Optimal Allocation Ratio Research Articles

Optimal sample size allocation for two-arm superiority and non-inferiority trials with binary endpoints.

The sample size of a clinical trial has to be large enough to ensure sufficient power for achieving the aim the study. On the other side, for ethical and economical reasons it should not be larger than necessary. The sample size allocation is one of the parameters that influences the required total sample size. For two-arm superiority and non-inferiority trials with binary endpoints, we performed extensive computations over a wide range of scenarios to determine the optimal allocation ratio that minimizes the total sample size if all other parameters are fixed. The results demonstrate, that for both superiority and non-inferiority trials the optimal allocation may deviate considerably from the case of equal sample size in both groups. However, the saving in sample size when allocating the total sample size optimally as compared to balanced allocation is typically small.

Optimal vaccine allocation strategy: Theory and application to the early stage of COVID-19 in Japan.

In this paper, we construct an age-structured epidemic model to analyze the optimal vaccine allocation strategy in an epidemic. We focus on two topics: the first one is the optimal vaccination interval between the first and second doses, and the second one is the optimal vaccine allocation ratio between young and elderly people. On the first topic, we show that the optimal interval tends to become longer as the relative efficacy of the first dose to the second dose (RE) increases. On the second topic, we show that the heterogeneity in the age-dependent susceptibility (HS) affects the optimal allocation ratio between young and elderly people, whereas the heterogeneity in the contact frequency among different age groups (HC) tends to affect the effectiveness of the vaccination campaign. A counterfactual simulation suggests that the epidemic wave in the summer of 2021 in Japan could have been greatly mitigated if the optimal vaccine allocation strategy had been taken.

Co-Cultivated Enzyme Constraint Metabolic Network Model for Rational Guidance in Constructing Synthetic Consortia to Achieve Optimal Pathway Allocation Prediction.

Synthetic consortia have emerged as a promising biosynthetic platform that offers new opportunities for biosynthesis. Genome-scale metabolic network models (GEMs) with complex constraints are extensively utilized to guide the synthesis in monocultures. However, few methods are currently available to guide the rational construction of synthetic consortia for predicting the optimal allocation strategy of synthetic pathways aimed at enhancing product synthesis. A standardized method to construct the co-cultivated Enzyme Constraint metabolic network model (CulECpy) is proposed, which integrates enzyme constraints and modular interaction scale constraints based on the research concept of "independent + global". This method is applied to construct several synthetic consortia models, which encompassed different target products, strains, synthetic pathways, and compositional structures. Analyzing the model, the optimal pathway allocation and initial inoculum ratio that enhance the synthesis of target products by synthetic consortia are predicted and verified. When comparing with the constructed co-culture synthesis system, the normalized root mean square error of all optimal theoretical yield simulations is found to be less than or equal to 0.25. The analyses and verifications demonstrate that the method CulECpy can guide the rational construction of synthetic consortia systems to facilitate biochemical synthesis.

Effects of Different Nitrogen Allocation Ratios and Period on Cotton Yield and Nitrogen Utilization

Choosing the proper fertilizer regime for a crop in a given location remains challenging to increase yield, profitability, environmental growth protection, and sustainability. However, the nutrient demand characteristics of cotton in the North China Plain are different at various growth stages. Therefore, we choose the local superior cotton variety (Lumian 532) with high yield as the material, in the present study, we assessed the cotton yield, biomass accumulation and distribution, nitrogen absorption and utilization efficiency, and other parameters by setting four nitrogen allocation ratios (3:5:2, 0:10:0, 3:7:0, and 0:7:3) when the nitrogen application rates were 0, 150, 220, and 300 kg hm−2. The results showed that when the nitrogen application rate was 300 kg hm−2, the growth index, biomass, nitrogen content, and yield of Lumian 532 were the highest, while the nitrogen partial productivity (12.2 and 12.8) was the lowest. When the nitrogen application rate was 220 kg hm−2 and the nitrogen allocation ratio was 3:5:2, the agronomic nitrogen use efficiency (3.2 and 3.5) and nitrogen physiological (24.8 and 25.0) was achieved. When the nitrogen application rate was 150 kg hm−2, the nitrogen partial productivity (20.6 and 20.9) was the highest. In conclusion, the biomass accumulation and distribution, nitrogen use efficiency, yield, and yield composition of Lumian 532 could be effectively regulated by appropriate nitrogen application rate and nitrogen allocation ratio. Therefore, to optimize the yield and improve the nitrogen use efficiency, the optimal nitrogen application rate of Lumian 532 was 220 kg hm−2, and the optimal nitrogen allocation ratio was 3:5:2 in the North China Plain. The results provided practical basis for nutrient demand, cotton yield and ecological protection in different growth stages of cotton in North China Plain.

Optimal vaccination strategies for COVID-19 in population migration between two regions scenario

ABSTRACT Population movements had a significant impact on the spread of COVID-19, and vaccination is considered the most effective means for humans to face viral infections. This study identifies the optimal control strategy for COVID-19 prevention and control, and explores the impact of short-term and long-term migration on the optimal proportion of vaccine allocation between two regions. We proposed to establish the SIR (Susceptible-Infectious-Recovered) model and determine the stability by calculating the disease free equilibrium and Jacobi matrix of the model. We then established the vaccine optimization model, solved the optimal vaccine distribution strategy by gradient descent method and explored the impact of short-term and long-term migration on the optimal vaccine allocation ratio. The stability analysis revealed that the virus could not be eliminated only by reducing the migration rates and infection rates. we introduced the vaccine methods and obtained the optimal vaccine allocation ratio in Shenzhen and Hong Kong as p 1 : p 2 = 0.000341 : 0.001739 , and the daily vaccination rate we need to impose in each region as p 1 : p 2 = 0.00068 : 0.001901 . The presence or absence of short-term migration had no greater impact on the distribution of the vaccine, whereas R v with long-term migration had a greater effect than no migration. We found that migration rates could not eliminate the outbreak in both regions and that adopting an effective vaccine distribution strategy could be more effective in eliminating the outbreak. And for different allocation scenarios with limited vaccine supply, we obtained the optimal allocation most favorable to control the epidemic.

The Effect of Fangcang Shelter Hospitals under Resource Constraints on the Spread of Epidemics.

Since the outbreak of the COVID-19 pandemic, Fangcang shelter hospitals have been built and operated in several cities, and have played a huge role in epidemic prevention and control. How to use medical resources effectively in order to maximize epidemic prevention and control is a big challenge that the government should address. In this paper, a two-stage infectious disease model was developed to analyze the role of Fangcang shelter hospitals in epidemic prevention and control, and examine the impact of medical resources allocation on epidemic prevention and control. Our model suggested that the Fangcang shelter hospital could effectively control the rapid spread of the epidemic, and for a very large city with a population of about 10 million and a relative shortage of medical resources, the model predicted that the final number of confirmed cases could be only 3.4% of the total population in the best case scenario. The paper further discusses the optimal solutions regarding medical resource allocation when medical resources are either limited or abundant. The results show that the optimal allocation ratio of resources between designated hospitals and Fangcang shelter hospitals varies with the amount of additional resources. When resources are relatively sufficient, the upper limit of the proportion of makeshift hospitals is about 91%, while the lower limit decreases with the increase in resources. Meanwhile, there is a negative correlation between the intensity of medical work and the proportion of distribution. Our work deepens our understanding of the role of Fangcang shelter hospitals in the pandemic and provides a reference for feasible strategies by which to contain the pandemic.

A Battery Capacity Configuration Method of a Photovoltaic and Battery System Applied in a Building Complex for Increased Self-Sufficiency and Self-Consumption

Photovoltaic (PV) systems have been growing in popularity as an energy conservation and carbon reduction approach. Generally, battery storage is integrated with a PV system to solve the intermittent and fluctuant problems of solar resources, enhancing the relative independence of the PV–battery (PVB) system. In consideration of the economic benefits and system efficiency, it is necessary to investigate battery capacity allocation methods. A battery capacity configuration method was established in this study to increase the self-sufficiency rate (SSR) and self-consumption rate (SCR) of the system for a building complex by exploiting the battery resources. The PVB system designed for the building complex is divided into two categories: distributed and centralized storage. The SSR and SCR significantly increase with the increasing battery capacity for both schemes. The SCR of centralized storage is always higher than that of distributed storage, considering different battery and PV capacities. However, the SSR of distributed storage scheme was found to be slightly higher than that of the centralized storage scheme when the energy generated by PV is half of the energy consumed by the building load. For instance, when the battery capacity is four, SSR values for optimal distributed and centralized storage schemes are 47.62% and 47.19%, respectively. For the distributed storage scheme, there is a slight difference between the optimal allocation ratios achieved by SSR and SCR, considering that they have the same total battery capacity. In addition, the effects of converter loss, complementarity in load curves, and centralized batteries were analyzed to achieve greater SSR and SCR. The comparison results of this study can be used as a guide for battery capacity design in the PVB systems of building complexes.

Experimental investigation and optimization analysis on thermoelectric water generator integrated with heat pipe

• Thermoelectric water generator integrated with heat pipe (HPTEWG) is proposed. • HPTEWG and thermoelectric water generator (TEWG) are compared experimentally. • HPTEWG can achieve higher cooling capacity than TEWG by 34.11W. • Maximum water generation increment in HPTEWG by 38.95ml/h can be achieved. • Structure configurations of HPTEWG are optimized to gain maximum water generation. As scare freshwater resources have been severely stressed by climate change, population growth and water pollution, demands of efficient water generation methods and devices urgently increase. To further improve the water generation capacity of thermoelectric water generator (TEWG), a novel TEWG integrated with heat pipe (HPTEWG) is proposed and studied by using experimental and simulation methods. Rather than the heat sink of the TEWG, the heat pipe is utilized to precool moisture air before the thermoelectric cooler to achieve the goal. Experimental results show that the maximum improvement in cooling capacity and water generation of HPTEWG can be 34.11W and 38.95ml/h when compared with TEWG under given operating condition. Besides, the effects of the input power of TEWG, inlet air temperature, relative humidity and mass flow rate on the performances of two system are experimentally investigated as well. In addition, a validated theoretical optimization model is built to optimize the structure configuration of the HPTEWG. The maximum water generation of the HPTEWG can be achieved when optimal area allocation ratio of HP and TEWG are chosen under constant total area condition. It is hope that the results can provide theoretical basis for the thermoelectric water generator development and application.

Does Bitcoin Contribute to Portfolio Performance?

This study analyzes the role of Bitcoin as an investment asset in a global multi-asset portfolio. For portfolio construction, we use a risk-based portfolio strategy that excludes estimates of future expected returns. We derive the optimal asset allocation ratio of Bitcoin included in the global multi-asset portfolio and compare the performance with the general portfolio. We find that the average investment weight of Bitcoin in the portfolio is 1.8%, and the portfolio containing Bitcoin shows superior investment performance compared to the portfolio without Bitcoin.

Using information from network meta-analyses to optimize the power and sample allocation of a subsequent trial with a new treatment

BackgroundA critical step in trial design is determining the sample size and sample allocation to ensure the proposed study has sufficient power to test the hypothesis of interest: superiority, equivalence, or non-inferiority. When data are available from prior trials and leveraged with the new trial to answer the scientific questions, the value of society’s investment in prior research is increased. When prior information is available, the trial design including the sample size and allocation should be adapted accordingly, yet the current approach to trial design does not utilize such information. Ensuring we maximize the value of prior research is essential as there are always constraints on resources, either physical or financial, and designing a trial with adequate power can be a challenge.MethodsWe propose an approach to increasing the power of a new trial by incorporating evidence from a network meta-analysis into the new trial design and analysis. We illustrate the methodology through an example network meta-analysis, where the goal is to identify the optimal allocation ratio for the new three-arm trial, which involves the reference treatment, the new treatment, and the negative control. The primary goal of the new trial is to show that the new treatment is non-inferior to the reference treatment. It may also be of interest to know if the new treatment is superior to the negative control. We propose an optimal treatment allocation strategy which is derived from minimizing the standard error of the log odds ratio estimate of the comparison of interest. We conducted a simulation study to assess the proposed methods to design a new trial while borrowing information from the existing network meta-analysis and compare it to even allocation methods.ResultsUsing mathematical derivation and simulations, we document that our proposed approach can borrow information from a network meta-analysis to modify the treatment allocation ratio and increase the power of the new trial given a fixed total sample size or to reduce the total sample size needed to reach a desired power.ConclusionsWhen prior evidence about the hypotheses of interest is available, the traditional equal allocation strategy is not the most powerful approach anymore. Our proposed methodology can improve the power of trial design, reduce the cost of trials, and maximize the utility of prior investments in research.

Altitude Optimization and Task Allocation of UAV-Assisted MEC Communication System.

Unmanned aerial vehicles (UAVs) are widely used in wireless communication systems due to their flexible mobility and high maneuverability. The combination of UAVs and mobile edge computing (MEC) is regarded as a promising technology to provide high-quality computing services for latency-sensitive applications. In this paper, a novel UAV-assisted MEC uplink maritime communication system is proposed, where an MEC server is equipped on UAV to provide flexible assistance to maritime user. In particular, the task of user can be divided into two parts: one portion is offloaded to UAV and the remaining portion is offloaded to onshore base station for computing. We formulate an optimization problem to minimize the total system latency by designing the optimal flying altitude of UAV and the optimal task allocation ratio. We derive a semi closed-form expression of the optimal flying altitude of UAV and a closed-form expression of the optimal task allocation ratio. Simulation results demonstrate the precision of the theoretical analyses and show some interesting insights.

Optimal Investment‐Consumption Strategy of Household Based on CEV Model

To maintain and increase household wealth, this study studies the optimal allocation ratio of household investment and consumption. When considering venture capital, it is assumed that the theoretical price of risky asset obeys the CEV model. Our goal was to maximize the expectation of household cumulative consumption and the discounted utility of terminal wealth and to solve the optimal consumption and investment ratio using the dynamic programming principle and HJB equation. Using logarithmic utility and isoelastic power utility function with residual utility, we get the analytical solution of the household investment‐consumption ratio by means of guessing and variable transformation. Finally, the influence of general parameters on the optimal ratio in the market is analyzed by numerical simulation and diagram, which is consistent with the description of actual situation. This study not only enriches portfolio theory but also provides investors with investment strategies.

Statistical considerations of phase 3 umbrella trials allowing adding one treatment arm mid-trial

Master protocols, in particular umbrella trials and platform trials, when evaluating multiple experimental treatments with a common control, could save patient resource, increase trial efficiency, and reduce drug development cost. Compared to the phase 3 platform trials that allow unlimited number of experimental arms to be added, it is more practical for individual companies to evaluate two experimental arms with a common control in an umbrella trial and allow the second experimental arm to be added at a later time. There have been limited research done in this type of trials in terms of statistical properties and guidance. In this article, we present statistical considerations of a phase 3 three-arm umbrella design including Type I error control and power, as well as the optimal allocation ratio. We intend to not only complement the existing literature, but more importantly to provide practical guidance to pave the way for its implementation by individual companies.

Traffic Allocation for Heterogeneous Links in Satellite Data Relay Networks

Efficient traffic allocation for heterogeneous links in satellite data relay networks (SDRNs) has been an attractive topic nowadays. However, different traffic types and link heterogeneity bring plenty of difficulties to the link delay evaluation which directly impacts the traffic allocation efficiency. Owing to the unique determination of the probability distribution of arrival processes, we succeed in characterizing any type of traffic with the help of the moment generating function (MGF). According to the alternation and discontinuity of satellite ground links (SGLs), we propose a Markov chain Monte Carlo embedded service matrix construction method to model the SGL service. Being apt at combining service processes, the stochastic network calculus based min-plus convolution is employed to depict the relay service. By deriving the tight upper bounds of the delay in heterogeneous links based on the MGF, min-plus convolution, and Markov chain, respectively, taking advantage of the Chernoff bound and Union bound, we calculate the optimal traffic allocation ratio in terms of minimum system delay. Finally, numerous simulations are conducted to show the relationships among the optimal traffic allocation ratio, traffic type, and link heterogeneity.

Optimal design of cluster randomized trials allowing unequal allocation of clusters and unequal cluster size between arms.

There are sometimes cost, scientific, or logistical reasons to allocate individuals unequally in an individually randomized trial. In cluster randomized trials we can allocate clusters unequally and/or allow different cluster size between trial arms. We consider parallel group designs with a continuous outcome, and optimal designs that require the smallest number of individuals to be measured given the number of clusters. Previous authors have derived the optimal allocation ratio for clusters under different variance and/or intracluster correlations (ICCs) between arms, allowing different but prespecified cluster sizes by arm. We derive closed-form expressions to identify the optimal proportions of clusters and of individuals measured for each arm, thereby defining optimal cluster sizes, when cluster size can be chosen freely. When ICCs differ between arms but the variance is equal, the optimal design allocates more than half the clusters to the arm with the higher ICC, but (typically only slightly) less than half the individuals and hence a smaller cluster size. We also describe optimal design under constraints on the number of clusters or cluster size in one or both arms. This methodology allows trialists to consider a range for the number of clusters in the trial and for each to identify the optimal design. Except if there is clear prior evidence for the ICC and variance by arm, a range of values will need to be considered. Researchers should choose a design with adequate power across the range, while also keeping enough clusters in each arm to permit the intended analysis method.

Optimal Allocation Ratios: A Square Root Relationship between the Ratios of Symbiotic Costs and Benefits.

AbstractAll organisms struggle to make sense of environmental stimuli in order to maximize their fitness. For animals, the responses of single cells and superorganisms to stimuli are generally proportional to stimulus ratios, a phenomenon described by Weber's law. However, Weber's law has not yet been used to predict how plants respond to stimuli generated from their symbiotic partners. Here we develop a model for quantitatively predicting the ratios of carbon (C) allocation to symbionts that provide nutrients to their plant host. Consistent with Weber's law, our model demonstrates that the optimal ratio of resources allocated to a less beneficial relative to a more beneficial symbiont scale to the ratio of the growth benefits of the two strains. As C allocation to symbionts increases, the ratio of C allocation to two strains approaches the square root of the ratio of symbiotic growth benefits (e.g., a worse symbiont providing one-fourth the benefits gets the C of a better symbiont). We document a compelling correspondence between our square root model prediction and a meta-analysis of experimental literature on C allocation. This type of preferential allocation can promote coexistence between more beneficial and less beneficial symbionts, offering a potential mechanism behind the high diversity of microbial symbionts observed in nature.

Performance evaluation and optimization of a task offloading strategy on the mobile edge computing with edge heterogeneity

With the development for the technology of mobile edge computing (MEC) and the grave situation for the shortage of global energy, the problem of computation offloading in a cloud computing framework is getting more attention by network managers. In order to improve the experience quality of users and increase the energy efficiency of the system, we focus on the issue of task offloading strategy in MEC system. In this paper, we propose a task offloading strategy in the MEC system with a heterogeneous edge. By considering the execution and transmission of tasks under the task offloading strategy, we present an architecture for the MEC system. We establish a system model composed of M/M/1, M/M/c and M/M/ $$\infty$$ queues to capture the execution process of tasks in local mobile device (MD), MEC server and remote cloud servers, respectively. Moreover, by trading off the average delay of tasks, the energy consumption level of the MD and the offloading expend of the system, we construct a cost function for serving one task and formulate a joint optimization problem for the task offloading strategy accordingly. Furthermore, under the constraints of steady state and proportion scope, we use the Lagrangian function and the corresponding Karush–Kuhn–Tucker (KKT) condition to obtain the optimal task offloading strategy with the minimum system cost. Finally, we carry out numerical experiments on the MEC system to investigate the influence of system parameters on the task offloading strategy and to obtain the optimal results. The experiment results show that the task offloading strategy proposed in this paper can balance the average delay, the energy consumption level and the offloading expend with the optimal allocation ratio.

Optimization for Wireless-Powered IoT Networks Enabled by an Energy-Limited UAV Under Practical Energy Consumption Model

This letter investigates an energy-limited unmanned aerial vehicle (UAV)-enabled wireless-powered Internet-of-Things (IoT) networks. Herein, we propose an energy-constrained/limited fly-and-hover energy harvest (EFH-EH) scheme. The UAV charges the IoT sensors during its flying time, while the hovering time of the UAV above each sensor is divided into two parts, one for energy transfer and the other for information transmission. In particular, a maximum available energy constraint is imposed on the UAV to capture UAV’s real-world energy-limited feature. In addition, a practical UAV energy consumption model is adopted, which differentiates the hovering, flying, and charging energy consumption of the UAV. Under these practical constraints, we study the optimal time allocation and hovering time ratio to maximize the sum throughput. Numerical results show that the proposed EFH-EH scheme outperforms existing schemes, and the maximum available energy constraint limits the system performance when the transmit power is high.

Optimal carbon tax income distribution and health welfare spillover effect based on health factors

Based on the Over Lapping Generation Model, this paper concerns the impact of environmental pollution and residents' health status on economic activities, and analyzes the relationship between tax revenue distribution proportion, economic activities and residents' social welfare. Through modeling, health welfare is introduced into welfare function, and time allocation proportion is introduced into health function and consumption budget. It is proved that the level of economic output and social welfare level can simultaneously optimal. Given the tax rate, we explore the optimal allocation ratio of carbon tax revenue when the per capita output of the economic steady-state equilibrium is optimal and the social welfare of the residents is optimal. Moreover, the evolutionary relationship among spillover effect, transfer payment, carbon tax, etc. is revealed. The stability analysis of qualitative conclusion is carried out and corresponding policies are put forward. It is proved that the optimal point of health welfare spillover effect exists. Then, under the steady-state equilibrium, in this paper the optimal effect of health welfare spillover is obtained.

Fairness-Aware Intragroup Cooperative Transmission in Wireless Powered Communication Networks

This article investigates fairness-aware transmission in a wireless powered communication network (WPCN), in which a group of adjacent users receive radio frequency energy and then cooperatively transmit information to a remote access point (AP) by using the harvested energy with time division multiple access (TDMA) scheme. Considering the constraints of practical energy harvesting electric circuits, a non-linear energy harvesting model is adopted in this paper. To guarantee both throughput fairness and signal-to-noise-ratio (SNR) fairness among users in the group, we propose a cooperative transmission protocol which contains three phases: wireless energy transmission (WET) phase, single information transmission phase and cooperative information transmission phase. Each user harvests wireless energy in WET phase, and then divides the harvested energy into two parts to be used in the rest two phases. In single information transmission phase, each user broadcasts its information to the AP and all the other users. In cooperative information transmission phase, all the users transmit information jointly to the AP. At the AP, the same signals in cooperative information transmission phase are combined with these in single information transmission phase by using maximum ratio combining (MRC) method. The common SNR of the received signals at the AP from all the users is achieved in both single information transmission phase and cooperative information transmission phase. Furthermore, the throughput fairness is achieved by common SNR and equal time allocation for information transmission at each user. Besides, we optimize the max-min throughput by joint WET time and harvested energy allocation. The optimal time allocation ratio and harvested energy allocation ratio are derived in closed forms. The cooperative diversity gain is achieved and numerical results demonstrate that the proposed protocol has low complexity and high reliability. Moreover, it also achieves a higher minimum throughput and is more energy-efficient in harsh transmission condition than other transmission protocols in the literature.