Boxicity and separation dimension

A family $\mathcal{F}$ of permutations of the vertices of a hypergraph $H$ is called 'pairwise suitable' for $H$ if, for every pair of disjoint edges in $H$, there exists a permutation in $\mathcal{F}$ in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for $H$ is called the 'separation dimension' of $H$ and is denoted by $\pi(H)$. Equivalently, $\pi(H)$ is the smallest natural number $k$ so that the vertices of $H$ can be embedded in $\mathbb{R}^k$ such that any two disjoint edges of $H$ can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph $H$ is equal to the 'boxicity' of the line graph of $H$. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.Comment: This is the full version of a paper by the same name submitted to WG-2014. Some results proved in this paper are also present in arXiv:1212.6756. arXiv admin note: substantial text overlap with arXiv:1212.675

Spectra of some new graph operations and some new classes of integral graphs

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs. Keywords: Duplication corona, Duplication edge corona, Duplication neighborhood corona, Cospectral graphs, Integral graphs

Griffiths phase-like behaviour and spin-phonon coupling in double perovskite Tb2_{2}NiMnO6_{6}

The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb$_2$NiMnO$_6$ are reported. The double perovskite compound crystallizes in monoclinic $P2_1/n$ space group and exhibits a magnetic phase transition at $T_c \sim$ 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie-Weiss law exhibited by 1/$\chi(T)$ curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions which arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below $T_c$ in Tb$_2$NiMnO$_6$ which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the {\it stretching} mode at 645 cm$^{-1}$ presents an anomaly which coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material.Comment: 17 pages, 8 figures; accepted in J. Appl. Phy

Boxicity of graphs on surfaces

The boxicity of a graph $G=(V,E)$ is the least integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap ... \cap E_k$. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface $\Sigma$ of genus $g$ is at most $5g+3$. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.Comment: 9 pages, 2 figure

Evaluation of efficacy of two drug regimens of anti-retro viral therapy

Background: CD4 count is an important marker to assess the effectiveness of treatment, mortality and survival rates in HIV patients on treatment. It is an important guide to treatment as it reflects drug resistance, treatment failure and need to switch over to different regimen. Objective of the study was to assess the efficacy of tenofovir (TDF) and efavirenz (EFV) versus zidovudine (AZT) and nevirapine (NVP), in combination with lamivudine (3TC) in HIV-infected patients taking basal and after treatment CD4 count levels as tools.Methods: A retrospective observational study on 40 adult HIV patients, receiving AZT+3TC+NPV (ZLN) (group I) and 18 patients on TDF+3TC+EFV (TLE) (group II) was carried out. Demographic profile, medication prescribed, baseline CD4 cell counts, serially monitored CD4 count values and Hb% were recorded from patient's medical record. Student’s paired ‘t’ test was done to compare CD4 counts before and after treatment in individual groups. Unpaired ‘t’ test was used for the comparison of CD4 counts between the groups.Results: A very highly significant (p<0.0001) increment in CD4 count was observed in group I after treatment. Improvement in CD4 count was highly significant in group II as well with p<0.0004. The extent of improvement was significantly better (p<0.05) in group I as compared to group II. Patients in group I were better staged clinically.Conclusions: We conclude that ART regimen containing AZT/3TC/NVP is proved to be superior to TDF/3TC/EFV. However further studies need to be done, by taking drug adherence into account in a larger patient population

When the optimal is not the best: parameter estimation in complex biological models

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results: We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions: The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system, and point to the need of a theory that addresses this problem more generally

Antigenic determinants on chicken riboflavin carrier protein. A study with monoclonal antibodies

Monoclonal antibodies raised against chicken egg white riboflavin carrier protein were classified into seven categories each recognizing a distinct epitope. Of these, six were directed against conformation dependent epitopes and one to a sequential epitope. The roles of lysine residues and the post-translationally attached phosphate and oligosaccharide moieties in the antigenicity of riboflavin carrier protein recognized by the monoclonal antibodies were investigated. The binding region of three monoclonal antibodies could be located within the 87-219 amino acid sequence of the protein and one antibody among these recognized a sequence of 182-204 amino acid residues. All the monoclonal antibodies were able to recognize riboflavin carrier proteins present in the sera of pregnant rats, cows and humans indicating that the epitopes to which they are directed are conserved through evolution from chicken to the human

Biochemical and immunological aspects of riboflavin carrier protein

Riboflavin carrier protein which is obligatorily involved in yolk deposition of the vitamin in the chicken egg, is a unique glycophosphoprotein present in both the yolk and white compartments. The yolk and egg white proteins are products of a single estrogen-inducible gene expressed in the liver and the oviduct respectively of egg laying birds. Despite the fact that the carbohydrate composition of the yolk and white riboflavin carrier proteins differ presumably due to differential post-translational modification, the proteins are immunologically similar and have identical amino acid sequence (including a cluster of 8 phosphoser residues towards the C-terminus) except at the carboxy terminus where the yolk riboflavin carrier protein lacks 13 amino acids as a consequence of proteolytic cleavage during uptake by oocytes. The protein is highly conserved throughout evolution all the way to humans in terms of gross molecular characteristics such as molecular weight and isoelectric point, and in immunological properties, preferential affinity for free riboflavin and estrogen inducibility at the biosynthetic locusviz., liver. Obligatory involvement of the mammalian riboflavin carrier protein in transplacental flavin transport to subserve fetal vitamin nutrition during gestation is revealed by experiments using pregnant rodent or subhuman primate models wherein immunoneutralisation of endogenous maternal riboflavin carrier protein results in fetal wastage followed by pregnancy termination due to selective yet drastic curtailment of vitamin efflux into the fetoplacental unit. Using monoclonal antibodies to chicken riboflavin carrier protein, it could be shown that all the major epitopes of the avian riboflavin carrier protein are highly conserved throughout evolution although the relative affinities of some of the epitopes for different monoclonal antibodies have undergone progressive changes during evolution. Using these monoclonal antibodies, an attempt is being made to map the different epitopes on the riboflavin carrier protein molecule with a view to delineate the immunodominant regions of the vitamin carrier to understand its structure-immunogenicity relationship