The pre-WDVV ring of physics and its topology

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex $\Delta_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Atmospheric Muon Flux at Sea Level, Underground, and Underwater

The vertical sea-level muon spectrum at energies above 1 GeV and the underground/underwater muon intensities at depths up to 18 km w.e. are calculated. The results are particularly collated with a great body of the ground-level, underground, and underwater muon data. In the hadron-cascade calculations, the growth with energy of inelastic cross sections and pion, kaon, and nucleon generation in pion-nucleus collisions are taken into account. For evaluating the prompt muon contribution to the muon flux, we apply two phenomenological approaches to the charm production problem: the recombination quark-parton model and the quark-gluon string model. To solve the muon transport equation at large depths of homogeneous medium, a semi-analytical method is used. The simple fitting formulas describing our numerical results are given. Our analysis shows that, at depths up to 6-7 km w. e., essentially all underground data on the muon intensity correlate with each other and with predicted depth-intensity relation for conventional muons to within 10%. However, the high-energy sea-level data as well as the data at large depths are contradictory and cannot be quantitatively decribed by a single nuclear-cascade model.Comment: 47 pages, REVTeX, 15 EPS figures included; recent experimental data and references added, typos correcte

On Eigenvalues of Random Complexes

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $k\geq 2$ and $n\in \mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/\sqrt{n}),1+O(1/\sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(\log n/n)$ and so tends to zero as $n\rightarrow \infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$.Comment: Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of Mathematic

An Efficient Targeted Drug Delivery through Apotransferrin Loaded Nanoparticles

BACKGROUND: Cancerous state is a highly stimulated environment of metabolically active cells. The cells under these conditions over express selective receptors for assimilation of factors essential for growth and transformation. Such receptors would serve as potential targets for the specific ligand mediated transport of pharmaceutically active molecules. The present study demonstrates the specificity and efficacy of protein nanoparticle of apotransferrin for targeted delivery of doxorubicin. METHODOLOGY/PRINCIPAL FINDINGS: Apotransferrin nanoparticles were developed by sol-oil chemistry. A comparative analysis of efficiency of drug delivery in conjugated and non-conjugated forms of doxorubicin to apotransferrin nanoparticle is presented. The spherical shaped apotransferrin nanoparticles (nano) have diameters of 25-50 etam, which increase to 60-80 etam upon direct loading of drug (direct-nano), and showed further increase in dimension (75-95 etam) in conjugated nanoparticles (conj-nano). The competitive experiments with the transferrin receptor specific antibody showed the entry of both conj-nano and direct-nano into the cells through transferrin receptor mediated endocytosis. Results of various studies conducted clearly establish the superiority of the direct-nano over conj-nano viz. (a) localization studies showed complete release of drug very early, even as early as 30 min after treatment, with the drug localizing in the target organelle (nucleus) (b) pharmacokinetic studies showed enhanced drug concentrations, in circulation with sustainable half-life (c) the studies also demonstrated efficient drug delivery, and an enhanced inhibition of proliferation in cancer cells. Tissue distribution analysis showed intravenous administration of direct nano lead to higher drug localization in liver, and blood as compared to relatively lesser localization in heart, kidney and spleen. Experiments using rat cancer model confirmed the efficacy of the formulation in regression of hepatocellular carcinoma with negligible toxicity to kidney and liver. CONCLUSIONS: The present study thus demonstrates that the direct-nano is highly efficacious in delivery of drug in a target specific manner with lower toxicity to heart, liver and kidney

Disproportionate Intrauterine Growth Intervention Trial At Term: DIGITAT

Contains fulltext : 65628.pdf ( ) (Open Access)BACKGROUND: Around 80% of intrauterine growth restricted (IUGR) infants are born at term. They have an increase in perinatal mortality and morbidity including behavioral problems, minor developmental delay and spastic cerebral palsy. Management is controversial, in particular the decision whether to induce labour or await spontaneous delivery with strict fetal and maternal surveillance. We propose a randomised trial to compare effectiveness, costs and maternal quality of life for induction of labour versus expectant management in women with a suspected IUGR fetus at term. METHODS/DESIGN: The proposed trial is a multi-centre randomised study in pregnant women who are suspected on clinical grounds of having an IUGR child at a gestational age between 36+0 and 41+0 weeks. After informed consent women will be randomly allocated to either induction of labour or expectant management with maternal and fetal monitoring. Randomisation will be web-based. The primary outcome measure will be a composite neonatal morbidity and mortality. Secondary outcomes will be severe maternal morbidity, maternal quality of life and costs. Moreover, we aim to assess neurodevelopmental and neurobehavioral outcome at two years as assessed by a postal enquiry (Child Behavioral Check List-CBCL and Ages and Stages Questionnaire-ASQ). Analysis will be by intention to treat. Quality of life analysis and a preference study will also be performed in the same study population. Health technology assessment with an economic analysis is part of this so called Digitat trial (Disproportionate Intrauterine Growth Intervention Trial At Term). The study aims to include 325 patients per arm. DISCUSSION: This trial will provide evidence for which strategy is superior in terms of neonatal and maternal morbidity and mortality, costs and maternal quality of life aspects. This will be the first randomised trial for IUGR at term. TRIAL REGISTRATION: Dutch Trial Register and ISRCTN-Register: ISRCTN10363217