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"optimal control theory"

Ehsan Shakeri, Gholamreza Latif-Shabgahi, Amir Esmaeili Abharian
In recent years, many efforts have been made to present optimal strategies for cancer therapy through the mathematical modelling of tumour-cell population dynamics and optimal control theory. In many cases, therapy effect is included in the drift term of the stochastic Gompertz model. By fitting the model with empirical data, the parameters of therapy function are estimated. The reported research works have not presented any algorithm to determine the optimal parameters of therapy function. In this study, a logarithmic therapy function is entered in the drift term of the Gompertz model...
April 2018: IET Systems Biology
Soyoung Kim, Aurelio A de Los Reyes, Eunok Jung
Tuberculosis (TB) is the sixth leading cause of morbidity and mortality in the Philippines. Although significant progress has been made in the detection and cure of TB under the Directly Observed Treatment Short Course, battling against the disease is still a burdensome task. It demands a concerted effort for specific and effective interventions. In this work, a mathematical TB model fitted to the Philippine data is developed to understand its transmission dynamics. Different control strategies such as distancing, latent case finding, case holding, active case finding controls, and combinations thereof are investigated within the framework of optimal control theory...
January 31, 2018: Journal of Theoretical Biology
Amit Ron, Evren U Azeloglu, Rhodora C Calizo, Mufeng Hu, Smiti Bhattacharya, Yibang Chen, Gomathi Jayaraman, Sunwoo Lee, Susana R Neves-Zaph, Hong Li, Ronald E Gordon, John C He, James C Hone, Ravi Iyengar
The shape of a cell within tissues can represent the history of chemical and physical signals that it encounters, but can information from cell shape regulate cellular phenotype independently? Using optimal control theory to constrain reaction-diffusion schemes that are dependent on different surface-to-volume relationships, we find that information from cell shape can be resolved from mechanical signals. We used microfabricated 3-D biomimetic chips to validate predictions that shape-sensing occurs in a tension-independent manner through integrin β3 signaling pathway in human kidney podocytes and smooth muscle cells...
December 15, 2017: Nature Communications
Evans Otieno Omondi, Titus Okello Orwa, Farai Nyabadza
In this paper, we present a model for onchocerciasis that considers mass administration of ivermectin, contact prevention controls and vector elimination. The model equilibria are computed and stability analysis carried out in terms of the basic reproduction number R0 . The model is found to exhibit a backward bifurcation so that for R0 less than unity is not sufficient to eradicate the disease from the population and the need is to lower R0 to below a certain threshold, R0 c for effective disease control. The model is fitted to data on individuals with onchocerciasis in Ghana...
March 2018: Mathematical Biosciences
Inkyung Ahn, Seongman Heo, Seunghyun Ji, Kyung Hyun Kim, Taehwan Kim, Eun Joo Lee, Jooyoung Park, Keehoon Sung
Much concern has arisen regarding serious epidemics due to the Middle East Respiratory Syndrome (MERS) coronavirus. The first MERS case of Korea was reported on 20 May 2015, and since then, the MERS outbreak in Korea has resulted in hundreds of confirmed cases and tens of deaths. Deadly infectious diseases such as MERS have significant direct and indirect social impacts, which include disease-induced mortality and economic losses. Also, a delayed response to the outbreak and underestimating its danger can further aggravate the situation...
October 12, 2017: Journal of Theoretical Biology
Dal Hyung Kim, Jungsoo Kim, João C Marques, Abhinav Grama, David G C Hildebrand, Wenchao Gu, Jennifer M Li, Drew N Robson
Calcium imaging with cellular resolution typically requires an animal to be tethered under a microscope, which substantially restricts the range of behaviors that can be studied. To expand the behavioral repertoire amenable to imaging, we have developed a tracking microscope that enables whole-brain calcium imaging with cellular resolution in freely swimming larval zebrafish. This microscope uses infrared imaging to track a target animal in a behavior arena. On the basis of the predicted trajectory of the animal, we applied optimal control theory to a motorized stage system to cancel brain motion in three dimensions...
November 2017: Nature Methods
Dan-Qing Liu, Zhen-Qiang Wu, Yu-Xin Wang, Qiang Guo, Jian-Guo Liu
Accurately describing the knowledge dissemination process is significant to enhance the performance of personalized education. In this study, considering the effect of periodic teaching activities on the learning process, we propose a periodic impulsive knowledge dissemination system to regenerate the knowledge dissemination process. Meanwhile, we put forward learning effectiveness which is an outcome of a trade-off between the benefits and costs raised by knowledge dissemination as objective function. Further, we investigate the optimal teaching strategy which can maximize learning effectiveness, to obtain the optimal effect of knowledge dissemination affected by the teaching activities...
2017: PloS One
Vincent Renault, Michèle Thieullen, Emmanuel Trélat
We use conductance based neuron models, and the mathematical modeling of optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals, and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls...
June 29, 2017: Journal of Mathematical Biology
K R Nandipati, Z Lan, H Singh, S Mahapatra
A first principles quantum dynamics study of N-H photodissociation of pyrrole on the S0-(1)πσ(*)(A21) coupled electronic states is carried out with the aid of an optimally designed UV-laser pulse. A new photodissociation path, as compared to the conventional barrier crossing on the πσ*1 state, opens up upon electronic transitions under the influence of pump-dump laser pulses, which efficiently populate both the dissociation channels. The interplay of electronic transitions due both to vibronic coupling and the laser pulse is observed in the control mechanism and discussed in detail...
June 7, 2017: Journal of Chemical Physics
Hamadjam Abboubakar, Jean Claude Kamgang, Leontine Nkague Nkamba, Daniel Tieudjo
In this paper, we derive and analyse a model for the control of arboviral diseases which takes into account an imperfect vaccine combined with some other control measures already studied in the literature. We begin by analysing the basic model without control. We prove the existence of two disease-free equilibrium points and the possible existence of up to two endemic equilibrium points (where the disease persists in the population). We show the existence of a transcritical bifurcation and a possible saddle-node bifurcation and explicitly derive threshold conditions for both, including defining the basic reproduction number, [Formula: see text], which provides whether the disease can persist in the population or not...
June 6, 2017: Journal of Mathematical Biology
Paul Coote, Clemens Anklin, Walter Massefski, Gerhard Wagner, Haribabu Arthanari
We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame...
August 2017: Journal of Magnetic Resonance
Giorgio Gnecco, Alberto Bemporad, Marco Gori, Marcello Sanguineti
Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with the classical linear quadratic gaussian (LQG) optimal control problem, of which the proposed learning paradigm is a nontrivial variation as it involves random matrices, are investigated. The obtained optimal solutions are compared with the Kalman filter estimate of the parameter vector to be learned...
May 31, 2017: Neural Computation
Pauline M Lefebvre, Eric Van Reeth, Hélène Ratiney, Olivier Beuf, Elisabeth Brusseau, Simon A Lambert, Steffen J Glaser, Dominique Sugny, Denis Grenier, Kevin Tse Ve Koon
This paper investigates the use of Optimal Control (OC) theory to design Radio-Frequency (RF) pulses that actively control the spatial distribution of the MRI magnetization phase. The RF pulses are generated through the application of the Pontryagin Maximum Principle and optimized so that the resulting transverse magnetization reproduces various non-trivial and spatial phase patterns. Two different phase patterns are defined and the resulting optimal pulses are tested both numerically with the ODIN MRI simulator and experimentally with an agar gel phantom on a 4...
May 22, 2017: Journal of Magnetic Resonance
Panayiotis Christodoulides, Yoshito Hirata, Elisa Domínguez-Hüttinger, Simon G Danby, Michael J Cork, Hywel C Williams, Kazuyuki Aihara, Reiko J Tanaka
Atopic dermatitis (AD) is a common chronic skin disease characterized by recurrent skin inflammation and a weak skin barrier, and is known to be a precursor to other allergic diseases such as asthma. AD affects up to 25% of children worldwide and the incidence continues to rise. There is still uncertainty about the optimal treatment strategy in terms of choice of treatment, potency, duration and frequency. This study aims to develop a computational method to design optimal treatment strategies for the clinically recommended 'proactive therapy' for AD...
June 28, 2017: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Brittany Stephenson, Cristina Lanzas, Suzanne Lenhart, Judy Day
The spore-forming, gram-negative bacteria Clostridium difficile can cause severe intestinal illness. A striking increase in the number of cases of C. difficile infection (CDI) among hospitals has highlighted the need to better understand how to prevent the spread of CDI. In our paper, we modify and update a compartmental model of nosocomial C. difficile transmission to include vaccination. We then apply optimal control theory to determine the time-varying optimal vaccination rate that minimizes a combination of disease prevalence and spread in the hospital population as well as cost, in terms of time and money, associated with vaccination...
December 2017: Journal of Mathematical Biology
Eric Van Reeth, Hélène Ratiney, Michael Tesch, Denis Grenier, Olivier Beuf, Steffen J Glaser, Dominique Sugny
This work investigates the use of MRI radio-frequency (RF) pulses designed within the framework of optimal control theory for image contrast optimization. The magnetization evolution is modeled with Bloch equations, which defines a dynamic system that can be controlled via the application of the Pontryagin Maximum Principle (PMP). This framework allows the computation of optimal RF pulses that bring the magnetization to a given state to obtain the desired contrast after acquisition. Creating contrast through the optimal manipulation of Bloch equations is a new way of handling contrast in MRI, which can explore the theoretical limits of the system...
April 21, 2017: Journal of Magnetic Resonance
Andress Laan, Raul Gil de Sagredo, Gonzalo G de Polavieja
Animals moving in groups coordinate their motion to remain cohesive. A large amount of data and analysis of movement coordination has been obtained in several species, but we are lacking theoretical frameworks that can derive the form of coordination rules. Here, we examine whether optimal control theory can predict the rules underlying social interactions from first principles. We find that a control rule which is designed to minimize the time it would take a pair of schooling fish to form a cohesively moving unit correctly predicts the characteristics of social interactions in fish...
April 12, 2017: Proceedings. Biological Sciences
Jung Eun Kim, Hyojung Lee, Chang Hyeong Lee, Sunmi Lee
Emerging and re-emerging dengue fever has posed serious problems to public health officials in many tropical and subtropical countries. Continuous traveling in seasonally varying areas makes it more difficult to control the spread of dengue fever. In this work, we consider a two-patch dengue model that can capture the movement of host individuals between and within patches using a residence-time matrix. A previous two-patch dengue model without seasonality is extended by adding host demographics and seasonal forcing in the transmission rates...
2017: PloS One
Santanu Biswas, Abhishek Subramanian, Ibrahim M ELMojtaba, Joydev Chattopadhyay, Ram Rup Sarkar
Visceral leishmaniasis (VL) is a deadly neglected tropical disease that poses a serious problem in various countries all over the world. Implementation of various intervention strategies fail in controlling the spread of this disease due to issues of parasite drug resistance and resistance of sandfly vectors to insecticide sprays. Due to this, policy makers need to develop novel strategies or resort to a combination of multiple intervention strategies to control the spread of the disease. To address this issue, we propose an extensive SIR-type model for anthroponotic visceral leishmaniasis transmission with seasonal fluctuations modeled in the form of periodic sandfly biting rate...
2017: PloS One
Wanping Liu, Shouming Zhong
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. The aim of this paper is to understand the propagation mechanisms of web malware and the impact of human intervention on the spread of malicious hyperlinks. Considering the characteristics of web malware, a new differential epidemic model which extends the traditional SIR model by adding another delitescent compartment is proposed to address the spreading behavior of malicious links over networks...
February 10, 2017: Scientific Reports
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