Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.     

Bio-economics of a renewable resource in a seasonally varying environment

In this paper we study the bio-economics of a renewable resource with governing dynamics described by two distinct growth functions (viz., logistic and Gompertz growth functions) in a seasonally varying environment. Seasonality is introduced into the system by taking the involved ecological parameters to be periodic. In this work, we establish a procedure to obtain the optimal path and compute the optimal effort policy which maximizes the net revenue to the harvester for a fairly general optimal control problem and apply this procedure to the considered models to derive some important conclusions. These problems are solved on the infinite horizon. We find that, for both the models, the optimal harvest policy and the corresponding optimal path are periodic after a finite time. We also obtain optimal solution, a suboptimal harvesting policy and the corresponding suboptimal approach path to reach this optimal solution. The key results are illustrated using numerical simulations and we compare the revenues to the harvester along the optimal and suboptimal paths. The general procedure developed in this work, for obtaining the optimal effort policy and the optimal path, has wider applicability.     

Investigation of optimal follower load path generated by trunk muscle coordination

It has been reported that the center of rotation of each vertebral body is located posterior to the vertebral body center. Moreover, it has been suggested that an optimized follower load (FL) acts posterior to the vertebral body center. However, the optimal position of the FL with respect to typical biomechanical characteristics regarding spinal stabilization, such as joint compressive force, shear force, joint moment, and muscle stress, has not been studied. A variation in the center of rotation of each vertebra was formulated in a three-dimensional finite element model of the lumbar spine with 117 pairs of trunk muscles. Then, the optimal translation of the FL path connecting the centers of rotations was estimated by solving the optimization problem that was to simultaneously minimize the compressive forces, the shear forces, and the joint moments or to minimize the cubic muscle stresses. An upright neutral standing position and a standing position with 200N in both hands were considered. The FL path moved posterior, regardless of the optimization criteria and loading conditions. The FL path moved 5.0 and 7.8mm posterior in upright standing and 4.1mm and 7.0mm posterior in standing with 200N in hands for each optimization scheme. In addition, it was presented that the optimal FL path may have advantages in comparison to the body center FL path. The present techniques may be important in understanding the spine stabilization function of the trunk muscles.     

Evaluation of a patient-specific cost function to predict the influence of foot path on the knee adduction torque during gait

A large external knee adduction torque during gait has been correlated with the progression of knee osteoarthritis (OA). Though foot path changes (e.g. toeing out) can reduce the adduction torque, no method currently exists to predict whether an optimal foot path exists for a specific patient. This study evaluates a patient-specific optimization cost function to predict how foot path changes influence both adduction torque peaks. Video motion and ground reaction data were collected from a patient with knee OA performing normal, toe out, and wide stance gait. Joint and inertial parameters in a dynamic, 27 degree-of-freedom, full-body gait model were calibrated to the patient's normal gait data. The model was then used in gait optimizations that predicted how the patient's adduction torque peaks would change due to changes in foot path. The cost function tracked the patient's normal gait data using weight factors calibrated to toe out gait and tested using wide stance gait. For both gait motions, the same cost function weights predicted the change in both adduction torque peaks to within 7% error. With further development, this approach may eventually permit the design of patient-specific rehabilitation procedures such as an optimal foot path for patients with knee OA.     

Grey-Theory-Based Optimization Model of Emergency Logistics Considering Time Uncertainty

Natural disasters occur frequently in recent years, causing huge casualties and property losses. Nowadays, people pay more and more attention to the emergency logistics problems. This paper studies the emergency logistics problem with multi-center, multi-commodity, and single-affected-point. Considering that the path near the disaster point may be damaged, the information of the state of the paths is not complete, and the travel time is uncertainty, we establish the nonlinear programming model that objective function is the maximization of time-satisfaction degree. To overcome these drawbacks: the incomplete information and uncertain time, this paper firstly evaluates the multiple roads of transportation network based on grey theory and selects the reliable and optimal path. Then simplify the original model under the scenario that the vehicle only follows the optimal path from the emergency logistics center to the affected point, and use Lingo software to solve it. The numerical experiments are presented to show the feasibility and effectiveness of the proposed method.     

Sensory feedback in a bump attractor model of path integration

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal’s current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal’s knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541–4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.     

A weighted constraint satisfaction approach to human goal-directed decision making

When we plan for long-range goals, proximal information cannot be exploited in a blindly myopic way, as relevant future information must also be considered. But when a subgoal must be resolved first, irrelevant future information should not interfere with the processing of more proximal, subgoal-relevant information. We explore the idea that decision making in both situations relies on the flexible modulation of the degree to which different pieces of information under consideration are weighted, rather than explicitly decomposing a problem into smaller parts and solving each part independently. We asked participants to find the shortest goal-reaching paths in mazes and modeled their initial path choices as a noisy, weighted information integration process. In a base task where choosing the optimal initial path required weighting starting-point and goal-proximal factors equally, participants did take both constraints into account, with participants who made more accurate choices tending to exhibit more balanced weighting. The base task was then embedded as an initial subtask in a larger maze, where the same two factors constrained the optimal path to a subgoal, and the final goal position was irrelevant to the initial path choice. In this more complex task, participants’ choices reflected predominant consideration of the subgoal-relevant constraints, but also some influence of the initially-irrelevant final goal. More accurate participants placed much less weight on the optimality-irrelevant goal and again tended to weight the two initially-relevant constraints more equally. These findings suggest that humans may rely on a graded, task-sensitive weighting of multiple constraints to generate approximately optimal decision outcomes in both hierarchical and non-hierarchical goal-directed tasks.     

Performance Evaluation of Shared Mesh Protection in WDM Networks

The efficient use of network capacity in shared restoration schemes strongly depends upon the path selection procedure. In this paper we propose and evaluate path selection algorithms for sharable and restorable connections in optical networks. Namely, two distributed path selection algorithms are proposed. The first approach maintains global information on network resource usage to determine link sharability and compute optimal shared paths. The second approach only relies upon local information maintained at each node. Subsequently, we present an analytical model to evaluate the performance of these path selection algorithms and show its accuracy through numerical examples. Results indicate that path selection algorithms that maximally exploit the use of reserved sharable channels do not necessarily result in fast restoration; rather these two optimality criteria can conflict most of the time. Additionally, algorithms that maximally exploit the sharability condition typically result in lower scalability and higher complexity.     

The most likely voltage path and large deviations approximations for integrate-and-fire neurons

We develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy integrate-and-fire (IF) neuron, given observations of the neuron’s superthreshold spiking activity. This optimal voltage path satisfies a second-order ordinary differential (Euler-Lagrange) equation which may be solved analytically in a number of special cases, and which may be solved numerically in general via a simple “shooting” algorithm. Our results are applicable for both linear and nonlinear subthreshold dynamics, and in certain cases may be extended to correlated subthreshold noise sources. We also show how this optimal voltage may be used to obtain approximations to (1) the likelihood that an IF cell with a given set of parameters was responsible for the observed spike train; and (2) the instantaneous firing rate and interspike interval distribution of a given noisy IF cell. The latter probability approximations are based on the classical Freidlin-Wentzell theory of large deviations principles for stochastic differential equations. We close by comparing this most likely voltage path to the true observed subthreshold voltage trace in a case when intracellular voltage recordings are available in vitro. Action Editor: Peter Latham     

Dynamically optimal strategies for managing resistance to genetically modified crops

This paper develops a dynamic model of the evolution of pest a population and pest resistance to characterize the socially optimal refuge strategy for managing a pest's resistance to genetically modified crops. Previous theoretical economic analyses of this problem focus on steady states; we also address refuge policies along the optimal path to the final equilibrium. To elaborate on our theoretical analysis of the resistance problem, we develop a simulation model calibrated to cotton (Gossypium spp.) production in China. Our results show the importance of fitness cost as a determinant of the qualitative nature of optimal refuge policies.     

The hippocampus as a cognitive graph

A theory of cognitive mapping is developed that depends only on accepted properties of hippocampal function, namely, long-term potentiation, the place cell phenomenon, and the associative or recurrent connections made among CA3 pyramidal cells. It is proposed that the distance between the firing fields of connected pairs of CA3 place cells is encoded as synaptic resistance (reciprocal synaptic strength). The encoding occurs because pairs of cells with coincident or overlapping fields will tend to fire together in time, thereby causing a decrease in synaptic resistance via long-term potentiation; in contrast, cells with widely separated fields will tend never to fire together, causing no change or perhaps (via long-term depression) an increase in synaptic resistance. A network whose connection pattern mimics that of CA3 and whose connection weights are proportional to synaptic resistance can be formally treated as a weighted, directed graph. In such a graph, a "node" is assigned to each CA3 cell and two nodes are connected by a "directed edge" if and only if the two corresponding cells are connected by a synapse. Weighted, directed graphs can be searched for an optimal path between any pair of nodes with standard algorithms. Here, we are interested in finding the path along which the sum of the synaptic resistances from one cell to another is minimal. Since each cell is a place cell, such a path also corresponds to a path in two-dimensional space. Our basic finding is that minimizing the sum of the synaptic resistances along a path in neural space yields the shortest (optimal) path in unobstructed two-dimensional space, so long as the connectivity of the network is great enough. In addition to being able to find geodesics in unobstructed space, the same network enables solutions to the "detour" and "shortcut" problems, in which it is necessary to find an optimal path around a newly introduced barrier and to take a shorter path through a hole opened up in a preexisting barrier, respectively. We argue that the ability to solve such problems qualifies the proposed hippocampal object as a cognitive map. Graph theory thus provides a sort of existence proof demonstrating that the hippocampus contains the necessary information to function as a map, in the sense postulated by others (O'Keefe, J., and L. Nadel. 1978. The Hippocampus as a Cognitive Map. Clarendon Press, Oxford, UK). It is also possible that the cognitive mapping functions of the hippocampus are carried out by parallel graph searching algorithms implemented as neural processes. This possibility has the great attraction that the hippocampus could then operate in much the same way to find paths in general problem space; it would only be necessary for pyramidal cells to exhibit a strong nonpositional firing correlate.     

A flat inclined modular photobioreactor for outdoor mass cultivation of photoautotrophs

A flat inclined modular photobioreactor (FIMP) for mass cultivation of photoautotrophic microorganisms is described. It consists of flat glass reactors connected in cascade facing the sun with the proper tilt angles to assure maximal exposure to direct beam radiation. The optimal cell density in reference to the length of the reactor light path was evaluated, and the effect of the tilt angle on utilization of both direct beam as well as diffuse sunlight was quantitatively assessed. The mixing mode and extent were also optimized in reference to productivity of biomass. The FIMP proved very successful in supporting continuous cultures of the tested species of photoautotrophs, addressing the major criteria involved in design optimization of photobioreactors: Made of fully transparent glass, inclined toward the sun and endowed with a high surface-to-volume ratio, it combines an optimal light path with a vigorous agitation system. The maximal exposure to the culture to solar irradiance as well as the substantial control of temperature facilitate, under these conditions, a particularly high, extremely light-limited optimal cell density. The integrated effects of these growth conditions resulted in record volumetric and areal output rates of Monodus subterraneus, Anabana siamensis, and Spirulina platensis. (c) 1996 John Wiley & Sons, Inc.     

A simple method to generate non-trivial alternate alignments of protein sequences

A major problem in sequence alignments based on the standard dynamic programming method is that the optimal path does not necessarily yield the best equivalencing of residues assessed by structural or functional criteria. An algorithm is presented that finds suboptimal alignments of protein sequences by a simple modification to the standard dynamic programming method. The standard pairwise weight matrix elements are modified in order to penalize, but not eliminate, the equivalencing of residues obtained from previous alignments. The algorithm thereby yields a limited set of alternate alignments that can differ considerably from the optimal. The approach is benchmarked on the alignments of immunoglobulin domains. Without a prior knowledge of the optimal choice of gap penalty, one of the suboptimal alignments is shown to be more accurate than the optimal.     

Local versus global optimal sports techniques in a group of athletes

Various optimization algorithms have been used to achieve optimal control of sports movements. Nevertheless, no local or global optimization algorithm could be the most effective for solving all optimal control problems. This study aims at comparing local and global optimal solutions in a multistart gradient-based optimization by considering actual repetitive performances of a group of athletes performing a transition move on the uneven bars. Twenty-four trials by eight national-level female gymnasts were recorded using a motion capture system, and then multistart sequential quadratic programming optimizations were performed to obtain global optimal, local optimal and suboptimal solutions. The multistart approach combined with a gradient-based algorithm did not often find the local solution to be the best and proposed several other solutions including global optimal and suboptimal techniques. The qualitative change between actual and optimal techniques provided three directions for training: to increase hip flexion–abduction, to transfer leg and arm angular momentum to the trunk and to straighten hand path to the bar.     

响应面法优化青枯病生防菌Hrp~-菌株的发酵条件

对工程菌Hrp-菌株的摇瓶发酵条件进行优化。首先采用Plackett-Burman设计法对影响Hrp-菌株活菌量的6个因素进行评价,筛选出具有显著效应的2个因素(发酵温度和摇床转速),再用最陡爬坡试验法接近重要因子的最优水平,最后应用中心组合设计确定重要因子的最优水平。确定优化后的发酵条件:初始pH 8.75、装液量为100 mL(500 mL三角瓶)、接种量6.25%、接种龄10 h、温度20℃、摇瓶转速205 r/min。实验结果表明:采用优化后的发酵条件,Hrp-菌株的发酵液菌量由最初的3.30×1010个/mL提高至4.42×1010个/mL,增幅为133.9%。     

Ant Navigation: Fractional Use of the Home Vector

Home is a special location for many animals, offering shelter from the elements, protection from predation, and a common place for gathering of the same species. Not surprisingly, many species have evolved efficient, robust homing strategies, which are used as part of each and every foraging journey. A basic strategy used by most animals is to take the shortest possible route home by accruing the net distances and directions travelled during foraging, a strategy well known as path integration. This strategy is part of the navigation toolbox of ants occupying different landscapes. However, when there is a visual discrepancy between test and training conditions, the distance travelled by animals relying on the path integrator varies dramatically between species: from 90% of the home vector to an absolute distance of only 50 cm. We here ask what the theoretically optimal balance between PI-driven and landmark-driven navigation should be. In combination with well-established results from optimal search theory, we show analytically that this fractional use of the home vector is an optimal homing strategy under a variety of circumstances. Assuming there is a familiar route that an ant recognizes, theoretically optimal search should always begin at some fraction of the home vector, depending on the region of familiarity. These results are shown to be largely independent of the search algorithm used. Ant species from different habitats appear to have optimized their navigation strategy based on the availability and nature of navigational information content in their environment.     

Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations

The Lotka–Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time horizon is large enough, optimal strategies are nearly steady-state. Such path is known as turnpike property. Some experiments are performed to observe such turnpike phenomenon in the hunting problem. Based on the turnpike property, we implement a variant of the single shooting method to solve the previous optimisation problem, taking the middle of the time interval as starting point.     

Population consequences of movement decisions in a patchy landscape

Complex, human‐dominated landscapes provide unique challenges to animals. In landscapes fragmented by human activity, species whose home ranges ordinarily consist of continuous habitat in pristine environments may be forced to forage among multiple smaller habitat patches embedded in an inhospitable environment. Furthermore, foragers often must decide whether to traverse a heterogeneous suite of landscape elements that differ in risk of predation or energetic costs. We modeled population consequences of foraging decisions for animals occupying patches embedded in a heterogeneous landscape. In our simulations, animals were allowed to use three different rules for moving between patches: a) optimal selection resulting from always choosing the least‐cost path; b) random selection of a movement path; and c) probabilistic selection in which path choice was proportional to an animal's probability of survival while traversing the path. The resulting distribution of the population throughout the landscape was dependent on the movement rule used. Least‐cost movement rules (a) produced landscapes that contained the highest average density of consumers per patch. However, optimal movement resulted in an all‐or‐none pattern of occupancy and a coupling of occupied patches into pairs that effectively reduced the population to a set of sub‐populations. Random and probabilistic rules, (b and c), in relatively safe landscapes produced similar average densities and 100% occupancy of patches. However, as the level of risk associated with travel between patches increased, random movement resulted in an all‐or‐none occupancy pattern while occupied patches in probabilistic populations went extinct independently of the other patches. Our results demonstrate strong effects of inter‐patch heterogeneity and movement decisions on population dynamics, and suggest that models investigating the persistence of species in complex landscapes should take into account the effects of the intervening landscape on behavioral decisions affecting animal movements between patches.     

Preventing LVAD implantation by early short-term mechanical support and prolonged inodilator therapy

Cardiogenic shock continues to be a life-threatening condition carrying a high mortality and morbidity, where the prognosis remains poor despite intensive modern treatment modalities. In recent years, mainly technical improvements have led to a more widespread use of short- and long-term mechanical circulatory support, such as veno-arterial extracorporeal membrane oxygenation (VA-ECMO) and left ventricular assist devices (LVADs). Currently, LVADs are indispensable as ‘bridge’ to cardiac recovery, heart transplantation (HTX), and/or as destination therapy Importantly, both LVADs and HTX put a vast burden on financial resources, besides significant short- and long-term risks of morbidity and mortality. These considerations underscore the importance of optimal timing and appropriate patient selection for LVAD therapy, avoiding as much as possible an unfortunate and costly clinical path. In this report, we present a series of three cases with acute refractory cardiogenic shock (‘crash and burn’, INTERMACS profile 1) successfully treated by ECMO and early optimal medical therapy preventing a certain path towards LVAD and/or HTX, for which they were initially referred. This conservative approach in INTERMACS profile one patients warrants very early introduction of adequate medical heart failure therapy under the umbrella of a combination of short-term mechanical circulatory and inotropic support by phosphodiesterase inhibitors. Therefore, this novel combined medical-mechanical approach could have important clinical implications for this extremely challenging patient category, as it may avoid an unnecessary and costly clinical path towards LVAD and/or heart transplantation.     

Shoot/root balance of plants: Optimal growth of a system with many vegetative organs

The optimal growth schedule of a plant with two vegetative parts is studied to investigate the balance between shoot and root. An intuitive justification of optimization procedures used in Pontryagin's maximum principle is obtained by defining the marginal values of shoot size, root size, and reproductive activity at various times of the season and deriving their differential equations and terminal conditions. The optimal growth pattern which maximizes the total reproductive activity during the season is composed of the convergence of a plant's shape to a balanced growth path, followed by simultaneous growth of shoot and root (balanced growth), ending with the reproductive growth. Along the balanced growth path, a plant has a root/shoot ratio which maximizes the daily net photosynthesis for a given total biomass. The model also shows a simultaneous stop of shoot and root growth when the reproduction begins, the dependence of root/shoot ratio on age, water and light availability, etc., the convergence of a plant's shape to the balanced growth after pruning or an environmental change.