What are relevant levels of description when investigating human language? How are these levels connected to each other? Does one description yield smoothly into the next one such that different models lie naturally along a hierarchy containing each other? Or, instead, are there sharp transitions between one description and the next, such that to gain a little bit accuracy it is necessary to change our framework radically? Do different levels describe the same linguistic aspects with increasing (or decreasing) accuracy? Historically, answers to these questions were guided by intuition and resulted in subfields of study, from phonetics to syntax and semantics. Need for research at each level is acknowledged, but seldom are these different aspects brought together (with notable exceptions). Here we propose a methodology to inspect empirical corpora systematically, and to extract from them, blindly, relevant phenomenological scales and interactions between them. Our methodology is rigorously grounded in information theory, multi-objective optimization, and statistical physics. Salient levels of linguistic description are readily interpretable in terms of energies, entropies, phase transitions, or criticality. Our results suggest a critical point in the description of human language, indicating that several complementary models are simultaneously necessary (and unavoidable) to describe it.

In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal front, well-distributed, maximally extended and fully filled. Therefore, an effective performance indicator must encompass these features as a whole and must be Pareto dominance compliant. Unfortunately, some of the known indicators often fail to properly reflect the quality of a solution set or cost a lot to compute. This paper demonstrates that the Degree of Approximation (DOA) quality indicator, is a weakly Pareto compliant unary indicator that gives a good estimation of the match between the approximated front and the Pareto-optimal front. Moreover, DOA computation is easy and fast.

This paper is focused on two topics very relevant in water distribution networks (WDNs): vulnerability assessment and the optimal placement of water quality sensors. The main novelty element of this paper is to represent the data of the problem, in this case all objects in a graph underlying a water distribution network, as discrete probability distributions. For vulnerability (and the related issue of re-silience) the metrics from network theory, widely studied and largely adopted in the water research community, reflect connectivity expressed as closeness centrality or, betweenness centrality based on the average values of shortest paths between all pairs of nodes. Also network efficiency and the related vulnerability measures are related to average of inverse distances. In this paper we propose a different approach based on the discrete probability distribution, for each node, of the node-to-node distances. For the optimal sensor placement, the elements to be represented as dis-crete probability distributions are sub-graphs given by the locations of water quality sensors. The objective functions, detection time and its variance as a proxy of risk, are accordingly represented as a discrete e probability distribution over contamination events. This problem is usually dealt with by EA algorithm. We’ll show that a probabilistic distance, specifically the Wasserstein (WST) distance, can naturally allow an effective formulation of genetic operators. Usually, each node is associated to a scalar real number, in the optimal sensor placement considered in the literature, average detection time, but in many applications, node labels are more naturally expressed as histograms or probability distributions: the water demand at each node is naturally seen as a histogram over the 24 hours cycle. The main aim of this paper is twofold: first to show how different problems in WDNs can take advantage of the representational flexibility inherent in WST spaces. Second how this flexibility translates into computational procedures.

The quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts that has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy ‘flips’ r binary variables to get a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, very high-quality solutions within a short CPU time.

Water management and soil pollution are hot issues in modern agriculture. While more production of food is required, this quantity has to be obtained using the minimum level of resources and the maximum amortization of assets. Moreover, studies show that in Europe, 30% of water consumption is for agriculture, which has a strong influence not only on the amount of water consumed, but also on its quality due to pollution caused by chemical fertilizers, pesticides and other pollutants used in this sector. Therefore, a major concern is related to the use of water, its efficient consumption, which requires optimal irrigation systems both in terms of water transport and distribution. In this context, but also in the context of a turbid environmental debate, the most important facts in agriculture are the protection of the environment on a long range of time. In order to obtain good results for an irrigation system, in this paper we will present a model for calculating the best suited material for a given geographical area and the optimal water content for irrigation

For the time being, public sector innovation gains new and complex forms of expression: managerial, institutional, technological or communication. This fact is also due to national and international important bodies’ interest for using innovation as resource and tool for public sector development. Characterised by complexity and adaptation, the innovative processes in the public sector embrace the form of medium and long term innovation strategies, holding high key socio-economic impact on the social utility of public sector innovation. The optimality of innovation strategies becomes a tool for improved decisions in public sector management, providing the methodology for their evaluation related to the objectives of development in the public sector.

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of \textit{"Higgs Boson like"} potentials among others.

One of the most effective image processing techniques is the use of convolutional neural networks, where we combine intensity values at grid points in the vicinity of each point. To speed up computations, researchers have developed a dilated version of this technique, in which only some points are processed. It turns out that the most efficient case is when we select points from a sub-grid. In this paper, we explain this empirical efficiency proving that the sub-grid is indeed optimal – in some reasonable sense. To be more precise, we prove that all reasonable optimality criteria, the optimal subset of the original grid is either a sub-grid, or a sub-grid-like set.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

Four decades of snooker rankings are analyzed in terms of prize money distributions. In particular, it is investigated how much these rankings are dominated by the top players, and also by players from the UK. The main conclusions are: (1) with an increasing amount of available prize money, the rankings are less dominated by the top players, and (2) players from the UK have historically earned a significantly larger share of the available prize money than could be reasonably expected based on the actual percentage of UK players.

In this paper we study a bilinear optimal control problem related to a 2D parabolic-elliptic chemo-repulsion system consider a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a result on the existence of Lagrange multipliers in Banach spaces, we derive an optimality system for a local optimal solution.

This study examines the potential of implementing a systematic approach to piloting desalination plants, with the objective of evaluating energy improvements in water desalination processes. The global scarcity of freshwater resources has significantly influenced the development of desalination technologies, with reverse osmosis emerging as one of the most prevalent and highly regarded methods. Pilot tests with the latest generation of reverse osmosis membranes in large desalination plants are becoming increasingly common. This is due to the fact that small-scale experiments are being carried out on the operation of new generation membranes with better salt rejection and lower energy consumption. The objective of this approach is to achieve the optimal water quality standard at the lowest possible cost. In this manner, pilot tests are being conducted prior to the determination of whether to alter the reverse osmosis membranes, as this represents a substantial investment. The objective of these tests is to minimise the risk of making an erroneous decision and to ensure optimal results in terms of energy consumption, operating costs and reduction of environmental impact, while complying with the requisite water quality standards. In this case, the Pareto analysis is employed to identify the two or three most significant causes whose treatment affects more than 80% of the potential energy savings to be implemented. This article introduces a novel approach to studying a total of 180 desalination plants at the territorial level in the Canaries.

Defects are considered one of the wastes in manufacturing systems that negatively affect the delivery times, cost and quality of products leading to manufacturing companies facing a critical situation with the customers and to not comply with the IPC-A-610E standard for the acceptability of electronic components. This is the case is a manufacturing company located in Tijuana, Mexico. Due to an increasing demand on the products manufactured by this company, several defects have been detected in the welding process of electronic boards, as well as in the components named Thru-Holes. It is for this reason that this paper presents a lean manufacturing application case study. The objective of this research is to reduce at least 20% the defects generated during the welding process. In addition, it is intended to increase 20% the capacity of 3 double production lines where electronic boards are processed. As method, the PDCA cycle, is applied. The Pareto charts and the flowchart are used as support tools. As results, defects decreased 65%, 79% and 77% in three analyzed product models. As conclusion, the PDCA cycle, the Pareto charts, and the flowchart are excellent quality tools that help decrease the number of defective components.

Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to flows, which, ultimately, are essential to life itself. Living beings are under the pressures of natural selection, thus are biological flows as well. At the same time, the maintenance of homeostatic conditions, the tenet of physiology, demands regulation of these flows by control of variables. However, due to the very nature of these systems, regulation of flows and control of variables become entangled in closed loops. Therefore, the search for adaptation in flows takes a different path than the search for adaptation in morphological traits. Being at the roots of transfer processes, thermodynamic criteria turn out to be as natural physical candidates. Likewise, being at the roots of physiology, control turns out to be as a natural biological candidate in that path. Here we show how to combine entropy generation, with respect to a generalized process, and control of parameters (in such a generalized process) in order to create a criterium of optimal ways to regulate changes in generalized flows.

This paper proposed a triangular inequality-based rewiring method for the Rapidly exploring Random Tree (RRT)-Connect robot path-planning algorithm that guarantees the planning time compared to the RRT algorithm, to bring it closer to the optimum. To check the proposed algorithm’s performance, this paper compared the RRT and RRT-Connect algorithms in various environments through simulation. From these experimental results, the proposed algorithm shows both quicker planning time and shorter path length than the RRT algorithm and shorter path length than the RRT-Connect algorithm with a similar number of samples and planning time.

This study explores the potential of piloting desalination plants in a systematic way to evaluate energy improvements in water desalination processes. Pilot tests with the latest generation of reverse osmosis membranes in large desalination plants are becoming increasingly common, as small-scale experiments are carried out on the operation of new generation membranes with better salt rejection and lower energy consumption. This approach aims to achieve optimal water quality standard at the lowest possible cost. In this way, pilot tests are being carried out before the decision is made whether to change the reverse osmosis membranes, as this represents a significant investment. By carrying out these tests, we hope to minimize the risk of making a mistake to ensure the best results in terms of energy consumption, operating costs and reducing the environmental impact while complying with the required water quality. In this case, the Pareto analysis is used to identify the two or three most significant causes whose treatment affects more than 80% of the possible energy improvement to be implemented. This article introduces a novel approach to studying a total of 180 desalination plants at the territorial level in the Canary Islands. The global scarcity of freshwater resources has greatly contributed to the development of desalination technologies, in which reverse osmosis is one of the most widely used and highly regarded methods.

This article investigates robust optimality and duality for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (in short, UNMPVC) via convexificators. Using the properties of convexificators, we introduce generalized standard Abadie constraint qualification (in short, GS-ACQ) for the considered problem UNMPVC. Moreover, we introduce generalized robust version of nonsmooth stationary conditions, namely, weakly stationary point (in short, RW-Stationary), T-stationary point (in short, RT-Stationary), M-stationary point (in short, RM-Stationary) and S-stationary point (in short, RS-Stationary) for UNMPVC. By employing GS-ACQ, we establish that the RS-Stationary is the necessary first-order optimality condition for a local Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we establish sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type (in short, WRD) and Mond-Weir-type (in short, MWRD) robust dual models corresponding to the primal problem UNMPVC.

The ratio between blade height and chord, named aspect ratio (AR), plays an important role in compressor aerodynamic design. Once selected, it influences stage performance, blade losses, and the stage stability margin. The choice of the design AR involves both aerodynamic and mechanical considerations, and a reasonable aim is frequently to achieve a desired operating range while maximizing efficiency. For a fixed set of aerodynamic and geometric parameters there will be an optimal choice in AR that achieves a maximum efficiency. However, for a state-of-the-art aero-engine design optimality means multi-objective optimality, that is reaching the highest possible efficiency for a number of operating points while achieving a sufficient stability margin. To this end, the influence of the AR on the performance of the first rotor row of a multistage multi-objective high-speed compressor design is analyzed. A careful setup of the high-speed aerodynamic design problem allows the effect of the AR to be isolated. Close to the optimal AR, only a modest efficiency variation is observed, but a considerable change in compressor stability margin (SM) is noted. Decreasing the AR allows for an increasing efficiency, but at the expense of a reduced surge margin. This allows the designer to trade efficiency for stability. Increasing the AR, however, is shown to reduce both surge margin and efficiency, hence a distinct optimality in stability is observed for the analyzed rotor blade row. In this work, the optimality in surge margin with respect to AR is observed whereas a close to optimal efficiency. The predicted range from AR=1.10 to AR=1.64, is only indicative, considering that the definition of a multi-objective optimality requires balancing efficiency and surge margin and that the choice of balancing these two criteria requires making a design choice along a pareto optimal front.

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

Forest planners have traditionally used expected growth and yield coefficients to predict future merchantable timber volumes. However, because climate change affects forest growth, the typical forest planning methods using expected value of forest growth can lead to sub-optimal harvest decisions. We proposed in this paper to formulate the harvest planning with growth uncertainty due to climate change problem as a multistage stochastic optimization problem and use sample average approximation (SAA) as a tool for finding the best set of forest units that should be harvested in the first period even though we have a limited knowledge of what future climate will be. The objective of the harvest planning model is to maximize the expected value of the net present value (NPV) considering the uncertainty in forest growth and thus in revenues from timber harvest. The proposed model was tested on a small forest with 89 stands and the numerical results showed that the approach allows to have superior solutions in terms of net present value and robustness in face of different climate scenarios compared to the approach using the expected growth and yield. The SAA methods requires to generate samples from the distribution of the random parameter. Our results suggested that a sampling scheme that focuses on generating high number of samples in distant future stages is favorable compared to having large sample sizes for the near future stages. Finally, we demonstrated that, depending on the level of forest growth change, ignoring this uncertainty can negatively affect forest resources sustainability.

In this study is considered the design and implementation of pilots in desalination plants, in a systematic way, to evaluate energy improvements in water desalination processes. Pilot tests with the latest generation of reverse osmosis membranes in large desalination plants are becoming increasingly common, as small-scale experiments are carried out on the operation of new generation membranes with better salt rejection and lower energy consumption, to achieve the best water quality required for each case at the lowest possible cost. In this way, pilot tests are being carried out before the decision is made whether or not to change the reverse osmosis membranes, as this represents a significant investment and we minimize the risk of making a mistake in order to ensure the best results in terms of energy consumption, operating costs and reducing the environmental impact while complying with the required water quality. In this case, the Pareto analysis is used to highlight the 2 or 3 most significant causes whose treatment affects more than 80% of the possible energy improvement to be implemented. In this sense, figure 3 below shows the Pareto diagram for the energy improvement of N plants in a given territory. A series of factors that can affect this energy improvement have been numbered from 1 to 7, such as the seawater intake, the decision on the membranes, the energy recuperators, the high-pressure pump, the decisions on the pre-treatment, the feed pump or the post-treatment. The Pareto diagram has been studied at territorial level with a total of 180 seawater desalination plants. The novelty of this article is to apply Pareto diagram to a study of a total of 180 seawater desali-nation plants at territorial level in Canary Islands.

We construct a repeated quantum game with public goods by the quantum entanglement and strong reciprocity. By using the paradigm of quantum game analysis, we obtain that both the quantum entanglement and strong reciprocity are helpful to intensify cooperation and achieving Pareto optimality. In addition, under an example which is greenhouse green viable planting industry, we verify that the quantum entanglement and strong reciprocity have a positive role in cooperation.

We proposed a deep learning based chemometric data analysis technique. We trained L2 regularized sparse autoencoder end-to-end for reducing the size of the feature vector to handle the classic problem of curse of dimensionality in chemometric data analysis. We introduce a novel technique of automatic selection of nodes inside hidden layer of an autoencoder through pareto optimization. Moreover, linear regression, ϵ-SVR , and Gaussian process regressor are applied on the reduced size feature vector for the regression. We evaluated our technique on orange juice and wine dataset and results are compared against state-of-the-art methods. Quantitative results are shown on Normalized Mean Square Error (NMSE) and the results show considerable improvement in the state-of- the-art.

New information suggests female autistic spectrum disorder (ASD) is much more common than previously thought, with a likely prevalence of 6% and with 80% undiagnosed at the age of 18. ASD then becomes a common comorbidity of female mental illness with nearly one in five women who develop a mental illness being autistic. ASD has heretofore been regarded as a pediatric condition and though now thought to be life long it is still not well recognized by adult health services. Most mental illness first presents in the teens and early twenties. Comorbid ASD is more difficult to diagnose due to diagnostic overshadowing, and ASD comorbidity maks the mental illness more severe and mor difficult to treat. Recognized ASD is readily treatable with an approach sympathetic to neurodiversity. Improving the pathway from adolescence to adulthood by increasing knowledge of autism in adult health services would dramatically improve female mental health at surprisingly little extra cost. It is low hanging fruit in a very fraught area of healthcare. This paper will examine the extent of the problem. It will explore solutions and quantify the gains of appropriate therapy.

The aim of the paper is to investigate Nash equilibria and correlated equilibria of classical and quantum games in the context of their Pareto optimality. We study four games: the prisoner's dilemma, battle of the sexes and two versions of the game of chicken. The correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device. We analyze the quantum extension of these games in the Eisert-Wilkens-Lewenstein formalism with the full SU(2) space of players’ strategy parameters. It has been shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counterparts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also analyzed.

Insulation systems for the floor, roof and external walls play a prominent role in providing a thermal barrier for the building envelope. Design decisions made for the insulation material type and thickness can alleviate potential impacts on the embodied energy and improve the building thermal performance. This design problem is often addressed using a BIM-integrated optimisation approach. However, one major weakness lies in the current studies is that BIM is merely used as the source for design parameters input. This study proposes a BIM-based envelope insulation optimisation design framework using a common software Revit to find the trade-off between the total embodied energy of the insulation system and the thermal performance of the envelope by considering the material type and thickness. In addition, the framework also permits data visualisation in a BIM environment, and subsequent material library mapping together with instantiating the optimal insulation designs. The framework is tested on a case study based in Sydney, Australia. By analysing sample designs from the Pareto front, it is found that slight improvement in the thermal performance (1.3399 to 1.2112 GJ/m2) would cause the embodied energy to increase by more than 50 times.

The incorporation of renewable energy into power systems poses serious challenges to the transmission and distribution power system operators (TSOs and DSOs). To fully leverage these resources there is a need for a new market design with improved coordination between TSOs and DSOs. In this paper we propose two coordination schemes between TSOs and DSOs: one centralised and another decentralised that facilitate the integration of distributed based generation; minimise operational cost; relieve congestion; and promote a sustainable system. To this end, we approximate the power equations with linearised equations so that the resulting optimal power flows (OPFs) in both the TSO and DSO become convex optimisation problems. In the resulting decentralised scheme, the TSO and DSO collaborate to optimally allocate all resources in the system. In particular, we propose an iterative bi-level optimisation technique where the upper level is the TSO that solves its own OPF and determines the locational marginal prices at substations. We demonstrate numerically that the algorithm converges to a near optimal solution. We study the interaction of TSOs and DSOs and the existence of any conflicting objectives with the centralised scheme. More specifically, we approximate the Pareto front of the multi-objective optimal power flow problem where the entire system, i.e., transmission and distribution systems, is modelled. The proposed ideas are illustrated through a five bus transmission system connected with distribution systems, represented by the IEEE 33 and 69 bus feeders.

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending results from the literature. We introduce the dual robust version of the above problem, prove the Mond-Weir type weak and strong duality theorems, and illustrate with an example.

We numerically investigate the relationship between the main parameters of thinned antenna arrays using a specifically designed evolutionary algorithm, the Multi-Objective Pareto Evolution for Thinning (MOPET). We provide some useful results that allow assessing the achievable performance of antenna arrays and help researchers and practitioners design radar, 5G, and 6G systems.

We give two examples of the appearance of heavy-tailed distributions in applications to social sciences. Among these distributions are the laws of Pareto, Lotka, and some new ones. The examples are illustrated by constructing suitable toy models.

This paper provides attempts to formalize Hayek’s theory of knowledge. It has been theoretically shown that exponential income distribution is a spontaneous order of the well-functioning market economy. We show that this theoretical result is supported by the empirical evidence from the United Kingdom and China. In particular, we empirically show how the income structure of China evolved towards an exponential distribution after the market-oriented economic reformation. Furthermore, we strictly prove that, if the income structure of an economy obeys an exponential distribution, the income summation over all households leads to an aggregate production function with Hicks-neutral-like technical progress, in which the technology factor is exactly equal to society’s information stock that is a result of combining all of decentralized decisions.

The growth of demand for metallic minerals has faced with the need for new techniques and improving technologies for all mine life cycle operations. Nowadays, the exploitation of old tailings and mine wastes facilities could represent a solution to this demand, with economic and environmental advantages. W-Sn Panasqueira Mine has been operating for more than 100 years. Its first processing plant “Rio” was located near Zêrere river being the mineral processing residues deposited on the top hillside on the margin of this river in Cabeço do Pião tailings dam. The lack of maintenance and monitoring of this enormous structure in the last twenty years represents high risks to the environment and population of the surrounding region. The re-mining of the tailings by hydrometallurgical methods was considered, in order to satisfy these two enounced conditions - metals demand and environmental risk, aiming for the sale of the metal to pay the environmental intervention. Field samples campaign allowed collecting data and results from laboratory tests driving to use regression optimization. The re-mining solution was studied, taking into account the technical, economic, social, and environmental aspects.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality which unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

We introduce and discuss a generalization of the classical multi-objective optimization to pairs of functions. This procedure is referred to as bi-multi-objective optimization. A justification of this general optimization procedure is presented, related both to multi-objective optimization under ambiguity concerning individual preferences and to Pareto optimality for a family of preferences with nontransitive indifference. Incidentally, the binary relation naturally associated to a bi-multi-objective optimization problem is represented by a finite bi-multi-utility, which generalizes to the nontransitive case the classical finite multi-utility representation. An important application is presented to Markowitz portfolio selection under ambiguity concerning both the vector of returns and the covariance matrix.

Our knowledge of physics and chemistry is relatively well defined. Results from that knowledge are predictable as, largely, are those of their technical offspring such as electrical, chemical, me-chanical and civil engineering. By contrast biology is relatively unconstrained and unpredictable. A factor common to all areas is the trade-off, which provides a means of defining and quantifying a problem and, ideally, its solution. In order to understand the anatomy of the trade-off and how to handle it, its development (as the dialectic) is tracked from Hegel and Marx to its implementa-tion as dialectical materialism in Russian philosophy and TRIZ, the Theory of Invention. With the ready availability of mathematical techniques, such as multi-objective analysis and the Pareto set, the trade-off is well-adapted to bridging the gaps between the quantified and the unquantifiable, allowing modelling and the transfer of concepts by analogy. It is thus an ideal tool for biomimet-ics. An intracranial endoscope can be derived with little change from the egg-laying tube of a wood wasp. More complex transfers become available as the technique is developed. Most im-portant, as more trade-offs are analyzed, their results are stored to be used again in the solution of problems. There is no other system in biomimetics which can do this.

In this paper we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyse the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash Equilibrium solution), a fully cooperative solution with all players following a joint course of action (a Pareto optimal solution), and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully cooperative solution yields the best results, the noncooperative solution fares worst, and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty country coming closest to the Pareto optimum.

We present a simple proof of the well-known axiomatic characterization of state-salient decision rules on the domain of all strict preference profiles, using Pareto property and Global Independence of Irrelevant Alternatives. Our proof appeals to Sen’s Impossibility Theorem and an extract from a proof of the same theorem, that is available in an earlier paper of this author.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

Abstract: Earth’s Phanerozoic history is marked by about 100 major events (“golden spikes”) indicating the beginnings of new stages in the Geologic Time Scale (GTS). Stage boundaries signify major deterministic events that are relatively well-known and can be correlated worldwide, mostly on the basis of appearances or disappearances of fossil species. The latest stage (Anthropocene) is human-made and currently involves rapid (approximately linear) increase in average atmospheric temperature. The main cause of Earth’s past and current temperature increases is addition of CO2 to the atmosphere. There is continuous exchange of greenhouse gases between atmosphere and oceans, which (per unit of volume) contain 50 to 60 times as much CO2 as the atmosphere. Abundance of new very precise worldwide observations is allowing multifractal modeling of weather and climate during the latest Quaternary stages during which some variables like temperature of the atmosphere and frequency of forest fires can be described by using the Pareto-lognormal frequency distribution model with parameters that are subject to continuous (deterministic) changes, similar to those in the earlier Phanerozoic.

The forest is a complex and dynamic ecosystem that requires integrated planning and management, considering economic, social, environmental, and ecological dimensions. Different stakeholders often have conflicting goals, making optimal management decisions challenging. This study aims to balance increasing economic benefits for forest users with reducing negative environmental impacts, aligning the interests of managers, government institutions, and policymakers. To achieve this, multi-objective optimization methods and game theory were used. The objectives were to maximize the net present value of wood harvesting and the amount of carbon sequestration. The study was conducted in the Shafarood forest in northern Iran. Data collected included stumpage prices, variable harvesting costs, tree density per ha, volume per ha, growth rates, interest rates, carbon sequestration, and labor costs. Using this data, models were developed for the expected mean price of various species, stored carbon, logistics growth, and labor. After adjusting the objective functions and model constraints, the range of Pareto optimal solutions for the multi-objective model and the Nash equilibrium for the game theory model were determined using the epsilon-constrain method. The results indicate that both modeling approaches can identify optimal points for balancing economic and environmental goals. The Pareto optimal range and Nash equilibrium allow for informed decision-making in managing the Hyrcanian forests, accommodating different user goals. Therefore, both models are effective tools for forest management planning and provide a framework for achieving sustainable management practices.

Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply "expectation," traditionally the probability-weighted outcome, regarded since the seventeenth century as the mathematical definition of "expectation." However, when considering the "expectation" of an individual confronted with a finite sequence of outcomes, particularly existential outcomes (e.g., a trader with a limited time to perform or lose his position in a trading operation), we find this individual "expects" the median terminal outcome over those finite trials, with the classical seventeenth-century definition being the asymptotic limit as trials increase to this. Since such finite-sequence "expectations" often differ in values from the classic one, so do the optimal allocations (e.g., growth-optimal). We examine these for fat-tailed distributions. The focus is on implementation, and the techniques described can be applied to all distributional forms.

Abstract: The ever-increasing use of motor vehicles causes a number of traffic safety and community issues, which are particularly severe in cities, accompanied with scarcity of parking spaces and challenges encountered in the road layout alteration projects. The commonly applied solutions include designation of through streets and implementation of on-street parking on residential streets and retrofitted traffic calming measures (TCMs). This article presents the results of the study conducted on a two-way street where Metered Parking System MPS was implemented together with diagonal and parallel parking spaces, refuge islands, horizontal deflection and lane narrowing by a single-sided chicane. The aim of this study was to identify those TCMs that effectively helped to reduce the island approach speed. Heuristic method was applied to assess the effect of the respective TCMs on reducing the island approach speed and the key speed reduction determinants were defined using cause and effect diagram and Pareto chart. Comparative analyses were carried out to rate the respective TCMs as effective, moderately effective or ineffective. Section 1 of this article presents the output of the literature review on urban parking analyses and TCM efficacy. Section 2 presents the study site and the applied heuristic method. The study results are presented in Section 3. Section 3 defines the determinants on the cause and effect diagram and analyses the determinants using the Pareto chart. The final conclusions and comments are given in Section 5. Although the study was limited to a single street in Poland, the findings may hold true in other countries where similar TCMs are used.

Drag reduction by laminarization, an innovative technology in aerodynamics design, provides the possibility to improve significantly the aerodynamic performance of aircraft and remains to be one of the most promising and effective technologies. In this paper, the design method for transonic natural laminar flow (NLF) wing at high Reynolds number is investigated in details and a new optimization model is established to solve conflicts between the increase of a laminar flow region and the shock wave strength at the trailing edge. In order to numerically handle this competitive situation efficiently, a two-objective hierarchical variable fidelity Pareto evolutionary optimization model based on search space contraction is proposed and implemented. Numerical experiments show that it can capture simultaneously a Pareto front of the two-objectives: a wave drag minimization and a laminar flow region maximization. The results also show that both wave drag and skin friction drag performances of non-dominated Pareto members can be significantly improved via the optimal laminar wing shape and shock wave control device. Nearly 40% of the laminar flow area on the wing surface is achieved at the Reynolds number of 107. It is concluded that the present hierarchical variable-fidelity multi-objective evolutionary optimization method is computationally efficient, and illustrate its potential for solving complex engineering design problems.

Delay in data transmission is one of key performance indicators (KPIs) of a network. The planning and project value of delay in network management is of crucial importance for the optimal allocation of network resources and their performance focuses. To create optimal solutions, predictive models, which are currently most often based on machine learning (ML), are used. This paper aims to investigate the training, testing and selection of the best predictive delay model for a VoIP service in an Long Term Evolution (LTE) network using three ML techniques - Neural Networks (NN), Support Vector Machines (SVM) and k-Nearest Neighbors (k-NN). The space of model input variables is optimized by dimensionality reduction techniques: RReliefF algorithm, Backward selection via the recursive feature elimination algorithm and the Pareto 80/20 rule. A three-segment road in the geo-space between the cities of Banja Luka (BL) and Doboj (Db) in the Republic of Srpska (RS), Bosnia and Herzegovina (BiH), covered by the cellular network (LTE) of the M:tel BL operator was chosen for the case study. The results show that, in all three optimization approaches, the k-NN model is selected as the best solution. For the RReliefF optimization algorithm, the best model has 6 inputs and minimum relative error (RE), RE=0.109; for the Backward selection via the recursive feature elimination algorithm, the best model has 4 inputs and RE=0.041; and for the Pareto 80/20 rule, the best model has 11 inputs and RE= 0.049. The comparative analysis of the results concludes that according to observed criteria for the selection of the final model, the best solution is an approach to optimizing the number of predictors based on the Backward selection via the recursive feature elimination algorithm.

This article analyzes 6 probability distributions from the Generalized Pareto family, with 3, 4 and 5 parameters, with main purpose to identify other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distributions use are presented like, the probability density functions, the complementary cumulative distribution functions, the quantile functions, the exact and approximate relations for estimating parameters, for both methods of parameters estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor river, to numerically present the analyzed distributions. The performance of this distributions is evaluated using relative mean error, relative absolute error and linear moments diagram.

Fractional differential systems have received much attention in recent decades likely due to its powerful ability in modeling memory processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. Obviously, bang-bang property is of a significant importance in optimal control theory. In this paper a Bang-Bang property and time-optimal control problem for time-Fractional Differential System (FDS) is under consideration. First we formulate our problem and we prove the existence theorem. We state and prove the bang-bang theorem. Finally we give the optimality conditions that characterized the optimal control. Some illustrate applications are given to clarify our results.

With the rapid development of renewable energy, accurately forecasting wind power is crucial for the stable operation of power systems and effective energy management. This paper proposes a short-term wind power forecasting method based on the Orthogonalized Maximal Information Coefficient (OMNIC) combined with an Adaptive Fractional Generalized Pareto Motion (fGPm) model. The method quantifies the influence of meteorological factors on wind power prediction and identifies the optimal set and number of influencing factors. The model accounts for long-range dependence (LRD) in time series data and constructs an uncertainty model using the properties and parameters of the fractional generalized Pareto distribution (GPD), significantly improving prediction accuracy under nonlinear conditions. The proposed approach was validated using a real dataset from a wind farm in northwest China and compared with other models such as Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) and Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU). Results demonstrate that the adaptive fGPm model significantly reduces wind power forecasting errors, offering high accuracy and robustness. This method provides practical value in alleviating peak voltage and frequency regulation challenges in power systems and in promoting the integration of wind power into the grid.

This study examines the potential of combining decision support approaches to identify optimal bundles of ecosystem services. A forested landscape, Zona de Intervenção Florestal of Paiva and Entre-Douro and Sousa (Portugal), is used to test and demonstrate this potential. The landscape extends over 14,000 ha, representing 1,976 stands. The property is fragmented into 376 holdings. The overall analysis was performed in three steps. First, we selected six alternative solutions (A to F) in a Pareto frontier generated by a multiple criteria method within a decision support system (SADfLOR) for subsequent analysis. Next, an aspatial strategic multi-criteria decision analysis (MCDA) analysis was performed with the Criterium DecisionPlus (CDP) component of another decision support system (EMDS) to assess the aggregate performance of solutions A to F for the entire forested landscape with respect to their utility for delivery of ecosystem services. For the CDP analysis, SADfLOR data inputs were grouped into two sets of primary criteria: Wood Harvested and Other Ecosystem Services. Finally, a spatial logic-based assessment of solutions A to F for individual stands of the study area was performed with the NetWeaver component of EMDS. The NetWeaver model was structurally and computationally equivalent to the CDP model, but the key NetWeaver metric is a measure of the strength of evidence that solutions for specific land stands were optimal for the unit. Solutions D and B performed best in the aspatial strategic MCDA analysis, and a composite of the maps generated by NetWeaver demonstrated the spatial basis for the performance of solutions D and B in individual land stands. We conclude with a discussion of how the combination of decision support approaches encapsulated in the two systems could be further automated.

Cryptocurrencies have obtained a crucial position in the international financial landscape. The cryptocurrency market has been perceived as a highly volatile market since the inception of Bitcoin. This study investigates the relevant performance of extreme value models (EVM) in estimating the Value-at-Risk (VaR) of Bitcoin and Ethereum returns. The extreme value mixture models, GPD-Normal-GPD (GNG) and GPD-KDE-GPD models are fitted to the returns of Bitcoin and Ethereum and the Kupiec likelihood backtesting procedure is performed on the VaR estimates to assess the fits. Both models’ results showed that the fits were a much more decent representation of the observed data when compared to the Normal distribution. The backtesting results showed that the GPD-KDE-GPD model’s fit was superior to that of the GPD-Normal-GPD for both sets of returns at all VaR risk levels except at the 99% level. The results of this study may assist with understanding the dynamics and risks associated with cryptocurrencies and can serve as a beneficial tool for decision-making and risk management to investors, traders, financial institutions and many other participants in the cryptocurrency ecosystem.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.