**Organizers: **

** **** Maria Cameron**, MATH 4105, cameron@math.umd.edu

** ****Kasso Okoudjou**, MATH 2111, kasso@math.umd.edu

**Meetings:**

**Fridays, 2:00 - 3:00 PM**

**MATH 1310**

**The organizational meeting:**

**Friday, Feb. 5**

**Synopsis: **The contemporary development of communications, information technologies and powerful computing resources has made networks a popular tool for data organization, representation and interpretation. Networks arising nowadays in various spheres of science and technology are often tremendously larger and more complex than the ones studied in the classic graph theory. Furthermore, they are often dynamic rather than static. We will consider a number of problems where complex networks can be used as a modeling tool and explore various approaches for their analysis.

**Schedule:**

**Feb. 5:** Organizational meeting

**Feb. 12:** Maria Cameron, UMCP Math, Erdos - Renyi Random Graphs

**Feb. 26:** Maria Cameron, UMCP Math, Random Graphs (Newman, Strogatz, Watts, 2001, Phys. Rev. E, Vol. 64, 026118)

**March 4:** Matthew Begue, UMCP Math, Support of Laplacian Eigenvectors on Graphs

**March 25:** Aaron Ostrander, UMCP Physics, Algebraic Analysis of Network Structure

**April 1:** Kasso Okoudjou, UMCP Math, Diffusion Maps and Diffusion Wavelets

**April 15:** 2-3 PM, Kasso Okoudjou, UMCP Math, Diffusion Maps and Diffusion Wavelets (continuation)

**April 22:** Michelle Girvan, UMCP, Physics: Elucidating the Role of Network Structure in Gene Regulation: Connecting Models and Data

Abstract: The complex process of genetic control relies upon an elaborate network of interactions between genes. Our goal is to combine simple mathematical models with empirical data to understand the role of network structure in gene regulation. Our modeling efforts focus primarily on Boolean systems, which have received extensive attention as useful models for genetic control. An important aspect of Boolean network models is the stability of their dynamics in response to small perturbations. Previous approaches to studying stability have generally assumed uncorrelated random network structure, even though real gene networks typically have nontrivial topology significantly different from the random network paradigm.

**April 29:** Siddharth Sharma, UMCP, Physics: Compressed Sensing and Spin Glasses

Abstract: Reconstruction of a signal from a limited number of measurements is a crucial problem in complex networks. This is especially true in cases where the observed behaviour is not completely explained by the mapped structure e.g. Gene-regulatory networks. Compressed sensing has been a major revolution in signal acquisition as it involves reconstructing a signal with a number of measurements lesser than the actual length of the signal. The technique relies on the signal being sparse in some basis so only the necessary ³compressed² part is required for full reconstruction. In this talk, I would discuss a probabilistic reconstruction which allows compressed sensing to be performed at acquisition rates approaching the theoretical optimal limits. The main idea would be to present the inference problem as a spin-glass and to then use results from statistical physics to reconstruct the signal through a belief propagation algorithm. A Bayesian optimality analysis leading to the Nishimori conditions will also be discussed.

**May 6:** William Rand, UMCP: Business School, Authority, Trust and Influence: The Complex Network of Social Media

Abstract: The dramatic feature of social media is that it gives everyone a voice; anyone can speak out and express their opinion to a crowd of followers with little or no cost or effort, which creates a loud and potentially overwhelming marketplace of ideas. Given this egalitarian competition, how do users of social media identify authorities in this crowded space? Who do they trust to provide them with the information and the recommendations that they want? Which tastemakers have the greatest influence on social media users? Using agent-based modeling, machine learning and network analysis we begin to examine and shed light on these questions and develop a deeper understanding of the complex system of social media.