The LMU Math Seminar is held on the first Wednesdays 3:00 PM  3:50 PM in Math Library. Please contact Dr. Thomas Laurent or Dr. Yanping Ma for more details.
Fall 2014
Oct. 

9 
Dr. Ryan Compton, HRL Laboratories Abstract: Geographically annotated social media is extremely valuable for modern information retrieval. However, when researchers can only access publiclyvisible data, one quickly finds that social media users rarely publish location information. In this work, we provide a method which can geolocate the overwhelming majority of active Twitter users, independent of their location sharing preferences, using only publiclyvisible Twitter data. Our method infers an unknown user's location by examining their friend's locations. We frame the geotagging problem as an optimization over a social network with a total variationbased objective and provide a scalable and distributed algorithm for its solution. Furthermore, we show how a robust estimate of the geographic dispersion of each user's ego network can be used as a peruser accuracy measure, allowing us to discard poor location inferences and control the overall error of our approach. Leavemanyout evaluation shows that our method is able to infer location for 101,846,236 Twitter users at a median error of 6.33 km, allowing us to geotag over 80% of public tweets. 
Nov. 

6 
Dr. Anael Verdugo, California State University, Fullerton Abstract: Computational and mathematical modeling has become an important tool for modern lifesciences research. Understanding the molecular interactions and metabolism of iron in healthy and cancer cells is the main goal of this work. We approach this problem by building a mathematical model using dynamical systems theory and experimental data. Our preliminary findings on healthy cells have started to elucidate some of the main pathways associated to a healthy iron regulation. In this talk, I will give a brief overview of iron metabolism and explain some of our experimental and computational findings in this new area of computational cancer biology. 
Dec. 

4 
Dr. Amanda Croll , Concordia University Irvine Abstract: Mathematics is often developed through a series of refinements rather than mathematicians making correct initial conjectures. One such example is Euler's polyhedron formula, which states that VE+F = 2, where V, E and F are the number of vertices, edges and faces, respectively, in a "nice" polyhedron. Regular polyhedra, such as the cube and icosahedron, are examples of "nice" polyhedra to which this formula applies. We will look at several different proofs of Euler's polyhedron formula and examine the historical development of precisely which polyhedra are "nice enough" for this formula to hold. 
Sring 2014
Jan. 

29 
Dr. Jesus Rosado, University of California, Los Angeles Abstract: Don't worry! You can find plenty of guides with useful tips that will help you survive it... provided you are human. But what about the other part involve? Have you ever thought, for instance, how difficult can it be to eat a good brain when you don't even have one of your own? In this talk, we will use mathematical tools to explore how a zombie community works: why do they pack together? How do they decide to move? How do their numbers increase? And since we are at it, give you some hints to better understand your mostliked screamy food." 

30 
Dr. Kamuela Yong, Arizona State University Applications of diffusion: from modeling the spread of infectious diseases to modeling pollination. 
Mar. 

12 
Dr. Anna Bargagliotti , Loyola Marymount University Abstract: The Central Limit Theorem is often referred to as the most important theorem in statistics. As such, statistics courses spend a significant amount of time teaching the theorem. Using simulations to teach the CLT is meant to provide students with sound conceptual understanding. However, this talk will show that simulations may actually mislead. Together we will simulate sampling distributions for the sample means using various samples sizes and number of samples to show how a misunderstanding about the mean can be inadvertently introduced or reinforced through simulation. From observing the patterns in a typical series of simulated sampling distributions constructed with increasing sample sizes, we will show that it is plausible to incorrectly, but reasonably, conclude that, as the sample size, n, increases, the mean approaches the population mean. 

Apr. 

2 
Dr. Nestor Guillen, University of California, Los Angeles Abstract: Examples of random structures in nature and our every day life abound, most often at the smallest spatial scales. How often does an object look smooth and featureless from afar, but shows a great deal of structure when you look at it under a microscope (a good example would be the piece of paper or the computer screen where you are reading this!). In mathematics, homogenization theory deals with the question of how smooth and "homogeneous" behavior can arise as the combined effect of many random and small scale factors. In this talk, I will illustrate a small portion of this vast theory by discussing how heat and electricity propagate through a composite material. Talk best suited for students with familiarity with linear algebra and multivariable calculus. 

25 
Katrina Sherbina , Math Senior, Loyola Marymount University Abstract: DNA microarrays were used to measure the effect of cold shock on gene expression in Saccharomyces cerevisiae, budding yeast. The wild type strain BY4741 and four transcription factor deletion strains were subjected to cold shock at 13ºC and allowed to recover at 30ºC. A modified ANOVA test was used to detect significant differences in gene expression between the control and experimental conditions and between strains. Expression of each gene in a regulatory network consisting of 21 transcription factors was modeled by a nonlinear differential equation describing the change in expression over time as the difference between the production and degradation rates. The fmincon function in MATLAB compared the differential equation model to the microarray data to find optimized weights and threshold constants by a nonlinear least squares fit criterion. The deletion strains were modeled by removing the gene from the dynamical system. Modeling production by MichaelisMenten kinetics instead of a sigmoid function more accurately described repression and the case of an OR transcriptional gate. The MichaelisMenten model accurately predicted that PHD1, the gene with the most connections in the network, is downregulated in the cin5 deletion strain but upregulated in the wild type strain. 

May 

7 
Alec Lewald, Math Senior, Loyola Marymount University Abstract: We develop theorems about spatial graphs and their twodimensional projections. This is done by applying previously known techniques used in knot theory to our more complex structures; the goal of these theorems is to distinguish which spatial graph projections are isotopically equivalent. In particular, we extend pcolorability, the knot determinant, and the Alexander polynomial to spatial graphs, and prove they are spatial graph invariants. We then investigate some properties of these invariants and present several examples. 

Fall 2013
Oct. 

3 
Dr. Thomas Laurent, Loyola Marymount University Geometry of patters appearing in systems of interacting particles Abstract: In this talk we will study patterns arising in large systems of selfassembling particles. In models arising from material sciences the particles can be molecules, proteins or nanoparticles. In applications to biological sciences the particles represent individuals in a social aggregate (e.g., a swarm of insects, a flock of birds, a school of fish or a colony of bacteria). We will see that simple rules of interaction between the particles lead to surprisingly complex patterns and structures. The goal is to understand what type of interaction rule leads to what type of structure. We will present some theorems which predict the dimensionality of these structures.


Nov. 

6 
Dr. ChiuYen Kao, Claremont McKenna College Shape Optimization Problems Involving Eigenvalues and Their Applications Abstract: Since Lord Rayleigh conjectured that the disk should minimize the first LaplaceDirichlet eigenvalue among all shapes of equal area more than a century ago, eigenvalue optimization problems have been active research topics with applications in various areas including mechanical vibration, electromagnetic cavities, photonic crystals, and population dynamics. In this talk, we will review some interesting classical problems and discuss some recent developments. 

Dec. 

4  Leesa Anzaldo, Ph.D. Candidate, University of California, Irvine Some examples of Schubert Calculus Abstract: Schubert calculus was developed in order to solve problems in enumerative projective geometry using cohomology. For example, one can show that there are two lines intersecting four general lines in P3. In this talk, we will provide a brief introduction to Schubert calculus and use it to prove that there are 27 lines on a general cubic surface in P3. 
