Browsing Rensselaer Libraries by Subject "Mathematics"
Now showing items 1-20 of 104
-
2D Log-Elastographic methods for tissue shear stiffness reconstruction using a 2D plane strain elastic system
(Rensselaer Polytechnic Institute, Troy, NY, 2009-12) -
A dynamic fiber composite continuum model of the tympanic membrane coupled to the ossicular chain and the outer ear
(Rensselaer Polytechnic Institute, Troy, NY, 1986-05) -
A new model of oscillatory chemical signaling in cellular slime mold aggregation
(Rensselaer Polytechnic Institute, Troy, NY, 1976-08)An algorithmic model for the behavior of individual aggregating slime mold amoebae consistent with experimental evidence is considered. A cell releases a pulse of acrasin (a chemical generally thought to be cyclic AMP) ... -
A numerical study of shock induced cavity collapse
(Rensselaer Polytechnic Institute, Troy, NY, 2010-08) -
A stochastic conditional value-at-risk approach to disaster relief planning
(Rensselaer Polytechnic Institute, Troy, NY, 2015-05)Following a major disaster, such as Hurricane Katrina or the Indian Ocean Tsunami, organization and efficiency of relief operations is vital to the safety of the affected population and to the speed of recovery. However, ... -
A stochastic method for simulating subdomains of weakly nonlinear dispersive wave systems
(Rensselaer Polytechnic Institute, Troy, NY, 2011-08) -
A theoretical analysis of outgoing isotropic time-harmonic linear elasticity in a half-space with traction-free boundary
(Rensselaer Polytechnic Institute, Troy, NY, 2018-05)Linear elastic wave propagation in a half-space is of fundamental interest in geophysics and has many applications in inverse problems, including imaging the Earth’s mantle, sub-seabed mineral exploration, and cancer ... -
A variational bayes approach to inferring neuronal network connectivity
(Rensselaer Polytechnic Institute, Troy, NY, 2022-12)Uncovering a neuronal circuit's structure is an important step toward developing a mechanistic understanding of that circuit's function. In this thesis, we develop an algorithm which can accurately reconstruct an ... -
Accelerated stochastic gradient methods with adaptive techniques and distributed computing
(Rensselaer Polytechnic Institute, Troy, NY, 2023-05)Stochastic gradient methods (SGMs) have gained widespread usage for solving stochastic optimization problems due to their simplicity and efficient computation as first-order methods. However, vanilla SGMs suffer from slow ... -
An examination of nonlinear waves in the cochlea utilizing asymptotic and numerical methods
(Rensselaer Polytechnic Institute, Troy, NY, 2013-05)In this work we develop a comprehensive, three-dimensional model for the active cochlear response. We expand upon other currently accepted linear modeling efforts in order to explain observed nonlinearities such as ... -
Analysis and applications of discontinuous Galerkin methods for hyperbolic equations
(Rensselaer Polytechnic Institute, Troy, NY, 2014-08)We also consider the Vlasov-Maxwell (VM) system which is a kinetic model to describe the time evolution of the plasma particles in the self-consistent electromagnetic field. The prevailing particle-in-cell methods make ... -
Analytical approach for opinion dynamics on social networks
(Rensselaer Polytechnic Institute, Troy, NY, 2012-12)Opinion dynamics is a class of agent based models arising from the study of the origins and evolutions of languages and now attracts a lot of interest. These models consist of a large number of individuals updating their ... -
Anomaly detection for batch manufacturing via greybox feedback control models
(Rensselaer Polytechnic Institute, Troy, NY, 2019-08)Results on the PI control simulated data indicate that our framework defeats two anomaly detection benchmarks by a large margin if the theoretical shape signatures are known a priori. Though they will not be known in ... -
Applications of 3-convexity
(Rensselaer Polytechnic Institute, Troy, NY, 2009-12) -
Applications of modal approximations to attenuation properties in sandy-silty sediments
(Rensselaer Polytechnic Institute, Troy, NY, 2010-12) -
Approximations and improvements to semidefinite relaxations of optimization problems
(Rensselaer Polytechnic Institute, Troy, NY, 2013-08)At the beginning of the 1990s, semidefinite programming (SDP) gained popularity as one of the major research areas of convex optimization and attracted many researchers from various disciplines. Today many engineers and ... -
Best simultaneous approximation in a normed linear space
(Rensselaer Polytechnic Institute, Troy, NY, 1976-12)The problem we consider is the approximation of m elements (xₗ,...,xₘ) in a normed linear space by one element in a subset of that normed linear space. To each element in the ordered m-tuple (xₗ,...,xₘ) we associate ... -
Bilevel programming algorithms for machine learning model selection
(Rensselaer Polytechnic Institute, Troy, NY, 2010-12) -
Central discontinuous Galerkin methods for Hamilton-Jacobi equations and ideal magnetohydrodynamics equations
(Rensselaer Polytechnic Institute, Troy, NY, 2011-08) -
Classifying microtubule networks using curvature calculation of discrete curves
(Rensselaer Polytechnic Institute, Troy, NY, 2015-08)Microtubules are structures within the cell that form a transportation network along which motor proteins tow cargo to destinations within the cell. To establish and maintain a structure capable of serving the cell's tasks, ...