Duality Principle Research Articles

How Low Can We Go? Minimizing Interaction Samples for Configurable Systems

Modern software systems are typically configurable, a fundamental prerequisite for wide applicability and reusability. This flexibility poses an extraordinary challenge for quality assurance, as the enormous number of possible configurations makes it impractical to test each of them separately. This is where t-wise interaction sampling can be used to systematically cover the configuration space and detect unknown feature interactions. Over the last two decades, numerous algorithms for computing small interaction samples have been studied, providing improvements for a range of heuristic results; nevertheless, it has remained unclear how much these results can still be improved. We present a significant breakthrough: a fundamental framework, based on the mathematical principle of duality , for combining near-optimal solutions with provable lower bounds on the required sample size. This implies that we no longer need to work on heuristics with marginal or no improvement, but can certify the solution quality by establishing a limit on the remaining gap; in many cases, we can even prove optimality of achieved solutions. This theoretical contribution also provides extensive practical improvements: Our algorithm SampLNS was tested on 47 small and medium-sized configurable systems from the existing literature. SampLNS can reliably find samples of smaller size than previous methods in 85 % of the cases; moreover, we can achieve and prove optimality of solutions for 63 % of all instances. This makes it possible to avoid cumbersome efforts of minimizing samples by researchers as well as practitioners, and substantially save testing resources for most configurable systems.

The Connections Between Attribute-Induced and Object-Induced Decision Rules in Incomplete Formal Contexts

For a given incomplete context, object-induced approximate concepts have been defined, and this type of approximate concept can induce a type of decision rule. Based on the duality principle, another set of approximate concepts can be defined from the perspective of attributes, i.e., attribute-induced approximate concepts. Although object induced approximate concepts and attribute induced approximate concepts are symmetrical by duality principle, their induced decision rules exhibit different properties and the connections between attribute induced decision rules and object induced decision rules in incomplete formal contexts are not clear. To this end, a type of attribute-induced approximate concept and a method of extracting attribute-induced decision rules are presented. More importantly, it is revealed that given a type of decision rules, there must be corresponding decision rules of the other type, and both of them can provide some useful information, but they are not equivalent to each other. In other words, each type of decision rule can provide some unique and irreplaceable information.

An Innovative Double-Frontier Approach to Measure Sustainability Efficiency Based on an Energy Use and Operations Management Perspective

China’s economic development has achieved great success in recent years, but the problems of energy scarcity and environmental pollution have become increasingly serious. To enhance the reliability and efficiency between energy, the environment and the economy, sustainable development is an inevitable choice. In the context of measuring sustainability efficiency, a network data envelopment analysis model is proposed to formulate the two-stage process of energy use and operations management. A double frontier is derived to optimize the available energy for sustainable development. Due to nonlinearity, previous linear methods are not directly applicable to identify the double frontier and calculate stage efficiencies for inefficient decision-making units. To address this problem, this study develops the primal-dual relationship between multiplicative and envelopment network models based on the Lagrange duality principle of parametric linear programming. The newly developed approach is used to evaluate the sustainability efficiency of 30 administrative regions in China. The results show that insufficient sustainability efficiency is a systemic problem. Different regions should take different measures to conserve energy and reduce pollutant emissions for sustainable development. To increase sustainability efficiency, regions should support energy-saving and emission-reducing technologies in production processes and strengthen their capacity for technological innovation. Compared with energy use efficiency, operations management efficiency in China has a wider range of changes. During the operations management stage, there is not much difference between the capacity and quantity of each region. Based on benchmark regions at the efficiency frontier, there is an opportunity to improve operations management in the near future. Blockchain technology can effectively improve energy allocation efficiency.

Linear–quadratic stochastic Volterra controls I: Causal feedback strategies

In this paper, we formulate and investigate the notion of causal feedback strategies arising in linear–quadratic control problems for stochastic Volterra integral equations (SVIEs) with singular and non-convolution-type coefficients. We show that there exists a unique solution, which we call the causal feedback solution, to the closed-loop system of a controlled SVIE associated with a causal feedback strategy. Furthermore, introducing two novel equations named a Type-II extended backward stochastic Volterra integral equation and a Lyapunov–Volterra equation, we prove a duality principle and a representation formula for a quadratic functional of controlled SVIEs in the framework of causal feedback strategies.

Categor´ıas del An´alisis Funcional

The objective of this article is to categorically focus on some aspects of Functional Analysis, aiming to present a high-level methodology for research and teaching. In section 1 the notions of category and subcategory are given; The Identification Convention and the Principle of Duality are stated; Some categories are presented and important properties of their objects and morphisms are stated. In section 2, functors and natural transformations are studied, showing their importance through examples that connect algebra and topology. In section 3 the important notions of limit of a functor and of adjunction of functors are given, and some examples are considered.

Optimizing local electricity markets: A bi-level primal-dual approach for integrating price-based demand response and distribution locational marginal pricing

This paper addresses the conundrum of optimizing electricity consumption patterns in response to fluctuations in demand and price, a task managed by both load aggregators and the distribution system operator (DSO). The conventional approaches in the literature to integrate demand response (DR) into optimal power flow (OPF) problems typically overlook the price responsiveness of consumers or simplify power flow equations to account for price-elastic demand.In this paper, we strive to close this gap by introducing a bi-level primal-dual optimization framework that incorporates aggregators' objectives into the market-clearing process while preserving the precision of the OPF equations. At the upper level, the model seeks to minimize both the total payment and peak load. The lower level, structured as a second-order conic (SOC) problem, aims to reduce overall generation costs subject to constraints of the second-order conic (SOC) branch flow model (BFM). The two levels interact through the optimal demand response and distribution locational marginal prices (DLMPs). The principles of convex duality principles together with the strong duality constraint are leveraged to transform the market-clearing problem into a single primal-dual problem. We also circumvent the non-linearity that stems from the DR payment term by incorporating discretizing loads and the big-M method, thus converting the problem into a mixed-integer SOC (MI-SOC) formulation. The merits of the proposed MI-SOC framework are validated through case studies conducted on the IEEE 33-bus test system, showcasing its potential to enforce price-elasticity demand response in distribution system's electricity markets.

Deriving Dependently-Typed OOP from First Principles

The expression problem describes how most types can easily be extended with new ways to produce the type or new ways to consume the type, but not both. When abstract syntax trees are defined as an algebraic data type, for example, they can easily be extended with new consumers, such as print or eval , but adding a new constructor requires the modification of all existing pattern matches. The expression problem is one way to elucidate the difference between functional or data-oriented programs (easily extendable by new consumers) and object-oriented programs (easily extendable by new producers). This difference between programs which are extensible by new producers or new consumers also exists for dependently typed programming, but with one core difference: Dependently-typed programming almost exclusively follows the functional programming model and not the object-oriented model, which leaves an interesting space in the programming language landscape unexplored. In this paper, we explore the field of dependently-typed object-oriented programming by deriving it from first principles using the principle of duality. That is, we do not extend an existing object-oriented formalism with dependent types in an ad-hoc fashion, but instead start from a familiar data-oriented language and derive its dual fragment by the systematic use of defunctionalization and refunctionalization. Our central contribution is a dependently typed calculus which contains two dual language fragments. We provide type- and semantics-preserving transformations between these two language fragments: defunctionalization and refunctionalization. We have implemented this language and these transformations and use this implementation to explain the various ways in which constructions in dependently typed programming can be explained as special instances of the general phenomenon of duality.

Non-dual Reality and Empirical Existence in Advaita Vedānta and Ghazālī’s Metaphysics of Unity

This essay explores the ways in which two distinct spiritual traditions, Ghazālī’s Ṣūfīsm and Śaṅkarian Advaita Vedānta, articulate an exclusive metaphysical affirmation of the Ultimate Reality with an empirical recognition of relative existence. Both perspectives are shown to be radically absolutist in their discernment of the Real and in their denying metaphysical reality to other-than-the-Absolute. This raises the question of the ontological status of relativity and empirical existence. Although Islam would seem to assign a greater reality to the world of relativity and human experience, Ghazālī’s most metaphysical treatise, Mishkāt al-anwār (The Niche of Lights), utterly denies the intrinsic reality of creatures in themselves. Similarly, Śaṅkara affirms the non-existence of māyā, the principle of ignorance and duality, as a superimposition upon ātman, the Divine Self immanent to all. Ghazālī concedes, however, that relative existence is “metaphorically” existent (majāz) while Śaṅkara acknowledges the “transactional” reality (vyāvahārika) of empirical existence. Such recognitions involve a multi-stratified view of reality that must account for both metaphysical consistency and empirical access to Reality. This essay shows that although fundamental parallels between the two worlds of meaning can be highlighted, their respective metaphysical perspectives and views of relativity are also quite distinct inasmuch as they are informed by profoundly different religious and traditional contexts.

Classically Computing Performance Bounds on Depolarized Quantum Circuits

Quantum computers and simulators can potentially outperform classical computers in finding ground states of classical and quantum Hamiltonians. However, if this advantage can persist in the presence of noise without error correction remains unclear. In this paper, by exploiting the principle of Lagrangian duality, we develop a numerical method to classically compute a certifiable lower bound on the minimum energy attainable by the output state of a quantum circuit in the presence of depolarizing noise. We provide theoretical and numerical evidence that this approach can provide circuit-architecture-dependent bounds on the performance of noisy quantum circuits. Published by the American Physical Society 2024

REENGINEERING THE EDUCATIONAL PROCESS IN HIGHER EDUCATION INSTITUTIONS ON A DUAL BASIS

The purpose of the paper is to present the authors' conclusions and practical recommendations regarding the restructuring of the educational process of higher education institutions – providers of educational services in partnership with specialised companies. Methodology. The following methods were used: structural-functional method – in the study of the internal structure of the educational process, based on the principles of duality, where each component has a corresponding purpose in the value chain of intellectual capital; graphical modelling – to systematically reflect the author's views on relevant aspects of the research. Results. The sequence of the reengineering cycle and the directions it should take have been defined. It is emphasised that reengineering includes the competences acquired by the recipients of educational services, their communication with teachers, curators from the company, teaching methods and technologies that make up the instrumental mix, the structure of which depends on the mix of expected professional competences. Practical implications. It is emphasised that an applicant should have the right to make an independent choice between the forms of education, taking into account his/her economic circumstances and plans for future professional life in a democratic country. For each of the options, guidelines are proposed for completing the standard number of classroom hours, independent work and other forms of academic activity.

A current sharing snubber of parallel IGBTs based on duality principle

Parallel connection of multiple insulated gate bipolar transistors (IGBTs) is an important approach to improve the current level of equipment in applications of power electronics. The key to ensure the safe and stable operation of parallel IGBTs is to realize current sharing for them. A novel current sharing snubber of parallel IGBTs is proposed for high-power applications, which is derived from a voltage sharing snubber of series IGBTs by duality principle. It not only effectively suppresses the overcurrent and static and dynamic current imbalance, but also possesses advantages of simple structure and easy implementation. The operating principle and deficiencies of the proposed snubber are first analyzed, and then the improved topology is presented. In order to apply the snubber to multiple IGBTs, various topologies and their derivation processes are given. The improvements are carried out and suitable structures are determined by analysis and comparison. In addition, the effectiveness and feasibility of the proposed snubber are verified by experiments. Finally, the proposed snubber is compared with other current sharing methods.

Trading strategies of energy storage participation in day-ahead joint market based on Stackelberg game

The goal of "carbon peak, carbon neutral" and the increasing expansion of new energy have helped to advance the development of energy storage. However, since the operating cost of energy storage is high, carbon emission trading and power market trading have emerged, effectively improving the efficiency. In this paper, a trading strategy and bidding framework of energy storage participation in the day-ahead joint market are studied. A market bidding model has been established in a framework based on the Stackelberg game. Finally, the "Day-Ahead and Intra-Day and Carbon Emission Trading (CET)" market clearing model has been constructed. It has been simplified to solve the equivalent mixed-integer linear programming (MILP) problem with equilibrium constraints through the use of the Karush–Kuhn–Tucker (KKT) optimality criterion and duality principle. The proposed model is validated through improved examples to obtain thermal unit output cuts of up to 32.2% during load trough periods, and up to 16.75% increase in clearing prices during peak load periods. The storage life is extended and the storage output variation is minimized.

Slow Invariant Manifolds of Memristor-Based Chaotic Circuits

This work presents an efficient approach for computing the slow invariant manifold of the fourth-order canonical memristor-based Chua circuits using the flow curvature method. First, the magnetic-flux and charge characteristic curve is generated from the classical circuit with a piecewise-linear function. Then, the characteristic curve is generated from the circuit with the piecewise-linear function replaced by a cubic function. Further, the duality principle is applied to studying such memristor-based circuits in the three-dimensional flux-linkage and charge phase space and then in the four-dimensional current–voltage phase space. It is demonstrated that the slow invariant manifolds of these fourth-order memristor-based chaotic circuits can be more directly computed for the first case than the second.

The Ushnus in the astronomy of the Inca culture

AbstractInferences are made about the relationship that existed between the Ushnus, pyramid‐shaped, terraced structures used by the Incas in the most important ceremonies of the Tawantinsuyo, and Inka Astronomy. We draw attention to Ayni, Kawsaypacha, Duality, and Tinkuy principles, multidimensional codes of conduct and wisdom that are at the root of the Andean cosmovision and on their perception of the world and the Cosmos. These principles, examined as postulates, allow to elaborate axiomatic propositions to identify the Ushnus with ancient Astronomy practices. In a complementary statement, starting from a bi‐conditional proposition, we may infer through reciprocal corollaries that the Inka earliest roots to a holistic learning and educational ambient in the Tawantinsuyo was not elitist, instead it was based on a epistemological construct that differs from the corresponding Western educational ambients. An epistemological and cognitive approach allows to identify an ancient elaborate process of knowledge construction, based on the four fundamental principles, corresponding to different levels of assimilation and comprehension. As a complementary aspect, we identify some of the most preserved Ushnus of the Inka “Empire.” Then we complement this contribution with a broader interpretation for the Ushnus.

An integrative review of secondary school quantum physics curricula in Malaysia

<span lang="EN-US">As a relatively new subject in the physics curriculum of Malaysian secondary schools, quantum physics (QP) raises questions about its relevance to students and the best approach for teaching it. This paper aims to analyze the content of the QP curriculum to provide students with a meaningful learning experience and expose them to the nature of science (NOS). To accomplish this, the Malaysian standard curriculum document known as </span><em><span lang="EN-US">Dokumen Standard Kurikulum dan Pentaksiran</span></em><span lang="EN-US"> (DSKP) and the textbook were analyzed through integrative review. Frameworks and perspectives identified by Stadermann and co-workers on the common trust of the QP curriculum in 15 different countries were used as a benchmark for this analysis. It is found that the QP curriculum in Malaysia focuses on the fundamental principle of understanding the quantum energy of light and its interaction with matter. However, it is also found that there are specific NOS aspects that can be highlighted to help students develop their scientific literacy. These might include emphasizing the philosophy of complementarity in explaining the wave-particle duality principle, the ultraviolet catastrophe, and the contradiction of classical physics interpretation with QP. It is suggested that the QP curriculum be improved by including these and other relevant examples to be on par with other countries. Overall, this analysis provides insight into the relevance and content of QP in Malaysian secondary schools. The proposed changes may help improve students’ learning experience and provide a more comprehensive understanding of the NOS.</span>

Duality for Nonlinear Filtering II: Optimal Control

This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to introduce a stochastic optimal control problem as a dual to the nonlinear filtering problem. The mathematical statement of the dual relationship between the two problems is given in the form of a duality principle. The constraint for the optimal control problem is the backward stochastic differential equation (BSDE) introduced in the companion paper. The optimal control solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The proposed duality is shown to be an exact extension of the classical Kalman-Bucy duality, and different from other types of optimal control and variational formulations given in literature.

Overview of Principles and Rules of Geometrical Product Specifications According to the Current ISO Standards

The article provides an overview of the philosophy of geometrical product specifications (GPS), which are, in addition to material specifications, a key component of effective planning and production of mechanical products as well as communication between partners in these processes. The principles and basic rules for precise and unambiguous specification of all requirements are embodied in a series of ISO GPS standards. It includes standards that describe the required accuracy of geometrical features of size and geometrical tolerances. An overview of the fundamental principles and rules imposed by the current ISO GPS standards and their content was carried out. This includes a description of the organization of the ISO GPS system and a summary of the content of the more relevant standards, which have recently undergone multiple revisions. The ISO GPS standards are based on the duality principle of specification and verification. In the present research, we focused primarily on geometrical specifications, while omitting the parallel pillar of verification, which, according to the ISO GPS matrix model, contains an even greater number of standards that define this area in more detail.

GREPHRO: Nature-inspired optimization duo for Internet-of-Things

The optimization techniques usually work with the maximization or minimization of the problem to obtain the local loci or cumulative global loci. Two-dimensional bio-inspired optimization techniques face convexing problems towards a global solution and use an increased number of iterations. Besides, the duality principle considers the dual optimization aspects of the problems leading to a large duality gap of uncertain deviations and optimization errors between any prime solution and its dual solution. Moreover, several problems exist where one objective function requires maximization and another objective function requires minimization using the same set of parameters and some chaining of the feedback process. In such cases, we generally use two different optimization problems as per the best suit to the problem environment and obtain the different sub-solutions of the individual problems. This increases the complexity of the system and often deviates from the original optimal solution. We address these problems of dual optimization in our present work.In this paper, we introduce the first optimization duo model for computing services. To be specific, our proposed model is the first optimization model that works in a dual combined mode with maximization and minimization simultaneously to obtain a global optimum value or loci. We call our model GREen PHotosynthesis and Respiratory-based Optimization (GREPHRO). GREPHRO is primarily motivated by the observation of plants’ photosynthesis and respiratory processes, which work on the same set of environmental variables and have a chaining process. Further, our proposed nature-inspired GREPHRO can value the global optima or infimum point considering a single objective function serving as maximization and minimization combined. GREPHRO uses the Lagrange dual principle and non-linear parameters to obtain a linear solution for the infimum optima. We use a set of experiments on the GREPHRO model in the domain of Wireless Sensor Network (WSN)-based Internet of Thing (IoT) to derive the use case of our proposed work. The experimental results and the comparative analysis with the two of our previous works show that GREPHRO takes fewer iterations with more stability of the optimum solution. Moreover, the computational and memory complexities are also less. Therefore, GREPHRO is efficient and suitable for two-dimensional optimization problems in resource-constrained environments for IoTs.

Stochastic maximum principle for a time-changed mean field game

This work studies a class of time-changed mean field game problems by the stochastic maximum principle, and establishes a duality principle for the derived forward backward stochastic differential equation. As an application, we provide an explicit solution for the mean of the subdiffusion under the framework of the linear-quadratic structure.

A dual principle for symmetric periodic solutions Bi-stability in noninterdigitated Comb-drive MEMS

A dual principle for symmetric periodic solutions Bi-stability in noninterdigitated Comb-drive MEMS