## September 2018

### Applied math organizational meeting

We will have an organizational meeting for the applied math seminar today. Anyone who is interested in suggesting speakers and/or organizing applied math seminar is welcome to come.

Find out more »### Diffusion, Social Networks, and Logic (Pavel Naumov, CMC)

Once a new commercial product, technology, political opinion, or social norm is adopted by a few people, these few often put peer pressure on others to consider adopting it as well. Those who adopt next put even more pressure on the rest of the population. This cascading “epidemic” effect is often called diffusion in social networks. There are many natural questions that can be asked about diffusion. Which initial group of people should get “infected” by a new product to…

Find out more »## October 2018

### Agent-Based and Continuous Models of Locust Hopper Bands: The Role of Intermittent Motion, Alignment, Attraction and Repulsion (Andrew J. Bernoff, HMC)

Locust swarms pose a major threat to agriculture, notably in northern Africa and the Middle East. In the early stages of aggregation, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust hopper bands that incorporates intermittent motion, alignment with neighbors, and social attraction, all behaviors that have been validated in experiments. Using a particle-in-cell computational method,…

Find out more »### Minimal Gaussian Partitions, Clustering Hardness and Voting (Steven Heilman, USC)

A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air. When two soap bubbles collide, they form a "double-bubble" composed of three spherical caps. The double-bubble minimizes total surface area among all sets enclosing two fixed volumes. This was proven mathematically in a landmark result by Hutchings-Morgan-Ritore-Ros and Reichardt using the calculus of variations in the early 2000s. The analogous case of three or more Euclidean sets is…

Find out more »## November 2018

### CFTP: the algorithm ERGM deserves, but not the one it needs right now (Matt Moores, University of Wollongong)

The exchange algorithm enables Bayesian posterior inference for models with intractable likelihoods, such as Ising, Potts, or exponential random graph models (ERGM). Crucially, this algorithm relies on an auxiliary Markov chain to obtain an unbiased sample from the generative distribution of the model. It was originally proposed to use coupling from the past (CFTP) for this purpose, but this requires the Markov chain to be uniformly ergodic. In the case of the Ising model, coupling time increases super-exponentially for parameter…

Find out more »### Digital sequences for frequency hopping CDMA systems (Lenny Fukshansky, CMC)

Frequency hopping is a method of transmitting signals by rapidly switching between many frequency channels, following some sequence of frequencies known to the transmitter and the receiver. This technique is used in the CDMA (code division multiple access) systems, and has many civilian and military applications. For successful transmission minimizing signal interference, we want to use sets of digital frequency sequences with minimal Hamming cross-correlation, which measures frequency overlaps with time shifts between two different sequences. We discuss a construction of a…

Find out more »### Turing mechanism for homeostatic control of synaptic density during C. elegans growth (Heather Zinn Brooks, UCLA)

It has been observed that motor neuron synapses in the worm C. elegans are remarkably evenly spaced, even during growth and development. In this work, we propose a novel mechanism for Turing pattern formation that provides a possible explanation for the regular spacing of synapses along the ventral cord of C. elegans during development. The model consists of two interacting chemical species, where one is passively diffusing and the other is actively trafficked by molecular motors; we identify the former…

Find out more »### A renormalization approach to existence of the blow-up solutions of the Navier-Stokes equations (Denis Gaidashev, Uppsala University, Sweden)

The Navier-Stokes existence and smoothness problem is one of the most important open problems in modern mathematics. Ya. Sinai and D. Li have proposed a renormalization approach to constructing a counter-example to existence. In this approach, existence of a blow-up solution (a solution whose energy becomes infinite in finite time) is equivalent to existence of fixed point of an appropriate operator in some functional space. We will explain a computer assited technique which can be conjecturally used to prove existence of…

Find out more »## December 2018

### A Martingale Approach to the Question of Fiscal Stimulus (Michael Imerman, CGU)

Joint work with Larry Shepp & Philip Ernst In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US say that government spending can be used to “grease the wheels’ of the economy, create wealth, and increase employment; the Republicans say that government spending is wasteful, discourages investment, and so increases unemployment. These arguments cannot both be correct, but both arguments seem meritorious. We address this economic question of…

Find out more »### Transfinite $\zeta$-metrics (Zair Ibragimov, CMC)

I will discuss the concept of transfinite ζ-metrics. In some details I will discuss transfinite Apollonian metric in the settings of semi-metric spaces. I will discuss specific examples of domains where the transfinite Apollonian metric can be computed explicitly. This is a preliminary work.

Find out more »## January 2019

### Applied Math Seminar Organizational Meeting

We will have an organizational meeting for the applied math seminar at 4:15pm in Emmy Noether Rm, Millikan 1021, Pomona on 1/28 (Monday). Anyone who in interested in suggesting speakers and/or organizing applied math seminar is welcome to come.

Find out more »## February 2019

### Estimating the physical location of Twitter users with the von Mises-Fisher distribution (Mike Izbicki, UC Riverside)

Approximately 500 million tweets are sent everyday. Scientists monitor these tweets to predict the spread of disease, better allocate social welfare services, help first responders during natural disasters, and many other important tasks. A key step in each of these tasks is estimating the location the tweet was sent from. In this talk, I discuss how to combine machine learning and the von Mises-Fisher distribution to estimate this location. The von Mises-Fisher distribution is the spherical analog of the Gaussian distribution, and this distribution lets us exploit…

Find out more »### Community structure in networks: the effect of communities on a preferential attachment model and epidemic spreading (Emily Fischer, Cornell)

Online social networks and other networks of interest are known to exhibit community structure, where a community is defined to be a highly interconnected group of nodes with possibly shared traits or features. However, classic network models, such as the preferential attachment model, do not account for community structure. In this talk, I will present the Community-Aware Preferential Attachment Model (CAPAM), which allows the user to specify community structure via edge probabilities. I will show that CAPAM retains desirable properties…

Find out more »### Applied Math Seminar: Measurement Error Modeling using Empirical Phase Functions (Prof. Cornelis Potgieter, Southern Methodist University)

Measurement error, formally defined as the difference between the measured value and the true value of a quantity of interest, is ubiquitous. When a doctor takes your blood pressure, the instrumentation may not be properly calibrated and the reading is subject to error. When completing an online Harry Potter Sorting Hat quiz, you may accidentally click the wrong option for a specific question and find yourself in House Slytherin!. The effect of measurement error is sometimes insignificant, but there are…

Find out more »### Applied Math Seminar: Eulerian Approaches based on the Level Set Method for Visualizing Continuous Dynamical Systems (Shingyu Leung, Department of Mathematics, HKUST)

One very important concept in understanding a dynamical system is coherent structure. Such structure segments the domain into different regions with similar behavior according to a quantity. When we try to partition space-time into regions according to a Lagrangian quantity advected along with passive tracers, such class of coherent structure is called the Lagrangian coherent structures (LCSs). Among many, a simple definition of an LCS uses the finite-time Lyapunov exponent (FTLE). It measures the rate of separation between adjacent particles…

Find out more »## March 2019

### Applied Math Seminar: Fluid mechanics at the microscale (Prof. Amy Buchmann, University of San Diego)

I will present mathematical and computational methods used to model interactions between a viscous fluid and elastic structures in biological processes. For example, microfluidic devices carry very small volumes of liquid through channels and may be used to gain insight into many biological applications including drug delivery and development, but mixing and pumping at this scale is difficult. Experimental work suggests that the flagella of bacteria may be used as motors in microfluidic devices, and mathematical modeling can be used…

Find out more »### Applied Math Talk: Cluster analysis on covariance stationary ergodic processes and locally asymptotically self-similar processes (Nan Rao, CGU)

We study the problems of clustering covariance stationary ergodic processes and locally asymptotically self-similar stochastic processes, when the true number of clusters is priorly known. A new covariance-based dissimilarity measure is introduced, from which efficient consistent clustering algorithms are obtained. As examples of application, clustering fractional Brownian motions and clustering multifractional Brownian motions are respectively performed to illustrate the asymptotic consistency of the proposed algorithms.

Find out more »## April 2019

### Applied Math Talk: Repurposing FDA-approved drugs as host-oriented therapies against infectious diseases (Prof. Mikhail Martchenko, KGI)

The traditional method of treating most human diseases is to direct a therapy against targets in the host patient, whereas conventional therapies against infectious diseases are directed against the pathogen. Unfortunately, the efficacy of pathogen-oriented therapies and their ability to combat emerging threats such as genetically engineered and non-traditional pathogens and toxins have been limited by the occurrence of mutations that render pathogen targets resistant to countermeasures. Our work shows that host proteins that are exploited by pathogens (Host Proteins…

Find out more »### Models of Biological Tissue Electrostatics and Molecular Transport (Jim Sterling, KGI)

In this presentation, some fundamentals of electrostatics in biology will be discussed with focus on the fact that most biological macromolecules including nucleic acids, carbohydrates, and proteins are negatively-charged. Electroneutrality requires cations to move toward the macromolecules where they both screen and bind to the negatively-charged groups. An important class of mathematical models of species-flux and electrostatics are known as the Poisson-Nernst-Planck, or PNP equations. These are partial differential equations describing some important biophysical consequences.

Find out more »### Applied Math Talk: Solving Complex Public Health Problems—Cancer, Obesity and Aging (Jessica Dehart, CGU)

Abstract: Remember smoking? What’s the new public health problem? In the US, we are currently entangled within three converging and intertwined complex problems: Cancer, Obesity, Aging. There are over 16 million cancer survivors living in the US as we speak. Over 50% of our society is overweight and/obese. Our society is aging and the age distribution is much older than a few years back. Cancer, obesity and aging share several risk factors, biological mechanisms and patterns. Given the multidimensionality and…

Find out more »### Applied Math Talk: Nonlocal problems for linear evolution equations (Prof. Smith David Andrew, Yale-NUS College, Singapore)

Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where one specifies some linear combination of the solution and its derivative evaluated at internal points of the spatial domain, and “nonlocal” specification of the integral over space of the solution against some continuous weight.

Find out more »### Applied Math Seminar: The Kaczmarz Algorithm and its Applications to Data Science (Anna Ma, UCSD)

Data is exploding at a faster rate than computer architectures can handle. For that reason, mathematical techniques to analyze large-scale data need be developed. Stochastic iterative algorithms have gained interest due to their low memory footprint and adaptability for large-scale data. In this talk, we will study the Randomized Kaczmarz algorithm for solving extremely large linear systems of the form Ax=y. In the spirit of large-scale data, this talk will proceed under the assumption that the entire data matrix A…

Find out more »## May 2019

### Applied math seminar: Topological descriptions of protein folding (Helen Wong, CMC)

Knotting in proteins was once considered exceedingly rare. However, systematic analyses of solved protein structures over the last two decades have demonstrated the existence of many deeply knotted proteins, and researchers now hypothesize that the knotting presents some functional or evolutionary advantage for those proteins. Unfortunately, there is very little known (whether experimentally, through computer simulations, or theoretically) about how proteins fold into knotted configurations. In this talk, we will discuss some of the theorized pathways from a topological point…

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