Trade-off Function Research Articles

The emergence of nonlinear evolutionary trade-offs and the maintenance of genetic polymorphisms.

Evolutionary models of quantitative traits often assume trade-offs between beneficial and detrimental traits, requiring modellers to specify a function linking trait values. The choice of trade-off function can be consequential; functions that assume diminishing returns (accelerating costs) typically lead to single equilibrium genotypes, while decelerating costs often lead to genetic polymorphisms. Despite their importance, our current theory has little to say on which trade-off functions are the most biologically plausible. To address this gap, we explored how the genetic determination of quantitative traits can lead to different trade-off functions, using resistance to infectious diseases as an example trait. We developed a model where alleles at separate loci pleiotropically increase resistance while decreasing fecundity. We then used this model to generate genotype landscapes and investigate how epistasis effects the trade-off function. Regardless of the strength of epistasis, our model consistently led to accelerating costs. We then incorporated our genotype model into an eco-evolutionary model of disease resistance. Unlike other models with accelerating costs, our approach often led to genetic polymorphisms. Our results suggest that accelerating costs are a strong null model for evolutionary trade-offs and that the eco-evolutionary conditions required for polymorphism may be more nuanced than previously thought.

Enhancing motor skill learning through multiple sessions of online high-definition transcranial direct current stimulation in healthy adults: insights from EEG power spectrum.

The purpose of this study was to evaluate the influence of high-definition transcranial direct current stimulation (HD-tDCS) on finger motor skill acquisition. Thirty-one healthy adult males were randomly assigned to one of three groups: online HD-tDCS (administered during motor skill learning), offline HD-tDCS (delivered before motor skill learning), and a sham group. Participants engaged in a visual isometric pinch task for three consecutive days. Overall motor skill learning and speed-accuracy tradeoff function were used to evaluate the efficacy of tDCS. Electroencephalography was recorded and power spectral density was calculated. Both online and offline HD-tDCS total motor skill acquisition was significantly higher than the sham group (P < 0.001 and P < 0.05, respectively). Motor skill acquisition in the online group was higher than offline (P = 0.132, Cohen's d =1.46). Speed-accuracy tradeoff function in the online group was higher than both offline and sham groups in the post-test. The online group exhibited significantly lower electroencephalography activity in the frontal, fronto-central, and centro-parietal alpha band regions compared to the sham (P < 0.05). The findings suggest that HD-tDCS application can boost finger motor skill acquisition, with online HD-tDCS displaying superior facilitation. Furthermore, online HD-tDCS reduces the power of alpha rhythms during motor skill execution, enhancing information processing and skill learning efficiency.

People are more error-prone after committing an error

Humans tend to slow down after making an error. A longstanding account of this post-error slowing is that people are simply more cautious. However, accuracy typically does not improve following an error, leading some researchers to suggest that an initial ‘orienting’ response may initially impair performance immediately following error. Unfortunately, characterizing the nature of this error-based impairment remains a challenge in standard tasks that use free response times. By exerting control over the timing of responses, we reveal the time course of stimulus-response processing. Participants are less accurate after an error even when given ample time to make a response. A computational model of response preparation rules out the possibility that errors lead to slower cognitive processing. Instead, we find that the efficacy of cognitive processing in producing an intended response is impaired following errors. Following an error, participants commit more slips of action that tend to be a repetition of the previous mistake. Rather than a strategic shift along a single speed-accuracy tradeoff function, post-error slowing observed in free response time tasks may be an adaptive response to impaired cognitive processing that reflects an altered relationship between the speed and accuracy of responses.

The Emergence of Non-Linear Evolutionary Trade-offs and the Maintenance of Genetic Polymorphisms.

Evolutionary models of quantitative traits often assume trade-offs between beneficial and detrimental traits, requiring modelers to specify a function linking costs to benefits. The choice of trade-off function is often consequential; functions that assume diminishing returns (accelerating costs) typically lead to single equilibrium genotypes, while decelerating costs often lead to evolutionary branching. Despite their importance, we still lack a strong theoretical foundation to base the choice of trade-off function. To address this gap, we explore how trade-off functions can emerge from the genetic architecture of a quantitative trait. We developed a multi-locus model of disease resistance, assuming each locus had random antagonistic pleiotropic effects on resistance and fecundity. We used this model to generate genotype landscapes and explored how additive versus epistatic genetic architectures influenced the shape of the trade-off function. Regardless of epistasis, our model consistently led to accelerating costs. We then used our genotype landscapes to build an evolutionary model of disease resistance. Unlike other models with accelerating costs, our approach often led to genetic polymorphisms at equilibrium. Our results suggest that accelerating costs are a strong null model for evolutionary trade-offs and that the eco-evolutionary conditions required for polymorphism may be more nuanced than previously believed.

Measuring and monitoring skill learning in closed-loop myoelectric hand prostheses using speed-accuracy tradeoffs

Objective. Closed-loop myoelectric prostheses, which combine supplementary sensory feedback and electromyography (EMG) based control, hold the potential to narrow the divide between natural and bionic hands. The use of these devices, however, requires dedicated training. Therefore, it is crucial to develop methods that quantify how users acquire skilled control over their prostheses to effectively monitor skill progression and inform the development of interfaces that optimize this process. Approach. Building on theories of skill learning in human motor control, we measured speed-accuracy tradeoff functions (SAFs) to comprehensively characterize learning-induced changes in skill—as opposed to merely tracking changes in task success across training—facilitated by a closed-loop interface that combined proportional control and EMG feedback. Sixteen healthy participants and one individual with a transradial limb loss participated in a three-day experiment where they were instructed to perform the box-and-blocks task using a timed force-matching paradigm at four specified speeds to reach two target force levels, such that the SAF could be determined. Main results. We found that the participants’ accuracy increased in a similar way across all speeds we tested. Consequently, the shape of the SAF remained similar across days, at both force levels. Further, we observed that EMG feedback enabled participants to improve their motor execution in terms of reduced trial-by-trial variability, a hallmark of skilled behavior. We then fit a power law model of the SAF, and demonstrated how the model parameters could be used to identify and monitor changes in skill. Significance. We comprehensively characterized how an EMG feedback interface enabled skill acquisition, both at the level of task performance and movement execution. More generally, we believe that the proposed methods are effective for measuring and monitoring user skill progression in closed-loop prosthesis control.

Privacy-Preserving Decentralized Inference With Graph Neural Networks in Wireless Networks

As an efficient neural network model for graph data, graph neural networks (GNNs) recently find successful applications for various wireless optimization problems. Given that the inference stage of GNNs can be naturally implemented in a decentralized manner, GNN is a potential enabler for decentralized control/management in the next-generation wireless communications. Privacy leakage, however, may occur due to the information exchanges among neighbors during decentralized inference with GNNs. To deal with this issue, in this paper, we analyze and enhance the privacy of decentralized inference with GNNs in wireless networks. Specifically, we adopt local differential privacy as the metric, and design novel privacy-preserving signals as well as privacy-guaranteed training algorithms to achieve privacy-preserving inference. We also define the SNR-privacy trade-off function to analyze the performance upper bound of decentralized inference with GNNs in wireless networks. To further enhance the communication and computation efficiency, we adopt the over-the-air computation technique and theoretically demonstrate its advantage in privacy preservation. Through extensive simulations on the synthetic graph data, we validate our theoretical analysis, verify the effectiveness of proposed privacy-preserving wireless signaling and privacy-guaranteed training algorithm, and offer some guidance on practical implementation.

Study on the Trade-Offs of Land Functions in the Central Plain of China for Sustainable Development

Properly managing the relationship between food security, ecological protection, and urbanization, and coordinating the trade-offs among these three factors for land demand are extremely important for environmental management and sustainable development. In this study, we attempt to analyze the state of land use trade-offs from a dynamic perspective in terms of both potential and efficiency. We have innovatively proposed a new land use trade-off analysis framework integrating the Estimation System for Land Productivity (ESLP) model, machine learning algorithms, ecosystem service value assessment, and spatial analysis method. By applying the framework, the potential and efficiency of the three land use functions of urban development, ecological protection, and agricultural production on the Huang-Huai-Hai (HHH) Plain were comprehensively estimated, and the trade-off relationship between the three land use functions was identified. The results showed a prominent conflict between urban development and agricultural production (around 8%) on the HHH Plain, especially in the Beijing–Tianjin–Hebei urban agglomeration and the southern Jiangsu urban agglomeration. In the mountainous areas, such as northern Hebei and central Shandong, there was an obvious trade-off between ecological land and agriculture land. Most cities had a trade-off between ecological land and urban land (approximately 6% of the study area), but it was relatively more relaxed in comparison. Finally, we found that on the HHH Plain, where land resources are fiercely competitive, spatial planning and land resource control depend not only on the suitability or potential of the land unit, but also on whether the efficiency of land use has reached an appropriate range. The smart way to use land resources is to scientifically trade-off different land use functions and improve the efficiency of land use to achieve maximum benefit.

A GIS-based maritime supply chain network design of distant-water fisheries

In the pursuit of efficient and cost-effective supply chain management within the marine capture fishery sector, this study introduces a novel approach that integrates the supply chain network for distant-water fisheries. This approach not only involves an integrated maritime location inventory routing problem (MLIRP) but also considers the identification of offshore fishing grounds based on geographic information system (GIS) techniques. The proposed model centers on critical decision variables, including selection of fishery production areas, strategic placement and sizing of perishable goods depots, and allocation of refrigerated vessels. Meanwhile, the model proposes two trade-off objective functions: one seeks to maximize the weighted coverage rate of fishery resource within selected production areas, while the other aims to minimize the total cost of the built network. To address the complex model, a method based on the k-means clustering and the multi-objective plant growth simulation algorithm (MO-PGSA) is adopted. Key elements, such as growth operators, dominant strength, crowding distance, and partially ordered sets, are involved to enhance algorithm performance. Finally, the effectiveness of the proposed model and method are discussed through numerical experiments based on the real-life case in the Spratly Islands.

Optimizing the use of forestry biomass producer gas in dual fuel engines: A novel emissions reduction strategy for a micro-CHP system

Low energy density fuels, like producer gas from biomass gasification, can be profitably used in compression ignition (CI) engines by means of a proper combustion strategy, such as the dual-fuel mode. Experimental investigations have proven the environmental benefits of the use of producer gas in terms of green-house gas emissions but critical issues related to their use in CI engines have been also highlighted. In particular, under specific operating conditions, the performance and the emissions of the engine might be derated reducing the attractiveness of the technology. In this work a new data-driven emission optimization strategy for a micro-cogeneration system based on an open-top biomass gasification unit coupled with a CI engine running in dual-fuel mode (producer gas/diesel) is presented and discussed. The main purpose of the work is to provide an appropriate tool to address one of the typical problems of dual-fuel systems, namely the nitrogen oxides (NOx) and carbon monoxide (CO) emission trade-off, by calculating the optimal diesel substitution rate (DSR) at a certain required power load. The methodology baseline is the experimental characterization and parametric modeling of the system in terms of NOx, CO, and electrical efficiency (ηe). Then a trade-off objective function (TOF) is defined. The novelties of the proposed approach stands in the building of an ad-hoc designed TOF so as to describe the problem with a single-objective optimization, and thus avoiding the computational and time complexity of a multi-objective optimization. Moreover, a second peculiar aspect is the introduction in the TOF of an internally dependent coefficient (namely the load factor Kl) able to take into account the effect of load and DSR on CO emissions: the adding of such a physical-related feature represents an effective enrichment of the minimization strategy, especially considering the nature of the optimization, which is purely data-driven. Finally, sequential quadratic programming (SQP) minimization of the TOF is carried out by means of the available MATLAB SQP libraries, and two optimization strategies – namely, CO-driven and efficiency-driven - are discussed. Results show (i) promising potentialities in identifying the best effective utilization range of dual-fuel combustion; (ii) high flexibility in the use of the optimization algorithm thanks to the definition of the TOF, which can be easily adapted to different objectives (e.g., NOx mitigation, maintenance of high electrical efficiencies, CO emission bounding) while maintaining external constraints; (iii) high robustness even in the extreme cases in which the imposition of a particular constraint (e.g., high electrical efficiency) is not compatible with the capabilities of the system.

The role of underspecification in relative clause attachment: Speed-accuracy tradeoff evidence.

A number of studies have found evidence for the so-called ambiguity advantage, that is, faster processing of ambiguous sentences compared with unambiguous counterparts. While a number of proposals regarding the mechanism underlying this phenomenon have been made, the empirical evidence so far is far from unequivocal. It is compatible with several theories, including strategic underspecification (Swets et al., 2008), race models (Logačev & Vasishth, 2016; Van Gompel et al., 2000), and a more recent coactivation-based account (Dillon et al., 2019). While all three classes of theories make matching predictions for the average time to complete relative clause (RC) attachment in ambiguous compared with unambiguous sentences, their predictions diverge with regard to the minimum completion times. The speed-accuracy tradeoff procedure was used to test the predictions of all three classes of theories. According to a hierarchical Bayesian model, the speed-accuracy tradeoff functions (SATFs) for ambiguous RC attachment conditions show an earlier departure from chance performance than in either high or low attachment conditions. The results further indicate increased asymptotic accuracy in the ambiguous condition but no increase in processing rate. Taken together, this pattern of results is compatible with the strategic underspecification model and coactivation-based accounts, but not with race models. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Bayesian adaptive method for estimating speed-accuracy tradeoff functions of multiple task conditions.

The speed-accuracy tradeoff (SAT) often makes psychophysical data difficult to interpret. Accordingly, the SAT experimental procedure and model were proposed for an integrated account of the speed and accuracy of responses. However, the extensive data collection for a SAT experiment has blocked its popularity. For a quick estimation of SAT function (SATf), we previously developed a Bayesian adaptive SAT method, including an online stimulus selection strategy. By simulations, the method was proved efficient with high accuracy and precision with minimal trials, adequate for practically applying a single condition task. However, it calls for extensions to more general designs with multiple conditions and should be revised to achieve improved estimation performance. It also demands real experimental validation with human participants. In the current study, we suggested an improved method to measure SATfs for multiple task conditions concurrently and to enhance robustness in general designs. The performance was evaluated with simulation studies and a psychophysical experiment using a flanker task. Simulation results revealed that the proposed method with the adaptive stimulus selection strategy efficiently estimated multiple SATfs and improved performance even for cases with an extreme parameter value. In the psychophysical experiment, SATfs estimated by minimal adaptive trials (1/8 of conventional trials) showed high agreement with those by conventional trials required for reliably estimating multiple SATfs. These results indicate that the Bayesian adaptive SAT method is reliable and efficient in estimating SATfs in most experimental settings and may apply to SATf estimation in general behavioral research designs.

Low-Intensity Focused Ultrasound Neuromodulation for Stroke Recovery: A Novel Deep Brain Stimulation Approach for Neurorehabilitation?

Stroke as the leading cause of adult long-term disability and has a significant impact on patients, society and socio-economics. Non-invasive brain stimulation (NIBS) approaches such as transcranial magnetic stimulation (TMS) or transcranial electrical stimulation (tES) are considered as potential therapeutic options to enhance functional reorganization and augment the effects of neurorehabilitation. However, non-invasive electrical and magnetic stimulation paradigms are limited by their depth focality trade-off function that does not allow to target deep key brain structures critically important for recovery processes. Transcranial ultrasound stimulation (TUS) is an emerging approach for non-invasive deep brain neuromodulation. Using non-ionizing, ultrasonic waves with millimeter-accuracy spatial resolution, excellent steering capacity and long penetration depth, TUS has the potential to serve as a novel non-invasive deep brain stimulation method to establish unprecedented neuromodulation and novel neurorehabilitation protocols. The purpose of the present review is to provide an overview on the current knowledge about the neuromodulatory effects of TUS while discussing the potential of TUS in the field of stroke recovery, with respect to existing NIBS methods. We will address and discuss critically crucial open questions and remaining challenges that need to be addressed before establishing TUS as a new clinical neurorehabilitation approach for motor stroke recovery.

The trade-off function of photorespiration in a changing environment

Abstract The photorespiratory pathway in plants comprises metabolic reactions distributed across several cellular compartments. It emerges from the dual catalytic function of Rubisco, i.e. ribulose-1,5-bisphosphate carboxylase/oxygenase. Rubisco either carboxylates or oxygenates ribulose-1,5-bisphosphate. Carboxylation reactions produce 3-phosphoglycerate molecules which are substrates for the central carbohydrate metabolism. However, oxygenation reactions additionally form 2-phosphoglycolate molecules which are (i) substrate for a multicompartmental recovery process, and (ii) inhibit several enzymes of the Calvin–Benson–Bassham cycle. Here, an approach of structural kinetic modelling is presented to investigate the extent of stabilization of the Calvin–Benson–Bassham cycle and carbohydrate metabolism by photorespiration. This method is based on a parametric representation of the Jacobian matrix of a metabolic system which offers a robust strategy for handling uncertainties associated with in vitro kinetic constants. Our findings indicate that oxygenation of ribulose-1,5-bisphosphate by Rubisco significantly stabilizes the Calvin–Benson–Bassham cycle. Hence, a trade-off function of photorespiration is suggested which reduces carbon assimilation rates but simultaneously stabilizes metabolism by increasing plasticity of metabolic regulation within the chloroplast. Furthermore, our analysis indicates that increasing carbon flux towards sucrose biosynthesis has a stabilizing effect. Finally, our findings shed light on the role of a multicompartmental metabolic pathway in stabilizing plant metabolism against perturbation induced by a dynamic environment.

Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a function of Bell linear functionals, conditioned on an eavesdropper&amp;apos;s quantum side information. In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting, where the analysis can be reduced to qubit systems, by combining entropy bounds for variants of the well-known BB84 protocol with quantum constraints on qubit operators on the bipartite system shared by Alice and Bob. The approach gives analytic bounds on the entropy, or semi-analytic ones in reasonable computation time, which are typically close to optimal. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key as well as on a more refined analysis of the original single-basis variant with respect to losses. We obtain in particular a detection efficiency threshold slightly below 80.26%, within reach of current experimental capabilities.

BIM-Based Multi-Objective Optimization of Low-Carbon and Energy-Saving Buildings

Global warming and other environmental problems are increasing the demand for green and low-carbon buildings. The development of high-performance computers and building information models has a significant impact on low-carbon buildings. Low-carbon building design needs to comprehensively consider geography, climate, material, cost and other factors, a highly complex multidisciplinary research problem. Therefore, it is urgent to use advanced modeling and simulation technology, involving BIM, parametric design, cloud platform and evolutionary algorithm. This paper proposes a BIM based low-carbon building design optimization framework, which realizes the comprehensive trade-off function of building low-carbon energy saving and daylighting performance through an improved genetic algorithm. The framework drives BIM through parameterization and integrates building environment information, geometric information and operation information, including six parts: BIM model establishment, parameter-driven development, building performance simulation, multi-objective optimization design, Pareto frontier analysis, and energy-saving decision-making and evaluation. The case study shows that the simulation results obtained through the framework can effectively achieve building energy conservation while maximizing the lighting performance of the building, providing a scientific basis and reference for construction professionals to design low-carbon buildings. Finally, the application advantages and limitations of the framework in low-carbon building design and its application prospects in low-carbon energy-saving building design are discussed. This research has made contributions to the multi-disciplinary low-carbon energy conservation research field, realized the multi-objective optimization strategy of building performance based on BIM, genetic algorithm and simulation, and is an important supplement to existing building energy conservation and emission reduction optimization design.

Trajectory Optimization for High-Speed Trains via a Mixed Integer Linear Programming Approach

This paper proposes a trajectory optimization approach for high-speed trains to reduce traction energy consumption and increase riding comfort. Besides, the proposed approach can also achieve energy-saving effects by optimizing the operation time between stations. First, an optimization model is developed by defining the objective function as a trade-off function of the traction energy consumption and riding comfort. In addition to constraints in the classic optimal train control model, three new factors–the discrete throttle settings, neutral zones, and sectionalized tunnel resistance–are considered. Then, the model is discretized and turned into a multi-step decision optimization problem. All the nonlinear constraints are approximated using piecewise affine (PWA) functions, and the trajectory optimization problem is turned into a mixed integer linear programming (MILP) problem which can be solved by existing solvers CPLEX and YALMIP. Finally, some case studies with real-world data sets are conducted to present the effectiveness of the proposed approach. The simulation results are compared with the practical running data of trains, which shows that the proposed model and the optimization approach save energy and improve the riding comfort.

Estimating speed-accuracy trade-offs to evaluate and understand closed-loop prosthesis interfaces

Objective. Closed-loop prosthesis interfaces, which combine electromyography (EMG)-based control with supplementary feedback, represent a promising direction for developing the next generation of bionic limbs. However, we still lack an understanding of how users utilize these interfaces and how to evaluate competing solutions. In this study, we used the framework of speed–accuracy trade-off functions (SAF) to understand, evaluate, and compare the performance of two closed-loop user-prosthesis interfaces. Approach. Ten able-bodied participants and an amputee performed a force-matching task in a functional box-and-block setup at three different speeds. All participants were subjected to both interfaces in a crossover study design with a 1 week washout period. Importantly, both interfaces used direct proportional control but differed in the feedback provided to the participant (EMG feedback vs. Force feedback). We estimated the SAFs afforded by the two interfaces and sought to understand how the participants planned and executed the task under the various conditions. Main results. We found that execution speed significantly influenced performance, and that EMG feedback afforded better overall performance, especially at medium speeds. Notably, we found that there was a difference in the SAF between the two interfaces, with EMG feedback enabling participants to attain higher accuracies faster than Force feedback. Furthermore, both interfaces enabled participants to develop flexible control policies, while EMG feedback also afforded participants the ability to generate smoother, more repeatable EMG commands. Significance. Overall, the results indicate that the performance of closed-loop prosthesis interfaces depends critically on the feedback approach and execution speed. This study showed that the SAF framework could be used to reveal the differences between feedback approaches, which might not have been detected if the assessment was performed at a single speed. Therefore, we argue that it is important to consider the speed–accuracy trade-offs to rigorously evaluate and compare user-prosthesis interfaces.

Unified trade-off optimization of quantum harmonic Otto engine and refrigerator.

We investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum Ω function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawl model which is a steady-state classical heat engine. For the sudden switch of frequencies, we obtain loop-like behavior of the efficiency-work curve, which is characteristic of irreversible heat engines. Finally, we discuss the behavior of cooling power at maximum Ω function.

Coevolutionary dynamics of host-pathogen interaction with density-dependent mortality.

This study explores the coevolutionary dynamics of host-pathogen interaction based on a susceptible-infected population model with density-dependent mortality. We assume that both the host’s resistance and the pathogen’s virulence will adaptively evolve, but there are inevitable costs in terms of host birth rate and disease-related mortality rate. Particularly, it is assumed that both the host resistance and pathogen virulence can affect the transmission rate. By using the approach of adaptive dynamics and numerical simulation, we find that the finally coevolutionary outcome depends on the strength of host-pathogen asymmetric interaction, the curvature of trade-off functions, and the intensity of density-dependent natural mortality. To be specific, firstly, we find that if the strengths of host-pathogen asymmetric interaction and disease-related mortality are relatively weak, or the density-dependent natural mortality is relatively strong, then the host resistance and pathogen virulence will evolve to a continuously stable strategy. However, if the strength of host-pathogen asymmetric interaction and disease-related mortality becomes stronger, then the host resistance and pathogen virulence will evolve periodically. Secondly, we find that if the intensities of both the birth rate trade-off function and the density-dependent natural mortality are relatively weak, but the strength of host-pathogen asymmetric interaction becomes relatively strong, then the evolution of host resistance will have a relatively strongly accelerating benefit, the evolutionary branching of host resistance will first arise. However, if the strength of host-pathogen asymmetric interaction is relatively weak, but the intensity of the trade-off function of disease-related mortality becomes relatively strong, then the evolution of pathogen virulence will have a relatively strongly decelerating cost, and the evolutionary branching of pathogen virulence will first arise. Thirdly, after the evolutionary branching of host resistance and pathogen virulence, we further study the coevolutionary dynamics of two-hosts-one-pathogen interaction and one-host-two-pathogens interaction. We find that if the evolutionary branching of host resistance arises firstly, then the finally evolutionary outcome contains a dimorphic host and a monomorphic pathogen population. If the evolutionary branching of pathogen virulence arises firstly, then the finally evolutionary outcome may contain a monomorphic host and a dimorphic pathogen population.

Optimal chance-constrained pension fund management through dynamic stochastic control

We apply a dynamic stochastic control (DSC) approach based on an open-loop linear feedback policy to a classical asset-liability management problem as the one faced by a defined-benefit pension fund (PF) manager. We assume a PF manager seeking an optimal investment policy under random market returns and liability costs as well as stochastic PF members’ survival rates. The objective function is formulated as a risk-reward trade-off function resulting in a quadratic programming problem. The proposed methodology combines a stochastic control approach, due to Primbs and Sung (IEEE Trans Autom Control 54(2):221–230, 2009), with a chance constraint on the PF funding ratio (FR) and it is applied for the first time to this class of long-term financial planning problems characterized by stochastic asset and liabilities. Thanks to the DSC formulation, we preserve the underlying risk factors continuous distributions and avoid any state space discretization as is typically the case in multistage stochastic programs (MSP). By distinguishing between a long-term PF liability projection horizon and a shorter investment horizon for the FR control, we avoid the curse-of-dimensionality, in-sample instability and approximation errors that typically characterize MSP formulations. Through an extended computational study, we present in- and out-of-sample results which allows us to validate the proposed methodology. The collected evidences confirm the potential of this approach when applied to a stylized but sufficiently realistic long-term PF problem.