Solving physics-driven inverse problems via structured least squares

Numerous physical phenomena are well modeled by partial differential equations (PDEs); they describe a wide range of phenomena across many application domains, from model- ing EEG signals in electroencephalography to, modeling the release and propagation of toxic substances in environmental monitoring. In these applications it is often of interest to find the sources of the resulting phenomena, given some sparse sensor measurements of it. This will be the main task of this work. Specifically, we will show that finding the sources of such PDE-driven fields can be turned into solving a class of well-known multi-dimensional structured least squares prob- lems. This link is achieved by leveraging from recent results in modern sampling theory – in particular, the approximate Strang-Fix theory. Subsequently, numerical simulation re- sults are provided in order to demonstrate the validity and robustness of the proposed framework

On a dynamic reaction-diffusion mechanism: The spatial patterning of teeth primordia in the alligator

It is now well established both theoretically and, more recently, experimentally, that steady-state spatial chemical concentration patterns can be formed by a number of specific reaction–diffusion systems. Reaction–diffusion models have been widely applied to biological pattern formation problems. Here we propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis, which, from a reaction–diffusion theory, introduces, among other things, a new element, namely the effect of domain growth on dynamic spatial pattern formation. Detailed embryological studies by Westergaard and Ferguson (B. Westergaard and M. W. J. Ferguson, J. Zool. Lond., 1986, 210, 575; 1987, 212, 191; Am. J. Anatomy, 1990, 187, 393) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction–diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw of A. mississippiensis. The results for the precise spatio temporal sequence compare well with detailed developmental experiments

A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology

Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the system's structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator

Dynamic weight parameter for the Random Early Detection (RED) in TCP networks

This paper presents the Weighted Random Early Detection (WTRED) strategy for congestion handling in TCP networks. WTRED provides an adjustable weight parameter to increase the sensitivity of the average queue size in RED gateways to the changes in the actual queue size. This modification, over the original RED proposal, helps gateways minimize the mismatch between average and actual queue sizes in router buffers. WTRED is compared with RED and FRED strategies using the NS-2 simulator. The results suggest that WTRED outperforms RED and FRED. Network performance has been measured using throughput, link utilization, packet loss and delay

Multidecadal variability in hydro-climate of Okavango river system, southwest Africa, in the past and under future climate

The focus of this paper is to understand the multi-decadal oscillatory component of variability in the Okavango River system, in southwestern Africa, and its potential evolution through the 21st century under climate change scenarios. Statistical analyses and hydrological modelling are used to show that the observed multi-decadal wet and dry phases in the Okavango River and Delta result from multi-decadal oscillations in rainfall, which are likely to be related to processes of internal variability in the climate system, rather than external natural or anthropogenic forcing. Analyses of changes in this aspect of variability under projected climate change scenarios are based on data from a multi-model ensemble of 19 General Circulation Models, which are used to drive hydrological models of the Okavango River and Delta. Projections for the 21st century indicate a progressive shift towards drier conditions attributed to the influence of increasing temperatures on water balance. It is, however, highly likely that multi-decadal oscillations, possibly of similar magnitude to that of 20th century, will be superimposed on the overall trend. These may periodically offset or amplify the mean drying trend. This effect should be accounted for in water and catchment management and climate change adaptation strategies

Suicide substrate reaction-diffusion equations: varying the source

The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of initial and boundary conditions are examined: one modelling an instantaneous point source, akin to an injection of substrate, the other, a continuous point source, akin to a continuing influx, or intravenous drip, of substrate. The quasi-steady-state assumption is applied to obtain analytical solutions for a limited parameter space. Finally, further applications of numerical and analytical experimentation on pharmaceutical mechanisms are described

Mixtures of Common Skew-t Factor Analyzers

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used

On the kinetics of suicide substrates

We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure to obtain accurate, approximate solutions analytically in terms of the rate equation parameters. This systematic technique provides more accurate approximations to the exact (numerical) solutions than other approximate methods which have been proposed based on a pseudo-steady state hypothesis