[Lowerbounds, Upperbounds]

(Updated on 2007-10-31 with simpler steps. This post assumes you are running Windows, but it’s actually applicable to Unix users if you replace the MiKTeX terms with their TeX Live counterparts. )

The most recent release of MiKTeX is 2.6 and it ships with pdfLaTeX 1.4. Unfortunately, it is incompatible with Ipe’s latest release 6.0pre28 because this version of Ipe cannot cope with the PDF generated by pdfLaTeX 1.4. As the next version of Ipe is not coming very soon (Otfried says “Certainly not before spring 2008.”), one solution would be to downgrade to MiKTeX 2.5 so that Ipe can use the pdfLaTeX 1.3 that ships with MiKTeX 2.5. But if you have upgraded to pdfLaTeX 1.4 with a reason (like having fun with microtype), then you can also keep the two installations side-by-side with some storage overhead (~100MB). Assuming that your MiKTeX 2.6 is installed in C:\texmf-2.6, here is how you might do the MiKTeX 2.5 installation:

1. Get a copy of basic-miktex-2.5.2580.exe. It’s the self-contained “basic installer” for MiKTeX 2.5 and contains some basic packages. This file does not seem to be available at the official MiKTeX download page any more, but Google can help you find a copy, or you can get a local copy hosted on this server.
2. Launch the basic installer and install MiKTeX 2.5 to, say, C:\texmf-2.5.
3. After the installation finishes, remove C:\texmf-2.5 from the PATH environment variable. That way, whenever you run latex, you are still running pdfLaTeX 1.4.
4. Run Yap 2.6 once and you will be prompted to associate .dvi files with it. (The 2.5 installer associates .dvi files with Yap 2.5, of course. And frankly, I recommend dviout over Yap.)
5. Set up an environment variable called IPEPDFLATEX to override IPE’s default pdflatex command, eg, IPEPDFLATEX=C:\texmf-2.5\miktex\bin\pdflatex.exe if that’s where you installed it to. At this moment, you may also be interested to set up something like IPELATEXDIR=C:\temp\iperun to control where Ipe generates the temp files.
6. If you don’t use any special packages in your Ipe files, then you can skip this step. But for completeness, we can let MiKTeX 2.5 know about the extra packages installed in MiKTeX 2.6. From the Start menu, run MiKTeX 2.5->Settings. In the Roots tab, add C:\texmf-2.6 to the bottom of the search list. Click OK and the filename database will be refreshed. (Unix users: this is the Kpathsea step. See here.)

At this point, the side-by-side installation is complete. Have fun!

Title: On a random graph evolving by degrees
Speaker: Boris Pittel (Ohio State University)
When: October 19, 15:30-16:30
Where: Wean Hall 5302
Abstract:

We consider a random (multi)graph growth process ${G_m}$ on a vertex set $[n]$, which is a special case of a more general process suggested by Laci Lovasz several years ago. $G_0$ is empty, and $G_{m+1}$ is obtained from $G_m$ by inserting a new edge $e$ at random. Specifically, the conditional probability that $e$ joins two currently disjoint vertices, $i$ and $j$ , is proportional to $(d_i + \alpha)(d_j + \alpha)$, where $d_i$ , $d_j$ are the degrees of $i$ ,$ $j in $G_m$, and $\alpha > 0$ is a fixed parameter. The limiting case $\alpha = \infty$ is the Erdos-Renyi graph process. We show that whp $G_m$ contains a unique giant component iff $c := 2m/n > c_{\alpha} = \alpha/(1 + \alpha)$, and the size of this giant is asymptotic to $n [1-(\frac{\alpha+c^*}{\alpha+c})^{\alpha}]$, where $c^* < c_{\alpha}$ is the root of $\frac{c}{(\alpha+c)^{2+\alpha}} = \frac{c^*}{(\alpha+c^*)^{2+\alpha}}$ . For the multigraph version, ${MG_m}$, we show that $MG_m$ is connected whp iff $m \gg m_n := n^{1+\alpha^{-1}}$, and we conjecture that, for $\alpha > 1$, $m_n$ is the threshold for connectedness of $G_m$ itself.