Trade-off Research Articles

Environmentally dependent interactions shape patterns in gene content across natural microbiomes.

Sequencing surveys of microbial communities in hosts, oceans and soils have revealed ubiquitous patterns linking community composition to environmental conditions. While metabolic capabilities restrict the environments suitable for growth, the influence of ecological interactions on patterns observed in natural microbiomes remains uncertain. Here we use denitrification as a model system to demonstrate how metagenomic patterns in soil microbiomes can emerge from pH-dependent interactions. In an analysis of a global soil sequencing survey, we find that the abundances of two genotypes trade off with pH; nar gene abundances increase while nap abundances decrease with declining pH. We then show that in acidic conditions strains possessing nar fail to grow in isolation but are enriched in the community due to an ecological interaction with nap genotypes. Our study provides a road map for dissecting how associations between environmental variables and gene abundances arise from environmentally modulated community interactions.

Green AI: exploring carbon footprints, mitigation strategies, and trade offs in large language model training

Prominent works in the space of Natural Language Processing (NLP) have long attempted to create new innovative models by improving upon previous model training approaches, altering model architecture, and developing more in-depth datasets to better their performance. However, with the quickly advancing field of NLP comes increased greenhouse gas emissions, posing concerns over the environmental damage caused by training LLMs. Gaining a comprehensive understanding of the various costs, particularly those pertaining to environmental aspects, that are associated with artificial intelligence serves as the foundational basis for ensuring safe AI models. Currently, investigations into the CO2 emissions of AI models remain an emerging area of research, and as such, we evaluate the CO2 emissions of well-known large language models, which have an especially high carbon footprint due to their significant amount of model parameters. We argue for the training of LLMs in a way that is responsible and sustainable by suggesting measures for reducing carbon emissions. Furthermore, we discuss how the choice of hardware affects CO2 emissions by contrasting the CO2 emissions during model training for two widely used GPUs. Based on our results, we present the benefits and drawbacks of our proposed solutions and make the argument for the possibility of training more environmentally safe AI models without sacrificing their robustness and performance.

Analysis of the privacy-performance tradeoff of reference testing in Forensic Investigative Genetic Genealogy.

During an investigation using Forensic Investigative Genetic Genealogy, which is a novel approach for solving violent crimes and identifying human remains, reference testing-when law enforcement requests a DNA sample from a person in a partially constructed family tree-is sometimes used when an investigation has stalled. Because the people considered for a reference test have not opted in to allow law enforcement to use their DNA profile in this way, reference testing is viewed by many as an invasion of privacy and by some as unethical. We generalize an existing mathematical optimization model of the genealogy process by incorporating the option of reference testing. Using simulated versions of 17 DNA Doe Project cases, we find that reference testing can solve cases more quickly (although many reference tests are required to substantially hasten the investigative process), but only rarely (<1%) solves cases that cannot otherwise be solved. Through a mixture of mathematical and computational analysis, we find that the most desirable people to test are at the bottom of a path descending from an ancestral couple that is most likely to be related to the target. We also characterize the rare cases where reference testing is necessary for solving the case: when there is only one descending path from an ancestral couple, which precludes the possibility of identifying an intersection (e.g., marriage) between two descendants of two different ancestral couples.

Scientific Integration of Operations Research and Machine Learning for Data Centre Optimization

In this study, we explore how to optimize data center operations by combining Operations Research (OR) and Machine Learning (ML) methodologies with Python-based categorization algorithms. Using Scikit-learn and TensorFlow, two Python libraries, we investigate how ML algorithms might be integrated with OR techniques like queuing theory and linear programming to forecast workloads and allocate resources more effectively. Problems with scheduling workloads, allocating resources, and managing energy consumption are at the heart of our research into data center optimization. The goal of this comprehensive framework is to create more effective and environmentally friendly data centre operations by systematically evaluating Python-based categorization models in response to changing workload demands and environmental circumstances. Introduction: The backbone of our digital infrastructure, data centers stand tall in the ever-changing world of contemporary technology. A vast variety of online services, including social media platforms, e-commerce websites, cloud computing, and big data analytics, rely on the servers, storage devices, networking gear, and other essential components housed in these expansive facilities. Meeting the ever-increasing demands for computational resources while simultaneously enhancing performance, efficiency, and cost-effectiveness is a daunting task for data centers, which are already struggling to keep up with the exponential growth in both the amount and complexity of digital data. Objectives: Our goal in writing this article is to delve into the ways in which data center optimization intersects with Operations Research and Machine Learning. Data center optimization presents a wide range of problems, and this course will explore the theory, methods, and best practices for using OR and ML to solve these problems. To develop an integrated framework that combines operations research (OR) and machine learning (ML) techniques to optimize the performance, energy efficiency, and reliability of data centers. Methods: Optimization strategies that improve data center operations in terms of performance, efficiency, and sustainability. These proposed strategies make use of both OL and ML techniques. Data center operators can optimize resource allocation, workload management, temperature control, energy consumption, and anomaly detection in real-time by formally stating the optimization problem in a mathematical framework. This allows for informed decision-making, systematic analysis of trade-offs, and the implementation of adaptive control strategies. Results: The visualization depicts the projected energy usage in terms of bandwidth for both approaches, compared to the actual values. In general, although both methods demonstrate potential, additional refinement and optimization may be necessary to attain superior outcomes in real-life situations. This discussion presents an analysis of the performance of both procedures and offers insights into their respective strengths and shortcomings, which can serve as a foundation for further investigation or improvement of the approaches. Conclusions: By using a comprehensive and multidisciplinary approach, we can optimize data centres in a way that boosts efficiency and performance while simultaneously encouraging innovation, resilience, and sustainability in data centre operations. Also, Data center gains in resource operators can achieve considerable utilization, energy efficiency, and overall system performance by integrating optimization algorithms, predictive analytics, and adaptive control strategies

Development of a method to assess synergy and competition for water use among water-energy-food nexus in the Yellow River basin: Water quantity-quality dimensions

Water, as an indispensable component of the water-energy-food (WEF) nexus, plays a pivotal role in shaping its stability and safety. The competition for water between the food and energy systems is accentuated in the concept of the nexus. However, existing quantitative frameworks and assessment mechanisms have limitations as they often neglect to consider water quality in water competition within the WEF nexus. Therefore, a WEF nexus synergy and competition assessment method was proposed by coupling water footprint theory and the Lotka-Volterra model in this paper. This method establishes two scenarios based on the water footprint perspective, namely, water quantity and water quality-quantity. It effectively addresses the deficiencies in quantitative analysis of WEF system trade-offs and synergies. To illustrate the application of the method, this study conducted a case study in the Yellow River Basin (YRB) of China, evaluating the complex competitive and synergistic mechanisms of water use in the energy and food industries. Compared to the water quantity scenario, the results reveals that the inclusion of gray water footprint intensifies the competition for water in the food and energy industries in the YRB from 2000 to 2020, particularly in resource-based and economically developed cities. The spatial distribution characteristics of water resource competition and synergy in the YRB’s WEF system align with WEF endowment and economic technology levels. To address water conflicts in the WEF nexus and enhance nexus security, this study proposes a regulatory pathway for WEF system synergistic security based on two aspects (water competition and synergy characteristics and resource endowment). It contributes to a more comprehensive understanding of water competition and synergy in the WEF nexus and provides valuable insights for resource management.

Controller design and energy analysis for stochastic differential systems with one-sided polynomial growth under finite-time attraction constraint

This article presents a novel controller design approach for stochastic nonlinear systems exhibiting one-sided polynomial growth. The objective is to achieve finite-time attractiveness and estimate control energy consumption. By constructing an appropriate controller and employing inequality techniques, sufficient conditions for achieving finite-time attractiveness in stochastic nonlinear systems are established. Moreover, the article introduces the concept of expected energy consumption for stochastic systems and provides upper bounds on control time and energy consumption. A comprehensive trade-off analysis between control time and energy consumption is conducted to identify the optimal control intensity. The proposed approach is validated through numerical examples, demonstrating its effectiveness in practice.

Goodness-of-fit, identifiability and extrapolation: Can the Two-Component Extreme Value distribution be used in at-site flood frequency analysis?

When fitting three-parameter flood frequency models to annual maximum (AM) flood series, the lack-of-fit can be mitigated by censoring potentially influential low flows (PILFs). An alternative and less-studied approach is to apply mixture probability models with four or more parameters, which trade off greater flexibility to fit AM series against the need to deal with degeneracy which arises when there is insufficient information to identify mixture components. However, the issue of degeneracy and the lack of a robust inference framework present a significant barrier to adoption. This study investigated the potential of the most parsimonious mixture model, the four-parameter Two-Component Extreme Value (TCEV) model. A Bayesian framework using Markov chain Monte Carlo sampling was developed to robustly characterize parameter uncertainty even in the presence of degeneracy. Two new posterior diagnostics based on the strength of the TCEV components were developed to aid identification of degeneracy. Armed with a robust inference framework, the study evaluated the potential of TCEV using a case study based on 31 catchments in eastern Australia with records exceeding 70 years. The evaluation used short to long records to compare TCEV and Log Pearson III fit and extrapolative uncertainty. The Log Pearson approach (LP3-PILF) censors PILFs following the approach described in Australian Rainfall and Runoff. With respect to goodness-of-fit, we found in most cases that TCEV fitted AM flood peaks well without the need to censor or stratify data, and overall, no clear difference emerged between TCEV and LP3-PILF. However, and contrary to expectation, TCEV produced high flow quantile confidence intervals consistently narrower than LP3-PILF even in the presence of degeneracy. While more case studies in different regions are needed to confirm the potential of TCEV, this study is a reminder that goodness-of-fit is a necessary but not sufficient criterion for selecting the probability model that best represents flood frequency.

A generalized integral equation formulation for pricing American options under regime-switching model

In this paper, we present a generalized and highly efficient integral equation formulation for the price of American put options under regime-switching model with a goal of improving computational efficiency in mind, particularly when the number of regimes is large. Our achieved high efficiency is based on a newly proved theorem, which facilitates the decoupling of a system with simultaneously coupled PDEs so that they can be solved recursively at the numerical solution stage. Such a high efficiency is also fueled further by that the integral equation approach being characterized with its excellent trade off between maximizing analytical tractability and minimizing numerical discretization. Upon providing some numerical examples to demonstrate the implementation of the new approach and its efficiency, we anticipate that the very same theorem can be used to reduce the computational burden if other numerical approaches are adopted, for this highly challenging nonlinear problem.

FlashSwift: A Configurable and More Efficient Range Proof With Transparent Setup

Bit-decomposition-based zero-knowledge range proofs in the discrete logarithm (DLOG) setting with a transparent setup, e.g., Bulletproof (IEEE S&amp;P 18), Flashproof (ASIACRYPT 22), and SwiftRange (IEEE S&amp;P 24), have garnered widespread popularity across various privacy-enhancing applications. These proofs aim to prove that a committed value falls within the non-negative range [0, 2^N-1] without revealing it, where N represents the bit length of the range. Despite their prevalence, the current implementations still suffer from suboptimal performance. Some exhibit reduced communication costs at the expense of increased computational costs while others experience the opposite. Presently, users are compelled to utilize these proofs in scenarios demanding stringent requirements for both communication and computation efficiency. In this paper, we introduce, FlashSwift, a stronger DLOG-based logarithmic-sized alternative. It stands out for its greater shortness and significantly enhanced computational efficiency compared with the cutting-edge logarithmic-sized ones for the most common ranges where N is no more than 64. It is developed by integrating the techniques from Flashproof and SwiftRange without using a trusted setup. The substantial efficiency gains stem from our dedicated efforts in overcoming the inherent incompatibility barrier between the two techniques. Specifically, when N=64, our proof achieves the same size as Bulletproof and exhibits 1.1 times communication efficiency of SwiftRange. More importantly, compared with the two, it achieves 2.3 times and 1.65 times proving efficiency, and 3.2 times and 1.7 times verification efficiency, respectively. At the time of writing, our proof also creates two new records of the smallest proof sizes, 289 bytes and 417 bytes, for 8-bit and 16-bit ranges among all the bit-decomposition-based ones without requiring trusted setups. Moreover, to the best of our knowledge, it is the first configurable range proof that is adaptable to various scenarios with different specifications, where the configurability allows to trade off communication efficiency for computational efficiency. In addition, we offer a bonus feature: FlashSwift supports the aggregation of multiple single proofs for efficiency improvement. Finally, we provide comprehensive performance benchmarks against the state-of-the-art ones to demonstrate its practicality.

Optimizing social costs in post-pandemic humanitarian distribution models

ABSTRACT In response to the COVID-19 pandemic, the Red Cross Society of China played a crucial role in distributing medical donations, but the initial efforts were inefficient and neglected medical personnel’s welfare. This study proposes a time-sensitive humanitarian distribution model that optimizes the social costs by integrating logistics and deprivation costs that cares about human suffering. We ues the Gini coefficient to evaluate delays in distribution, aiding trade-off analysis between logistics efforts and social welfare. Our findings show that the proposed model improves the Gini coefficient by an average of 33.96% across 500 scenarios. Additionally, investing 23.7% more in logistics costs reduces the Gini coefficient by 0.1, enhancing the social welfare of medical supplies distribution. Sensitivity analysis examines the impact of time delay and cost investment on the Gini coefficient, offering insights into balancing logistics investments and social welfare.

INTEGRATED ASSESSMENT OF CLIMATE CHANGE ADAPTATIONS FOR THE RESILIENT AGRICULTURAL PRODUCTION SYSTEM IN SOUTH PUNJAB, PAKISTAN

Agricultural production systems are multidimensional, interlinked, complex and diverse, and need special attention to cope with changing climate, technology and changes in input and output market structure. Climate change is an evident phenomenon that drastically affects the agricultural production system. The developing countries mainly rely on farming activities for the needs of food and Fiber. This study aims to find climate change impacts and economic analysis of proposed adaptations and to formulate a climate-resilient agricultural production system. The primary and secondary data were collected by conducting a well-designed South Punjab survey. The secondary data about historical crop yields, socioeconomic profiles, climate data, and crop simulation results are incorporated into the model. The TOA-MD (Tradeoff analysis multidimensional impact assessment) model was used for the economic analysis. The results showed substantial negative impacts of climate change on farm income. The adaptations regarding climatic variations are present and increase the net farm returns adopted by farming communities, which are projected in public policies. The financial inclusion of the farming community is needed in terms of farm insurance and finance.

선삭 절삭력 예측을 위한 지식 기반 툴 개발

In this study, a knowledge-based tool is developed to enhance the manufacturing efficiency of mechanical components, particularly those requiring the removal of large components, such as the struts of airplane landing gears. Using this tool, knowledge is extracted and implemented during the turning process. The cutting forces and material-removal quantities are calculated based on the obtained knowledge. User-friendly graphical user interfaces are provided for user interactions. They can be used to input various parameters, such as the workpiece, cutting tool, and machining conditions, including the cutting material, rotational speed, and cut depth. The tool outputs essential parameters, such as the cutting forces, torque, power consumption, and material-removal rate, under different cutting conditions. More importantly, the tool enables users to conduct trade-off analyses, thus enabling the identification of near-optimal cutting conditions while accounting for factors such as tool life and production efficiency. This study contributes to the machining of high-strength materials by providing a useful tool for efficient industrial manufacturing.

An Engineered Assessment System to Manage Demand Reduction Initiatives

The Joint Warfighting Concept is a framework for how the United States will fight in the future security landscape. To successfully carry out these new concepts, the military services must find ways to lessen the logistics burden at the strategic, operational, and tactical levels. Only by reducing the demands on its current and planned sustainment systems can the United States continue to be a dominant force on the world stage. However, defense agencies such as the Logistics Functional Capability Board lack a quantitative, credible, repeatable process to effectively assess and manage demand reduction initiatives. This paper is based on work from a student/faculty team that created an assessment system for demand reduction initiatives. Discussion highlights the systems engineering techniques that were used in the effort, which includes but is not limited to stakeholder analysis, functional analysis, morphological analysis, and value modeling. The blended qualitative and quantitative methods focused on user and stakeholder needs to create a process system to evaluate technologically disparate, multicriteria systems. The team expects that the resultant assessments system’s applicability to a range of demand reduction initiatives would be of interest to organizations that must prioritize technology proposals, as well as perform trade-off analysis. Additionally, the approach to create the assessment system has the flexibility to adapt to changes in the stakeholders’ requirements from the reduction initiatives, as well as the ongoing evolution of the warfighting concepts.

Efficiency and longevity trade-off analysis and real-time dynamic health state estimation of solid oxide fuel cell system

Solid oxide fuel cell (SOFC) is a promising energy conversion technology due to its advantages of high efficiency, low emissions, and fuel adaptability. Addressing the balance between efficiency and longevity is crucial for their application on a large scale. Accurate estimation and prediction of the health state of SOFC systems is essential for the study of optimization between system efficiency and degradation. In this work, the influence law of degradation, the relationship between efficiency and longevity, and their joint optimization, alongside the state of health (SOH) estimation of the SOFC system have been deeply investigated, based on a rigorously validated model of a degraded SOFC system. First, the influential variables that predominantly influence system degradation are identified and analyzed via principal component analysis, including stack average temperature, stack temperature gradient, and fuel utilization. Then, the exploration of the trade-off relationship between system efficiency and longevity under all operating conditions is conducted, and the influence laws of influential variables on system degradation are revealed. In light of the lack of accuracy during load changes and the high time cost for existing SOH estimation methodologies, a novel improved SOH estimation strategy, considering both stack voltage and current-related states, is proposed for real-time estimation of system SOH under varying fuel compositions and dynamic power scenarios. The performance of the proposed method is demonstrated by comparing with existing methodologies. This comprehensive study lays the groundwork for the effective and sustainable health management of SOFC systems, ensuring their efficiency and longevity are maintained at an optimal balance.

Free-breathing, fat-corrected T1 mapping of the liver with stack-of-stars MRI, and joint estimation of T1, PDFF, , and .

Quantitative T1 mapping has the potential to replace biopsy for noninvasive diagnosis and quantitative staging of chronic liver disease. Conventional T1 mapping methods are confounded by fat and inhomogeneities, resulting in unreliable T1 estimations. Furthermore, these methods trade off spatial resolution and volumetric coverage for shorter acquisitions with only a few images obtained within a breath-hold. This work proposes a novel, volumetric (3D), free-breathing T1 mapping method to account for multiple confounding factors in a single acquisition. Free-breathing, confounder-corrected T1 mapping was achieved through the combination of non-Cartesian imaging, magnetization preparation, chemical shift encoding, and a variable flip angle acquisition. A subspace-constrained, locally low-rank image reconstruction algorithm was employed for image reconstruction. The accuracy of the proposed method was evaluated through numerical simulations and phantom experiments with a T1/proton density fat fraction phantom at 3.0 T. Further, the feasibility of the proposed method was investigated through contrast-enhanced imaging in healthy volunteers, also at 3.0 T. The method showed excellent agreement with reference measurements in phantoms across a wide range of T1 values (200 to 1000 ms, slope = 0.998 (95% confidence interval (CI) [0.963 to 1.035]), intercept = 27.1 ms (95% CI [0.4 54.6]), r2 = 0.996), and a high level of repeatability. In vivo imaging studies demonstrated moderate agreement (slope = 1.099 (95% CI [1.067 to 1.132]), intercept = -96.3 ms (95% CI [-82.1 to -110.5]), r2 = 0.981) compared to saturation recovery-based T1 maps. The proposed method produces whole-liver, confounder-corrected T1 maps through simultaneous estimation of T1, proton density fat fraction, and in a single, free-breathing acquisition and has excellent agreement with reference measurements in phantoms.

The Nexus between Poverty and Elections in Africa: A Case Study of Somaliland and the Gambia

This article explores the states of democracy and the conduct of elections in Somaliland and the Gambia. The article examines the democratic and electoral institutions responsible for the conduct of elections in the two countries and assesses their level of effectiveness for a free and transparent election. The article uses multiple case studies as the research design to generate data on elections in Somaliland and the Gambia. Triangulation was also adopted as a method of obtaining multiple data to test their validity and relevance for this study. The study adopted content analysis as the technique for data analysis. The study found that the conduct of elections in both Somaliland and the Gambia has been influenced by vote buying which is the consequence of poverty. The study found that limited economic opportunities in both countries make citizen trade off their votes for favors during elections. The study recommends widening economic opportunities and strengthening the media and civil society organizations for civic education and capacity building of political parties and government officials.

Optimizing lunar regolith for vat polymerization and sintering: pre-processing & mineral composition impact

Lunar regolith is the most abundant resource on the lunar surface, which can be used for in-situ fabrication and repair technologies. Vat photopolymerization-based additive manufacturing is among the most promising techniques, capable of producing precise ceramic parts of complex shapes from the lunar regolith feedstock for the needs of future crewed exploration missions to the Moon. One of the under-studied aspects of additive manufacturing with lunar regolith is the pre-and post-treatment procedures, which would ensure optimal energy and material consumption and the best printing performance. The goal of the present article was to define the influence of the mineral composition of lunar regolith simulants and the parameters of their pre-processing on the properties of sintered regolith ceramics. It was found that the highland regolith could be sintered to higher relative density compared to the mare regolith. The optimal sintering temperature was determined to be 1150 °C for both types of lunar regolith. An optimal mineral and fractional composition for the regolith feedstock was determined based on the trade-off analysis between lunar regolith sinterability and its printability via vat photopolymerization-based additive manufacturing. Vat-polymerization was performed to produce complex-shaped ceramic parts, yielding 95 % of relative density and a mean ultimate flexural strength of 106 ± 5 MPa, confirming the proposed trade-off point.

Rationale, conceptual issues, and resultant protocol for a mixed methods Person Trade Off (PTO) and qualitative study to estimate and understand the relative value of gains in health for children and young people compared to adults.

Economic evaluation of healthcare typically assumes that an identical health gain to different patients has the same social value. There is some evidence that the public may give greater value to gains for children and young people, although this evidence is not always consistent. We present a mixed methods study protocol where we aim to explore public preferences regarding health gains to children and young people relative to adults, in an Australian setting. This study is a Person Trade Off (PTO) choice experiment that incorporates qualitative components. Within the PTO questions, respondents will be asked to choose between treating different groups of patients that may differ in terms of patient characteristics and group size. PTO questions will be included in an online survey to explore respondent views on the relative value of health gains to different age groups in terms of extending life and improving different aspects of quality of life. The survey will also contain attitudinal questions to help understand the impact of question style upon reported preferences. Additionally, the study will test the impact of forcing respondents to express a preference between two groups compared with allowing them to report that the two groups are equivalent. One-to-one 'think aloud', semi-structured interviews will be conducted to explore a sub-sample of respondents' motivations and views in more detail. Focus groups will be conducted with members of the public to discuss the study findings and explore their views on the role of public preferences in health care prioritisation based on patient age. Our planned study will provide valuable information to healthcare decision makers in Australia who may need to decide whether to pay more for health gains for children and young people compared with adults. Additionally, the methodological test of forcing respondent choice or allowing them to express equivalence will contribute towards developing best practice methods in PTO studies. The rationale for and advantages of the study approach and potential limitations are discussed in the protocol.

Economic shocks and skill acquisition: Evidence from a national online learning platform at the onset of COVID-19

We study how large shocks impact individuals’ skilling decisions using data from a large, government-sponsored, online learning platform in Saudi Arabia. The onset of the COVID-19 pandemic brought about a massive increase in online skilling, and demand shifted towards courses that offered skills, such as telework, likely to be immediately valuable during the pandemic. Consistent with a model where individuals trade off reskilling costs with their expectations of future labor market conditions and their duration of work, we find that shifts into telework courses were largest for older workers. In contrast, younger workers increased enrollments in courses related to new skills, such as general, occupation-specific, and computer-related skills. Using national administrative employment data, we provide descriptive evidence that these investments in skills in early 2020 helped users maintain employment over the course of the pandemic.

Evaluating alternatives to improve drinking water supply within a complex and uncertain human-environment system: case of the Port-au-Prince Metropolitan Region

ABSTRACT Improving decision making in urban water supply systems under a wide range of changing human-environmental scenarios represents a challenging issue, especially when there is a high level of uncertainty and the available information is limited or scarce. To address this concern, the present study applied a decision aiding process to evaluate long-term planning solutions for the Port-au Prince Metropolitan Region’s water supply in Haiti, which is recognized for having a low coverage of water services and great lack of monitoring data. The methodological framework assessed pre-specified alternatives to face uncertain future conditions, with the main emphasis of being aware of how these uncertainties can be framed in the water management practices. To discover the most robust management solutions, a tradeoff analysis and multi-objective optimization allowed to explore the performance of alternatives across many future states of the world and multiple criteria. The results highlighted that human factors associated with the increase of per-capita water use and population growth posed a greater risk on water supply coverage than climatic factors. In addition, the decision support can offer a comprehensive representation of potential supply/demand futures, and provides decision-makers with the opportunity to discuss a posteriori the most appropriate water supply solution under an extensive variety of information with severe uncertainty.