On the Homoclinic Tangles of Henri Poincar
DateTuesday, February 12, 2019 - 12:30pm
AbstractThis talk is on the dynamics of the time-periodic second order equations.
We assert that Smale’s horseshoe, SRB measure of Benedick-Carleson and Young, and
Newhouse sinks are all participating elements of the homoclinic tangles of this equation.
We further assert that homoclinic tangles of different structures are arranged in a fixed
pattern and this pattern is repeated indefinitely in parameter space.
The Control of Growth, Patterning and Drug Response of the Intestinal Epithelium
DateTuesday, February 12, 2019 - 4:00pm
AbstractThe epithelial lining of the human intestine is a prime example of tight homeostatic control of cell proliferation, organization and fate determination. Estimated to have a surface area the size of a tennis court, it continuously receives mechanical, chemical and pathogen-derived insults and is in constant turnover, completely renewing every five days. Amazingly, this active process produces multiple cell types at just the right ratios and locations throughout our life span. Failure of this exquisite control is the basis for diseases including inflammatory bowel disease and cancers of the esophagus, stomach, small and large intestine. To accelerate our ability to study control of cell fate and discover new therapies, we have developed the culture of intestinal stem cells (ISCs) in a high-throughput, quantitative, two-dimensional format. Using this novel “enteroid monolayer” system, we have systematically perturbed intrinsic and extrinsic WNT/BMP signaling to reveal a core morphogenic feedback pathway that controls tissue growth and patterning. Our work demonstrates that the intestinal epithelium, without contributions from the mesenchyme or 3-D crypt geometry, has the intrinsic ability to regulate proliferation and patterning through morphogen-mediated feedback. Additionally we explored Glycogen Synthase Kinase 3 (GSK-3), a protein kinase that is uniquely positioned to act as a signaling by-pass for cancer cells to evade targeted therapies. We found GSK-3 suppression can affect the cellular sensitivities to a broad spectrum of chemotherapies and targeted oncology drugs (e.g., inhibitors of RTKs, mTOR, PLK1). Combined with a kinome-wide RNAi screen, we have shown GSK-3 is a central drug response modulator that affects potency of ~50% of current, clinically relevant kinase-targeted drugs. Our findings suggest small molecule activators of GSK-3 would have potent anti-tumor activity as single agents or in combination therapies.
Fundamental Limits of Low Probability of Detection/Intercept Communications: Core Results and Future Directions
DateThursday, February 14, 2019 - 12:30pm
AbstractHiding transmitted signals is of paramount importance in many communication settings. While traditional security (e.g., encryption) prevents unauthorized access to message content, detection of the mere presence of a message by the adversary can have significant negative impact. This necessitates the use of low probability of detection/interception (LPD/LPI) communication, which not only protects the information contained in a transmission from unauthorized decoding, but also prevents the detection of a transmission in the first place. In this talk, I will present the fundamental classical and quantum limits of LPD/LPI communication, and overview future research directions.
Resonance States and Non-Hermittian Quantum Mechanics: An Application to Nano-Tips
DateFriday, February 15, 2019 - 12:00pm
AbstractThe resonance states or quasi stationary states have been known from scattering theory of quantum systems. These states are like stationary states but with a finite life time after which they will not remain localized. They arise in various problems and we can consider them as the eigen functions of a non-Hermittian Hamiltonian. Using these states to describe the time evolution of the system can be of great advantage over the standard Hermittian formalism in some classes of problems. In addition to providing us with a better understanding of physics of the system in consideration, it is sometimes the only possible way to computationally model the system. In my research, I am solving a simplified model for metallic nano-tips using these resonance states. In this talk, I will show the power of this formalism in attacking some problems including our simplified model, and then I briefly talk about the current state of my research.
Multiscale Stochastic Transcription Models
DateFriday, February 15, 2019 - 3:00pm
AbstractThe formalism of stochastic reaction networks (SRNs) provides building blocks for number of models in mathematical biology both at molecular and population levels (e.g., gene transcription or epidemic outbreak). In particular the SRNs allow to naturally incorporate both delay and multi-scale phenomena. In the first case the resulting models may be often expressed in the language of queuing theory, in the second case they lead to stochastic diffusions and ODE/PDE approximations. In this talk I will provide a brief overview of the applications of SRNs to modeling molecular biological systems emphasizing the recent work on multi-scaling for simple stochastic gene transcription model.