Wilson Loop Invariants from WNW_N Conformal Blocks

Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for $W_N$ conformal blocks with one component in the fundamental representation and another in a rectangular representation of $SU(N)$, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of $W_N$ algebra.Comment: 20 pages, 2 figure

Universality of stochastic Laplacian growth

We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domain with a sharp boundary which evolves under a change in the size of matrices. This evolution can be interpreted as a stochastic growth process. We show that the most probable growth scenario is similar to deterministic Laplacian growth. The other scenarios involve Laplacian growth in the presence of fluctuations. We use the random matrix approach to determine a probability distribution function of fluctuations. The partition function of fluctuations is shown to be universal. It does not depend on the shape of the initial domain and depends on the strength of fluctuations and the geometry of the problem only.Comment: 16 page

Depletion of the histone chaperone tNASP inhibits proliferation and induces apoptosis in prostate cancer PC-3 cells

<p>Abstract</p> <p>Background</p> <p>NASP (Nuclear Autoantigenic Sperm Protein) is a histone chaperone that is present in all dividing cells. NASP has two splice variants: tNASP and sNASP. Only cancer, germ, transformed, and embryonic cells have a high level of expression of the tNASP splice variant. We examined the consequences of tNASP depletion for prostate cancer PC-3 cells.</p> <p>Methods</p> <p>tNASP was depleted from prostate cancer PC-3 cells, cervical cancer HeLa cells, and prostate epithelial PWR-1E cells using lentivirus expression of tNASP shRNA. Cell cycle changes were studied by proliferation assay with CFSE labeling and double thymidine synchronization. Gene expression profiles were detected using RT²Profiler PCR Array, Western and Northern blotting.</p> <p>Results</p> <p>PC-3 and HeLa cells showed inhibited proliferation, increased levels of cyclin-dependant kinase inhibitor p21 protein and apoptosis, whereas non-tumorigenic PWR-1E cells did not. All three cell types showed decreased levels of HSPA2. Supporting in vitro experiments demonstrated that tNASP, but not sNASP is required for activation of HSPA2.</p> <p>Conclusions</p> <p>Our results demonstrate that PC-3 and HeLa cancer cells require tNASP to maintain high levels of HSPA2 activity and therefore viability, while PWR-1E cells are unaffected by tNASP depletion. These different cellular responses most likely arise from changes in the interaction between tNASP and HSPA2 and disturbed tNASP chaperoning of linker histones. This study has demonstrated that tNASP is critical for the survival of prostate cancer cells and suggests that targeting tNASP expression can lead to a new approach for prostate cancer treatment.</p