Some new Menon designs with parameters (196,91,42)

There are exactly 54 symmetric (196,91,42) designs admitting an automorphism group isomorphic to $Frob_{13 cdot 6} times Z_3$ acting with orbit size distribution (1,13,13,13,39,39,39,39) for blocks and points. For 50 of these designs the full automorphism group has order 234 and is isomorphic to $Frob_{13 cdot 6} times Z_3$. The remaining four designs have $Frob_{13 cdot 6} times Frob_{7 cdot 3}$ as a full automorphism group.Among these designs there are 18 self-dual designs and 18 pairs of mutually dual ones. The derived designs (with respect to the fixed block) of the four designs with a full automorphism group of order 1638 are cyclic

On path graphs of incidence graphs

For a given graph $G$ and a positive integer $k$ the $P_k$-path graph $P_k(G)$ has for vertices the set of paths of length $k$ in $G$. Two vertices are connected in $P_k(G)$ when the intersection of the corresponding paths forms a path of length $k-1$ in $G$, and their union forms either a cycle or a path of length $k+1$. Path graphs were proposed as a generalization of line graphs. In this article we investigate some properties of path graphs of bipartite graphs, especially path graphs of incidence graphs of configurations

Unique symmetric (66,26,10) design admitting an automorphism of order 55

We have proved that the first known symmetric (66,26,10) design, constructed by Tran van Trung, is up to isomorphism the only symmetric (66,26,10) design admitting an automorphism of order 55. A full automorphism group of that design is isomorphic to Frob_{55}times D_{10}

A class of Siamese twin Menon designs

A{0,±1}-matrix S is called a Siamese twin design sharing the entries of I, if S = I + K − L, where I, K, L are non-zero {0, 1}-matrices and both I + K and I + L are incidence matrices of symmetric designs with the same parameters. Let p and 2p−1 be prime powers and p ≡ 3 (mod 4). We describe a construction of a Siamese twin Menon design with parameters (4p², 2p² −p, p² −p), yielding a Siamese twin Hadamard design with parameters (4p ²− 1, 2p ²− 1, p² − 1)

BF Actions for the Husain-Kuchar Model

We show that the Husain-Kuchar model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative QFT techniques or the spin-foam formalism introduced in the space-time description of General Relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.Comment: 21 pages (in DIN A4 format), minor typos corrected; to appear in Phys. Rev.

The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell \Gr of the Sato Grassmannian $Gr$. This is a consequence of a well-defined continuum limit in which the string equation has the simple form \lb \cp ,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- $2\times 2$ matrices of differential operators. These conditions on $V_1$ and $V_2$ yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate the two modified-KdV \t-functions whose product gives the partition function of the Unitary Matrix Model.Comment: 21 page

Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets

We quantize the space of 1/2 BPS configurations of Type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), directly in supergravity. We use the Crnkovic-Witten-Zuckerman covariant quantization method to write down the expression for the symplectic structure on this entire space of solutions. We find the symplectic form explicitly around AdS_5 x S^5 and obtain a U(1) Kac-Moody algebra, in precise agreement with the quantization of a system of N free fermions in a harmonic oscillator potential, as expected from AdS/CFT. As a cross check, we also perform the quantization around AdS_5 x S^5 by another method, using the known spectrum of physical perturbations around this background and find precise agreement with our previous calculation.Comment: 22 Pages + 2 Appendices, JHEP3; v3: explanation of factor 2 mismatch added, references reordered, published versio

Expression of inhibitor of apoptosis protein Livin in renal cell carcinoma and non-tumorous adult kidney

The antiapoptotic Livin/ML-IAP gene has recently gained much attention as a potential new target for cancer therapy. Reports indicating that livin is expressed almost exclusively in tumours, but not in the corresponding normal tissue, suggested that the targeted inhibition of livin may present a novel tumour-specific therapeutic strategy. Here, we compared the expression of livin in renal cell carcinoma and in non-tumorous adult kidney tissue by quantitative real-time reverse transcription-PCR, immunoblotting, and immunohistochemistry. We found that livin expression was significantly increased in tumours (P=0.0077), but was also clearly detectable in non-tumorous adult kidney. Transcripts encoding Livin isoforms α and β were found in both renal cell carcinoma and normal tissue, without obvious qualitative differences. Livin protein in renal cell carcinoma samples exhibited cytoplasmic and/or nuclear staining. In non-tumorous kidney tissue, Livin protein expression was only detectable in specific cell types and restricted to the cytoplasm. Thus, whereas the relative overexpression of livin in renal cell carcinoma indicates that it may still represent a therapeutic target to increase the apoptotic sensitivity of kidney cancer cells, this strategy is likely to be not tumour-specific

Background-Independence

Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.Comment: Forthcoming in General Relativity and Gravitatio