Minimax Research Articles

Robustly optimized hybrid intensity-modulated proton therapy for craniospinal irradiation.

The aim of the study was to investigate the hybrid robust optimization planning approach in intensity-modulated proton therapy (IMPT) of craniospinal irradiation (CSI). Five IMPT-based adult CSI plans in supine position were created using Raystation treatment planning system (TPS) modelled for Proteus plus proton therapy system. A hybrid planning strategy was implemented, where clinical target volume was robustly optimized (RB) for set up uncertainties and planning target volume was optimized for target coverage using minimax algorithm in the TPS. Beam angle selection, optimization, and dose calculation approach were carefully performed to ensure optimum organ at risk (OAR) sparing, even with potential setup and range errors. The complementary dose gradients in junctions were generated using spot assignment and RB technique. Dosimetric outcomes in both nominal plan and the 16 error scenarios (±3 mm setup and 3.5% range) were analyzed using standard dose volume histogram. This planning approach resulted in a homogeneous dose distribution in the target volume of CSI, including the junction regions, by explicitly reducing number of robust optimization scenarios. The proposed technique was also able to achieve excellent coverage to cribriform plate with lower lens doses and minimal dose to other OARs. Target and OAR doses in the nominal plans as well as in the worst case scenarios with setup and range errors were able to meet the predefined clinical goal. This proposed planning technique is efficient, robust against the uncertainties. It could be adopted in other proton therapy centers.

A Causal Framework for Distribution Generalization.

We consider the problem of predicting a response Y from a set of covariates X when test- and training distributions differ. Since such differences may have causal explanations, we consider test distributions that emerge from interventions in a structural causal model, and focus on minimizing the worst-case risk. Causal regression models, which regress the response on its direct causes, remain unchanged under arbitrary interventions on the covariates, but they are not always optimal in the above sense. For example, for linear models and bounded interventions, alternative solutions have been shown to be minimax prediction optimal. We introduce the formal framework of distribution generalization that allows us to analyze the above problem in partially observed nonlinear models for both direct interventions on X and interventions that occur indirectly via exogenous variables A. It takes into account that, in practice, minimax solutions need to be identified from data. Our framework allows us to characterize under which class of interventions the causal function is minimax optimal. We prove sufficient conditions for distribution generalization and present corresponding impossibility results. We propose a practical method, NILE, that achieves distribution generalization in a nonlinear IV setting with linear extrapolation. We prove consistency and present empirical results.

Trajectory Optimization of Autonomous Surface Vehicles with Outliers for Underwater Target Localization

Location awareness is crucial for underwater applications; without it, gathered data would be essentially useless. However, it is impossible to directly determine the location of an underwater target because GPS-reliant methods cannot be utilized in the underwater environment. To this end, the underwater target localization technique has become one of the most critical technologies in underwater applications, wherein GPS-equipped autonomous surface vehicles (ASVs) are typically used to assist with localization. It has been proved that, under the assumption of Gaussian noise, an appropriate geometry among ASVs and the underwater target can enhance localization accuracy. Unfortunately, the conclusion may not hold if outliers arise and the closed-form expression of Cramér–Rao lower bound (CRLB) cannot be established. Eventually, it becomes hard to derive the accepted geometry, particularly for the received signal strength (RSS)-based ranging scenario. Therefore, this work optimizes the trajectory of ASVs with RSS-based ranging and in the presence of outliers to optimally estimate the location of an underwater target. The D-optimality criterion is applied in conjunction with the Monte Carlo method to determine the closed-form expression of the function, which then transforms the problem into an optimized framework. Nevertheless, the framework cannot be solved in the absence of the target location. In this case, the paper presents two methodologies to overcome the issue and achieve the optimum configuration without identifying the target location. (1) A min–max strategy that assumes that the target location drops in an uncertain region for a single or two ASVs is proposed; and (2) a two-phase localization approach (TPLA) that calculates the target location at each time slot for three ASVs is developed. Finally, the optimal trajectories of ASVs are constructed by a series of waypoints based on an analytically tractable measurement model in various conditions.

Tree Search Algorithms For Chinese Chess

Computer Games are an important aspect of Artificial Intelligence (AI) which has produced many representative algorithms of optimal strategies. Therefore, many AI researchers have applied game theory to various board games in an attempt to find the essence of games and grasp the core of AI behaviour. AlphaGo is a very famous and typical chess-playing program that uses Monte Carlo tree search (MCTS) to estimate the value of each node in the search tree and optimize the possible results. Chinese chess is one of the traditional chess versions with its typical strategy. However, due to its late start and high complexity, there are many more technical problems to be solved. In this paper, we recommend two commonly used search frameworks for Chinese chess: the minimax algorithm and the alpha-beta pruning algorithm. On this basis, to deal with the complex and changeable situation, the Chinese chess algorithm based on Monte Carlo tree search and appropriate neural network evaluation function is studied.

An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem

AbstractIn this article, an effective finite element method based on dimension reduction scheme is proposed for a fourth-order Steklov eigenvalue problem in a circular domain. By using the Fourier basis function expansion and variable separation technique, the original problem is transformed into a series of radial one-dimensional eigenvalue problems with boundary eigenvalue. Then we introduce essential polar conditions and establish the discrete variational form for each radial one-dimensional eigenvalue problem. Based on the minimax principle and the approximation property of the interpolation operator, we prove the error estimates of approximation eigenvalues. Finally, some numerical experiments are provided, and the numerical results show the efficiency of the proposed algorithm.

OAM Mode Selection for High-Speed Optical Communications: A Bit Loading Approach

Occupying more channels increases transmission rate, however, crosstalk increases to an unacceptable level long before all 24 channels can be exploited. The crosstalk is not uniform between modes, hence occupying different subsets of channels leads to vastly different achievable transmission capacities. In addition to optimizing occupied subsets of channels, we adopt a bit loading approach. We examine several resource allocation strategies in a coherent detection system, starting with typical OAM mode group granularity (all channels in a group occupied) and ending with single channel granularity. By exhaustive search at mode group granularity, we find a bit load increasing the total capacity by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 15% compared to a minimax solution for mode group allocation. Single channel granularity imposes great computational effort to optimize bit loading. We propose search algorithms that are computationally tractable and improve capacity by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 30% vis-à-vis the minimax solution for mode groups. Finally, we examine the impact of signal-to-noise ratio (SNR) and receiver digital signal processing (DSP) complexity on the overall capacity. We include a discussion of DSP with limited or with no multi-input, multi-output (MIMO) processing.Our algorithms could be applied to any mode multiplexing fiber, as it only relies on knowledge of the crosstalk matrix across modes.

Planning the Number of Aircraft in a Group Flight with their Survivability and the Required Observation Duration of Ground Objects

In the interests of improving the quality of a group aircraft flight planning, the developing algorithms problem formulation for the operational determination of the permissible observation duration for ground objects is formulated. An algorithm for determining the observation duration when servicing the next request to be described in the form of a fuzzy logic procedure is proposed. To implement the algorithm for determining the duration of observation, a specialized expert system has been developed. The input of the expert system receives values that describe the influence of the factors in assessing the priority of servicing the next object. At the output of the expert system, an alternative is formed to continue searching for an object or to stop. A new approach to solving the target distribution problem between aircraft in a group flight is proposed. It is based on the joint use of two dynamic priorities in the minimax algorithm for selecting observation objects and for assigning service aircraft. An original approach to determine the rational aircrafts composition in one flight is proposed. This is done with the help of the queuing theory apparatus, which takes into account the random nature of the dynamic situation. To estimate the required aircrafts composition when servicing the flow of requests, the countermeasures process is described using two nonlinear differential equations (of the Riccati type). A general formula for determining aircrafts composition in one flight has been obtained. Mathematical model of the aircraft survivability loss in the form of the Bernoulli equation is formed. Computer simulation of the aircraft survivability losses in one flight was carried out for three cases: with weak interference, with equal opposing forces, with strong counteraction.

Singular Values of Dual Quaternion Matrices and Their Low-Rank Approximations

The dual quaternion matrix is an important and powerful tool for the study of multi-agent formation control. However, many basic properties of dual quaternion matrices are still not studied, due to the difficulty incurred by the non-commutativity of multiplication and existence of zero divisors of dual quaternion numbers. In this paper, we study some basic properties of dual quaternion matrices, including the polar decomposition theorem, the minimax principle and Weyl’s type monotonicity inequality for singular values, spectral norm and the Pythagoras theorem. Based upon these, we further present the best low-rank approximations for dual quaternion matrices, and discuss the relationship between the approximation degree characterizations of the best low-rank approximations in the sense of Frobenius norm and spectral norm, in addition to proving a fundamental property of the best low-rank approximation of dual quaternion matrices in a given subspace. These results are of importance to the applications in rigid body motion and data reduction.

A Novel Intelligent Deep Learning-Based Uncertainty-Guided Network Training in Market Price

In this article, we introduce an intelligent probabilistic uncertainty-guided prediction model for energy market price modeling based on the lower–upper bound estimation method. The proposed method borrows the prediction interval (PI) concept to replace the traditional point–point estimation process. Making use of the PI, the forecast error would be captured within the upper and lower bounds of the PI. The proposed method uses the long–short term networks to learn the complex and nonlinear dataset of market prices with high accuracy. Considering the conflicting nature of the prediction indices, a fuzzy min–max solution is introduced to get into a compromised solution. From the optimization point of view, a new method based on the grey wolf algorithm (GWA) is proposed to adjust the model hyperparameters suitably. Moreover, a new modification is introduced to increase the diversity of the GWA and, thus, enhance its search capability. To validate the proposed model, a standard dataset from the New South Wales electricity market is used to assess the high accuracy of the model to capture the prediction error.

Quantum walks do not like bridges

We consider graphs with two cut vertices joined by a path with one or two edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has no other vertex. We achieve this result by applying the 1-sum lemma for the characteristic polynomial of graphs, the neutrino identities that relate entries of eigenprojectors and eigenvalues, and variational principles for eigenvalues (Cauchy interlacing theorem, Weyl inequalities and Wielandt minimax principle). We see our result as an intermediate step to broaden the understanding of how connectivity plays a key role in quantum walks, and as further evidence of the conjecture that no tree on four or more vertices admits state transfer. We conclude with some open problems.

Fully computable a posteriori error bounds for eigenfunctions

For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple eigenvalues, under the settings of target eigenvalue problems. Algorithm I is based on the Rayleigh quotient and the min-max principle that characterizes the eigenvalue problems. The formula for the error estimate provided by Algorithm I is easy to compute and applies to problems with limited information of Rayleigh quotients. Algorithm II, as an extension of the Davis–Kahan method, takes advantage of the dual formulation of differential operators along with the Prager–Synge technique and provides greatly improved accuracy of the estimate, especially for the finite element approximations of eigenfunctions. Numerical examples of eigenvalue problems of matrices and the Laplace operators over convex and non-convex domains illustrate the efficiency of the proposed algorithms.

Portföy Optimizasyonuna Yönelik Ampirik Bir Karşılaştırma: Oyun Teorisi ve Modern Portföy Teorisi

Portföy optimizasyonu gerçekleştirebilmek için menkul kıymetlerin ne zaman ve ne oranda portföye dâhil edilmesi gerektiğinin belirlenmesine ihtiyaç duyulmaktadır. Bu doğrultuda kullanılan modellerden oyun teorisi, minimaks ilkesi ile en düşük risk seviyesinde gerçekleşebilecek en yüksek getirili portföyü oluşturmayı amaçlamaktadır. Modern portföy teorisi ise, verilen risk düzeyinde en yüksek getiriyi sunan ya da verilen getiri düzeyinde riski en düşük portföylere ulaşmayı hedeflemektedir. Çalışmada, Borsa İstanbul'da 2013-2021 yılları arasında kesintisiz her ay işlem gören, işlem hacmi en yüksek 200 hisse senedi kullanılarak, oyun teorisi minimaks ilkesi kapsamında 12 ayrı doğrusal programlama modeli ve modern portföy teorisi kapsamında 12 ayrı kuadratik programlama modeli çözülerek her ay için optimum portföylerin oluşturulması amaçlanmıştır. Her iki teori kapsamında ulaşılan portföylerin performansları, gerek kendi aralarında gerekse alternatif yatırım araçlarının getirisi ile karşılaştırılmıştır. Elde edilen bulgular, geçmişe dönük analizde modern portföy teorisinin; geleceğe dönük uygulamada oyun teorisinin oluşturduğu portföylerin daha başarılı sonuçlar verdiğini ortaya koymaktadır.

On minimax principles and sets with convex sections

On minimax principles and sets with convex sections

Network data envelopment analysis with two-level maximin strategy

Network data envelopment analysis (NDEA), one of the most important branches of recent DEA developments, has been developed for examining the decision making units (DMUs) of a system with complex and internal component divisions. In this study we apply a maximin strategy to network DEA at two levels. At the individual DMU level, we evaluate the system’s performance by maximizing the minimum of the divisions efficiencies, which is based on the weak-link approach. At the all DMUs level, we evaluate the system’s performance by maximizing the minimum of the DMUs’ efficiencies, which is based on the maximin ratio efficiency model. With such two-level maximin strategy, we propose the two-level maximin NDEA model to evaluate efficiencies of all divisions as well as all DMUs at the same time. The model will provide unique and unbiased efficiency scores for all divisions in a system and improve incomparable efficiency scores and weak discrimination power of traditional DEA models. In addition, we discuss the cross efficiency evaluation based on the two-level maximin NDEA model. The proposed models are applied to the efficiency evaluation of supply chains for illustrations.

On Minimax Detection of Gaussian Stochastic Sequences with Imprecisely Known Means and Covariance Matrices

We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. An alternative is independent identically distributed zero-mean Gaussian random variables with unit variances. For a given false alarm (1st-kind error) probability, the quality of minimax detection is given by the best miss probability (2nd-kind error probability) exponent over a growing observation horizon. We study the maximal set of means and covariance matrices (composite hypothesis) such that its minimax testing can be replaced with testing a single particular pair consisting of a mean and a covariance matrix (simple hypothesis) without degrading the detection exponent. We completely describe this maximal set.

An accelerated minimax algorithm for convex-concave saddle point problems with nonsmooth coupling function

In this work we aim to solve a convex-concave saddle point problem, where the convex-concave coupling function is smooth in one variable and nonsmooth in the other and not assumed to be linear in either. The problem is augmented by a nonsmooth regulariser in the smooth component. We propose and investigate a novel algorithm under the name of OGAProx, consisting of an optimistic gradient ascent step in the smooth variable coupled with a proximal step of the regulariser, and which is alternated with a proximal step in the nonsmooth component of the coupling function. We consider the situations convex-concave, convex-strongly concave and strongly convex-strongly concave related to the saddle point problem under investigation. Regarding iterates we obtain (weak) convergence, a convergence rate of order mathcal {O}(frac{1}{K}) and linear convergence like mathcal {O}(theta ^{K}) with theta < 1, respectively. In terms of function values we obtain ergodic convergence rates of order mathcal {O}(frac{1}{K}), mathcal {O}(frac{1}{K^{2}}) and mathcal {O}(theta ^{K}) with theta < 1, respectively. We validate our theoretical considerations on a nonsmooth-linear saddle point problem, the training of multi kernel support vector machines and a classification problem incorporating minimax group fairness.

Optimal Design of Honeycomb Beams with Unit Cell Structure Based on Multiobjective Optimization Algorithm

In order to promote the development of honeycomb composite reinforcements, the mechanical properties and optimization methods of honeycomb beams are studied. A structural optimization design method is proposed based on natural frequency and stiffness and the lightest weight. According to the vibration frequencies and mechanical analysis, the equivalent density and equivalent stiffness of the section in the unit length are deduced, which is considered a typical example. The geometric parameters of the structure system are trained by multiobjective optimization minimax algorithm (MOMA), and the Pareto optimal solution of variable combination is obtained. The results show that optimized objects are significantly better than that previously. Therefore, the optimized scheduling algorithm has some reference value and prospects for practical application.

From commons to resilience grabbing: Insights from historically-oriented social anthropological research on African peasants

AbstractThis paper aims to show the relevance that institutions governing common-pool resources (CPRs) play in peasant resilience. It outlines nine variables for resilience taken from socio-economic and ecological anthropological theories focusing on subsistence and minimax strategies and used for the comparative historical analysis of African case studies. These include drylands (Morocco, Ghana), semi-arid areas (Sierra Leone, Malawi, Tanzania) and wetlands (Cameroon, Kenya, Zambia). The variables could be found under pre-colonial common property but were no longer operating during colonial and postcolonial institutional change from common to state property and privatisation via land grabbing, leading to commons and resilience grabbing.

Fairness in Influence Maximization through Randomization

The influence maximization paradigm has been used by researchers in various fields in order to study how information spreads in social networks. While previously the attention was mostly on efficiency, more recently fairness issues have been taken into account in this scope. In the present paper, we propose to use randomization as a mean for achieving fairness. While this general idea is not new, it has not been applied in this area.&#x0D; Similar to previous works like Fish et al. (WWW ’19) and Tsang et al. (IJCAI ’19), we study the maximin criterion for (group) fairness. In contrast to their work however, we model the problem in such a way that, when choosing the seed sets, probabilistic strategies are possible rather than only deterministic ones. We introduce two different variants of this probabilistic problem, one that entails probabilistic strategies over nodes (node-based problem) and a second one that entails probabilistic strategies over sets of nodes (set-based problem). After analyzing the relation between the two probabilistic problems, we show that, while the original deterministic maximin problem was inapproximable, both probabilistic variants permit approximation algorithms that achieve a constant multiplicative factor of 1 − 1/e minus an additive arbitrarily small error that is due to the simulation of the information spread. For the node-based problem, the approximation is achieved by observing that a polynomial-sized linear program approximates the problem well. For the set-based problem, we show that a multiplicative-weight routine can yield the approximation result.&#x0D; For an experimental study, we provide implementations of multiplicative-weight routines for both the set-based and the node-based problems and compare the achieved fairness values to existing methods. Maybe non-surprisingly, we show that the ex-ante values, i.e., minimum expected value of an individual (or group) to obtain the information, of the computed probabilistic strategies are significantly larger than the (ex-post) fairness values of previous methods. This indicates that studying fairness via randomization is a worthwhile path to follow. Interestingly and maybe more surprisingly, we observe that even the ex-post fairness values, i.e., fairness values of sets sampled according to the probabilistic strategies computed by our routines, dominate over the fairness achieved by previous methods on many of the instances tested.

Locust Mayfly Optimization-Tuned Neural Network for AI-Based Pruning in Chess Game

The art of mimicking a human’s responses and behavior in a programming machine is called Artificial intelligence (AI). AI has been incorporated in games in such a way to make them interesting, especially in chess games. This paper proposes a hybrid optimization tuned neural network (NN) to establish a winning strategy in the chess game by generating the possible next moves in the game. Initially, the images from Portable Game Notation (PGN) file are used to train the NN classifier. The proposed Locust Mayfly algorithm is utilized to optimally tune the weights of the NN classifier. The proposed Locust Mayfly algorithm inherits the characteristic features of hybrid survival and social interacting search agents. The NN classifier involves in finding all the possible moves in the board, among which the best move is obtained using the mini-max algorithm. At last, the performance of the proposed Locust mayfly-based NN method is evaluated with help of the performance metrics, such as specificity, accuracy, and sensitivity. The proposed Locust mayfly-based NN method attained a specificity of 98%, accuracy of 98%, and a sensitivity of 98%, which demonstrates the productiveness of the proposed mayfly-based NN method in pruning.