Characteristic Function Form Research Articles

Effect of the duration of vehicles’ idleness at transfer hubs of urban passenger transport on the conditions of synchronization of passenger transfers

Problem. The task of synchronizing the time of passengers' transfers between routes has been defined as one of the important directions for improving the operation of urban passenger transport in the transport and transfer hub. The simultaneous presence of route vehicles within the stops makes it possible to transfer passengers without waiting. Due to the action of external factors, compliance with the terms of coordination of the vehicles’ arrival at the transport hub is significantly complicated, which leads to a decrease in the efficiency of synchronization of passenger transfers and requires the implementation of additional management measures. Goal. The purpose of the work is to determine the effect of the duration of idleness of route vehicles in a transport interchange on the parameters of synchronization of passenger transfers and conflicting traffic within the stops. Methodology. The methodological basis for establishing the effect of the duration of vehicles’ idleness in a transport interchange on the efficiency of synchronization of passenger transfers is the developed structural model of the interaction of incoming route flows. Such a model describes the functional relationship between the traffic parameters of route vehicles, the distance between the initial stopping point of the route and the transfer point, the technical speed on network sections, the traffic intensity on routes, the idle time at intermediate stopping points, the average time of a passenger transfer and the number of conflict situations. Results. In the process of analyzing the object of the study, it was determined that it is possible to improve the conditions of synchronization of passenger transfers by increasing the duration of the stay of route vehicles at the stops. It was determined that the key role in synchronizing the transfer of passengers is played by the determination of the departure time of route vehicles from the initial stopping point, accounting for external impacts and laws of distribution of random values of the technical speed and the idle time at intermediate points. The developed circuit of functional communication allows to present the process of finding vehicles in a transport interchange as a complex system of synchronization of the route flows interaction. Originality. It is proposed to use a rational time of route vehicles idleness at the stop points of the transport and transfer hub, which allows to partially compensate for the decrease in the effectiveness of the synchronization of passenger transfers. When determining the time of vehicles idleness, the frequency of traffic conflicts that occur with adjacent routes at stopping points is also taken into account. The obtained regularities are presented in the form of characteristic functions, which allow to evaluate the effect of the duration of route vehicles stay in the transport interchange hub on the parameters of the efficiency of route flows interaction. Practical value. According to the results of experimental studies, the dependences of changes in the average passenger transfer time and conflicting traffic of route vehicles were established for the transport and transfer hub "Odeska St." (Kharkiv). It was determined that in the conditions of synchronization of the traffic schedule, the idle time of route vehicles within 180 seconds is rational. This enables to reduce the time of inter-route transfer of passengers and ensure a low level of conflict of the route vehicles traffic.

The Bessel function expression of characteristic function

In this article, we give a unified method to derive the classical characteristic functions of all elliptical and related distributions in terms of Bessel functions. The approach is based on the stochastic representation of an elliptical random variable and the characteristic function of uniform distribution on the unit sphere surface in ℝ n . In particular, we present the simple closed form of characteristic functions for commonly used distributions such as multivariate t, Pearson Type II, Pearson Type VII, Kotz type, and Bessel distributions. Some extensions are also being investigated.

Game-Theoretic Models of Coopetition in Cournot Oligopoly

Coopetition means that in economic interactions, both competition and cooperation are presented in the same time. We built and investigated analytically and numerically game theoretic models of coopetition in normal form and in the form of characteristic function. The basic model in normal form reflects competition between firms in Cournot oligopoly and their cooperation in mutually profitable activities such as marketing, R&D, and environmental protection. Each firm divides its resource between competition and cooperation. In the model in normal form we study Nash and Stackelberg settings and compare the results. In cooperative setting we consider Neumann–Morgenstern, Petrosyan–Zaccour, and Gromova–Petrosyan versions of characteristic functions and calculate the respective Shapley values. The payoffs in all cases are compared, and the respective conclusions about the relative efficiency of different ways of organization for separate agents and the whole society are made.

Weighted shapley value: A cooperative game theory for loss allocation in distribution systems

This paper proposes a new method for assigning distribution system (DS) losses to consumers and distributed generations in the framework of a liberalized energy market. The architecture of the proposed method is based on a synthesis of electrical network analytical theory and cooperative game theory (CGT). Weighted shapely value (WSV) is a solution idea that is regarded to be efficient in CGT for n-player games with characteristic function form. By retaining the notion of electrical networks, the axioms of game theory will be preserved while employing the WSV in loss allocation theory. To allocate system losses, the proposed method estimates the average marginal contribution of each participant to all conceivable coalitions and also determines the weight of the marginal contribution of each participant based on its power rating. Rather than a sequential branch-oriented approach, the proposed methodology is node-oriented. Additionally, a majority rule game is used to constrain the population of a coalition without jeopardizing the efficacy of the solutions to achieve a fair allocation of losses. The results of the proposed method are presented and contrasted with those obtained using the conventional pro-rata method and the well-known Shapley value solution concept in CGT.

Coordination of two competing closed-loop supply chains: A cooperative game approach

In the development of end-of-life (EOL) products recycling, coordinating competing closed-loop supply chains (CLSCs) with restricted coalition has become an important topic that has yet to be thoroughly investigated. In this study, we first investigate the possible coalitions for two CLSCs composed of manufacturers and third-party recyclers under a restricted coalition structure, which is used for deriving the characteristic functions representing the bargaining powers of different coalitions and allocating the overall profits. Subsequently, to fairly allocate the maximal profit, we establish a cooperative game in the form of characteristic function for the two CLSCs and use an advanced solution concept (average tree value) to coordinate them. We find that: compared to other non-cooperative and partial cooperative models, the centralized model can always achieve the best performance, e.g., the highest recovery rate. And the profit of the fully centralized model increases linearly with the increase of the cooperation coefficient. When the third-party recyclers of two CLSCs form alliance, the profit of the manufacturer is positively or negatively correlated with the cooperation coefficient due to the difference of the model and price elasticity coefficient. Under the cooperation of two CLSCs third-party recyclers, the relationship between the profit of the third-party recycler, the profit of the single chain system or the profit of the double chain system and the cooperation coefficient increases first and then decreases, but the inflection point is different. The coordination of two competing CLSCs can be well addressed by the allocation scheme proposed in this study, while satisfying the collective and individual rationalities.

A game-theoretic approach for pollution control initiatives

There are numerous regional, national, and international efforts to establish mechanisms to curb pollution and emissions. In this paper, we mainly focus on emissions trading systems. Using a static Cournot oligopoly game, we investigate a multi-product multi-pollutant market in which several supply chains compete in a non-cooperative manner in their product markets. This study characterizes conditions under which an efficient solution procedure converges to the unique Nash equilibrium of the oligopoly. Meanwhile, its partners establish a cooperative triopoly game within each supply chain in a nonsuperadditive characteristic function form. Drawing on the cooperative game theory literature, we provide a closed-form solution for a rational distribution of joint rewards between the supply chain’s partners.

A balance for fairness: fair distribution utilising physics

The problem of ‘uneven distribution of wealth’ accelerated during the COVID-19 pandemic. In the chaotic modern society, there is an increasing demand for the realisation of true ‘fairness’. In this study, we propose a fair distribution method ‘using physics’, which imitates the Greek mythology, Themis, having a ‘balance of judgement’ in her left hand, for the profit in games of characteristic function form. Specifically, we show that the linear programming problem for calculating ‘nucleolus (a solution for the fair distribution)’ can be efficiently solved by considering it as a physical system in which gravity works. In addition to significantly reducing the computational complexity, the proposed scheme provides a new perspective to open up a physics-based policymaker that is adaptable to real-time changes. We will be able to implement it not only in liquid systems but also in many other physical systems, including semiconductor chips. The fair distribution problem can be solved immediately using physical systems, which should reduce disputes and conflicts based on inaccurate information and misunderstandings, eliminating fraud and injustice.

Asymptotic behavior and calibration of short-time option prices under the normal tempered stable model

In recent years, small-time asymptotics of option prices have received much attention. In this paper, we derive short-time first-order expansions for price and implied volatility of at-the-money call options under the exponential Normal Tempered Stable model in two methods. The first method is similar to the approach used by Figueroa-López and Forde for the CGMY model. The other is based on the explicit form of characteristic functions of the Normal Tempered Stable processes. Our numerical results show that the expansions herein remarkably approximate the prices obtained by Fourier transform, even for options with maturities as long as a few years. For this reason, our expansions can be used for parameter calibration and model testing in a simple and efficient way.

Mesh-Sequenced Realizations for Evaluation of Subgrid-Scale Models for Turbulent Combustion

This paper develops a new approach for analysis of subgrid closures for turbulent combustion as modeled using direct quadrature (finite-rate chemistry) techniques. The approach, termed multiresolution analysis through mesh-sequenced realizations (MRA-MSR), conducts simultaneous, constrained large-eddy simulations on a set of hierarchically coarsened meshes. The availability of underlying fine-mesh (subgrid) data corresponding to coarse-mesh locations allows a clearer assessment of the effects of unresolved fluctuations on apparent reactivity. A key to MRA-MSR is the correlation of eddy structures at coarser mesh levels, which is facilitated by the transfer of filtered fine-mesh velocity information. A seven-mesh MRA-MSR hierarchy using three resolution levels is applied to one of the Sydney bluff-body stabilized methane–hydrogen flames. Analysis of the simultaneously evolved data at different resolution levels reveals several interesting trends. First, at high Damköhler numbers, there is clear evidence of attenuation of apparent reactivity due to the effects of unresolved fluctuations. Secondly, single-point, single-time filtered density functions of a normalized subgrid Damköhler number show a characteristic beta probability density function (PDF) form and display evidence of scale similarity. Interrogation of the MRA-MSR database also shows that the recently-proposed least-squares minimization (LSM) turbulence–chemistry interaction model can account for the observed diminishment in reactivity at high Damköhler numbers but cannot reduce scatter significantly. A new form of the LSM model, which makes use of the normalized subgrid Damköhler number beta PDF distribution, performs slightly better than the original model, illustrating the potential of MRA-MSR both in assessing existing closure concepts and in developing new ones.

A class of goodness-of-fit tests for circular distributions based on trigonometric moments

We propose a class of goodness–of–fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.

On a Simplified Method of Defining Characteristic Function in Stochastic Games

In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of the characteristic function is based on a calculation of the maximin values of zero-sum games between a coalition and its anti-coalition for each state of the game. The proposed characteristic function has some advantages in comparison with previously defined characteristic functions for stochastic games. In particular, the advantages include computation simplicity and strong subgame consistency of the core calculated with the values of the new characteristic function.

Voltammetry coupled with impedance spectroscopy

Dynamic EIS (dEIS) is the joint use of cyclic voltammetry and electrochemical impedance spectroscopy. A method is planned for data evaluation which involves transformations yielding potential program invariant forms of certain characteristic functions. This way of calculation is illustrated by the analysis of two archetypes of electrochemical kinetics. A future task is to develop the related theories and to perform demonstration experiments aimed at establishing dEIS as a robust, general-purpose technique for characterizing electrochemical systems.

Chandrasekhar’s H-function revisited

The Chandrasekhar H-function plays an important role in a wide class of problems of analytical radiative transfer theory. The H-function is the solution of well-known integral equations, both non-linear and linear. The physics of a particular problem under consideration determines the form of the so-called characteristic and dispersion functions, Ψ(μ) and T(μ), respectively. They appear in H-equations and determine their solutions. We show that Ψ(μ) and T(μ) can be restructured in such a way that the solutions of H-equations transforms from H(μ) to Hn(μ),n=2,3,4,… provided Ψ(μ) and T(μ) are replaced with Ψn(μ) and Tn(μ). The structure of the non-linear and linear H-equations does not change under this transformation. The basis of this restructuring is a recursion relation that gives Ψn(μ) and Tn(μ) in terms of Ψ(μ) and T(μ).

Coalitional bargaining with consistent counterfactuals

We propose a new solution concept for TU cooperative games in characteristic function form, the SCOOP, which builds on the symmetric Nash Bargaining Solution (NBS) by adding a consistency requirement for negotiations inside every coalition. The SCOOP specifies the probability of success and the payoffs to each coalition. The players share the surplus of a coalition according to the NBS. The disagreement payoffs are computed as the expectation of payoffs in other coalitions, using a common probability distribution that is derived from the prior distribution. The predicted outcome can be probabilistic or deterministic, but only an efficient coalition can succeed with probability one. We discuss the necessary and sufficient conditions for an efficient solution. In either case, the SCOOP always exists, is generically unique for superadditive games, and is easy to compute. Moreover, in the spirit of the Nash program, we propose a non-cooperative protocol whose stationary equilibrium identifies the SCOOP as the limit equilibrium outcome.

A generalized European option pricing model with risk management

Risk control systems in financial markets with numerous innovative financial products are characterized by infrequent and significant fluctuations (e.g., financial crises and minor disturbances occurring anytime and anywhere). Given that the traditional Black–Scholes (BS) model is difficult to adapt to ever-changing financial markets, to better describe real financial markets, this paper presents a generalized European option-pricing model with stochastic volatility and stochastic interest rates and pure jumps under Levy processes, which are stochastic processes with both stationary and independent increments. We use the Levy–Ito formula and measurement tools to transform logarithmic stock prices into conditions under risk neutral measures, and the characteristic functions of logarithmic stock prices are obtained using the decomposed characteristic function form. We in turn obtain a characteristic function solution based on the Fourier and inverse Fourier transform. Finally, we conduct a Monte Carlo (MC) simulation which highlight the adaptability, accuracy and efficiency of the FFT algorithm. The proposed model is superior from an economic and mathematics perspective, as it not only inherits advantages of the BS model but also better depicts the leptokurtosis and jump phenomenon in option markets.

Ak-mean characteristic function for optimizing short- and long-term-average-ratio-based detection of microseismic events

Event detection is an essential component of microseismic data analysis. This process is typically carried out using a short- and long-term-average-ratio (STA/LTA) method, which is simple and computationally efficient but often yields inconsistent results for noisy data sets. We have aimed to optimize the performance of the STA/LTA method by testing different input forms of 3C waveform data and different characteristic functions (CFs), including a proposed [Formula: see text]-mean CF. These tests are evaluated using receiver operating characteristic (ROC) analysis and are compared based on synthetic and field data examples. Our analysis indicates that the STA/LTA method using a [Formula: see text]-mean CF improves the detection sensitivity and yields more robust event detection on noisy data sets than some previous approaches. In addition, microseismic events are detected efficiently on field data examples using the same detection threshold obtained from the ROC analysis on synthetic data examples. We recommend the use of the Youden index based on ROC analysis using a training subset, extracted from the continuous data, to further improve the detection threshold for field microseismic data.

A cooperative game in Asian international electric power integration

The paper examines effects of long-term international integration in the field of electric power industry. An advantage of integration is provoked by the fact that the cost of introducing new generation capacities significantly exceeds the cost of new power lines and transmission of the energy from existing power station of another country. When countries form a coalition, the problem is to allocate the coalition’s surplus over its participants. It can be solved by notions of cooperative game theory. The present investigation is based on the real data on six countries of the Northeast Asian region: Russia, Mongolia, China, North Korea, South Korea and Japan. Electric power system is described by the ORIRES model. This model optimizes power generation, power flows, and the development of generation capacities and power lines of the system. We formulate corresponding cooperative game in characteristic function form, and specify the Core and the Shapley value. Effects of international integration are discussed.

Modeling transfer profits as externalities in a cooperative game-theoretic model of natural gas networks

Existing cooperative game theoretic studies of bargaining power in gas pipeline systems are based on the so called characteristic function form (CFF). This approach is potentially misleading if some pipelines fall under regulated third party access (TPA). TPA, which is by now the norm in the EU, obliges the owner of a pipeline to transport gas for others, provided they pay a regulated transport fee. From a game theoretic perspective, this institutional setting creates so called “externalities”, the description of which requires partition function form (PFF) games. In this paper we propose a method to compute payoffs, reflecting the power structure, for a pipeline system with regulated TPA. The method is based on an iterative flow mechanism to determine gas flows and transport fees for individual players and uses the recursive core and the minimal claim function to convert the PPF game back into a CFF game, which can be solved by standard methods. We illustrate the approach with a simple stylized numerical example of the gas network in Central Eastern Europe with a focus on Ukraine's power index as a major transit country.

Cooperative game approaches to coordinating a three-echelon closed-loop supply chain with fairness concerns

This paper investigates a three-echelon closed-loop supply chain (CLSC) consisting of a manufacturer, a distributor, and a retailer, where the retailer exhibits fairness concerns. Cooperative and non-cooperative game theoretic analyses are employed to characterize interactions among different parties. Analytical results confirm the conventional wisdom: with the retailer's fairness concerns, the channel profits under the decentralized and partial-coalition models underperform that under the centralized model. To find an appropriate profit allocation scheme to coordinate the supply chain system with fairness concerns, we resort to the cooperative game theory. To this end, we first derive the characteristic function form of the cooperative game based on the equilibrium profits under centralized, decentralized and different partial-coalition models. Subsequently, we propose three coordination mechanisms based on the Shapley value, nucleolus solution, and equal satisfaction to allocate surplus profit. The three mechanisms are then evaluated by using numerical experiments. We further examine how the retailer's fairness concerns affect profit allocation under the three mechanisms. The key innovation is to incorporate the retailer's fairness concerns into the coordination of a three-echelon CLSC. Our contributions are twofold: First, cooperative game-theoretic mechanisms are put forward to coordinate the three-echelon CLSC with a fairness-minded retailer. Second, we investigate how the retailer's fairness concerns affect the CLSC members' pricing decision and surplus profit allocation. Our studies confirm that the resulting profit allocation schemes satisfy both individual and collective rationality and fall in the core of the cooperative game, thereby making the grand coalition stable and suggesting viable options to coordinate the CLSC system. Further analyses reveal that different coordination mechanisms benefit the three CLSC members differently. These research findings help CLSC managers to understand what options are available and identify possible pathways for them to foster cooperation and achieve equitable allocation of surplus profit.

Computing optimal coalition structures in polynomial time

The optimal coalition structure determination problem is in general computationally hard. In this article, we identify some problem instances for which the space of possible coalition structures has a certain form and constructively prove that the problem is polynomial time solvable. Specifically, we consider games with an ordering over the players and introduce a distance metric for measuring the distance between any two structures. In terms of this metric, we define the property of monotonicity, meaning that coalition structures closer to the optimal, as measured by the metric, have higher value than those further away. Similarly, quasi-monotonicity means that part of the space of coalition structures is monotonic, while part of it is non-monotonic. (Quasi)-monotonicity is a property that can be satisfied by coalition games in characteristic function form and also those in partition function form. For a setting with a monotonic value function and a known player ordering, we prove that the optimal coalition structure determination problem is polynomial time solvable and devise such an algorithm using a greedy approach. We extend this algorithm to quasi-monotonic value functions and demonstrate how its time complexity improves from exponential to polynomial as the degree of monotonicity of the value function increases. We go further and consider a setting in which the value function is monotonic and an ordering over the players is known to exist but ordering itself is unknown. For this setting too, we prove that the coalition structure determination problem is polynomial time solvable and devise such an algorithm.