Bubbling 1/4 BPS solutions in type IIB and supergravity reductions on S^n x S^n

We extend the construction of bubbling 1/2 BPS solutions of Lin, Lunin and Maldacena (hep-th/0409174) in two directions. First we enquire whether bubbling 1/2 BPS solutions can be constructed in minimal 6d supergravity and second we construct solutions that are 1/4 BPS in type IIB. We find that the S^1 x S^1 bosonic reduction of (1,0) 6d supergravity to 4d gravity coupled to 2 scalars and a gauge field is consistent only provided that the gauge field obeys a constraint (F \wedge F=0). This is to be contrasted to the case of the S^3 x S^3 bosonic reduction of type IIB supergravity to 4d gravity, 2 scalars and a gauge field, where consistency is achieved without imposing any such constraints. Therefore, in the case of (1,0) 6d supergravity we are able to construct 1/2 BPS solutions, similar to those derived in type IIB, provided that this additional constraint is satisfied. This ultimately prohibits the construction of a family of 1/2 BPS solutions corresponding to a bubbling AdS_3 x S^3 geometry. Returning to type IIB solutions, by turning on an axion-dilaton field we construct a family of bubbling 1/4 BPS solutions. This corresponds to the inclusion of back-reacted D7 branes to the solutions of Lin, Lunin and Maldacena.Comment: 30 pages, Latex citations adde

Congruences for powers of the partition function

Let $p_{-t}(n)$ denote the number of partitions of $n$ into $t$ colors. In analogy with Ramanujan's work on the partition function, Lin recently proved in \cite{Lin} that $p_{-3}(11n+7)\equiv0\pmod{11}$ for every integer $n$. Such congruences, those of the form $p_{-t}(\ell n + a) \equiv 0 \pmod {\ell}$, were previously studied by Kiming and Olsson. If $\ell \geq 5$ is prime and $-t \not \in \{\ell - 1, \ell -3\}$, then such congruences satisfy $24a \equiv -t \pmod {\ell}$. Inspired by Lin's example, we obtain natural infinite families of such congruences. If $\ell\equiv2\pmod{3}$ (resp. $\ell\equiv3\pmod{4}$ and $\ell\equiv11\pmod{12}$) is prime and $r\in\{4,8,14\}$ (resp. $r\in\{6,10\}$ and $r=26$), then for $t=\ell s-r$, where $s\geq0$, we have that \begin{equation*} p_{-t}\left(\ell n+\frac{r(\ell^2-1)}{24}-\ell\Big\lfloor\frac{r(\ell^2-1)}{24\ell}\Big\rfloor\right)\equiv0\pmod{\ell}. \end{equation*} Moreover, we exhibit infinite families where such congruences cannot hold

Using mobile group dynamics and virtual time to improve teamwork in large-scale collaborative virtual environments

Mobile group dynamics (MGDs) assist synchronous working in collaborative virtual environments (CVEs), and virtual time (VT) extends the benefits to asynchronous working. The present paper describes the implementation of MGDs (teleporting, awareness and multiple views) and VT (the utterances of 23 previous users were embedded in a CVE as conversation tags), and their evaluation using an urban planning task. Compared with previous research using the same scenario, the new MGD techniques produced substantial increases in the amount that, and distance over which, participants communicated. With VT participants chose to listen to a quarter of the conversations of their predecessors while performing the task. The embedded VT conversations led to a reduction in the rate at which participants traveled around, but an increase in live communication that took place. Taken together, the studies show how CVE interfaces can be improved for synchronous and asynchronous collaborations, and highlight possibilities for future research

Evolution of New cis-Regulatory Motifs Required for Cell-Specific Gene Expression in Caenorhabditis

Patterning of C. elegans vulval cell fates relies on inductive signaling. In this induction event, a single cell, the gonadal anchor cell, secretes LIN-3/EGF and induces three out of six competent precursor cells to acquire a vulval fate. We previously showed that this developmental system is robust to a four-fold variation in lin-3/EGF genetic dose. Here using single-molecule FISH, we find that the mean level of expression of lin-3 in the anchor cell is remarkably conserved. No change in lin-3 expression level could be detected among C. elegans wild isolates and only a low level of change-less than 30%-in the Caenorhabditis genus and in Oscheius tipulae. In C. elegans, lin-3 expression in the anchor cell is known to require three transcription factor binding sites, specifically two E-boxes and a nuclear-hormone-receptor (NHR) binding site. Mutation of any of these three elements in C. elegans results in a dramatic decrease in lin-3 expression. Yet only a single E-box is found in the Drosophilae supergroup of Caenorhabditis species, including C. angaria, while the NHR-binding site likely only evolved at the base of the Elegans group. We find that a transgene from C. angaria bearing a single E-box is sufficient for normal expression in C. elegans. Even a short 58 bp cis-regulatory fragment from C. angaria with this single E-box is able to replace the three transcription factor binding sites at the endogenous C. elegans lin-3 locus, resulting in the wild-type expression level. Thus, regulatory evolution occurring in cis within a 58 bp lin-3 fragment, results in a strict requirement for the NHR binding site and a second E-box in C. elegans. This single-cell, single-molecule, quantitative and functional evo-devo study demonstrates that conserved expression levels can hide extensive change in cis-regulatory site requirements and highlights the evolution of new cis-regulatory elements required for cell-specific gene expression

How long does it take to pull an ideal polymer into a small hole?

We present scaling estimates for characteristic times $\tau_{\rm lin}$ and $\tau_{\rm br}$ of pulling ideal linear and randomly branched polymers of $N$ monomers into a small hole by a force $f$. We show that the absorbtion process develops as sequential straightening of folds of the initial polymer configuration. By estimating the typical size of the fold involved into the motion, we arrive at the following predictions: $\tau_{\rm lin}(N) \sim N^{3/2}/f$ and $\tau_{\rm br}(N) \sim N^{5/4}/f$, and we also confirm them by the molecular dynamics experiment.Comment: 4 pages, 3 figure

Combustion of Pure, Hydrolyzed and Methyl Ester Formed of Jatropha Curcas Lin Oil

The density and viscosity of vegetable oil are higher than that of diesel oil. Thus its direct combustion in the diesel engine results many problems. This research was conducted to investigate the flame characteristics of combustion of jatropha curcas lin in pure, hydrolyzed and methyl ester form. The results indicated that the combustion of pure jatropha curcas lin occurs in three stages, hydrolyzed in two stages and methyl ester in one stage. For pure jatropha curcas lin, in the first stage, unsaturated fatty acid burned for 0.265 s. It is followed by saturated fatty acid, burned for 0.389 s in the second stage. And, in the last stage is the burned of glycerol for 0.560 s. Meanwhile for hydrolyzed one, in the first stage, unsaturated fatty acid burned for 0.736 s, followed by saturated fatty acid, burned for 0.326 s in the second stage. And the last, for methyl ester is the burned for 0.712 s. The highest burning rate was for methyl ester which was 0.003931cc/s. The energy releasing rate of methyl ester, which was for 13,628.67 kcal/(kg.s) resembled that of diesel oil the most, while the lowest rate was for pure jatropha curcas lin which was 8,200.94 kcal/(kg.s). In addition, massive explosion occurred in the fuel containing unsaturated fatty acid and glycero