottle disappeared rather quickly. This was irresistible wine.
The lesson? Bubbles are indeed great for celebrations. But when you can get a wine of this quality at this kind of price, a wine that puts a smile on your face so effortlessly, why on earth wouldn't you drink it more often? There's always something to celebrate, no?


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Home » Roccat Kave XTD 5.1 Digital PC Gaming Headset is an Affordable Performer for Any Level Gamer [Review] » DSC_0129
About Stormy Beach
I have been a tech nut for many years. Android has had a special place in my heart since it originally made its debut with the T-Mobile G1. Prior to that I sported a number of windows devices including the T-Mobile Wing. After I was married and we had our 3rd child, is when I really got into phones. Since then my passion for tech and has grown into somewhat of a monster. Always looking for something that I haven't seen a million times everywhere else. Always looking for things that will benefit me, my family and people long term, not just for the few short months they have a certain device. I don't claim to know everything, but one of the best parts of tech is, and always will be, learning as much as possible.
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The Oscar nominations were released yesterday, and the joy in poring through each category is trying to figure out who got a surprise nomination and, more important, who got hosed. Because what's the Oscars without pettiness and jealousy? Let's dive in.
The Blind Side (Best Picture): A nomination for Sandra Bullock was expected (Bullock and Meryl Streep are the favorites to win Best Actress), but a Best Picture Nomination was far more of a long shot. But the smash hit made it into the category thanks to the Academy's expansion to 10 nominees. The Academy accomplished precisely what it wanted to with this category: making enough room so that more popular movies could make the cut. If the category had not been expanded, it's clear (at least to me) that hits like "The Blind Side," "District 9," and "Up" would be out of the running by now.
Jeremy Renner (Best Actor): The nomination itself isn't as much of a surprise as Renner's story is. Renner was a complete unknown until "The Hurt Locker" came out. Now he and Sam Worthington represent the next wave of full-blooded male acting superstars. His arrival is most welcome in a world where Russell Crowe gets a little older and a little sloppier each year.
Woody Harrelson (Best Supporting Actor): In a year where Harrelson reemerged with a hit comedy ("Zombieland"), he also scores a nod for his extremely serious turn in a little-seen but well-regarded movie about the after-effects of the Iraq War ("The Messenger" also got a screenplay nod). Harrelson will end up losing in this category to Christopher Waltz. Regardless, it's nice to see him nominated, and it would be nice to see him one day fully rewarded. He's an awesome acceptance speech waiting to happen.
Clint Eastwood (Best Director): I suppose you could be indignant about Clint not making the cut for "Invictus," except the movie is just okay and Clint seems to get nominated every year these days.
The Hangover (Best Picture): The Golden Globe Best Comedy winner had an outside shot at getting into the Best Picture Oscar category, only to be denied. Yet another snub for comedy, which is annoying. Any person who isn't funny will tell you comedy is hard to do.
The Lovely Bones (Best Picture): Count this movie, "It's Complicated," and "Nine" as films that would have earned Best Picture nominations if they hadn't stunk.
(500) Days of Summer (Best Picture): The beloved indie comedy didn't prove to be this year's "Juno," getting shut out of Best Picture. Know who I blame for it? The parentheses in the title. Such a hipster thing to do.


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Note As of 15 November 2015, the Zune service has been discontinued. This may cause errors when attempting to stream or download content or update the service.
This article describes how to view pictures or a slideshow on your Xbox 360 console, and how to set a picture as the Xbox 360 Dashboard background.
The Xbox 360 console can read JPEG, BMP, and PNG files from the following sources:
Note Not all devices, networks, and CD/DVD media are supported. If one source doesn't work, try another. For example, if your Xbox 360 console can't display images that are on a USB flash drive, try a different USB flash drive or copying the photos to a CD or a DVD.
You can stream pictures over your home network to your Xbox 360 console by using Windows Media Player, the Zune Music + Video software, or Microsoft Windows Media Center Extender. For more information, see Stream media using Groove, Movies & TV, or Windows Media Player with Xbox 360.
To view pictures or images on your Xbox 360 console, follow these steps:
To start a slideshow, follow these steps:
If you push the left thumbstick in any direction while you're playing a slideshow, you'll see a control panel displaying the following options:
To set a picture or an image as the Xbox 360 Dashboard background, follow these steps:
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Online Training
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Interact and learn with your peers, and have an expert instructor to answer questions and provide valuable, timely feedback. Our unique instructor-facilitated courses are designed to fit your schedule and budget. You can take all of our courses from the comfort of your home or office, when it's most convenient for you.


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Last updated: February 26, 2012
NHGRI Pays Tribute to a Giant of Medical Genetics
NHGRI Pays Tribute to a Giant of Medical Genetics
Renowned Father of Medical Genetics, Victor Almon McKusick, 1921-2008
Rarely can one person be credited with establishing an entire branch of medicine, but such is the case for Victor McKusick, M.D., and the field of medical genetics. The much-admired researcher, who almost single-handedly placed genetics into the mainstream of clinical medicine and helped to pioneer the Human Genome Project, died July 22 at his home near Baltimore at the age of 86.
"Victor McKusick is widely and accurately known as the 'Father of Medical Genetics.' His tireless and creative contributions over more than half a century have provided a permanent foundation for a field that now occupies the center of modern medicine," said National Human Genome Research Institute (NHGRI) Director Francis S. Collins, M.D., Ph.D.
NHGRI's Deputy Director, Alan E. Guttmacher, M.D., also fondly remembers the sweeping influence of Dr. McKusick, who was University Professor of Medical Genetics at the Johns Hopkins School of Medicine. "His wisdom and dedication to advancing knowledge and health were remarkable, as was his perpetual willingness to help whenever a colleague had a challenging clinical question. He served as a mentor not only for his numerous trainees at Johns Hopkins, but also for virtually all of us who chose to follow in his footsteps in medical genetics. He will be missed as a scientist, a physician, a role model and a kind man."
Dr. McKusick earned his M.D. from the Johns Hopkins University School of Medicine in 1946 and joined the faculty of the School of Medicine as a cardiologist the same year, studying heart sounds and murmurs. He held joint professorships in epidemiology in the Johns Hopkins University School of Public Health and in biology at the Johns Hopkins University.
He quickly developed an interest in the inheritance of disease, studying patients afflicted with Marfan syndrome, a connective tissue disease marked by unusually tall height, heart defects and other abnormalities. The experience prompted Dr. McKusick to begin cataloging and mapping genes on chromosomes, relating their location to human diseases.
In 1957, he founded the Division of Medical Genetics, which he headed until 1973, when he became the William Osler Professor and chairman of the Department of Medicine, and physician in chief of the Johns Hopkins Hospital. He held these posts until 1985, when he was named University Professor of Medical Genetics.
During the 1960s, McKusick conducted studies of inherited disorders in the Amish that discovered previously unrecognized, inherited conditions, and served as a model for studies in similarly isolated populations. In 1966, he published the first edition of his master compendium of disorders and genetic factors in disease, formally titled Mendelian Inheritance in Man: Catalogs of Autosomal Recessive, and X-Linked Phenotypes. Now known as Online Mendelian Inheritance in Man (OMIM), this landmark resource is continually updated at www.ncbi.nlm.nih.gov/omim and is considered an essential reference for medical geneticists around the globe.
In 1997, when Dr. McKusick was the recipient of the Albert Lasker Award for Lifetime Achievement in Medical Science, Dr. Collins had a conversation with the genetics pioneer about how important Mendelian Inheritance in Man had been to him as a first-year medical genetics fellow at Yale University in 1981. Dr. Collins was confronted with the puzzling case of a young infant where imaging studies suggested a sort of jejunal atresia, a type of intestinal obstruction. Sure enough, there was a family history of an identical lesion in a sibling.
Dr. Collins described the case to his attending physician, Dr. Uta Francke and both were quite puzzled until they looked at Dr. McKusick's book where they found the entry "*243600, Familial Apple Peel Jejunal Atresia."
"There it was, an absolute perfect description of the condition that we had just seen," remembered Dr. Collins. "Whereupon, Uta said,'This is wonderful. Victor should win the Nobel Prize!' "
While editing Mendelian Inheritance in Man was a passion for Dr. McKusick, it was just one of his many ideas that revolutionized the field of medical genetics. In 1969, he proposed mapping all human genes — an idea nearly two decades ahead of its time. In fact, he was an early proponent and skillful architect of the Human Genome Project, which in 2003 successfully completed its effort to sequence all 3.1 billion DNA letters in the human genetic blueprint. Today, the importance of recognizing and understanding the links between various genes and disease proves the merit and the widespread acceptance of Dr. McKusick's fundamental approach to studying disease.
During a career that spanned an impressive 60 years, Dr. McKusick received many accolades in addition to the Lasker Award. These honors included the John Phillips Award of the American College of Physicians for distinguished contributions in internal medicine (1972); the Gairdner International Award (1977); the William A. Allan Award of the American Society of Human Genetics (1977); the James Murray Luck Award from the National Academy of Sciences (1982); the Sanremo International Prize for Genetic Research (1983); the American Association of Physicians' George M. Kober Medal (1990); the National Medal of Science (2001); and the Japan Prize in Medical Genetics and Genomics (2008). McKusick is also a member of the National Academy of Sciences.
"Many of us would not be where we are today without him," Dr. Collins said. "As a geneticist, internist, cardiologist, teacher, mentor, role model, editor and academic leader, he was a giant of our time. We will miss him greatly."
Last Reviewed: February 26, 2012


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In the days before internet usage became widespread, buying lottery tickets 'offline' was a much more time-consuming process: players would need to visit a participating retailer, fill out lines on a ticket slip and pay, and then watch the televised draw to find out whether their lucky numbers had come up. Playing online is in some ways much easier (in terms of convenience) but in other ways more complicated, as the range of features and games on offer has increased considerably. Listed below are the key differences between online and 'offline'.
As discussed above, one of the key differences between offline and online play is the location where you buy your tickets: in-store versus on a dedicated website, for example National-Lottery.co.uk. When you buy offline, there's very little in the way of setup (although some UK retailers may ask for ID to verify that customers meet the 16-years age limit). By contrast, when playing online, users have to register for an account and provide personal details such as name, address, date of birth, gender and email address – as well as debit card details in order to process payments.
Another significant difference is the level of security and assurance available online. For example, if you buy a ticket in a shop and subsequently lose it, it's very difficult to prove the win and claim the prize. Likewise, if a player forgets to check the results of a draw, they may also fail to claim their prize in the event of a win. On the other hand, with an online lottery ticket, there is a permanent digital record of all transactions and numbers, and players will typically receive email alerts within 24 hours if they've won a prize, with the funds often being transferred straight to their account. The exception to this is in cases where players scoop a jackpot or other large prize – this will usually require the winner to either collect the prize in-person or to accept delivery by cheque.
Buying lottery tickets online comes with the benefit of several convenient features, such as
In the UK, online players have access to the country's four major draws via the National Lottery website – Lotto, EuroMillions, Thunder Ball and Lotto Hotpicks. One key difference from the offline experience, however, is the selection of scratch card options on offer: online players will find a very wide selection of instant win games to choose from (more than you would expect to find in-store) – and, unlike a shop, there's no risk of your favourite scratch card being out of stock.
Another key advantage of playing online is the opportunity to participate in lotteries from around the world, some of which (like the Mega Millions, Italy's SuperEnalotto or Spain's La Primitiva draw) routinely rack up enormous jackpots. Lottery concierge websites like TheLotter and GiantLottos work by either sending out local staff members to purchase tickets in the relevant country on behalf of overseas online players, or by acting as a betting service, whereby players pick their numbers and effectively bet on the outcome of the draw (without actually purchasing a ticket).
These websites also offer the chance to join online syndicates for major overseas draws (in which players buy 'shares' in exchange for a proportion of any winnings) which can boost individuals' chances of winning, thanks to collective purchasing power – without the effort and admin involved in organising an offline syndicate.


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DeLAND, Fla. - A Volusia County gun shop has offered a free gun to George Zimmerman, the former neighborhood watch leader acquitted in the shooting death of Trayvon Martin.
In a letter to Zimmerman's attorney, former Local 6 legal analyst Mark O'Mara, Pompano Pats in DeLand said it's offering a free firearm to Zimmerman after hearing media reports that he could not obtain his Kel-Tec PF-9 from authorities.
"Upon receiving your confirmation that he is well within his legal rights to concealed carry, our company would like to offer Mr. Zimmerman a free firearm. We currently have the same model in stock, or he could (choose) another weapon suitable for concealed carry," the letter states.
It also says, "We have read numerous reports of death threats against your client and believe no good would come from harming him."
The letter, which also says the company is not trying to make a political statement, was signed by Pompano Parts President Pat Johnson.
After Saturday's not guilty verdict was read, rallies, marches and demonstrations in support of Martin have been held across the county and many more are scheduled this weekend.
Watch Local 6 News and stay with ClickOrlando.com for more on this story.
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Countless blessings
Each year in November, we write a letter to the editor about adoption and this year is no different. November is National Adoption Month and is a great time to be thankful for the option of adoption.
Our kids are growing up fast but that doesn't mean we forget how we got them. For us, becoming parents was only possible through adoption.
To hold a baby in your arms after waiting for so long is absolutely one of the best feelings in the world.
Over time, we have been lucky to be able to help other couples adopt and have developed many friendships because of it.
And now we see those couples helping others. Through adoption the creation of a family is still possible.
This month, please remember all birth parents, couples considering adoption, those waiting for "the call" and those who have adopted. All of us have countless blessings, but the best blessing of all is your family.
Wade and Lisa Althouse


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Please send me the research paper for this.
Its not a secret that the nosocomial infections are worse in India... The resistance bacteria or the protein (the gene for it) comes primeraly from India.
(origin of the gene is south asia according to the research)
Pito, so all clean hospitals have no nosocomial infections???
if you are from India, you should know that there are still a lot of dirty places (hospitals) where the medical care is not really good/clean.
For this, I find no basis. Like you said, Medical tourism is high, so the numbers will be high. But you cant say all antibiotic resistant bacteria originate from India or Asia or America for that matter.
Its for example allready very clear that the medical tourism to India is becoming a big problems. If you look at the problems in the UK==> almost all due to medical tourism. All the problem cases due to resitant bacteria are almost all related to India (people that came for India with the bacterium, holding the gene for resistance)
Look up Burkholderia, is that Indian as well?
And why is the NDM-1 a big problems and the others not? Very simple: NDM-1 offers much more protection then other protein... Other proteins only work against a few antibioticclasses, NDM-1 against many more.
And yes, its not only India , Bangladesh and Pakistan play an important role too. And yes, India is going to review certain treatments
And yes, India isnt the only country doing things wrong. China is also doing things wrong.. the thing is:china is "more closed" , so not much information is gathered from china..
Same with african countries: major problems there too.. but less research, so less information.
The problem with India is the medical tourism etc... and the "industrial revolution" over there.
These are just patronizing statements.
You did say that antibiotics are prescribed on a regular basis by Medical doctors (who spend years in medical school... )
BTW: I never said that the biggest problems are caused by medical doctors prescribing antibiotics... like said: fishindustry for example plays a major role too.
And what do you mean with "How exactly are you supporting the use of alternative medicines, if you are bent upon using anibiotics?" Killing bacteria or getting rid off a bacterial infection is done bj antibiotics.. so I dont get the idea? You mean other medicins that are not antibiotics but work against bacteria? I dont understand what you mean by this?
What is your idea of alternative medicines? Do you think that the only way of ending infections is using antibiotics?
I will agree that central healthcare in India needs improvement, training and regulation but convicting a nation/ region for "granting antibiotic resistance" is like being a 10 yr old and saying "I dint do it, He did it". Modern Medicine being practised around the world is Western in origin, so should I blame the technology transfer methods adopted in the first place for all nosocomial infections? Why play this blame game, when we know that we all are responsible.
Our basic problem has been not understanding the potential of nature itself. Like Venter, who made synthetic DNA, but could not put it in a man-made cell, we are still too naive about how things work around us and within us.


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Why Even Good Hospitals And Doctors Are An Obstacle To Better, Cheaper Healthcare
from the perverse-incentives dept
As we noted in the context of antibiotics, it's well recognized that financial incentives cause the pharmaceutical industry to engage in research that tends to maximize profits rather than maximizing the health of the public. But a widely-circulated article in the Washington Post reveals another kind of bias that may stop us from adopting better ways of keeping people healthy that would also reduce healthcare costs.
This flows from the fact that countries with advanced healthcare systems are no longer dealing mainly with infectious diseases like turberculosis, as they once did, but with chronic ones like heart disease, diabetes, AIDS and many cancers. The key here is how best to manage the disease, particularly among elderly patients, and for that, doctors in hospitals aren't necessarily the best way:
Medicine has been so focused on what doctors can do in the hospital that it has barely even begun to figure out what can be done in the home. But the home is where elderly patients spend most of their time. It's where they take their medicine and eat their meals, and it's where they fall into funks and trip over the corner of the carpet. It's where a trained medical professional can see a bad turn before it turns into a catastrophe. Medicine, however, has been reluctant to intrude into homes.
One company, Health Quality Partners, has focused on doing precisely that:
The program enrolls Medicare patients with at least one chronic illness and one hospitalization in the past year. It then sends a trained nurse to see them every week, or every month, whether they're healthy or sick. It sounds simple and, in a way, it is. But simple things can be revolutionary.
The results certainly are:
According to an independent analysis by the consulting firm Mathematica, HQP has reduced hospitalizations by 33 percent and cut Medicare costs by 22 percent.
And yet Medicare is planning to shelve this pilot program, citing various bureaucratic reasons why it can't continue. Although some supporters of the home-based system maintain that it would be possible to overcome these problems, there remains a more fundamental obstacle to rolling out the Health Quality Partners approach more widely:
Hospitals make money when they do more to patients. They lose money when their beds are empty. Put simply, Health Quality Partners makes hospitals lose money.
So again we seem to be confronted by perverse incentives at the heart of our current healthcare. The better and cheaper way would mean scaling back key parts of the system by instituting regular home visits by nurses, thus reducing the number people sent into hospitals to be treated by physicians. That implies taking on very profitable and thus very powerful business interests, including the doctors themselves. Given that resistance, and Medicare's apparent reluctance to force change by backing the Health Quality Partners system, it seems likely that we will be stuck with an inferior, more costly approach to treating chronic diseases despite knowing what looks like a much better way to do it. Some might call that pretty sick.
Follow me @glynmoody on Twitter or identi.ca, and on Google+
Filed Under: economics, healthcare, incentives


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Welcome to Hyperion Records, an independent British classical label devoted to presenting high-quality recordings of music of all styles and from all periods from the twelfth century to the twenty-first.
Hyperion offers both CDs, and downloads in a number of formats. The site is also available in several languages.
Please use the dropdown buttons to set your preferred options, or use the checkbox to accept the defaults.
from notes by Meurig Bowen © 1998
extrait des notes rédigées par Meurig Bowen © 1998
Français: Hypérion
aus dem Begleittext von Meurig Bowen © 1998
Deutsch: Anke Vogelhuber
|Pärt: Berliner Messe & Magnificat
Here is some of the most spiritually uplifting music of our generation, sung by that most virtuosic of choirs, Polyphony. Arvo Pärt has succeeded in capturing the attention of a broad public through his consummate ability to weave a sense of inevi ...» More
|Pärt: Tintinnabuli
"It is with great pleasure that we present our tribute to Arvo Pärt in his 80th year. Tintinnabuli (from the Latin for 'bell') is the compositional style created by Arvo Pärt which informs every work on this recording. In all my searchings for ins ...» More
|A Christmas Present from Polyphony
'Stephen Layton directs the performances and deserves major credit for the very high standards evident on this compilation' (BBC Music Magazine)
'This is a disc for listening to in peace, after the Christmas Day festivites are over and the visitors have gone' (The Daily Telegraph)» More


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Mere Mehboob Qayamat Hogi - Kishore KumarsOnline Media
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Minnesota Man Gets Twenty Years For Child's Murder
ADA, Minn. (AP) - A western Minnesota man has been sentenced to 20 years in prison for killing his girlfriend's young daughter.
Raul Perez of Dilworth pleaded guilty to second-degree murder. He was accused of killing 22-month-old Ariel Reyes.
Ariel died of head and neck trauma last year. She was injured while Perez was watching her and her older brother.
Perez admitted he became angry because the girl wouldn't stop crying and threw her into her crib.
Reports say Perez read an apology to the victim's family before sentencing Monday in Norman County.
Perez got a stiffer sentence than court guidelines recommend because of aggravating factors, including the fact that the girl's now-6-year-old brother witnessed the crime.
But the girl's father says he wishes Perez had gotten an even harsher sentence.


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Rest for Restless Hearts
Stroll into a bookstore these days and you will likely find a large area labeled "Self-Help," "Motivation," or "Personal Transformation." Go ahead, browse the volumes found here. Some are curiously interesting, and some will just make you laugh. Several books …Read More
He Who Has Ears…
Everyone loves a story. Whether young or old, we all enjoy hearing, reading, or seeing a good story unfold. Stories are remarkably powerful things. They stir-up our imaginations and excite our affections. They instruct us and inspire us. They intoxicate …Read More
Scott Anderson
Scott Anderson is president and CEO of Desiring God Ministries in Minneapolis, Minnesota.


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If imitation is the sincerest form of flattery, then Hyundai Motor America marketing executives should be blushing bright red as General Motors Corporation and Ford Motor Company followed it today with buyer payment protection plans that emulate its breakthrough Hyundai Assurance Program that has boosted sales by at least 10% in Hyundai's estimation.
In the face of frightening U.S. sales declines in February that made it the lowest February sales on record going back to 1967, automakers are desperately trying to reassure customers that now is the time to buy with a variety of incentive packages. (February year-over-year comparisons ranged from -53% at GM, -48% Ford, -44% Chrysler, and -35 to -37% at Toyota, Honda and Nissan.) Auto sales in the first two weeks of March were down 40% compared to a year ago, and running at a dismal annual rate of 9.2 million units, according to J. D. Power and Associates.
Automakers are increasingly using as an inducement guaranteed-payment of car loans, if the buyer loses his or her job — certainly a very real threat at domestic car companies, if not for workers in the slumping economy as a whole.
A controversial bill has also been introduced in the U.S. House of representatives (H.R. 1550, or the CARS Act) could help kick-start the American automotive market by providing cash incentives of up to $5,000 for those who trade in a vehicle at least eight years old for a limited selection of fuel-efficient products produced in North America. The legislation, as initially proposed, would offer the biggest tax credits for U.S.-made vehicles, though products made in the NAFTA countries, Canada and Mexico, would also qualify. (more…)


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The City of Tacoma has updated the link required for landlords to use in the tenant screening criteria.
Tacoma landlords need to update the link in their screening criteria
Posted on February 7, 2019 by LandlordSolutions in Uncategorized
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