A Mathematical Model for the Effect of Enzymes on Metabolism of Pharmacologically Active Substances

Addiction is a societal issue with many negative effects. Substances that cause addictive reactions are easily ingested and interact with some part of the neural pathway. This paper describes a mathematical model for the systemic level of a substance subject to degradation (via metabolism) and reversible binding to psychoactive sites. The model allows the determination of bound substance levels during the processing of a dose, and how the maximum level depends on system parameters. The model also allows the study of a particular periodic repetitive dosing described by a rapid ingestion if a dose is at constant intervals.

A Mathematical Model for Nutrient Metabolic Chemistry

A model based on chemical kinetics for the rate of utilization and/or storage of carbohydrates, fats and proteins is derived and analyzed. This system is studied under different conditions of supply and usage and for short term dynamics and long term dynamics. Both the short term and long term models indicate that starting above an equilibrium threshold leads to growth of the stored species. Results from the short-term and long-term submodels show that the qualitative behavior depends on the levels of certain enzymes. The analysis of a model for enzyme dynamics indicates that the steady-state level of an enzyme should depend on the rate of supply of the substrate.

A Within-Host Model of Dengue Infection with a Non-Constant Monocyte Production Rate

In this paper we modify previous models to develop a new model of within-host dengue infection without the assumption that monocyte production is constant. We show that this new model exhibits behavior not seen in previous models. We then proceed by obtaining an expression for the net reproductive rate of the virus and thus establish a stability result. We also perform a sensitivity analysis to test various treatment strategies and find that two strategies might be fruitful. One is the reduction of the infection rate of monocytes by viruses and the other, more effective, theoretical approach is to reduce the number of new viruses per infected monocyte.

A Direct Algorithm for the Vertical Generalized Complementarity Problem Associated with <i>P</i>-Matrices

We present a direct algorithm for solving the vertical generalized linear complementarity problem, first considered by Cottle and Dantzig, when the associated matrix is a vertical block P-matrix. The algorithm converges to a unique solution in a finite number of steps, without an assumption of nondegeneracy on the given problem. The algorithm is simple, efficient, and easy to implement.

Exact Solution for Thermal Stagnation-Point Flow with Surface Curvature and External Vorticity Effects

Exact solution of the steady Navier-Stokes equations has been obtained for the thermal stagnation-point flow at the leading edge of a turbine blade under the assumptions of constant nose radius and external vorticity, and fluid properties independent of temperature. The solutions reveal that curvature affects local heat transfer and skin friction while external vorticity does not. The effect of external vorticity is to shift the zero skin friction point away from the stagnation point. This solution is valid for all Reynolds number, external vorticity, and nose radius. In the limit of nose radius going to infinity and external vorticity, going to zero, the exact solution for two-dimensional plane stagnation-point flow is recovered identically. In addition, it can be shown that the velocity field around the stagnation point of a rotating curved surface is the same as that around the stagnation point of a stationary curved surface with an external vorticity which equals to twice of the rotational speed. This realization renders the present solution equally valid for thermal stagnation point flow at the leading edge of centrifugal impeller blades.

CONVERGENCE OF BACKPRIOPAG ATION WITH MOMENTUM FOR NETWORK A RCHITECTURES WITH SKIP CONNECTIONS

We study a class of deep neural networks with architectures that form a directed acyclic graph(DAG).For backpropagation defined by gradient descent with adaptive momentum,we show weights converge for a large class of nonlinear activation functions.'The proof generalizes the results of Wu et al.(2008)who showed convergence for a feed-forward network with one hidden layer.For an example of the effectiveness of DAG architectures,we describe an example of compression through an AutoEncoder,and compare against sequential feed-forward networks under several metrics.

On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

Recent years have witnessed the surge of asynchronous parallel(asyncparallel)iterative algorithms due to problems involving very large-scale data and a large number of decision variables.Because of asynchrony,the iterates are computed with outdated information,and the age of the outdated information,which we call delay,is the number of times it has been updated since its creation.Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly.However,the maximum delay is practically unknown.This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint,and it allows for large unbounded delays.An explicit formula of stepsize that guarantees convergence is given depending on delays’statistics.With p+1 identical processors,we empirically measured that delays closely follow the Poisson distribution with parameter p,matching our theoretical model,and thus,the stepsize can be set accordingly.Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative,often slows down the convergence of the algorithm.

Randomized Primal–Dual Proximal Block Coordinate Updates

In this paper,we propose a randomized primal–dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints.Assuming mere convexity,we establish its O(1/t)convergence rate in terms of the objective value and feasibility measure.The framework includes several existing algorithms as special cases such as a primal–dual method for bilinear saddle-point problems(PD-S),the proximal Jacobian alternating direction method of multipliers(Prox-JADMM)and a randomized variant of the ADMM for multi-block convex optimization.Our analysis recovers and/or strengthens the convergence properties of several existing algorithms.For example,for PD-S our result leads to the same order of convergence rate without the previously assumed boundedness condition on the constraint sets,and for Prox-JADMM the new result provides convergence rate in terms of the objective value and the feasibility violation.It is well known that the original ADMM may fail to converge when the number of blocks exceeds two.Our result shows that if an appropriate randomization procedure is invoked to select the updating blocks,then a sublinear rate of convergence in expectation can be guaranteed for multi-block ADMM,without assuming any strong convexity.The new approach is also extended to solve problems where only a stochastic approximation of the subgradient of the objective is available,and we establish an O(1/√t)convergence rate of the extended approach for solving stochastic programming.

ROBUST FRAME BASED X-RAY CT RECONSTRUCTION

As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the in- terior tomography scheme which only illuminates a region-of-interest （ROI）, one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three differ- ent parts： cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART＋TV methods in terms of preservation of sharp edges, mean structural similarity （SSIM）, contrast-to-noise ratio, relative error and correlation- s. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART^TV methods need more than 200 projections. Additionally, the proposed ro- bust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART＋TV methods.

Homogenization Theory for a Replenishing Passive Scalar Field

Homogenization theory provides a rigorous framework for calculating the effective diffusivity of a decaying passive scalar field in a turbulent or complex flow.The authors extend this framework to the case where the passive scalar fluctuations are continuously replenished by a source (and/or sink).The basic structure of the homogenized equations carries over,but in some cases the homogenized source can involve a non-trivial coupling of the velocity field and the source.The authors derive expressions for the homogenized source term for various multiscale source structures and interpret them physically.