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## Theoretical Neuroscience Journal Club

#### Cognitive memory and mapping in a brain-like system for robotic Navigation

### Abstract

The paper is: ‘Cognitive memory and mapping in a brain-like system for robotic Navigation’ By Huajin Tang, Weiwei Huang, Aditya Narayanamoorthy, Rui Yan, Neural Networks 87:27-37, 2017.## Analysis and its Applications Seminar

#### Characterization of Steady Solutions for the 2D Euler Equation

### Abstract

The motion of an ideal fluid on a 2D surface is described by the incompressible Euler equation, which can be regarded as a Hamiltonian system on coadjoint orbits of the symplectic diffeomorphisms group. Using a combinatorial description of these orbits in terms of graphs with some additional structures, we give a characterization of coadjoint orbits which may admit steady solutions of then Euler equation (steady fluid flows). It turns out that when the genus of the surface is at least one, most coadjoint orbits do not admit steady fluid flows, while the set of orbits admitting such flows is a convex polytope. This is a joint work with B.Khesin.## Quantitative Biology Colloquium

#### Beagle in a flask: Adaptive laboratory evolution of ancient proteins in bacteria

### Abstract

Our living world is the result of a complex history spanning billions of years. Scientists have access to artifacts of this history, namely the fossil record and the genomes of many different living organisms. But there are surprisingly limited means with which to infer the exact evolutionary history that resulted in modern biota. It is difficult to reconcile fossil morphology on the one hand, and genetic composition and diversification over time on the other, when so little about the biological behavior of ancestral organisms can be reconstructed to link these data. This limitation makes it difficult to approach intriguing questions of whether the evolutionary paths that produced modern organisms were highly deterministic (i.e., life as a factory) or inherently dominated by chance (i.e., life as a casino parlor). Did life in the past function or evolve similarly to life today? Did the biology of ancestral organisms, the functions of their proteins or other factors inherently limit their ability to evolve into modern forms? To attempt to overcome these historical limitations, we resurrected 1.3 to 3.6 billion year old genes inside modern E. coli microbes. By engineering revenant proteins inside modern organisms, we can characterize their biological function and observe the holistic effects that they have on the cell’s behavior.## Brown Bag Seminar

#### Topics in Nonparametric Regression for High Dimensional Data

### Abstract

Nonparametric regression suffers from needing exponentially much data samples as dimensions. We will discuss methods to get around that. We will also highlight recent work done in dealing with missing data and shape constraints.## Applied Math Colloquium

#### Nonlinear Dynamics of Aortic Prostheses Conveying Pulsatile Flow

### Abstract

The nonlinear dynamics of thin-walled shells conveying pulsatile flow is of particular interest in cardiovascular biomedical applications. In this talk, I will discuss the dynamical behavior of woven Dacron thoracic prostheses subjected to physiological pulsatile blood flow and pressure. The artificial vessel is modeled with the nonlinear Novozhilov shell theory applied to an orthotropic circular cylindrical slightly corrugated shell. In Dacron implants, surface waves of the corrugation are in longitudinal direction and they can be modelled introducing a sinusoidal geometric imperfection on the circular cylindrical shell geometry for both axial and radial displacement. A pulsatile time-dependent blood flow model is considered by applying physiological waveforms of velocity and pressure during the heart beating period approximated through Fourier series with eight harmonics. The fluid is assumed to be Newtonian and the pulsatile flow is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Residual stresses because of pulsatile pressurization are evaluated and included in the model. Coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow will be presented for shells with both fixed boundary conditions and boundary conditions allowing radial displacement at both ends. The last ones boundary conditions are meant to reproduce the simple interrupted suture technique that can be performed by surgeons. Several superharmonic resonance peaks appear in the physiological frequency range by including higher harmonics in the Fourier expansion of the physiological waveforms of pressure and velocity. Large amplitude oscillations are observed in the physiological frequency range during exercise conditions. Since vibrations of the artificial vessel walls are activated for certain heart rates, the related high stress concentration combined with the fatigue cycles of the heart beats, could reduce the long term patency of the prosthesis. For very low damping values, flow-induced asymmetric vibration of the aortic prosthesis is possible in case of fixed boundary conditions. A period-doubling bifurcation appears at HR = 191.4 bpm giving a dynamic instability characterized by a periodic response with two times the excitation period (2T). This vibration can cause high stress concentration which, combined with the fatigue cycles of the heart beats, could contribute to material deterioration. In addition, by simply approximating the pulsatile blood flow velocity and pressure with only the first term of the Fourier series, geometrically nonlinear vibrations show interesting and intricate nonlinear dynamics (chaos, amplitude modulation and period-doubling bifurcations) for frequencies out of the physiological range. Results will be presented via frequency-response curves, time histories, bifurcation diagrams and Poincaré maps. The growing understanding of the dynamic behavior of vascular prostheses currently used in clinical practice could help controlling their common long-term adverse effects and could inspire the design of a new generation prosthesis with physiological properties more similar to the host arteries.