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This paper proposes a new framework for investigating neural signals sufficient for a conscious sensation of movement and their role in motor control. We focus on signals sufficient for proprioceptive awareness, particularly from muscle spindle activation and from primary motor cortex (M1). Our review of muscle vibration studies reveals that afferent signals alone can induce conscious sensations of movement. Similarly, studies employing peripheral nerve blocks suggest that efferent signals from M1 are sufficient for sensations of movement. On this basis, we show that competing theories of motor control assign different roles to sensation of movement. According to motor command theories, sensation of movement corresponds to an estimation of the current state based on afferent signals, efferent signals, and predictions. In contrast, within active inference architectures, sensations correspond to proprioceptive predictions driven by efferent signals from M1. The focus on sensation of movement provides a way to critically compare and evaluate the two theories. Our analysis offers new insights into the functional roles of movement sensations in motor control and consciousness.

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Non-pharmaceutical personal protective (NPP) measures such as face masks use, and hand and respiratory hygiene can be effective measures for mitigating the spread of aerosol/airborne diseases, such as COVID-19, in the absence of vaccination or treatment. However, the usage of such measures is constrained by their inherent perceived cost and effectiveness for reducing transmission risk. To understand the complex interaction of disease dynamics and individuals decision whether to adopt NPP or not, we incorporate evolutionary game theory into an epidemic model such as COVID-19. To compare how self-interested NPP use differs from social optimum, we also investigated optional control from a central planner's perspective. We use Pontryagin's maximum principle to identify the population-level NPP uptake that minimizes disease incidence by incurring the minimum costs. The evolutionary behavior model shows that NPP uptake increases at lower perceived costs of NPP, higher transmission risk, shorter duration of NPP use, higher effectiveness of NPP, and shorter duration of disease-induced immunity. Though social optimum NPP usage is generally more effective in reducing disease incidence than self-interested usage, our analysis identifies conditions under which both strategies get closer. Our model provides new insights for public health in mitigating a disease outbreak through NPP.

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The aim of the current study is to demonstrate the feasibility of radiofrequency (RF) pulses generated via an optimal control (OC) algorithm to perform magnetic resonance elastography (MRE) and quantify the mechanical properties of materials with very short transverse relaxation times (T2 < 5 ms) for the first time. OC theory applied to MRE provides RF pulses that bring isochromats from the equilibrium state to a fixed target state, which corresponds to the phase pattern of a conventional MRE acquisition. Such RF pulses applied with a constant gradient allow to simultaneously perform slice selection and motion encoding in the slice direction. Unlike conventional MRE, no additional motion-encoding gradients (MEGs) are needed, enabling shorter echo times. OC pulses were implemented both in turbo spin echo (OC rapid acquisition with refocused echoes [RARE]) and ultrashort echo time (OC UTE) sequences to compare their motion-encoding efficiency with the conventional MEG encoding (classical MEG MRE). MRE experiments were carried out on agar phantoms with very short T2 values and on an ex vivo bovine tendon. Magnitude images, wave field images, phase-to-noise ratio (PNR), and shear storage modulus maps were compared between OC RARE, OC UTE, and classical MEG MRE in samples with different T2 values. Shear storage modulus values of the agar phantoms were in agreement with values found in the literature, and that of the bovine tendon was corroborated with rheometry measurements. Only the OC sequences could encode motion in very short T2 samples, and only OC UTE sequences yielded magnitude images enabling proper visualization of short T2 samples and tissues. The OC UTE sequence produced the best PNRs, demonstrating its ability to perform anatomical and mechanical characterization. Its success warrants in vivo confirmation in further studies.

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Bortezomib and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts protein degradation in cells, leading to the accumulation of unfolded proteins that induce apoptosis. On the other hand, virotherapy uses genetically modified oncolytic viruses (OVs) to infect cancer cells, trigger cell lysis, and activate anti-tumor response. Despite progress in cancer treatment, identifying administration protocols for therapeutic agents remains a significant concern, aiming to strike a balance between efficacy, minimizing toxicity, and administrative costs. In this work, optimal control theory was employed to design a cost-effective and efficient co-administration protocols for bortezomib and OVs that could significantly diminish the population of cancer cells via the cell death program with the NF$ \kappa $B-BAX-RIP1 signaling network. Both linear and quadratic control strategies were explored to obtain practical treatment approaches by adapting necroptosis protocols to efficient cell death programs. Our findings demonstrated that a combination therapy commencing with the administration of OVs followed by bortezomib infusions yields an effective tumor-killing outcome. These results could provide valuable guidance for the development of clinical administration protocols in cancer treatment.

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COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

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Phase contrast velocimetry relies on bipolar gradients to establish a direct and linear relationship between the phase of the magnetic resonance signal, and the corresponding fluid motion. Despite its utility, several limitations and drawbacks have been reported, the most important being the extended echo time due to the encoding after the excitation. In this study, we elucidate a new approach based on optimal control theory that circumvents some of these disadvantages. An excitation pulse, termed FAUCET (flow analysis under controlled encoding transients), is designed to encode velocity into phase already during the radiofrequency excitation. As a result of concurrent excitation and flow encoding, and hence elimination of post-excitation flow encoding, FAUCET achieves a shorter echo time than the conventional method. This achievement is a matter of significance not only because it decreases the loss of signal due to spin-spin relaxation and B0 inhomogeneity, but also because a shorter echo time is always preferred in order to reduce the dimensionless dephasing parameter and the required residence time of the flowing sample in the detection coil. The method is able to establish a non-linear bijective relationship between phase and velocity, which can be employed to enhance the resolution over a specific range of velocities, for example along flow boundaries. A computational comparison between the phase contrast and optimal control methods reveals that the latter's encoding is more robust against remnant higher-order-moment terms of the Taylor expansion for faster voxels, such as acceleration, jerk, and snap.

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The effects of habitat heterogeneity on a diffusing population are investigated here. We formulate a reaction-diffusion system of partial differential equations to analyze the effect of resource allocation in an ecosystem with resource having its own dynamics in space and time. We show a priori estimates to prove the existence of state solutions given a control. We formulate an optimal control problem of our ecosystem model such that the abundance of a single species is maximized while minimizing the cost of inflow resource allocation. In addition, we show the existence and uniqueness of the optimal control as well as the optimal control characterization. We also establish the existence of an optimal intermediate diffusion rate. Moreover, we illustrate several numerical simulations with Dirichlet and Neumann boundary conditions with the space domain in 1D and 2D.

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We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way. For classical control, we used the relative displacement between the ball and the trolley as the controller to study the anharmonic effect of the cartpole. Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range.

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Energy pumping is a way to gain kinetic energy based on an active vertical center of mass movement in rollers in sports like skateboarding, skicross, snowboard cross and BMX. While the principle of the energy transfer from the vertical movement to the horizontal movement is well understood, the question of how to achieve the optimal energy transfer is still unresolved. In this paper, we introduce an inverse pendulum model to describe the movement of the center of mass of an athlete performing energy pumping. On this basis, the problem of identifying the optimal movement pattern is formulated as an optimal control problem. We solve the discretized optimal control problem with the help of a SQP-algorithm. We uncover that the optimal movement pattern consists of a jumping, flying, and landing phase, which has to be timed precisely. We investigate how the maximal horizontal speed depends on parameters like rollers height and maximal normal force of the athlete. Additionally, we present a qualitative comparison of our results with measured results from BMX-racing. For athletes and coaches, we advice on the basis of our results that athlete's performance is optimized by using maximal force and adopt an exact and proper timing of the movement pattern.

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In response to the widespread adoption of vehicle-following systems in autonomous applications, the demand for collision warning to enable safer functionalities is increasing. This study provides an approach for automated vehicle guidance to follow the preceding vehicles longitudinally and puts emphasis on the performance of collision avoidance. The safety distance model is established, which contains a distance compensation algorithm to deal with the special case on curved roads. By introducing the algorithm of velocity and distance prediction, the collision risks are detected and measured in real time. The objective function is established based on optimal control theory to solve the desired following acceleration. The control system designed with the method of proportion integration differentiation combines throttle percentage and brake pressure as outputs to compensate acceleration. In the Carsim and Simulink co-simulation platform, the control system for longitudinal collision avoidance is simulated and analysed for four typical working conditions: the preceding vehicle drives at a constant speed on straight and curved roads, while the preceding vehicle drives at various speeds on straight and curved roads. The results validate the feasibility and effectiveness of the proposed method, which can be used for the longitudinal control of vehicle-following active collision avoidance.

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In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.

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We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.

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Motivated by regulating/eliminating the population of herbivorous pests, we investigate a discrete-time plant-herbivore model with two different constant control strategies (removal versus reduction), and formulate the corresponding optimal control problems when its dynamics exhibits varied types of bi-stability and fluctuating environments. We provide basic analysis and identify the critical factors to characterize the optimal controls and the corresponding plant-herbivore dynamics such as the control upper bound (the effectiveness level of the implementation of control measures) and the initial conditions of the plant and herbivore. Our results show that optimal control could be easier when the model has simple dynamics such as stable equilibrium dynamics under constant environment or the model exhibits chaotic dynamics under fluctuating environments. Due to bistability, initial conditions are important for optimal controls. Regardless of with or without fluctuating environments, initial conditions taken from the near the boundary makes optimal control easier. In general, the pest is hard to be eliminated when the control upper bound is not large enough. However, as the control upper bound is increased or the initial conditions are chosen from near the boundary of the basin of attractions, the pest can be manageable regardless of the fluctuating environments.

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Epidemics can particularly threaten certain sub-populations. For example, for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here, we use optimal control theory to identify strategies to optimally protect a 'high-value' sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding 'buffer region' can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high-value region is often optimal. However, priority should sometimes switch from the buffer region to the high-value region only as the local outbreak grows. We characterize how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.

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Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

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When someone masters a skill, their performance looks to us like second nature: it looks as if their actions are smoothly performed without explicit, knowledge-driven, online monitoring of their performance. Contemporary computational models in motor control theory, however, are instructionist: that is, they cast skillful performance as a knowledge-driven process. Optimal motor control theory (OMCT), as representative par excellence of such approaches, casts skillful performance as an instruction, instantiated in the brain, that needs to be executed-a motor command. This paper aims to show the limitations of such instructionist approaches to skillful performance. We specifically address the question of whether the assumption of control-theoretic models is warranted. The first section of this paper examines the instructionist assumption, according to which skillful performance consists of the execution of theoretical instructions harnessed in motor representations. The second and third sections characterize the implementation of motor representations as motor commands, with a special focus on formulations from OMCT. The final sections of this paper examine predictive coding and active inference-behavioral modeling frameworks that descend, but are distinct, from OMCT-and argue that the instructionist, control-theoretic assumptions are ill-motivated in light of new developments in active inference.

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The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented by u 1 ( t ) , u 2 ( t ) and u 3 ( t ) , respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge-Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.

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A dynamical system entrains to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input, the state converges to a unique equilibrium point for any initial condition. We consider the problem of maximizing a weighted average of the system's output along the periodic attractor. The gain of entrainment is the benefit achieved by using a non-constant periodic input relative to a constant input with the same time average. Such a problem amounts to optimal allocation of resources in a periodic manner. We formulate this problem as a periodic optimal control problem, which can be analysed by means of the Pontryagin maximum principle or solved numerically via powerful software packages. We then apply our framework to a class of nonlinear occupancy models that appear frequently in biological synthesis systems and other applications. We show that, perhaps surprisingly, constant inputs are optimal for various architectures. This suggests that the presence of non-constant periodic signals, which frequently appear in biological occupancy systems, is a signature of an underlying time-varying objective functional being optimized.

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The approved coronavirus disease (COVID-19) vaccines reduce the risk of disease by 70-95%; however, their efficacy in preventing COVID-19 is unclear. Moreover, the limited vaccine supply raises questions on how they can be used effectively. To examine the optimal allocation of COVID-19 vaccines in South Korea, we constructed an age-structured mathematical model, calibrated using country-specific demographic and epidemiological data. The optimal control problem was formulated with the aim of finding time-dependent age-specific optimal vaccination strategies to minimize costs related to COVID-19 infections and vaccination, considering a limited vaccine supply and various vaccine effects on susceptibility and symptomatology. Our results suggest that "susceptibility-reducing" vaccines should be relatively evenly distributed among all age groups, resulting in more than 40% of eligible age groups being vaccinated. In contrast, "symptom-reducing" vaccines should be administered mainly to individuals aged 20-29 and ≥60 years. Thus, our study suggests that the vaccine profile should determine the optimal vaccination strategy. Our findings highlight the importance of understanding vaccine's effects on susceptibility and symptomatology for effective public health interventions.