Disjunctive Form Research Articles

Disjunctive answer options complicate communication – a linguistic analysis of the danish EQ-5D (5 L) version

Introduction: EQ-5D is an internationally acknowledged tool for assessing health-related quality of life. Our aim was to examine how pragmatic dynamics may influence answers to the EQ-5D-5 L in items where the structure of answer options is disjunctive. Methods: We performed a 3-step linguistic analysis building on the seminal work of Grice, including (1) examination of the lexical meanings of the answer options, (2) considerations of how conversational maxims might affect the respondent’s interpretation of compatible answer options under a single item, and (3) analysis of how the questionnaire’s context might counteract the problem of omitted answer options by shifting the meaning of context-sensitive expressions. Results: All items with disjunctive answer options exhibit both compatibilities and omissions. In combination with the disjunctive form of answer options these features of the EQ-5D-5 L complicates the communicative task for respondents relying on conversational norms to identify the most suitable answers to the instrument’s questions. Discussion: In items where answer options have a disjunctive structure, respondents relying on Gricean conversational maxims will have to depend on their individual understanding of fine-grained details concerning the questionnaire’s purpose and may have to weigh how conflicting norms should be balanced. While such dynamics are likely to go undetected in cognitive interviews, linguistic analysis may help to identify them.

Disjunctive writing in the urban skinscape: Bodies, borders and the physiology of attention in a Rio de Janeiro favela

This article offers a creative disjunctive feminist analysis of affective rhythms within a complexly bordered complex of favelas in Rio de Janeiro. It explores the gendered atmospheric constitution of authority in the favela’s violent border spaces, arguing that authority is partly embodied through a channelling of attention. Attention is conceptualised as involving not just conscious intentions, perceptions and emotions, but also non-conscious rhythms of autonomous affective self-regulation. The article is structured through a tripartite disjunctive form that expresses the bordering of city, body and experience. Drawing on qualitative interview data, quantitative electrodermal activity physiological data and creative writing, the article dwells with the materiality of words and the forms of affects to express material and physiological aspects of emotion and affect in journeys around the internal border-spaces of the city. Adapting the modernist tradition of ‘stream of consciousness’ writing, we style a ‘stream of attention’ form of writing that expresses multiple modes of embodied, conscious and preconscious attention.

Theory of Extended Forms of Switching Function

In switching algebra, there exist standard forms of Boolean functions such as the disjunctive or conjunctive form. This paper discusses the theory of the extended standard forms of Boolean functions. In addition to the four existing standard forms, two further forms are introduced and thus expanded to six basic forms. On the one hand, the existence of the extended forms is presented and on the other hand new formulas and equations are illustrated. Equations relating to the resolution and/or solution of conjunction/disjunctions are detailed and proven to be valid. In addition, equations for conversion between forms are exemplified. Finally, certain formal relations between the basic forms that are valid under certain conditions are featured.

Utilization of the Karnaugh Map in Exploring Cause-effect Relations Modeled by Partially-defined Boolean Functions

This paper utilizes a modern regular and modular eight-variable Karnaugh map in a systematic investigation of cause-effect relationships modeled by partially-defined Boolean functions (PDBF) (known also as incompletely specified switching functions). First, we present a Karnaugh-map test that can decide whether a certain variable must be included in a set of supporting variables of the function, and, otherwise, might enforce the exclusion of this variable from such a set. This exclusion is attained via certain don’t-care assignments that ensure the equivalence of the Boolean quotient w.r.t. the variable, and that w.r.t. its complement, i.e., the exact matching of the half map representing the internal region of the variable, and the remaining half map representing the external region of the variable, in which case any of these two half maps replaces the original full map as a representation of the function. Such a variable exclusion might be continued w.r.t. other variables till a minimal set of supporting variables is reached. The paper addresses a dominantly-unspecified PDBF to obtain all its minimal sets of supporting variables without resort to integer programming techniques. For each of the minimal sets obtained, standard map methods for extracting prime implicants allow the construction of all irredundant disjunctive forms (IDFs). According to this scheme of first identifying a minimal set of supporting variables, we avoid the task of drawing prime-implicant loops on the initial eight-variable map, and postpone this task till the map is dramatically reduced in size. The procedure outlined herein has important ramifications for the newly-established discipline of Qualitative Comparative Analysis (QCA). These ramifications are not expected to be welcomed by the QCA community, since they clearly indicate that the too-often strong results claimed by QCA adherents need to be checked and scrutinized.

Using Eight-Variable Karnaugh Maps to Unravel Hidden Technicalities in Qualitative Comparative Analysis

We use a regular and modular eight-variable Karnaugh map to reveal some technical details of Boolean minimization usually employed in solving problems of Qualitative Comparative Analysis (QCA). We utilize as a large running example a prominent eight-variable political-science problem of sparse diversity (involving a partially-defined Boolean function (PDBF), that is dominantly unspecified). We recover the published solution of this problem, showing that it is merely one candidate solution among a set of many equally-likely competitive solutions. We immediately obtain one of these rival solutions, that looks better than the published solution in two aspects, namely: (a) it is based on a smaller minimal set of supporting variables, and (b) it provides a more compact Boolean formula. However, we refrain from labelling our solution as a better one, but instead we stress that it is simply un-comparable with the published solution. The comparison between any two rival solutions should be context-specific and not tool-specific. In fact, the Boolean minimization technique, borrowed from the area of digital design, cannot be used as is in QCA context. A more suitable paradigm for QCA problems is to identify all minimal sets of supporting variables (possibly via integer programming), and then obtain all irredundant disjunctive forms (IDFs) for each of these sets. Such a paradigm stresses inherent ambiguity, and does not seem appealing as the QCA one, which usually provides a decisive answer (irrespective of whether it is justified or not).The problem studied herein is shown to have at least four distinct minimal sets of supporting variables with various cardinalities. Each of the corresponding functions does not have any non-essential prime implicants, and hence each enjoys the desirable feature of having a single IDF that is both a unique minimal sum and the complete sum. Moreover, each of them is unate as it is expressible in terms of un-complemented literals only. Political scientists are invited to investigate the meanings of the (so far) abstract formulas we obtained, and to devise some context-specific tool to assess and compare them.

Conventional and Improved Inclusion-Exclusion Derivations of Symbolic Expressions for the Reliability of a Multi-State Network

This paper deals with an emergent variant of the classical problem of computing the probability of the union of n events, or equivalently the expectation of the disjunction (ORing) of n indicator variables for these events, i.e., the probability of this disjunction being equal to one. The variant considered herein deals with multi-valued variables, in which the required probability stands for the reliability of a multi-state delivery network (MSDN), whose binary system success is a two-valued function expressed in terms of multi-valued component successes. The paper discusses a simple method for handling the afore-mentioned problem in terms of a standard example MSDN, whose success is known in minimal form as the disjunction of prime implicants or minimal paths of the pertinent network. This method utilizes the multi-state inclusion-exclusion (MS-IE) principle associated with a multi-state generalization of the idempotency property of the ANDing operation. The method discussed is illustrated with a detailed symbolic example of a real-case study, and it produces a more precise version of the same numerical value that was obtained earlier. The example demonstrates the notorious shortcomings and the extreme inefficiency that the MS-IE method suffers, but, on the positive side, it reveals the way to alternative methods, in which such a shortcoming is (partially) mitigated. A prominent and well known example of these methods is the construction of a multi-state probability-ready expression (MS-PRE). Another candidate method would be to apply the MS-IE principle to the union of fewer (factored or composite) paths that is converted (at minimal cost) to PRE form. A third candidate method, employed herein, is a novel method for combining the MS-PRE and MS-IE concepts together. It confines the use of MS-PRE to ‘shellable’ disjointing of ORed terms, and then applies MS-IE to the resulting partially orthogonalized disjunctive form. This new method makes the most of both MS-PRE and MS-IE, and bypasses the troubles caused by either of them. The method is illustrated successfully in terms of the same real-case problem used with the conventional MS-IE.

Formation Mission Design for Commercial Aircraft Using Switched Optimal Control Techniques

In this article, the formation mission design problem for commercial aircraft is studied. Given the departure times and the departure and arrival locations of several commercial flights, the relevant weather forecast, and the expected fuel savings during formation flight, the problem consists in establishing how to organize them in formation or solo flights and in finding the trajectories that minimize the overall direct operating cost of the flights. Each aircraft can fly solo or in different positions inside a formation. Therefore, the mission is modeled as a switched dynamical system, in which the discrete state describes the combination of flight modes of the individual aircraft and logical constraints in disjunctive form establish the switching logic among the discrete states of the system. The formation mission design problem has been formulated as an optimal control problem of a switched dynamical system and solved using an embedding approach, which allows switching decision among discrete states to be modeled without relying on binary variables. The resulting problem is a classical optimal control problem which has been solved using a knotting pseudospectral method. Several numerical experiments have been conducted to demonstrate the effectiveness of this approach. The obtained results show that formation flight has great potential to reduce fuel consumption and emissions.

Математическое описание функций управления двухфазным вентильным двигателем с двухсекционной фазной обмоткой

The mathematical description of a digital control device for a modern electric drive based on a switched two-phase motor with two-sectional phase windings is presented. For all possible winding sec-tion connection schemes and their basic usage methods involving the application of a four-arm or four-switch power amplifier, the cyclic sequences of control signals are determined and analytical expressions for them are derived that take into account the motor rotor rotation in both directions. Compact versions of representing them in form of Zhegalkin's polynomial or in the disjunctive form are obtained. Analytical dependencies of the rotor position digital signals received from Hall sensors are obtained, and their in-terrelation with the base vectors and number of pole pairs on the rotor magnet is revealed. Combined methods for using the phase winding sections are elaborated, which make it possible to obtain the base vectors uniformly distributed over the rotation circumference with their amplitudes minimally differing from each other. The derived mathematical expressions can be used in designing a digital electric drive and implementing high-speed algorithms based on programmable logic circuits and systems on a chip.

Choosing of Asynchronous Motor Protection Equipment in Production Environment

The current article is devoted to the topic problem of decision making concerning the choice of the protective means for asynchronous motors operated within industrial shop electric circuits under challenging conditions of improper electric supply. In this paper we show how energy economizing model for the asynchronous motor can be presented in the form of predicate disjunction and be applied with the pattern recognition algorithm for making solutions. The major advantage of a new model is its open character and the possibility of knowledge accumulation with respect to electromechanical equipment. We submit the information on the software and hardware complex applied for the research on the characteristics of the circuit voltage and the asynchronous motors in the real time mode directly within the enterprise industrial shop. The publication also reports on the searching for the best protective solution for asynchronous motors. This work is based on the known recognition algorithm of statistical optimization for non-linear objects given as the aggregates of predicates. The algorithm fruitfully applies the local selection principle. The approach proposed in this publication has been approbated at the protective means selection procedure for the asynchronous motor of 7.5 kW capacity, which performance is 80% of the working cycle under conditions of improper electric energy supply in the experimental shop of Ukrspetsservis.

Disjoint Sum of Products by Orthogonalizing Difference-Building ⴱ

AbstractThe orthogonalization of Boolean functions in disjunctive form, that means a Boolean function formed by sum of products, is a classical problem in the Boolean algebra. In this work, the novel methodologyORTH[ⴱ] of orthogonalization which is an universally valid formula based on the combination technique »orthogonalizing difference-building ⴱ« is presented. Therefore, the technique ⴱ is used to transform Sum of Products into disjoint Sum of Products. The scope of orthogonalization will be solved by a novel formula in a mathematically easier way. By a further procedure step of sorting product terms, a minimized disjoint Sum of Products can be reached. Compared to other methods or heuristicsORTH[ⴱ] provides a faster computation time.

Multi-periodic Refinery Scheduling Based on Generalized Disjunctive Programming

Refinery complex production process usually involves some distinct or implied production rules and expert experiences. Representation and utilizing these heuristic rules is conducive to efficient scheduling optimization. In this paper, the heuristic rules were formulated using disjunctive form and logical proposition, and a discrete-time based multi-periodic generalized disjunctive programming (GDP) scheduling model was built. Due to the combining of logic expressions and algebra expressions, heuristic rules were utilized by the proposed model, while scheduling optimization was ensured. The formulated model was used to deal with a refinery scheduling problem. Case study shows the model’s feasibility and efficiency.

Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints

This paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obstacle or storm avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle avoidance is especially demanding in terms of modeling efforts. Indeed, in general, separation constraints require the introduction of auxiliary integer variables in the model; for passage constraints, a multiphase optimal control approach is used, and for obstacle avoidance constraints, geometric approximations of the obstacles are introduced. Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this paper, an embedding approach is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the optimal control problem with logical constraints is converted into a smooth optimal control problem which is solved using traditional techniques, thereby reducing the computational complexity of finding the solution. The effectiveness of the approach is demonstrated through several numerical experiments by computing the optimal trajectories of multiple aircraft in converging and intersecting arrival routes with time-based separation constraints, distance-based separation constraints, and operational constraints.

Multi-aircraft optimal 4D online trajectory planning in the presence of a multi-cell storm in development

This paper studies the trajectory planning problem for multiple aircraft in converging arrival routes in the presence of a multi-cell storm in development. Storm avoidance constraints are enforced by approximating each cell of the storm as a moving and size-changing ellipsoid. Besides storm avoidance constraints, operational constraints, such as, following an arrival procedure or time-based separation between aircraft, are also considered. The problem is solved using nonlinear model predictive control based on hybrid optimal control with logical constraints in disjunctive form. Logical constraints in disjunctive form arise in modelling of both storm avoidance and operational constraints and also in modelling general decision making processes during flight, such as, establishing which among two or more actions should be taken to solve a contingency. The evolution of the storms is tackled using the nonlinear model predictive control scheme, which iteratively re-plans the trajectories as a new estimation of the state of the storms is available. The presence of this feedback mechanism in the trajectory planning scheme makes it substantially different from open-loop trajectory planning methods. Since it is intended for trajectory planning with very short time horizon before the departure or during the flight, it has been herein called online trajectory planning. An embedding approach is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the hybrid optimal control problem is converted into a smooth optimal control problem, thereby reducing the computational complexity of finding the solution. The effectiveness of the approach is demonstrated through several numerical experiments.

Impact of Structural Heterozygosity on Pollen Fertility and Chiasma Frequency in <i>Leontopodium jacotianum</i> from the Cold Deserts of Ladakh (Jammu and Kashmir), India

Meiotic studies have been carried out on three plants of Leontopodium jacotianum from Cold deserts of Ladakh. The chromosome number of n=24 counted in all the plants adds a new tetraploid cytotype for the species. The plants collected from Zoji-La showed a normal meiotic course leading to high pollen fertility. However, the plants collected from Sankoo region of cold deserts of Ladakh, Jammu, and Kashmir showed abnormal meiosis caused by structural heterozygosity for reciprocal translocations. The structural heterozygosity was observed for the first time in the species. Chiasma frequency was also calculated by using one-way analysis of variance (ANOVA) in the plants to see the effect of reciprocal translocations. Besides reciprocal translocation, the plant also showed various meiotic abnormalities in the form of early disjunction of bivalents, chromatin bridges, and laggards. Structural heterozygosity and other meiotic abnormalities in the plant seem to be responsible for a reduction in pollen fertility.

Lagrangian duality and saddle points for sparse linear programming

The sparse linear programming (SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved. In this paper, by rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of the Lagrangian dual problem for the SLP, in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality under bi-dual sparsity consistency. Furthermore, we show a saddle point theorem based on the strong duality and analyze two classes of stationary points for the saddle point problem. At last, we extend these results to SLP with the lower bound zero replaced by a certain negative constant.

A Case of Structural Heterozygosity Affecting Chiasma Frequency and Pollen Fertility in Natural Populations of <i>Artemisia roxburghiana</i>

Meiotic studies have been carried out on six accessions of Artemisia roxburghiana from four regions of Western Himalayas. The accessions collected from Chamba, Kinnaur and Kullu districts of Himachal Pradesh and Kargil district of Jammu and Kashmir showed a normal meiotic course leading to high pollen fertility. However, the accession collected from Drass region of cold deserts of Ladakh, Jammu, and Kashmir showed abnormal meiosis caused by structural heterozygosity for reciprocal translocations. The present study adds the first report of structural heterozygosity in the species. Chiasma frequency was also calculated in the accessions to see the effect of reciprocal translocations. Besides, reciprocal translocation, the accession also showed various meiotic abnormalities in the form of the early disjunction of bivalents, chromatin bridges and laggards leading to abnormal microsporogenesis. Structural heterozygosity and other meiotic abnormalities in the accession seem to be responsible for a reduction in pollen fertility.

ЛОГИКИ С ВЕКТОРНОЙ СЕМАНТИКОЙ КАК СРЕДСТВО ВЕРИФИКАЦИИ БАЗ ЗНАНИЙ

The paper discusses the general issues of automated search of artifacts in rule-based knowledge bases (KB) based on logic with vector semantics in the VTF-logic variant. Cases of falsity of antecedent of rules at all admissible values of truth of input premises, existence of terms which are not used anywhere and generation of uncertain values of truth, emergence of contradictions are considered. Automation is considered as the organization of the direct attached logical inference opening artifacts of KB. The first two cases are identified by counting the number of each rule triggering and identifying terms that are not tied to the rules. The contradiction is revealed by the verification of the truth of the conclusions-hypotheses. The presence of a conclusion with truth (1; 1) (complete contradiction) signals a contradiction at one of the stages of reasoning, which is set by the back trace of the logical chain. A necessary stage of inference is to combine the evidence using 11-composition (the second form of disjunction). The paper also presents the principle of calculating the truth of the conclusion based on the truth of the premises, the strategy of combining evidence, numerical measures that can be used in the conclusion.

Disjointed sum of products by a novel technique of orthogonalizing ORing

AbstractThis work presents a novel combining method called ‘orthogonalizing ORing◯∨$\bigcirc\!\!\!\!\!\!\vee $’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, axioms and rules for this linking technique are also defined which have to be considered getting correct results. Additionally, a novel equation, based on orthogonalizing ORing, is set up for orthogonalization of every Boolean function of disjunctive form. Thus, disjointed Sum of Products can be easily calculated in a mathematical way by this equation.

Data-driven context-sensitivity for points-to analysis

We present a new data-driven approach to achieve highly cost-effective context-sensitive points-to analysis for Java. While context-sensitivity has greater impact on the analysis precision and performance than any other precision-improving techniques, it is difficult to accurately identify the methods that would benefit the most from context-sensitivity and decide how much context-sensitivity should be used for them. Manually designing such rules is a nontrivial and laborious task that often delivers suboptimal results in practice. To overcome these challenges, we propose an automated and data-driven approach that learns to effectively apply context-sensitivity from codebases. In our approach, points-to analysis is equipped with a parameterized and heuristic rules, in disjunctive form of properties on program elements, that decide when and how much to apply context-sensitivity. We present a greedy algorithm that efficiently learns the parameter of the heuristic rules. We implemented our approach in the Doop framework and evaluated using three types of context-sensitive analyses: conventional object-sensitivity, selective hybrid object-sensitivity, and type-sensitivity. In all cases, experimental results show that our approach significantly outperforms existing techniques.

DISTRIBUTION OF CONJUNCTIVE AND DISJUNCTIVE FORMS IN XITSONGA

The conjunctive and disjunctive forms in Xitsonga are examined with the purpose of presenting the distribution of these forms. While verbs in the conjunctive form are followed by some elements, the disjunctive is used when no element follows a verb. Xitsonga follows these basic patterns observed in other Bantu languages, but previous theories cannot explain all the occurrences of the distinction between the conjunctive/disjunctive forms. In previous work, three major approaches have been proposed: the constituency approach, the focus-based approach and the information packaging approach. Xitsonga shows support as well as counter evidence for all these approaches. This paper will also reexamine the claim that the presence of conjunctive/disjunctive distinctions only exists in the present tense. Following Creissels (2014), we report that the conjunctive/disjunctive dichotomy is present in other tenses as well when prosodic patterns such as penultimate lengthening are further examined.