Unknown Quantities Research Articles

Towards cross-Canada monitoring of the unregulated street drug supply

BackgroundThe well-being of people who use drugs (PWUD) continues to be threatened by substances of unknown type or quantity in the unregulated street drug supply. Current efforts to monitor the drug supply are limited in population reach and comparability. This restricts capacity to identify and develop measures that safeguard the health of PWUD. This study describes the development of a low-barrier system for monitoring the contents of drugs in the unregulated street supply. Early results for pilot sites are presented and compared across regions.MethodsThe drug content monitoring system integrates a low-barrier survey and broad spectrum urine toxicology screening to compare substances expected to be consumed and those actually in the drug supply. The system prototype was developed by harm reduction pilot projects in British Columbia (BC) and Montreal with participation of PWUD. Data were collected from harm reduction supply distribution site clients in BC, Edmonton and Montreal between May 2018–March 2019. Survey and urine toxicology data were linked via anonymous codes and analyzed descriptively by region for trends in self-reported and detected use.ResultsThe sample consisted of 878 participants from 40 sites across 3 regions. Reported use of substances, their detection, and concordance between the two varied across regions. Methamphetamine use was reported and detected most frequently in BC (reported: 62.8%; detected: 72.2%) and Edmonton (58.3%; 68.8%). In Montreal, high concordance was also observed between reported (74.5%) and detected (86.5%) cocaine/crack use. Among those with fentanyl detected, the percentage of participants who used fentanyl unintentionally ranged from 36.1% in BC, 78.6% in Edmonton and 90.9% in Montreal.ConclusionsThis study is the first to describe a feasible, scalable monitoring system for the unregulated drug supply that can contrast expected and actual drug use and compare trends across regions. The system used principles of flexibility, capacity-building and community participation in its design. Results are well-suited to meet the needs of PWUD and inform the local harm reduction services they rely on. Further standardization of the survey tool and knowledge mobilization is needed to expand the system to new jurisdictions.

Optimization model in the flexible manufacture

Flexible manufacturing shop is examined. Multilevel control system of the shop is built. The demands to the system construction are listed. The existing input information is insufficient for building of the inventory model, for choice and realization of the optimal model of the manufacture. By this reason the situation of the uncertainties is arise. For the purpose to find needed data and to receive necessary knowledge the following intelligence procedures are suggested: ”Pendulum” – for stock foundation and for construction of the inventory model, “Symmetry in the arithmetical progression” – to define the values of the coefficients with unknown quantities in the aim function of the optimal task. With the help of the procedure “Pendulum” the equal corteges of the quantum of time are building. Cortege of the quantum of time is the unit of the stock and the direction for selection of the kind of the optimization model. The optimization model of location is suggested to use. Building of the indicated models (they are small dimension and equal dimension) give the opportunity to organize the parallel calculations.

Fiscal Integration in an Experimental Union: How Path-Breaking Was the EU's Response to the COVID-19 Pandemic?

Fiscal Integration in an Experimental Union: How Path-Breaking Was the EU's Response to the COVID-19 Pandemic?

Type System Based Rational Lazy IDA*

Meta-reasoning can improve numerous search algorithms, but necessitates collection of statistics to be used as probability distributions, and involves restrictive meta-reasoning assumptions. The recently suggested scheme of type systems in search algorithms is used in this paper for collecting these statistics. The statistics are then used to better estimate the unknown quantity of expected regret of computing a heuristic in Rational Lazy IDA* (RLIDA*), and also facilitate a second improvement due to relaxing one of the unrealistic meta-reasoning assumptions in RLIDA*.

On the long-only minimum variance portfolio under single factor model

The minimum-variance portfolio (MVP) has become an essential part of modern portfolio theory, largely due to the availability of its analytical formula and its good out-of-sample performance. When extra constraints such as the long-only constraints are added, MVP in general does not admit an analytical formula anymore. An exceptional case is when the single-factor model holds among the securities considered. It is known that there exists a semi-closed form formula, which relies on an unknown quantity called the long-only beta threshold (βL). This note conducts a detailed study of βL and establishes its optimality property that it is the smallest among all possible thresholds. We also develop a simple bisection method for computing βL. Finally we include a mathematical proof for this semi-closed form formula. The results reported provide a deep understanding how the long-only MVP are constructed.

More Than Three Meals per Day

More Than Three Meals per Day

Stress intensity factors of square cracks in one-layered transversely isotropic halfspaces subject to internal expansion or tensile traction

This paper studies the stress intensity factors of square cracks horizontally placed in one-layered transversely isotropic halfspaces using the dual boundary element method (DBEM). This DBEM uses the point load fundamental solution of a transversely isotropic bi-material fullspace. On the uncracked boundary, the infinite boundary elements are used to consider the influence of the domain far from the crack. On the crack surface, special crack-front elements are introduced to capture the crack-tip behavior. The relative crack opening displacements on the crack surface are treated as unknown quantities. The crack opening displacements near the crack tip are used to calculate the stress intensity factors. Numerical results illustrate that the proposed method can obtain highly accurate results of the three stress intensity factors for the crack problems in one-layered transversely isotropic halfspaces. The square cracks in homogeneous or bi-material halfspaces under internal expansion or tensile traction are analyzed in detail. Results show that the material anisotropy of transversely isotropic materials exerts a strong influence on the stress intensity factors.

A Case of Heart Transplantation after Ischaemic Preconditioning

A case of successful heart transplantation from a donor that suffered an out of hospital cardiac arrest lasting approximately one hour is presented. The recipient, a 27-year-old female nurse, was diagnosed with arrhythmogenic right ventricular cardiomyopathy in 2012. The donor was a 24-year-old male who after consuming an unknown quantity of alcohol and cocaine aboard a yacht was found floating face-down in the sea. The patient to be pulseless and CPR commenced after 7 minutes. The length of time that he spent in the sea was unknown. Return of spontaneous circulation (ROSC) occurred after 20 minutes of CPR on site. However, the patient arrested again in the ambulance and CPR was performed until he arrived Hospital, still in cardiac arrest. The patient arrested three more times before achieving a stable circulation. He was transferred to the intensive care unit on high doses of Noradrenaline and Adrenaline to maintain an adequate mean arterial blood pressure. An initial echocardiogram (ECHO) revealed a hypocontractile left ventricle (LV) with an estimated ejection fraction (EF) of 30%.Over the following 3 days the patient’s cardiac function improved. He was weaned off inotropic support and a repeat ECHO showed a normal LV with an EF of 70%. A brain MRI showed diffuse swelling consistent with global hypoxic injury with wide areas of cortical and basal ganglia infarction. The patient’s parents gave their consent and he was offered for organ transplantation on day 6. The operation was successful, with the recipient making an uneventful recovery. She received immunosuppressive treatment with cyclosporine, prednisolone and azathioprine and experienced one episode of early mild rejection with full resolution. She remains well 8 months later.

Analysis of two Weibull populations under joint progressively hybrid censoring

Joint Type-I progressive hybrid censoring scheme has been proposed to terminate the life-test experiment at maximum time that the experimenter can afford to continue. This article deals with the problem of estimating the two Weibull population parameters with the same shape parameter under joint Type-I progressively hybrid censoring scheme on the two samples using maximum likelihood and Bayesian inferential approaches. Using Fisher information matrix, the two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are developed using squared-error loss function. Since the Bayes estimators cannot be expressed in closed forms, hence, Gibbs within Metropolis-Hastings algorithm is proposed to carry out the Bayes estimates and also to construct the corresponding credible intervals. Moreover, some popular joint censoring plans are generalized and can be obtained as a special cases from our results. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To determine the optimal progressive censoring plan, two different optimality criteria are considered. Finally, to show the applicability of the proposed methods in real phenomenon, a real-life data set is analyzed.

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system's radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. The DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

Rollover dynamics modelling and analysis of self-propelled combine harvester

This study investigated the rollover phenomenon of a self-propelled combine harvester during short-distance cross-region travel on a road. The mathematical model of the unsteady lateral multi-degree-of-freedom (multi-DOF) motion of the combine harvester was established with consideration to rear wheel steering, front wheel braking, wheel sideslip, and tyre lateral deflection. By carrying out complex kinematics analysis for the entire vehicle and rotational dynamics analysis for the wheels, the mathematical relationships among the lateral deflection angles of the tyres, the kinematic parameters of the combine harvester centroid, the steering angles of the rear wheels, and the speed components of the wheel centroids along their longitudinal directions were derived and used to transform the established mathematical model into a novel form that considers the steering angles and kinematic parameters as unknown quantities. The lateral load transfer ratio (LTR) model of the combine harvester was established to assess the harvester's rollover critical state. Finally, by considering the steering angles of the rear wheels and the braking torque of the front wheels as model inputs, the rollover mechanism and effects of the structural geometry, steering angles, and braking torque on the LTR of the combine harvester were revealed through numerical calculation, and the safety intervals of the parameters were obtained. The results obtained by this study can provide theoretical and technical support for the dynamic design, control, and rollover protection of combine harvesters. • The rear-wheel steering instability analysis method of a combine is proposed. • An unsteady lateral motion model of the combine is established. • Mathematical relationships among the multiple kinematic parameters are established. • The parameter effects and rollover mechanism of the combine are revealed. • Results give a theoretical basis to the anti-rollover design, control and warning.

Multiple Leak Detection in Water Distribution Networks Following Seismic Damage

Water pipe leaks due to seismic damage are more difficult to detect than bursts, and such leaks, if not repaired in a timely manner, can eventually reduce supply pressure and generate both pollutant penetration risks and economic losses. Therefore, leaks must be promptly identified, and damaged pipes must be replaced or repaired. Leak-detection using equipment in the field is accurate; however, it is a considerably labor-intensive process that necessitates expensive equipment. Therefore, indirect leak detection methods applicable before fieldwork are necessary. In this study, a computer-based, multiple-leak-detection model is developed. The proposed technique uses observational data, such as the pressure and flow rate, in conjunction with an optimization method and hydraulic analysis simulations, to improve detection efficiency (DE) for multiple leaks in the field. A novel approach is proposed, i.e., use of a cascade and iteration search algorithms to effectively detect multiple leaks (with the unknown locations, quantities, and sizes encountered in real-world situations) due to large-scale disasters, such as earthquakes. This method is verified through application to small block-scale water distribution networks (WDNs), and the DE is analyzed. The proposed detection model can be used for efficient leak detection and the repair of WDNs following earthquakes.

LAMB’S PROBLEM AND CHARACTERISTIC OF ENERGY TRANSMISSION IN UNSATURATED HALF-SPACE

Because unsaturated soil is widely distributed on the earth’s surface, when the traditional saturated two-phase medium theory is used for dynamic analysis, the results are often inconsistent with the actual situation. Aiming at this problem, this paper takes unsaturated elastic half-space as the research object, firstly based on continuum mechanics and porous media theory, and then considers the basic equations of mass conservation equation, momentum conservation equation, constitutive equation and effective stress principle of each phase in unsaturated porous media, and finally, we established a dynamic control equation in which skeleton displacement, pore water pressure and pore gas pressure are basically unknown quantities. Aiming at the dynamic response and energy transmission of the unsaturated half-space surface under the action of vertical concentrated harmonic loads, an axisymmetric calculation model of the classical Lamb problem in the frequency domain is established. The Helmholtz decomposition method is used and the displacement component of the skeleton uses the potential function Φ and Ψ to represent, and combined with the constitutive equation, the analytical solutions of physical quantities such as the displacement field and energy field of the half-space surface under different boundary conditions are obtained. Finally, influencing factors such as load parameters (excitation frequency) and material parameters (saturation, permeability coefficient) are analyzed and discussed through numerical examples. The results show that: (1) An increase in saturation or a decrease in excitation frequency will increase the surface displacement amplitude of the unsaturated half-space; (2) When the permeability coefficient drops to a critical value, the surface displacement amplitude will tend to a limit value, and the influence of permeability coefficient under permeable (gas) boundary and impermeable (gas) boundary conditions shows obvious difference.

Partial wave basis adapted to exterior boundary conditions of an elastic plate

An approach to describing normal elastic vibration modes in confined systems is presented. In a standard treatment of the problem, the displacement field is represented by a superposition of partial waves of a general form, e.g., plane waves. The unknown coefficients of superposition are then obtained from the equation of motion and the full set of boundary conditions. In the proposed approach, the functional form of partial waves is chosen in such a way as to satisfy the boundary conditions on exterior surfaces identically, i.e., even if the unknown quantities determined by the remaining constraints are found in an approximation, numerically or analytically. Some examples of solutions for composite elastic plates are discussed to illustrate the efficiency of the approach and its relevance for applications.

Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot’s consolidation model

We consider the quasi-static Biot’s consolidation model in a three-field formulation with the three unknown physical quantities of interest being the displacement u of the solid matrix, the seepage velocity v of the fluid and the pore pressure p. As conservation of fluid mass is a leading physical principle in poromechanics, we preserve this property using an H(div)-conforming ansatz for u and v together with an appropriate pressure space. This results in Stokes and Darcy stability and exact, that is, pointwise mass conservation of the discrete model.The proposed discretization technique combines a hybridized discontinuous Galerkin method for the elasticity subproblem with a mixed method for the flow subproblem, also handled by hybridization. The latter allows for a static condensation step to eliminate the seepage velocity from the system while preserving mass conservation. The system to be solved finally only contains degrees of freedom related to u and p resulting from the hybridization process and thus provides, especially for higher-order approximations, a very cost-efficient family of physics-oriented space discretizations for poroelasticity problems.We present the construction of the discrete model, theoretical results related to its uniform well-posedness along with optimal error estimates and parameter-robust preconditioners as a key tool for developing uniformly convergent iterative solvers. Finally, the cost-efficiency of the proposed approach is illustrated in a series of numerical tests for three-dimensional test cases.

Solving inverse problems in stochastic models using deep neural networks and adversarial training

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. We demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.

The Bistatic Radar as an Effective Tool for Detecting and Monitoring the Presence of Phytoplankton on the Ocean Surface

A massive dust storm formed over the Sahara Desert in June 2020. The African dust cloud, which traveled over the tropical Atlantic’s main development region for hurricanes, resulted in the highest aerosol optical thickness (AOT) for the past two decades. Dust particles contained in dust clouds are at some point deposited on the ocean surface, impacting the ocean biogeochemistry through the supply of nutrients. Although there are remote sensing systems that can map the AOT, the locations of the aerosol particles deposited on the ocean surface remain unknown quantities with remote sensing measurements. In addition, the supplied nutrients are not static and are displaced by ocean currents. Nutrients trigger the phytoplankton (algae) blooms, which form a film on the ocean surface and affect the ocean surface tension. The change in ocean surface tension causes a local decrease of ocean surface roughness over the areas covered with phytoplankton. Bistatic radar data from the CYclone Global Navigation Satellite System (CYGNSS) mission can detect changes in the ocean surface roughness, expressed as an increase in reflectivity when the surface becomes smoother. Therefore, decreased ocean surface roughness correlated with a recent dust storm represents a key indicator of the presence of phytoplankton. In this paper, we present for the first time the capability of bistatic radar measurements to provide an effective tool to map information of areas covered with phytoplankton, establishing bistatic radar as the most reliable remote sensing tool for detecting phytoplankton blooms and monitoring their presence across the ocean surface. We present the analysis of low ocean roughness signatures in the bistatic radar measurements from the CYGNSS mission observed in the Gulf of Mexico after the Sahara’s dust storm circulation from Africa to the American continent from May to July 2020. CYGNSS data offer an unprecedented spatial and temporal coverage that allows for the analysis of those signatures at time scales of 1-day, robust to the presence of clouds and dust clouds. The described capability benefits the improvement of models, promoting a better constraint of the supply of dust into the ocean surface and a better understanding of the excess of nutrients that triggers the phytoplankton blooms. This new bistatic radar application enhances our understanding on the role of dust storms on ocean biogeochemistry and the global carbon cycle.

Robust optimal control for a batch nonlinear enzyme-catalytic switched time-delayed process with noisy output measurements

In this paper, we consider a nonlinear switched time-delayed (NSTD) system with an unknown time-varying function describing the batch culture. The output measurements are noisy. According to the actual fermentation process, this time-varying function appears in the form of a piecewise-linear function with unknown kinetic parameters and switching times. The quantitative definition of biological robustness is given to overcome the difficulty of accurately measuring intracellular material concentrations. Our main goal is to estimate these unknown quantities by using noisy output measurements and biological robustness. This estimation problem is formulated as a robust optimal control problem (ROCP) governed by the NSTD system subject to continuous state inequality constraints. The ROCP is approximated as a sequence of nonlinear programming subproblems by using some techniques. Due to the highly complex nature of these subproblems, we propose a hybrid parallel algorithm, based on Nelder–Mead method, simulated annealing and the gradients of the constraint functions, for solving these subproblems. The paper concludes with simulation results.

Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems

‎This paper presents a numerical fuzzy indirect method based on the fuzzy basis functions technique to solve an optimal control problem governed by Poisson's differential equation‎. The considered problem may or may not be accompanied by a control box constraint‎. ‎The first-order necessary optimality conditions have been derived, which may contain a variational inequality in function space‎. ‎In the presented method‎, ‎the obtained optimality conditions have been discretized using fuzzy basis functions and a system of equations introduced as the discretized optimality conditions‎. ‎The derived system mostly contains some nonsmooth equations and conventional system solvers fail to solve it‎. A fuzzy-system-based semi-smooth Newton method has also been introduced‎ ‎to deal with the obtained system‎. ‎Solving optimality systems by the presented method gets us unknown fuzzy quantities on the state and control fuzzy expansions‎. ‎Finally‎, ‎some test problems‎ ‎have been studied to demonstrate the efficiency and accuracy of the presented fuzzy numerical technique‎.

On the solvability of a nonlinear difference boundary value problem in the case of parametric resonance

We construct necessary and sufficient conditions for the existence of solution of seminonlinear boundary value problem for a parametric excitation system of difference equations. The convergent iteration algorithms for the construction of the solutions of the semi-nonlinear boundary value problem for a parametric excitation system difference equations in the critical case have been found. The investigation of periodic and Noetherian boundary-value problems in the critical cases is traditionally performed under the assumption that the differential equation and boundary conditions are known and fixed. As a rule, the study of periodic problems in the case of parametric resonance is reduced to the investigation of the problems of stability. At the same time, due to numerous applications in electronics, geodesy, plasma theory, nonlinear optics, mechanics, and machine-building, the analysis of periodic boundary-value problems in the case of parametric resonance requires not only to find the solutions but also to determine the eigenfunctions of the corresponding differenсе equation. The investigation of autonomous Noetherian boundary-value problems is also reduced to the study of Noetherian boundary-value problems in the case of parametric resonance because the change of the independent variable in the critical case gives a nonautonomous boundary-value problem with an additional unknown quantity. The aim of the present paper is to construct the solutions of Noetherian boundary-value problems in the case of parametric resonance whose solvability is guaranteed by the corresponding choice of the eigenfunction of the analyzed boundary-value problem. The applied classification of Noetherian boundary-value prob\-lems in the case of parametric resonance depending on the simplicity or multiplicity of roots of the equation for generating constants noticeably differs from a similar classification of periodic problems in the case of parametric resonance and corresponds to the general classification of periodic and Noetherian boundary-value problems. The equation for generating constants obtained for the Noetherian boundary-value problems in the case of parametric resonance strongly differs from the conventional equation for generating constants in the absence of parametric resonance by the dependence both of the equation and of its roots on a small parameter, which leads to noticeable corrections of the approximate solutions as compared with the approximations obtained by the Poincare method. Using the convergent iteration algorithms we expand solution of seminonlinear two-point boundary value problem for a parametric excitation Mathieu type difference equation in the neighborhood of the generating solution. Estimates for the value of residual of the solutions of the seminonlinear two-point boundary value problem for a parametric excitation Mathieu type difference equation are found.