On eigenspaces of some compound complex unit gain graphs

Let T be the multiplicative group of complex units, and let L (Φ) denote the Laplacian matrix of a nonempty T-gain graph Φ = (Γ, T, γ). The gain line graph L (Φ) and the gain subdivision graph S (Φ) are defined up to switching equivalence. We discuss how the eigenspaces determined by the adjacency eigenvalues of L (Φ) and S (Φ) are related with those of L (Φ)

Line graphs of complex unit gain graphs with least eigenvalue -2

Let T be the multiplicative group of complex units, and let L(φ) denote a line graph of a T-gain graph φ. Similarly to what happens in the context of signed graphs, the real number min Spec(A(L(φ)), that is, the smallest eigenvalue of the adjacency matrix of L(φ), is not less than -2. The structural conditions on φ ensuring that min Spec(A(L(φ)) = -2 are identified. When such conditions are fulfilled, bases of the -2-eigenspace are constructed with the aid of the star complement technique

On the multiplicity of α as an A_α (Γ)-eigenvalue of signed graphs with pendant vertices

A signed graph is a pair Γ = (G; ), where x = (V (G);E(G)) is a graph and E(G) -> {+1;−1} is the sign function on the edges of G. For any > [0; 1] we consider the matrix Aα(Γ) = αD(G) + (1 −α )A(Γ); where D(G) is the diagonal matrix of the vertex degrees of G, and A(Γ) is the adjacency matrix of Γ. Let mAα(Γ) be the multiplicity of α as an A(Γ)-eigenvalue, and let G have p(G) pendant vertices, q(G) quasi-pendant vertices, and no components isomorphic to K2. It is proved that mA(Γ)() = p(G) − q(G) whenever all internal vertices are quasi-pendant. If this is not the case, it turns out that mA(Γ)() = p(G) − q(G) +mN(Γ)(); where mN(Γ)() denotes the multiplicity of as an eigenvalue of the matrix N(Γ) obtained from A(Γ) taking the entries corresponding to the internal vertices which are not quasipendant. Such results allow to state a formula for the multiplicity of 1 as an eigenvalue of the Laplacian matrix L(Γ) = D(G) − A(Γ). Furthermore, it is detected a class G of signed graphs whose nullity – i.e. the multiplicity of 0 as an A(Γ)-eigenvalue – does not depend on the chosen signature. The class G contains, among others, all signed trees and all signed lollipop graphs. It also turns out that for signed graphs belonging to a subclass G ` G the multiplicity of 1 as Laplacian eigenvalue does not depend on the chosen signatures. Such subclass contains trees and circular caterpillars

Line and subdivision graphs determined by T4-gain graphs

Let T4 = (±1, ±i) be the subgroup of fourth roots of unity inside T, the multiplicative group of complex units. For a T4-gain graph Φ = (Γ,T4, ϕ), we introduce gain functions on its line graph L(Γ) and on its subdivision graph S(Γ). The corresponding gain graphs L(Φ) and S(Φ) are defined up to switching equivalence and generalize the analogous constructions for signed graphs. We discuss some spectral properties of these graphs and in particular we establish the relationship between the Laplacian characteristic polynomial of a gain graph Φ, and the adjacency characteristic polynomials of L(Φ) and S(Φ). A suitably defined incidence matrix for T4-gain graphs plays an important role in this contex

Activation of IκB Kinase by Herpes Simplex Virus Type 1 A NOVEL TARGET FOR ANTI-HERPETIC THERAPY

Herpes simplex viruses (HSV) are ubiquitous pathogens causing a variety of diseases ranging from mild illness to severe life-threatening infections. HSV utilize cellular signaling pathways and transcription factors to promote their replication. Here we report that HSV type 1 (HSV-1) induces persistent activation of transcription factor NF-κB, a critical regulator of genes involved in inflammation, by activating the IκB kinase (IKK) in the early phase of infection. Activated NF-κB enhances HSV-1 gene expression. HSV-1-induced NF-κB activation is dependent on viral early protein synthesis and is not blocked by the anti-herpetic drug acyclovir. IKK inhibition by the anti-inflammatory cyclopentenone prostaglandin A1 blocks HSV-1 gene expression and reduces virus yield by more than 3000-fold. The results identify IKK as a potential target for anti-herpetic drugs and suggest that cyclopentenone prostaglandins or their derivatives could be used in the treatment of HSV infection

15-Deoxy-Δ12,14-prostaglandin J2 induces apoptosis in human malignant B cells: an effect associated with inhibition of NF-κB activity and down-regulation of antiapoptotic proteins

AbstractCyclopentenone prostaglandins are potent inhibitors of nuclear factor-κB (NF-κB), a transcription factor with a critical role in promoting inflammation and connected with multiple aspects of oncogenesis and cancer cell survival. In the present report, we investigated the role of NF-κB in the antineoplastic activity of the cyclopentenone prostaglandin 15-deoxy-Δ12,14-PGJ2 (15d-PGJ2) in multiple myeloma (MM) and Burkitt lymphoma (BL) cells expressing constitutively active NF-κB. 15d-PGJ2 was found to suppress constitutive NF-κB activity and potently induce apoptosis in both types of B-cell malignancies. 15d-PGJ2-induced apoptosis occurs through multiple caspase activation pathways involving caspase-8 and caspase-9, and is prevented by pretreatment with the pan-caspase inhibitor ZVAD (z-Val-Ala-Asp). NF-κB inhibition is accompanied by rapid down-regulation of NF-κB-dependent antiapoptotic gene products, including cellular inhibitor-of-apoptosis protein 1 (cIAP-1), cIAP-2, X-chromosome-linked inhibitor-of-apoptosis protein (XIAP), and FLICE-inhibitory protein (cFLIP). These effects were mimicked by the proteasome inhibitor MG-132, but not by the peroxisome proliferator-activated receptor-γ (PPAR-γ) agonist troglitazone, suggesting that 15d-PGJ2-induced apoptosis is independent of PPAR-γ. Knockdown of the NF-κB p65-subunit by lentiviral-mediated shRNA interference also resulted in apoptosis induction in malignant B cells with constitutively active NF-κB. The results indicate that inhibition of NF-κB plays a major role in the proapoptotic activity of 15d-PGJ2 in aggressive B-cell malignancies characterized by aberrant regulation of NF-κB. (Blood. 2005;105:1750-1758

West Greenland Peregrine Falcon Survey, 1978

This brief report describes results of a survey project which has been banding West Greenland peregrines annually since 1972. Statistics on number of eyries, sex ratios, and number of young hatched per eyrie are given