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Series: Other Talks

Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess¹s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess¹s paradox is ubiquitous in expander graphs. Specifically, we prove that Braess¹s paradox occurs in a large class of expander graphs with continuous convex latency functions. Our results extend previous work which held only when the graph was both denser and random and for random linear latency functions. We identify deterministic sufficient conditions for a graph with as few as a linear number of edges, such that Braess¹s Paradox almost always occurs, with respect to a general family of random latency functions. Joint work with Fan Chung and Wenbo Zhao. (* Note that this is an ARC/Theory Seminar and is in Klaus 1116W *)

Series: Other Talks

(**This is at Emory and is a joint Emory - Georgia Tech Combinatorics Seminar. **) The KLR conjecture of Kohayakawa, Luczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G(n,p) satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and Rödl. We prove a variant of this conjecture which is sufficient for most applications to random graphs. In particular, our result implies a number of recent probabilistic threshold results. We also discuss several further applications. This joint work with Conlon, Gowers, and Samotij.

Series: Other Talks

Host: David Hu. Refreshments will be served.

<a href="http://www2.me.gatech.edu/www/calendar/view_seminar.asp?speaker=Evelyn%2... target="_blank">Speaker's Bio</a>

Nanoengineered surfaces offer new possibilities to manipulate fluidic
and thermal transport processes for a variety of applications
including lab-on-a-chip, thermal management, and energy conversion
systems. In particular, nanostructures on these surfaces can be
harnessed to achieve superhydrophilicity and superhydrophobicity, as
well as to control liquid spreading, droplet wetting, and bubble
dynamics. In this talk, I will discuss fundamental studies of droplet
and bubble behavior on nanoengineered surfaces, and the effect of such
fluid-structure interactions on boiling and condensation heat
transfer. Micro, nano, and hierarchical structured arrays were
fabricated using various techniques to create superhydrophilic and
superhydrophobic surfaces with unique transport properties. In pool
boiling, a critical heat flux >200W/cm2 was achieved with a surface
roughness of ~6. We developed a model that explains the role of
surface roughness on critical heat flux enhancement, which shows good
agreement with experiments. In dropwise condensation, we elucidated
the importance of structure length scale and droplet nucleation
density on achieving the desired droplet morphology for heat transfer
enhancement. Accordingly, with functionalized copper oxide
nanostructures, we demonstrated a 20% higher heat transfer coefficient
compared to that of state-of-the-art dropwise condensing copper
surfaces. These studies provide insights into the complex physical
processes underlying fluid-nanostructure interactions. Furthermore,
this work shows significant potential for the development and
integration of nanoengineered surfaces to advance next generation
thermal and energy systems.

Series: Other Talks

A discussion of the paper "Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks" by Shmulevich et al.

Series: Other Talks

Further discussion of co-transcriptional RNA folding, and the potential for trap models to capture these dynamics.

Series: Other Talks

We will continue discussing co-transcriptional RNA folding, and the potential for trap models to capture these dynamics.

Series: Other Talks

We will discuss how best to model and predict the co-transcriptional effects of RNA folding. That is, using the fact that the RNA molecule begins folding as the sequence is still being transcribed, can we find better predictions for the secondary structure? And what is a good mathematical model for the process?

Series: Other Talks

Organizational meeting.

Series: Other Talks

This is a summer school (June 18th - July 6th) in computational algebraic geometry intended for graduate students, however, everyone is welcome to attend. For details and schedule see aga.gatech.edu.
The first day's schedule has been slightly altered; we will give introductory lectures at
9:30 (Anton Leykin -- Computer Algebra and Numerical Algebraic Geometry),
11:30 (Greg Blekherman -- Convexity), and 2:00 (Josephine Yu -- Tropical Geometry).

Series: Other Talks

Over the past 30 years, researchers have developed successively faster
algorithms for the maximum flow problem. The best strongly polynomial
time algorithms have come very close to O(nm) time. Many researchers
have conjectured that O(nm) time is the "true" worst case running time.
We resolve the issue in two ways. First, we show how to solve the max
flow problem in O(nm) time. Second, we show that the running time is
even faster if m = O(n). In this case, the running time is O(n^2/log n).