Towards a New Spatial Representation of Bone Remodeling

Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology. Different approaches to modeling give insight into different aspects of a phenomena so it is useful to have an arsenal of various computational and mathematical models. Here we develop a mathematical representation of bone remodeling that can effectively describe many aspects of the complicated geometries and spatial behavior observed. There is a sharp interface between bone and marrow regions. Also the surface of bone moves in and out, i.e. in the normal direction, due to remodeling. Based on these observations we employ the use of a level-set function to represent the spatial behavior of remodeling. We elaborate on a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes. We exhibit simulations based on our computational model that show the motion of the interface between bone and marrow as a consequence of bone remodeling. The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur \emph{in vitro} and \emph{in vivo}. By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling. By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as \emph{in vitro} and \emph{in vivo}. This makes it possible to perform \emph{in silica} experiments more closely resembling experimental observations.Comment: Math. Biosci. Eng., 9(2), 201

Pairing Fluctuations Determine Low Energy Electronic Spectra in Cuprate Superconductors

We describe here a minimal theory of tight binding electrons moving on the square planar Cu lattice of the hole-doped cuprates and mixed quantum mechanically with pairs of them (Cooper pairs). Superconductivity occurring at the transition temperature T_c is the long-range, d-wave symmetry phase coherence of these Cooper pairs. Fluctuations necessarily associated with incipient long-range superconducting order have a generic large distance behaviour near T_c. We calculate the spectral density of electrons coupled to such Cooper pair fluctuations and show that features observed in Angle Resolved Photo Emission Spectroscopy (ARPES) experiments on different cuprates above T_c as a function of doping and temperature emerge naturally in this description. These include `Fermi arcs' with temperature-dependent length and an antinodal pseudogap which fills up linearly as the temperature increases towards the pseudogap temperature. Our results agree quantitatively with experiment. Below T_c, the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with some recent ARPES experiments, especially the observed `bending' or deviation of the superconducting gap from the canonical d-wave form.Comment: 14 pages, 8 figures (to appear in Phys. Rev. B

Modeling and Simulation of the Effects of Cyclic Loading on Articular Cartilage Lesion Formation

We present a model of articular cartilage lesion formation to simulate the effects of cyclic loading. This model extends and modifies the reaction-diffusion-delay model by Graham et al. 2012 for the spread of a lesion formed though a single traumatic event. Our model represents "implicitly" the effects of loading, meaning through a cyclic sink term in the equations for live cells. Our model forms the basis for in silico studies of cartilage damage relevant to questions in osteoarthritis, for example, that may not be easily answered through in vivo or in vitro studies. Computational results are presented that indicate the impact of differing levels of EPO on articular cartilage lesion abatement

AN EFFECTIVE APPROACH OF BILATERAL FILTER IMPLEMENTATION IN SPARTAN-3 FIELD PROGRAMMABLE GATE ARRAY

This paper presents the Field Programmable Gate Array (FPGA) implementation of Bilateral Filter, in order to achieve high performance and low power consumption. Bilateral filtering is a technique to smooth images while preserving edges by means of a nonlinear combination of nearby image values. This method is nonlinear, local, and simple. We give an idea that bilateral filtering can be accelerated by bilateral grid scheme that enables fast edge-aware image processing. Nowadays, most of the applications require real time hardware systems with large computing potentiality for which fast and dedicated Very Large Scale Integration (VLSI) architecture appears to be the best possible solution. While it ensures high resource utilization, that too in cost effective platforms like FPGA, designing such architecture does offers some flexibilities like speeding up the computation by adapting more pipelined structures and parallel processing possibilities of reduced memory consumptions. Here we have developed an effective approach of bilateral filter implementation in Spartan-3 FPGA

A Pathwise Ergodic Theorem for Quantum Trajectories

If the time evolution of an open quantum system approaches equilibrium in the time mean, then on any single trajectory of any of its unravelings the time averaged state approaches the same equilibrium state with probability 1. In the case of multiple equilibrium states the quantum trajectory converges in the mean to a random choice from these states.Comment: 8 page

Extremely Correlated Quantum Liquids

We formulate the theory of an extremely correlated electron liquid, generalizing the standard Fermi liquid. This quantum liquid has specific signatures in various physical properties, such as the Fermi surface volume and the narrowing of electronic bands by spin and density correlation functions. We use Schwinger's source field idea to generate equations for the Greens function for the Hubbard operators. A local (matrix) scale transformation in the time domain to a quasiparticle Greens function, is found to be optimal. This transformation allows us to generate vertex functions that are guaranteed to reduce to the bare values for high frequencies, i.e. are ``asymptotically free''. The quasiparticles are fractionally charged objects, and we find an exact Schwinger Dyson equation for their Greens function. We find a hierarchy of equations for the vertex functions, and further we obtain Ward identities so that systematic approximations are feasible. An expansion in terms of the density of holes measured from the Mott Hubbard insulating state follows from the nature of the theory. A systematic presentation of the formalism is followed by some preliminary explicit calculations.Comment: 40 pages, typos remove