Mobile Stroke Units (MSUs) are specialized ambulances that can diagnose and treat stroke patients; hence, reducing the time to treatment for stroke patients. Optimal placement of MSUs in a geographic region enables to maximize access to treatment for stroke patients. We contribute a mathematical model to optimally place MSUs in a geographic region. The objective function of the model takes the tradeoff perspective, balancing between the efficiency and equity perspectives for the MSU placement. Solving the optimization problem enables to optimize the placement of MSUs for the chosen tradeoff between the efficiency and equity perspectives. We applied the model to the Blekinge and Kronoberg counties of Sweden to illustrate the applicability of our model. The experimental findings show both the correctness of the suggested model and the benefits of placing MSUs in the considered regions.
A mobile stroke unit (MSU) is a special type of ambulance, where stroke patients can be diagnosed and provided intravenous treatment, hence allowing to cut down the time to treatment for stroke patients. We present a discrete event simulation (DES) model to study the potential benefits of using MSUs in the southern health care region of Sweden (SHR). We included the activities and actions used in the SHR for stroke patient transportation as events in the DES model, and we generated a synthetic set of stroke patients as input for the simulation model. In a scenario study, we compared two scenarios, including three MSUs each, with the current situation, having only regular ambulances. We also performed a sensitivity analysis to further evaluate the presented DES model. For both MSU scenarios, our simulation results indicate that the average time to treatment is expected to decrease for the whole region and for each municipality of SHR. For example, the average time to treatment in the SHR is reduced from 1.31h in the baseline scenario to 1.20h and 1.23h for the two MSU scenarios. In addition, the share of stroke patients who are expected to receive treatment within one hour is increased by a factor of about 3 for both MSU scenarios.
The numerical simulation of the induction heating process can be computationally expensive, especially if ferromagnetic materials are studied. There are several analytical models that describe the electromagnetic phenomena. However, these are very limited by the geometry of the coil and the workpiece. Thus, the usual method for computing more complex systems is to use the finite element method to solve the set of equations in the multiphysical system, but this easily becomes very time consuming. This paper deals with the problem of solving a coupled electromagnetic - thermal problem with higher computational efficiency. For this purpose, a semi-analytical modeling strategy is proposed, that is based on an initial finite element computation, followed by the use of analytical electromagnetic equations to solve the coupled electromagnetic-thermal problem. The usage of the simplified model is restricted to simple geometrical features such as flat or curved surfaces with great curvature to skin depth ratio. Numerical and experimental validation of the model show an average error between 0.9% and 4.1% in the prediction of the temperature evolution, reaching a greater accuracy than other analyzed commercial softwares. A 3D case of a double-row large size ball bearing is also presented, fully validating the proposed approach in terms of computational time and accuracy for complex industrial cases.
We prove that the minimum line covering problem and the minimum guard covering problem restricted to 2-link polygons are APX-hard.
We investigate parallel searching on $m$ concurrent rays. We assume that a target $t$ is located somewhere on one of the rays; we are given a group of $m$ point robots each of which has to reach $t$. Furthermore, we assume that the robots have no way of communicating over distance. Given a strategy $S$ we are interested in the competitive ratio defined as the ratio of the time needed by the robots to reach $t$ using $S$ and the time needed to reach $t$ if the location of $t$ is known in advance. If a lower bound on the distance to the target is known, then there is a simple strategy which achieves a competitive ratio of~9 --- independent of $m$. We show that 9 is a lower bound on the competitive ratio for two large classes of strategies if $m\geq 2$. If the minimum distance to the target is not known in advance, we show a lower bound on the competitive ratio of $1 + 2 (k + 1)^{k + 1} / k^k$ where $k = \left\lceil\log m\right\rceil$ where $\log$ is used to denote the base 2 logarithm. We also give a strategy that obtains this ratio.
In this paper we propose a Bayesian approach for describing the position distribution of the endocardium in cardiac ultrasound image sequences. The problem is formulated using a latent variable model, which represents the inside and outside of the endocardium, for which the posterior density is estimated. As the Rayleigh distribution has been previously shown to be a suitable model for blood and tissue in cardiac ultrasound image, we start our construction by assuming a Rayleigh mixture model and estimate its parameters by expectation maximization. The model is refined by incorporating priors for spatial and temporal smoothness, in the form of total variation, preferred shapes and position, by using the principal components and location distribution of manually segmented training shapes. The posterior density is sampled by a Gibbs method to estimate the expected latent variable image which we call the Bayesian Probability Map, since it describes the probability of pixels being classified as either heart tissue or within the endocardium. Our experiments showed promising results indicating the usefulness of the Bayesian Probability Maps for the clinician since, instead of producing a single segmenting curve, it highlights the uncertain areas and suggests possible segmentations.
We present a convex variational active contour model with shape priors, for spatio-temporal segmentation of the endocardium in 2D B-mode ultrasound sequences, which can be solved by Continuous Cuts. A four component (signal dropout, echocardiographic artifacts, blood and tissue) Rayleigh mixture model is proposed for modeling the inside and outside of the endocardium. The parameters of the mixture model are determined by Expectation Maximization, for the sequence. Annotated data is used to provide prior data, by which prior distributions for the inside and outside of the endocardium are constructed. Segmentation is then achieved by minimizing the Hellinger distance between prior and estimated distributions, under the constraints of a statistical shape prior built from principal eigenvectors of the annotated data. Since our model is convex, we can employ a fast optimization method: the Split-Bregman algorithm. Promising segmentation results and quantitative measures are provided.
In this paper we present the coupled active contours (CAC) model, which is applied to segmentation of the endocardium in ultrasonic images assuming Rayleigh distributed intensities. Comparative experiments, both real and synthetic, with a standard prior model are presented. In the CAC model the prior acts, by affine transformation, on the same image information as the active contour, in addition to the traditional interaction between prior and active contour. By this higher convergence rate and robustness, w.r.t artifacts and poor initialization, is achieved.
The accuracy of a numerical fission gas release algorithm developed by Forsberg and Massih for solving the problem of diffusive flow to a spherical grain boundary is analysed. Estimates of numerical errors are derived for both steady-state and time varying conditions. We also present a method through which the accuracy of the algorithm can be improved or optimised for most applications.
Boken behandlar programmering och beräkningar i Octave. Den vänder sig till en bred grupp av användare, från nybörjare som vill lära sig grunderna i programmering till mera vana användare som vill använda Octave för avancerade beräkningsuppgifter. Önskvärda förkunskaper är en inledande kurs i matematik på högskolenivå. Övningar finns efter varje kapitel.
It is shown that a minimum spanning tree of $n$ points in $R^d$ under any fixed $L_p$-metric, with $p=1,2,\ldots,\infty$, can be computed in optimal $O(T_d(n,n) )$ time in the algebraic computational tree model. $T_d(n,m)$ denotes the time to find a bichromatic closest pair between $n$ red points and $m$ blue points. The previous bound in the model was $O( T_d(n,n) \log n )$ and it was proved only for the $L_2$ (Euclidean) metric. Furthermore, for $d = 3$ it is shown that a minimum spanning tree can be found in $O(n \log n)$ time under the $L_1$ and $L_\infty$-metrics. This is optimal in the algebraic computation tree model. The previous bound was $O(n \log n \log \log n)$.
In this paper we determine the oxygen profile in a biofilm on suspended carriers in two ways: firstly by microelectrode measurements and secondly by a simple mathematical model. The Moving Bed Biofilm Reactor is well-established for wastewater treatment where bacteria grow as a biofilm on the protective surfaces of suspended carriers. The flat shaped BiofilmChipTM P was developed to allow good conditions for transport of substrates into the biofilm. Firstly, the oxygen profile was measured in situ the nitrifying biofilm with a microelectrode and secondly, the profile was simulated with a one-dimensional mathematical model. We refined a classical model by adding a dynamical tank equation, to connect the tank to the biofilm through the boundary conditions. This proved to be an important key in achieving relevant simulations. We also estimated the erosion parameter λ to increase the concordance between the measured and simulated profiles. Promising results have been obtained from our mathematical model. The accordance improved when simulating profiles without the boundary layer. Microelectrode measurements are a valuable tool in design of new suspended carriers.
We consider a mathematical model for the nitrification of municipal waste water in a moving bed biofilm reactor. The model consists of two interacting parts. The first part is an essentially one-dimensional mixed-culture biofilm model, based on the classical differential equation paradigm introduced by Wanner and Gujer (Biotech. Bioeng. 28, 1986). This part models nutrient transport, growth and internal composition of the bacterial film located on the inside of the individual AnoxKaldnes-carrier chips in the reactor. The second part of the model describes the nutrient concentrations in the reactor tank. Here we use the standard differential equations for a completely mixed (continuously stirred) reactor. The interaction between the two parts of the system is comprised in the boundary conditions, i.e. the nutrient concentrations at the biofilm-water interface.
Mathematical modeling of biofilm development has been an active research topic during the latest years. The main purpose of these models is to understand and predict biofilm growth and development. One of the first mathematical model was the so called Wanner-Gujer model, where a one-dimensional model capable of describing multiple species development was proposed. Later on, more advanced models, incorporating more dimensions, eps-production, cell-to-cell-signalling and other properties have been developed. The major obstacle when trying to predict biofilm development using these mathematical models is that a huge number of parameters are needed, such as parameters in the bacterial metabolism, growth and detachment rates. Some of these parameters are possible to measure in experimental conditions, but others are more difficult, such as the detachment rate. In this paper, we will propose a methodology for estimating parameters in mathematical models of biofilm development from comparison of model prediction and experimental data. The proposed method is based on parameter identification methods used in automatic control theory. We will especially focus on the determination of the detachment rate in the Wanner-Gujer model.
We present a fast algorithm for computing a watchman route in a simple polygon that is at most a constant factor longer than the shortest watchman route. The algorithm runs in $O(n\log n)$ time as compared to the best known algorithm that computes a shortest watchman route which runs in $O(n^6)$ time.
We consider the watchman route problem for a k-transmitter watchman: standing at point p in a polygon P, the watchman can see �∈� if ��¯ intersects P’s boundary at most k times—q is k-visible to p. Traveling along the k-transmitter watchman route, either all points in P or a discrete set of points �⊂� must be k-visible to the watchman. We aim for minimizing the length of the k-transmitter watchman route.
We show that even in simple polygons the shortest k-transmitter watchman route problem for a discrete set of points �⊂� is NP-complete and cannot be approximated to within a logarithmic factor (unless P=NP), both with and without a given starting point. Moreover, we present a polylogarithmic approximation for the k-transmitter watchman route problem for a given starting point and �⊂� with approximation ratio �(log2(|�|⋅�)loglog(|�|⋅�)log|�|) (with |�|=�).
We present new results on two types of guarding problems for polygons. For the first problem, we present an optimal linear time algorithm for computing a smallest set of points that guard a given shortest path in a simple polygon having 𝑛n edges. We also prove that in polygons with holes, there is a constant 𝑐>0c>0 such that no polynomial-time algorithm can solve the problem within an approximation factor of 𝑐log𝑛clogn, unless P=NP. For the second problem, we present a (𝑘+ℎ)(k+h)-FPT algorithm for computing a shortest tour that sees 𝑘k specified points in a polygon with ℎh holes. We also present a 𝑘k-FPT approximation algorithm for this problem having approximation factor 2‾√2. In addition, we prove that the general problem cannot be polynomially approximated better than by a factor of 𝑐log𝑛clogn, for some constant 𝑐>0c>0, unless P=NP.
Additive manufacturing (AM), also known as 3D-printing, has made it possible to produce components made of bulk metallic glass (BMG) which have remarkable properties compared to parts made of conventional alloys. A metallic glass is a metastable noncrystalline alloy that form if a melt is quenched with a sufficient cooling rate. Research on systems with low critical cooling rates have made the maximum dimensions of these alloys to grow to what is called BMG's. The high local cooling rate obtained during AM makes it in principle possible to bypass the dimension restrictions that otherwise have been present when creating these alloys but the procedure is complex. It is believed that oxygen impurities in the powder feedstock material used during AM of Zr-based alloys makes it favourable for nucleation of stable crystalline phases at lower activation energies which hinders fully glass features to develop. The purpose of this thesis is to investigate how the limiting solute concentration in the bulk of the AM produced alloy AMZ4 (Zr_{59.3}Cu_{28.8}Al_{10.4}Nb_{1.5}(at\%)) impact the nucleation. Using a numerical model based on classical nucleation theory (CNT) that couples the interfacial and long range fluxes makes it possible to study how impurities impact the nucleation event. However, missing oxygen dependent data makes this a study on how limiting solute impact the nucleation in AMZ4. The numerical model is validated against earlier work and the results obtained from the simulations on AMZ4 shows a strong connection between the nucleation event and the limiting solute concentration. Further investigations on phase separation energies and the production of concentration dependent time-temperature-transformation (TTT) diagrams are needed to fully describe the connection to oxygen concentration. Nevertheless, the implemented model captures important features that the classical model cannot describe which needs to be taken into account when describing the nucleation in AMZ4.