Incompatibility Relations Research Articles

Approximation algorithms for job scheduling with block-type conflict graphs

The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model.The presented model stems from a well-established line of research combining scheduling theory with methods relevant to graph coloring. Recently, cluster graphs and their extensions like block graphs were given additional attention. We complement hardness results provided by other researchers for block graphs by providing approximation algorithms. In particular, we provide a 2-approximation algorithm for P|G=block graph|Cmax and a PTAS for the case when the jobs are unit time in addition. In the case of uniform machines, we analyze two cases. The first one is when the number of blocks is bounded, i.e. Q|G=k − block graph|Cmax. For this case, we provide a PTAS, improving upon results presented by D. Page and R. Solis-Oba. The improvement is two-fold: we allow richer graph structure, and we allow the number of machine speeds to be part of the input. Due to strong NP-hardness of Q|G=2 − clique graph|Cmax, the result establishes the approximation status of Q|G=k − block graph|Cmax. The PTAS might be of independent interest because the problem is tightly related to the NUMERICAL k-DIMENSIONAL MATCHING WITH TARGET SUMS problem. The second case that we analyze is when the number of blocks is arbitrary, but the number of cut-vertices is bounded and jobs are of unit time. In this case, we present an exact algorithm. In addition, we present an FPTAS for graphs with bounded treewidth and a bounded number of unrelated machines.The paper ends with extensive tests of the selected algorithms.

Deep distortions in everyday memory: Fact memory is illogical, too.

A distinction has recently been drawn between surface distortions and deep distortions in false memory, where the former are conventional errors of commission and the latter are illogical relations among multiple memories of items. The deep distortions that have been studied to date are violations of the logical rules that govern incompatibility relations, such as additivity and countable additivity. Because that work is confined to laboratory word-list tasks, it is subject to the ecological validity criticism that memory for everyday facts may not exhibit such phenomena. We report evidence that memory for everyday facts displays the same deep distortions as laboratory tasks. We developed a version of the conjoint-recognition paradigm that measures memory for incompatible general knowledge facts, similar to those found on the quiz program Jeopardy! In experiments with university participants, four deep distortions were detected (violations of the additivity, countable additivity, universal set, and compensation rules), with participants consistently remembering more than what is logically possible. The distortions were more robust than in laboratory experiments, and memories of incompatible facts (e.g., Jupiter and Saturn cannot both be the largest planet in the solar system) did not suppress each other. These patterns were replicated in subsequent experiments with older and more diverse participant samples. Consistent with the notion that deep distortions are by-products of gist memory, conjoint-recognition modeling analyses revealed that memory for everyday facts was even more reliant on gist than memory for word lists, and that verbatim memory was near-floor. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Normativity of meaning: An inferentialist argument

This paper presents a new argument to defend the normativity of meaning, specifically the thesis that there are no meanings without norms. The argument starts from the observation inferentialists have emphasized that incompatibility relations between sentences are a necessary part of meaning as it is understood. We motivate this approach by showing that the standard normativist strategy in the literature, which is developed in terms of veridical reference that may swing free from the speaker’s understanding, violates the ought-implies-can principle, but ours does not. In addition, our approach is superior because, unlike the dominant approach, it can be extended from declarative sentences to non-representational uses of language. In this paper, however, we only formulate the argument for the base case that involves incompatibility relations between declarative sentences. The goal is not to derive norms from something that is not normative, but to explicate the distinctive type of normativity that is built into meaning as it is understood by language-users. The explication proceeds in two steps. (1) For any sentence s a speaker understands, there is another sentence s’ that is (and is understood by the speaker as) incompatible with s. (2) In virtue of understanding this incompatibility of meanings, she ought not to be committed to both s and s’. This prohibition is not derived from instrumental practical reason, nor is it based on representational correctness, but its source is the incompatibility of meanings.

Functional content and architecture of software laboratory for ontological data analysis

The article presents the functionality and architecture of the software laboratory for ontological analysis and through this prism the methodology of this analysis. The methodological complex of ontological analysis and the procedure for its application provide extraction from the data of multidimensional observations and measurements of the knowledge domain of its semantic model in the form of a formal ontology a set of formal concepts, each of which is determined by extent and intent. In the set of formal concepts, a partial order is revealed (a binary relation of generalization) and intensional relations are revealed that reflect the connections between the elements of the concepts extents. The developed software laboratory differs from the well-known tools for constructing formal ontologies based on empirical object-feature data (i.e., based on data presented in the generally recognized form of a measurement results registration protocol), first of all, by taking into account the realities of accumulating information about the knowledge domain under study. In the general case, they cause the incompleteness and inconsistency of the initial data, for the processing of which the apparatus of multi-valued vector logic is involved. Another unique difference of the software laboratory is the consideration of a priori known (i.e., known before measurements) constraints on the properties existence during the primary processing of empirical data binary relations of conditionality and incompatibility of objects properties of the studied knowledge domain. The presented software laboratory is implemented on the Excel table processor platform and the programming language Visual Basic for Application. The main motive for this choice was to ensure the availability and facilitate the familiarization of ontological data analysis technology by a very wide range of users who use Excel in their professional work.

Truthmakers, Incompatibility, and Modality

This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications of the framework, including proofs of soundness and completeness theorems for a number of logics, one way to use compatibility states to mirror Kripke frames, and an exploration of a way to use the new framework to provide truthmaking clauses for modal formulas.

Fair Allocation of Indivisible Items with Conflict Graphs

We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to this classical problem. Namely, we introduce an incompatibility relation between pairs of items described in terms of a conflict graph. Every subset of items assigned to one agent has to form an independent set in this graph. Thus, the allocation of items to the agents corresponds to a partial coloring of the conflict graph. Every agent has its own profit valuation for every item. Aiming at a fair allocation, our goal is the maximization of the lowest total profit of items allocated to any one of the agents. The resulting optimization problem contains, as special cases, both Partition and Independent Set. In our contribution we derive complexity and algorithmic results depending on the properties of the given graph. We show that the problem is strongly NP-hard for bipartite graphs and their line graphs, and solvable in pseudo-polynomial time for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. Each of the pseudo-polynomial algorithms can also be turned into a fully polynomial approximation scheme (FPTAS).

Polymer dynamics via cliques: New conditions for approximations

Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of compatible polymers. Various approximation problems reduce to approximating the partition function of a polymer model. Central to the existence of such approximation algorithms are weight conditions of the respective polymer model. Such conditions are derived either via complex analysis or via probabilistic arguments. We follow the latter path and establish a new condition—the clique dynamics condition—, which is less restrictive than the ones in the literature. We introduce a new Markov chain where the clique dynamics condition implies rapid mixing by utilizing cliques of incompatible polymers that naturally arise from the translation of algorithmic problems into polymer models. This leads to improved parameter ranges for several approximation algorithms, such as a factor of at least 21/α for the hard-core model on bipartite α-expanders.

Outline of a Theory of Reasons

AbstractThis paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences.

Defects and metric anomalies in Föppl–von Kármán surfaces

A general framework is developed to study the deformation and stress response in Föppl–von Kármán shallow shells for a given distribution of defects, such as dislocations, disclinations and interstitials, and metric anomalies, such as thermal and growth strains. The theory includes dislocations and disclinations whose defect lines can both pierce the two-dimensional surface and lie within the surface. An essential aspect of the theory is the derivation of strain incompatibility relations for stretching and bending strains with incompatibility sources in terms of the various defect and metric anomaly densities. The incompatibility relations are combined with balance laws and constitutive assumptions to obtain the inhomogeneous Föppl–von Kármán equations for shallow shells. Several boundary value problems are posed, and solved numerically, by first considering only dislocations and then disclinations coupled with growth strains.

Scheduling with complete multipartite incompatibility graph on parallel machines: Complexity and algorithms

In this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine.The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality: Cmax (makespan) and ∑Cj (total completion time). The problems are considered for a variety of machine types: identical, uniform and unrelated. The results consist of delimitation of the easy (polynomial) and NP-hard problems within these constraints. Also, polynomial-time exact algorithms are provided for easier problems and algorithms with a guaranteed constant worst-case approximation ratio for harder ones.In particular, there is provided a polynomial-time approximation scheme (PTAS) for scheduling with respect to ∑Cj on uniform machines, when the number of parts (i.e. sets of vertices constituting the mentioned graph) is bounded. The problem is addressed by developing a linear programming relaxation technique with appropriate rounding. This technique together with an exhaustive search (albeit in a manner controlled by the precision parameter) allows to provide the desired algorithm. For Cmax a PTAS is provided for the case of unit time jobs, but when the number of parts is part of the input. Interestingly, the latter result shows a connection between the considered problem of scheduling and covering problems.

Polymer Dynamics Via Cliques: New Conditions for Approximations

Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of compatible polymers. Various approximation problems reduce to approximating the partition function of a polymer model. Central to the existence of such approximation algorithms are weight conditions of the respective polymer model. Such conditions are derived either via complex analysis or via probabilistic arguments. We follow the latter path and establish a new condition---the clique dynamics condition---, which is less restrictive than the ones in the literature. We introduce a new Markov chain where the clique dynamics condition implies rapid mixing by utilizing cliques of incompatible polymers that naturally arise from the translation of algorithmic problems into polymer models. This leads to improved parameter ranges for several approximation algorithms, such as a factor of at least $2^{1/\alpha}$ for the hard-core model on bipartite $\alpha$-expanders.

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

In this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. We provide several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality: Cmax (makespan) and ∑Cj (total completion time). We consider a variety of machine types in our paper: identical, uniform, and unrelated. Our results consist of delimitation of the easy (polynomial) and NP-hard problems within these constraints. We also provide algorithms, either polynomial exact algorithms for the easier problems, or algorithms with a guaranteed constant worst-case approximation ratio. In particular, we fill the gap on research for the problem of finding a schedule with the smallest ∑Cj on uniform machines. We address this problem by developing a linear programming relaxation technique with an appropriate rounding, which to our knowledge is a novelty for this criterion in the considered setting.

Asymmetrical reproductive barriers in sympatric jewelflowers: are floral isolation, genetic incompatibilities and floral trait displacement connected?

Abstract Floral visitors influence reproductive interactions among sympatric plant species, either by facilitating assortative mating and contributing to reproductive isolation, or by promoting heterospecific pollen transfer, potentially leading to reproductive interference or hybridization. We assessed preference and constancy of floral visitors on two co-occurring jewelflowers [Streptanthus breweri and Streptanthus hesperidis (Brassicaceae)] using field arrays, and quantified two floral rewards potentially important to foraging choice – pollen production and nectar sugar concentration – in a greenhouse common garden. Floral visitors made an abundance of conspecific transitions between S. breweri individuals, which thus experienced minimal opportunities for heterospecific pollen transfer from S. hesperidis. In contrast, behavioural isolation for S. hesperidis was essentially absent due to pollinator inconstancy. This pattern emerged across multiple biotic environments and was unrelated to local density dependence. S. breweri populations that were sympatric with S. hesperidis had higher nectar sugar concentrations than their sympatric congeners, as well as allopatric conspecifics. Previous work shows that S. breweri suffers a greater cost to hybridization than S. hesperidis, and here we find that it also shows asymmetrical floral isolation and floral trait displacement in sympatry. These findings suggest that trait divergence may reduce negative reproductive interactions between sympatric but genetically incompatible relatives.

Acupuncture Treating Heart Diseases Based on Sixty JiaZi and Eight Palaces <br/>—Mathematical Reasoning of Treatment Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Medicine (V)

Theory of Sixty JiaZi (60 甲子) is useful in understanding a human body disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Medicine (TCM), this paper demonstrates the treatment principle: “seize the momentum of development, hasten lucky avoids disaster” (顺势而为, 趋吉避凶). Sixty JiaZi is hidden behind eight palaces. The first or second transfer law of human body energies of Sixty JiaZi changes according to the different blood pH values of a human body whether in the normal range or not, respectively, assuming that the range of blood pH values of a human body is divided into four parts from small to large. Both second and third are for a healthy human body. Both the root-cause and symptoms come from the first transfer law of human body energies. And both first and fourth are for an unhealthy human body. Both the root-cause and symptoms come from the second transfer law of human body energies. The treating disease of a human body should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, acupuncture is used to treat atrial premature beats as congenital heart disease.

RPI inflation rate from 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II)

RPI (Retail Price Index) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE) or Traditional Chinese Science (TCS), this paper demonstrates that for the RPI inflation rate of industry economic society, the normal range of theory is nearly to . The first or second transfer law of economic diseases changes according to the different RPI inflation rate whether in the normal range or not. The treatment principle:“Don’t have economic disease cure cure non-ill” () is abiding by the first or second transfer law of economic diseases. Assume that the range of the RPI inflation rate is divided into four parts from small to large. Both second and third are for a healthy economy. Our works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law. And both first and fourth are for an unhealthy economy. Our works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship.

PPI inflation rate from 1% to 6% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II)

PPI (Producer Price Index) is useful in understanding industry economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE) or Traditional Chinese Science (TCS), this paper demonstrates that for the PPI inflation rate of industry economic society, the normal range of theory is nearly to . The first or second transfer law of economic diseases changes according to the different PPI inflation rate whether in the normal range or not. The treatment principle:“Don’t have economic disease cure cure non-ill” () is abiding by the first or second transfer law of economic diseases. Assume that the range of PPI inflation rate is divided into four parts from small to large. Both second and third are for a healthy economy. Our works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law. And both first and fourth are for an unhealthy economy. Our works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship.

Основные парадигматические отношения в семантическом поле концепта лето/summer

Article is based on the materials of a comprehensive study of the concepts summer and autumn from the point of view of their perception by representatives of Russian and English linguistic cultures. This paper shows the features of the paradigmatic relations of Russian and English concept summer. The study was built on the identification of synonymous (quasi-synonymous), antonymic, (hypo) hyperonymic, or genus-species relationships, as well as the incompatibility relations of this concept. Study is based on the materials of the explanatory dictionaries and dictionaries of synonyms and antonyms of the Russian and English languages; illustrative material was taken from the National corpus of the Russian language and the British National Corpus. The analysis made it possible to conclude that the paradigmatic explication of the content of the concept summer most clearly actualizes only one of the four previously identified cognitive features of the concept, namely the sign ‘time of year, season’.

A Study of Extra Marital Relations in Urdu Dramas: A Qualitative Analysis

It is highly perceived that most of the stories of Urdu televise dramas in Pakistan are revolving around the problems of wedded couple. It is point of discussion that plots of the contemporary Pakistani Urdu televise dramas is depicting more extramarital relations. Through narrative structure analysis, the current study revealed that drama serials start with a family and then a quarrel arises between married couple. At that point, a protagonist enters in the scene which also becomes as catalyst in making separation between the married spouses. The bad and harsh attitude of the husband appears to be the enough reason to bend toward extramarital relation. Divorce seems to be the only solution in case of incompatible relations between the spouses. Consequently, the divorced lady marries with her protagonist and starts living a happy life with her second husband. It is apparent that these dramas are promoting extramarital relations in positive ways. The current bombardment of such issues by electronic media seems to be trying to legitimize the illegitimate relation. The analyses depict that televise Urdu dramas of Pakistan are violating the family values and promoting the extramarital relations in positive ways.

GDP 6% to 16%<br/>—Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II)

GDP (Gross Domestic Product) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE), this paper demonstrates that for the GDP inflation rate of economic society, the normal range of theory is [5.8114%, 16.359%] nearly to [6%, 16%], and center is 10.208% nearly to 10%. The first or second transfer law of economic diseases changes according to the different GDP inflation rate whether in the normal range or not. The treatment principle: “Don’t have economic disease cure cure non-ill” (不治已病治未病) is abiding by the first or second transfer law of economic diseases. Assume that the range of the GDP inflation rate is divided into four parts from small to large. Both second and third are for a healthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law. And both first and fourth are for an unhealthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, the Chinese GDP inflation rate is used for the water system of steady multilateral system.

CPI from 2% to 5%– Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II)

CPI (Consumer Price Index) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE), this paper demonstrates that for the CPI inflation rate of economic society, the normal range of theory is [1.8828%, 5.2216%] nearly to [2%, 5%] and the center is 3.2741% nearly to 3%. The first or second transfer law of economic diseases changes according to the different CPI inflation rate whether in the normal range or not. The treatment principle: “Don’t have economic disease cure cure non-ill” (不治已病治未病) is abiding by the first or second transfer law of economic diseases. Assume that the range of a CPI inflation rate is divided into four parts from small to large. Both second and third for are for a healthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law; And both first and fourth are for an unhealthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, the Chinese CPI inflation rate is used for the earth subsystem how to do works based on studying the sick subsystem of steady multilateral systems.