Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph

For a given graph G and an associated class of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdiere in connection with the Strong Arnold Property, two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities. These new properties are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Finally, these ideas are applied to the minimum number of distinct eigenvalues associated with G, denoted by q(G). The graphs for which q(G) is at least the number of vertices of G less one are characterized.Comment: 26 pages; corrected statement of Theorem 3.5 (a

Integrated Genomic Analysis of Sézary Syndrome

Sézary syndrome (SS) is a rare variant of primary cutaneous T-cell lymphoma. Little is known about the underlying pathogenesis of S. To address this issue, we used Affymetrix 10K SNP microarray to analyse 13 DNA samples isolated from 8 SS patients and qPCR with ABI TaqMan SNP genotyping assays for the validation of the SNP microarray results. In addition, we tested the impact of SNP loss of heterozygosity (LOH) identified in SS cases on the gene expression profiles of SS cases detected with Affymetrix GeneChip U133A. The results showed: (1) frequent SNP copy number change and LOH involving 1, 2p, 3, 4q, 5q, 6, 7p, 8, 9, 10, 11, 12q, 13, 14, 16q, 17, and 20, (2) reduced SNP copy number at FAT gene (4q35) in 75% of SS cases, and (3) the separation of all SS cases from normal control samples by SNP LOH gene clusters at chromosome regions of 9q31q34, 10p11q26, and 13q11q12. These findings provide some intriguing information for our current understanding of the molecular pathogenesis of this tumour and suggest the possibility of presence of functional SNP LOH in SS tumour cells

The Chief Student Affairs Officer: What Constitutes Effective Leadership?

The leadership characteristics of a 21 chief student affairs officers (CSAOs) within four-year, postsecondary institutions in the Southeast were examined using The Leadership Practices Inventory (LPI) developed by Kouzes and Posner. The LPI measures five fundamental leadership factors: challenge the process, inspire a shared vision, enable others to act, model the way, and encourage the heart. Each of these factors was investigated in relation to length of time in the current position, length in the student affairs profession, gender, and geographic location. Statistical analyses of performance on the LPI suggest that CSAOs tend to be most effective in leadership practices of challenge the process, enable others to act, and encourage the heart. CSAOs seem to be effective in the leadership practices of model the way and inspire a shared vision. Gender and geographic location were not found to be statistically significant to any of the leadership factors

Improving biochemical yields with MixoFerm

Acetyl-CoA is a primary hub for metabolism and is the building block for most biochemicals of interest. However, the yields for biochemicals derived from acety-CoA are inherently limited because of the decarboxylation of pyruvate to acetyl-CoA which releases CO2. To overcome this limitation, White Dog Labs (WDL) developed a fermentation technology call MixoFerm™ (also known as anaerobic, non-photosynthetic mixotrophy). This technology uses microorganisms capable of concurrently utilizing both organic (e.g., sugars) and inorganic (e.g., CO2) substrates. Using MixoFerm, CO2 can be fixed back into acetyl-CoA and thus improve biochemical yields (g product/g substrate consumed). Here, we demonstrate simultaneous utilization of both fructose and syngas by Clostridium ljungdahlii and Clostridium autoethanogenum. We next engineered C. ljungdahlii to produce the non-native metabolite acetone at a yield 35% greater than the theoretical maximum acetone yield without mixotrophy. Finally, we designed and generated a strain of C. ljungdahlii capable of consuming glucose, which the wild-type strain is unable to do. With the ability to improve biochemical yields, MixoFerm™ is a robust and flexible platform technology to improve process economics and product life-cycle analysi

The inverse nullity pair problem and the strong nullity interlacing property

The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph $G$. In this paper, we refer to the $i$-nullity pair of a matrix $A$ as $(\operatorname{null}(A), \operatorname{null}(A(i))$, where $A(i)$ is the matrix obtained from $A$ by removing the $i$-th row and column. The inverse $i$-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair

Expected values of parameters associated with the minimum rank of a graph

We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdière-type parameters. Let G(v,p) denote the usual Erdős-Rényi random graph on v vertices with edge probability p. We obtain bounds for the expected value of the random variables mr(G(v,p)), M(G(v,p)), ν(G(v,p)) and ξ(G(v,p)), which yield bounds on the average values of these parameters over all labeled graphs of order v

Upregulation of FOXM1 induces genomic instability in human epidermal keratinocytes

<p>Abstract</p> <p>Background</p> <p>The human cell cycle transcription factor FOXM1 is known to play a key role in regulating timely mitotic progression and accurate chromosomal segregation during cell division. Deregulation of FOXM1 has been linked to a majority of human cancers. We previously showed that FOXM1 was upregulated in basal cell carcinoma and recently reported that upregulation of FOXM1 precedes malignancy in a number of solid human cancer types including oral, oesophagus, lung, breast, kidney, bladder and uterus. This indicates that upregulation of FOXM1 may be an early molecular signal required for aberrant cell cycle and cancer initiation.</p> <p>Results</p> <p>The present study investigated the putative early mechanism of UVB and FOXM1 in skin cancer initiation. We have demonstrated that UVB dose-dependently increased FOXM1 protein levels through protein stabilisation and accumulation rather than de novo mRNA expression in human epidermal keratinocytes. FOXM1 upregulation in primary human keratinocytes triggered pro-apoptotic/DNA-damage checkpoint response genes such as p21, p38 MAPK, p53 and PARP, however, without causing significant cell cycle arrest or cell death. Using a high-resolution Affymetrix genome-wide single nucleotide polymorphism (SNP) mapping technique, we provided the evidence that FOXM1 upregulation in epidermal keratinocytes is sufficient to induce genomic instability, in the form of loss of heterozygosity (LOH) and copy number variations (CNV). FOXM1-induced genomic instability was significantly enhanced and accumulated with increasing cell passage and this instability was increased even further upon exposure to UVB resulting in whole chromosomal gain (7p21.3-7q36.3) and segmental LOH (6q25.1-6q25.3).</p> <p>Conclusion</p> <p>We hypothesise that prolonged and repeated UVB exposure selects for skin cells bearing stable FOXM1 protein causes aberrant cell cycle checkpoint thereby allowing ectopic cell cycle entry and subsequent genomic instability. The aberrant upregulation of FOXM1 serves as a 'first hit' where cells acquire genomic instability which in turn predisposes cells to a 'second hit' whereby DNA-damage checkpoint response (eg. p53 or p16) is abolished to allow damaged cells to proliferate and accumulate genetic aberrations/mutations required for cancer initiation.</p