Models are useful when they are compared with data. Whether this comparison should be qualitative or quantitative depends on circumstances, but in many cases some statistical comparison of model and data is useful and enhances objectivity. Unfortunately, ecological dynamic models tend to contain assumptions and simplifications which enhance tractability, promote insight, but spoil model fit and...

co-channel interference is a major factor in limiting the capacity and link quality in cellular communications. as the co-channel interference is modeled by lognormal distribution, sum of the co-channel interferences of neighboring cells is represented by the sum of lognormal random variables (rvs) which has no closed-form expression. assuming independent, identically distributed (iid) rvs, the...

Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electric...

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an externa...

As electronic data becomes widely available, the need for tools that help people gain insight from data has arisen. A variety of techniques from statistics, machine learning, and neural networks have been applied to databases in the hopes of mining knowledge from data. Multiple regression is one such method for modeling the relationship between a set of explanatory variables and a dependent var...

Our ignorance of dark energy is generally described by a two-parameter equation of state. In these approaches, a particular ad hoc functional form is assumed, and only two independent parameters are incorporated. We propose a model-independent, multiparameter approach to fitting dark energy and show that next-generation surveys will constrain the equation of state in three or more independent r...

PURPOSE To perform a preliminary exploration with a simplistic mathematical cancer stem cell (CSC) interaction model to determine whether the tumor-intrinsic heterogeneity and dynamic equilibrium between CSCs and differentiated cancer cells (DCCs) can better explain radiation therapy treatment response with a dual-compartment linear-quadratic (DLQ) model. METHODS AND MATERIALS The radiosensit...

Temperature-dependent development influences production rates of arthropods, including crustaceans important to fisheries and agricultural pests. Numerous candidate equation types (development functions) exist to describe the effect of temperature on development time, yet most studies use only a single type of equation and there is no consensus as to which, if any model predicts development rat...

Consistently fitting vanilla option surfaces is an important issue when it comes to modeling in finance. As far as local and stochastic volatility models are concerned, this problem boils down to the resolution of a nonlinear integro-differential pde. The non-locality of this equation stems from the quotient of two integral terms and is not defined for all bounded continuous functions. In this ...

A novel two-thermocouple sensor characterisation method for use in variable velocity flow environments is described. A difference equation method, recently developed by the authors for constant velocity flow applications, is extended to accommodate variable velocity flows using polynomial parameter fitting on a sliding data window. In particular, by using a novel difference equation formulation...