We develop two mathematical lumped parameter models for blood pressure distribution in the Fontan blood flow circulation: an ODE based spatially homogeneous model and a PDE based spatially inhomogeneous model. Numerical simulations of the ODE model with physiologically consistent input parameters and cardiac cycle pressure-volume outputs, reveal the existence of a critical value for pulmonary resistance above which the cardiac output dramatically decreases. We also analyze the existence of solutions for two initial-boundary value problems for a non-linear parabolic partial differential equation (PDE model) with switching in time dynamic boundary conditions which model the blood pressure distribution in the cardiovascular system with and without Fontan surgery. We obtain necessary conditions for parameter values of the PDE model for existence and uniqueness of physiologically relevant non-negative bounded periodic solutions. These results suggest the use of our model for creation of synthetic data to overcome a lack of training data that currently is considered to be one of the main challenges for the use of machine learning for classification of healthy and failing Fontan patients.
We solve the gas dynamics (Euler) equations, augmented by adding a fourth equation governing the fraction of unburnt gas, in a number of cylindrically symmetric configurations of the pipe system.
PURPOSE:We provide methods for determining the repeatability of airborne electromagnetic surveys when conducted at different altitudes over a number of repeated flights. Our data arise from the TELLUS project carried out by the Geological Surveys of Ireland and Northern Ireland and we examine the repeatability of the apparent resistivity at different frequencies.METHODS:After considering a number of issues with the data, we propose two different models from the functional data analysis literature; a Weiner process with random effects, and a penalised spline smoother.RESULTS:Both methods arrive at the same conclusion regarding repeatability of the data; results obtained are more repeatable for flights at lower altitudes.CONCLUSIONS:The target altitude for aircraft carrying out airborne electromagnetic surveys should be as low as possible.
In this article we consider a difficult combinatorial optimization problem arising from the operation of a system for testing electronic circuit boards (ECB). This problem was proposed to us by a company that makes a system for testing ECBs and is looking for an efficient way of planning the tests on any given ECB. Because of its difficulty, we first split the problem into a covering subproblem and a sequencing subproblem. We also give a global formulation of the test planning problem. Then we present and discuss results pertaining to the covering and sequencing subproblems. These results demonstrate that their solution yields testing plans that are much better than those currently used by the company. Finally we conclude our article by outlining avenues for future research.
A blind source signal separation problem that was brought to a Study Group in Limerick in 2013 required a way to prevent the gait of a jogger from masking the heartbeat, when detected by a simple photodiode that measures light transmission through a jogger’s wrist tissues. The group was successful in discovering a singular value decomposition (SVD) approach, which not only allows accurate detection of heart rate but also allows recovery of a good facsimile of the entire blood pressure time series from the mixed photodiode signal.
This paper develops mathematical models for a proposed production logging tool, which uses capacitance sensors to measure liquid annulus thickness and liquid type for a primarily gas-carrying wellbore. A semi-analytical method is devised which uses Fourier analysis to account for the complicated system geometry and reduces the problem to singular integral equations over a sensor electrode. Approximate solutions of these integral equations give expressions for capacitance, which is calculated for different liquids and varying liquid annuli thicknesses and electrode positions. These results are compared with capacitance values found using COMSOL Multiphysics, a finite element package. Good agreement is obtained between these two methods, with a discrepancy range of 1–8 %. Capacitance values obtained range from 32 to 93 pF/m, and sensitivity is estimated to range from 0.8 to 60 %, depending mainly on the proximity of the electrode to the liquid and also on the permittivity and thickness of the liquid layer. Practical implications of the study are also discussed. Realistically useful measurements, where ~0.2 mm of liquid is detectable, can potentially be made using an electrode 4–6 mm away from the inner wellbore wall.
At the 2014 Fields-MPrime Industrial Problem Solving Workshop, PerkinElmer presented a design problem for mass spectrometry. Traditionally, mass spectrometry is done via three methods: using magnetic fields to deflect charged particles whereby different masses bend differently; using a time-of-flight procedure where particles of different mass arrive at different times at a target; and using an electric quadrupole that filters out all masses except for one very narrow band. The challenge posed in the problem was to come up with a new design for mass spectrometry that did not involve magnetic fields and where mass fractions could be measured in an entire sample on a continuous basis. We found that by sending the sample particles down a channel of line charges oscillations would be induced with a spatial wavelength being mass dependent thereby allowing different masses to be separated spatially and potentially detected on a continuous basis, without the use of magnetic fields. In this paper, we present the analysis of our design and illustrate how this principle could be used for mass spectrometry.
In aircraft components maintenance shops, components are distributed amongst repair groups and their respective technicians based on the type of repair, on the technicians skills and workload, and on the customer required dates. This distribution planning is typically done in an empirical manner based on the group leader’s past experience. Such a procedure does not provide any performance guarantees, leading frequently to undesirable delays on the delivery of the aircraft components. Among others, a fundamental challenge faced by the group leaders is to decide how to distribute the components that arrive without customer required dates. This paper addresses the problems of prioritizing the randomly arriving of aircraft components (with or without pre-assigned customer required dates) and of optimally distributing them amongst the technicians of the repair groups. We proposed a formula for prioritizing the list of repairs, pointing out the importance of selecting good estimators for the interarrival times between repair requests, the turn-around-times and the man hours for repair. In addition, a model for the assignment and scheduling problem is designed and a preliminary algorithm along with a numerical illustration is presented.
The use of gas turbines is widespread in several industries such as; hydrocarbons, aerospace, power generation. However, despite to their many advantages, they are subject to multiple exploitation problem that need to be solved. Indeed, the purpose of the present paper is to develop mathematical models of this industrial system using an adaptive fuzzy neural network inference system. Where the knowledge variables in this complex system are determined from the real time input/output data measurements collected from the plant of the examined gas turbine. It is obvious that the advantage of the neuro-fuzzy modeling is to obtain robust model, which enable a decomposition of a complex system into a set of linear subsystems. On the other side, by focusing on the membership functions for residual generator to get consistent settings based on the used data structure classification and selection, where the main goal is to obtain a robust system information to ensure the supervision of the examined gas turbine.
Expansion of the NHL hockey league is of current interest. Success of an expansion team will rely on approved geographic locations, and most importantly fan support. Fan allegiance can be likened to infectious disease transmission, whereby individuals are susceptible, infected and recovered from a current team’s hockey season. We employ an infectious disease model to assess the viability of certain Canadian and American cities that have been discussed as potential locations for NHL expansion in the past decade. We find that Quebec City presents an ideal location for expansion, where as, Las Vegas is suboptimal.
Gas turbines are currently a popular power generation technology in countries with access to natural gas resources. However they are very complex systems the operation of which at peak performance is challenging. This paper proposes the use of a hybrid approach based on an Adaptive Neuro-Fuzzy Inference System (ANFIS) for the control of the speed and the exhaust temperature of a gas turbine. The main aim is to maintain turbine operation at optimum performance. The results obtained, based on the use of the Rowen model, clearly show the effectiveness of the proposed hybrid speed/exhaust temperature control approach for the gas turbine.
This paper studies liquidity and volatility commonality in the Canadian stock market. We show that five various liquidity measures display strong evidence of commonality at both market-wide and industry specific levels. Our findings extend the results of previous studies in liquidity commonality, and show that even after controlling for individual determinants of liquidity such as price, volume, and volatility, liquidity commonality remains. In addition to demonstrating liquidity commonality, we also investigated the causal relationship between liquidity and volatility. Our evidence indicates that depth, proportional effective spread, and liquidity changes predict volatility changes for bid-ask spread, depth, and proportional effective spread.
Understanding domestic electricity consumption behaviour is very important for planners and operators of electrical networks. Distribution Network Operators (DNOs) are installing monitoring devices at the low-voltage (LV) substation level. However, monitoring devices need to be allocated with consideration. This paper seeks to quantify the relationship between key information from a substation electricity profile, and the type of properties it supplies. Often the number of properties is the most significant predictor for key substation features. Additionally, the proportion of properties which are small-to-medium enterprises (SMEs) affects nearly all key features considered: from the overall load mean and variance, to the annual trend, to peak behaviour. Knowing substation key features is of direct use, for example where to prioritise monitoring. However we also demonstrate how these key features can be used within a so-called ‘buddying’ framework to estimate the load every half-hour for individual properties.
Maintenance cost of machinery, equipment and tooling are main contributor to total cost of production in processing industry. The aim of study is to explore selection of optimum maintenance strategy for steam generating unit (SGU) in a coal fired thermal power plant using various MADM and graphical approach. The novelty of research work is selection of strategy based on agile enabler attributes and use of graphical approaches for decision making. This selection procedure allows for speedy conflux of large number of attributes, which gives the decision maker an effective tool select optimum strategy.
Credit value adjustment (CVA) is an adjustment to an existing trading price based on the counterparty-risk premium. Currently, CVA is computed with an implicit assumption that the replacement contract is default-free after the original counterparty defaults, with the assumption that those trades will not re-assigned. In the actual counterparty default settlement, it is the norm that trades will be re-assigned, especially on the buy side. Since the counterparty of the replacement contract could also default within the lifetime of an existing contract, ignoring the possibility of counterparty defaults of replacement contracts will either under or over estimate the cost of the risk. An important practical question is, therefore, how to estimate under/over pricing of CVA under current practice. In this paper, we considered the pricing of credit contingent interest rate swap (CCIRS) or credit contingent default swap (CCDS), which is considered the CVA hedge for interest rate swaps (IRS). We derived partial differential Eqs. (PDEs) satisfied by the approximated CVA with the assumption that the replacement contracts do not default. For comparison purposes, we also derived the PDEs for the cost of CVA by relaxing the assumption of default-free replacement contracts with a finite number of counterparty defaults. It shows that the no-default and two default cases can be derived within the same analytical solution framework, similar to the Funding Valuation Adjustment (FVA) problem where continuous funding is a reasonable assumption. The finite number of default case is non-trivial. The PDE for the two default case is derived in this paper. We calibrate our model based on market data and carry out extensive computations for the purpose of comparing these three CVAs. Our basic finding is that the values of the two CVAs are close for top rated counterparties. On the other hand, for counterparties with lower credit ratings, the difference among the two CVAs can be significant.
A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. Using a standard method (Matlab function fminsearch) to calculate the parameter values led to unacceptable run times or non-convergence. Consequently we developed an algorithm which first finds the most important model parameters and uses these as a basis for a four stage process which accurately determines all parameter values. This process is then applied to data from three ICU patients. Good agreement between the model and measured arterial pressure is demonstrated in all cases.
A model is presented for the gravity-driven flow of rainwater descending through the soil layer of a green roof, treated as a porous medium on a flat permeable surface representing an efficient drainage layer. A fully saturated zone is shown to occur. It is typically a thin layer, relative to the total soil thickness, and lies at the bottom of the soil layer. This provides a bottom boundary condition for the partially saturated upper zone. It is shown that after the onset of rainfall, well-defined fronts of water can descend through the soil layer. Also the rainwater flow is relatively quick compared with the moisture uptake by the roots of the plants in the roof. In separate models the exchanges of water are described between the (smaller-scale) porous granules of soil, the roots and the rainwater in the inter-granule pores.
