Effective subdirect decomposition: a case study

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special cases of the constraint satisfaction problem (CSP), which is the problem of determining whether a set of constraints is satisfiable. In this paper we study the worst-case time complexity of NP-complete CSPs. Our main interest is in the CSP problem parameterized by a constraint language Gamma (CSP(Gamma)), and how the choice of Gamma affects the time complexity. It is believed that CSP(Gamma) is either tractable or NP-complete, and the algebraic CSP dichotomy conjecture gives a sharp delineation of these two classes based on algebraic properties of constraint languages. Under this conjecture and the ETH, we first rule out the existence of subexponential algorithms for finite domain NP-complete CSP(Gamma) problems. This result also extends to certain infinite-domain CSPs and structurally restricted CSP(Gamma) problems. We then begin a study of the complexity of NP-complete CSPs where one is allowed to arbitrarily restrict the values of individual variables, which is a very well-studied subclass of CSPs. For such CSPs with finite domain D, we identify a relation SD such that (1) CSP({SD}) is NP-complete and (2) if CSP(Gamma) over D is NP-complete and solvable in O(c^n) time, then CSP({SD}) is solvable in O(c^n) time, too. Hence, the time complexity of CSP({SD}) is a lower bound for all CSPs of this particular kind. We also prove that the complexity of CSP({SD}) is decreasing when |D| increases, unless the ETH is false. This implies, for instance, that for every c>1 there exists a finite-domain Gamma such that CSP(Gamma) is NP complete and solvable in O(c^n) time.

An algebra or relational system usually is called rigid if its automorphism group or endomorphism monoid is trivial, i.e. consists of the indentity only. Sometimes constants are also considered as trivial what gives rise to the notion of a C-rigid system (cf. [Lan-P 841). In this paper, which is an extended version of a talk given in Budapest at the Conference on Ordered Structures and Universal Algebra in honour of L. Fuchs on the occasion of his 70 ” birthday, we shall generalize the concept of rigidity simply by enlarging the set of functions to be considered as trivial. Thus, for a set H of functions, H-rigid means that the automorphisms, endomorphisms or in general the polymorphisms belong to H. Our aim is to give a criterion for H-rigidity. This will be done in terms of so-called H-minimal clones (see Theorem 2.1). Of course, for applications it remains the problem to determine these H-minimal clones. As an example, they are determined for some few special cases on a twoor three-element base set.

Cardinal sequences

In this article, an “algebra” (sometimes also called a “universal algebra”) is a nonempty set X together with a set of “basic operations”; each operation is a finitary total function on X , i.e., a function ƒ : X n → X for some n ∈ {1, 2, …}. While our operations always have finite arity, we allow infinitely many basic operations in our algebras. Clone theory investigates the structure of all algebras on a given set. It turns out that several questions originating in algebra can be solved (or at least attacked) with set-theoretic methods. This article collects a few examples of this approach, based on recent results of Pinsker, Shelah and the author. Background . A large part of universal algebra investigates the relations between the basic operations of an algebra; here we take a different point of view—all term operations are considered to live an an equal level; thus we will, for example, not distinguish between a Boolean algebra and the corresponding Boolean ring, because each ring operation can be written as composition of operations of the Boolean algebra, and conversely. This point of view is motivated by the observation that many properties of algebras depend only on the clone of its term functions or polynomials, without any need to distinguish basic operations; for example, an equivalence relation is a congruence relation iff it is closed under all unary polynomials.

Cyclotomic Gaudin models with irregular singularities

In the algebra there are several kinds of structure theorems which can be formulated without operations, using only homological tools. For instance, the wellknown fact that any universal algebra can be subdirectly embedded in a direct product of subdirectly irreducible algebras, can be formulated in a pure categorytheoretical manner. Now the question arises what its dual statement asserts. Our purpose is to give such a category which satisfies certain selfdual conditions, and making use of these, to prove structure theorems and their dual statements. The structure theorems themselves are, of course, well-known statements for algebraic stuctures. However, their duals yield some theorems of unusual type. About the possibility of the dualization there occurs some trouble. The most of the difficulties is at finding selfdual conditions being necessary to prove the theorems. So we must not make use of the condition 'every epimorphism is a normal one' which is fulfilled for groups, since its dual is false. Further the lattice of all congruencerelations of any universal algebra is a so-called compactly generated lattice. This fact plays a very important role in the proof of the theorem according to subdirect embeddings of universal algebras, nevertheless compactly generating is not a se!fdual notion. Applying the theorems proved for certain categories, we establish some particular theorems for rings, groups, modules, respectively. In w 2 we give a detailed enumeration of the usual notions and assertions of the theory of categories with respect to the importance of the dual notions and assertions, moreover, we form a system of selfdual conditions which will be satisfied by the category we are dealing with. w 3 is devoted to the investigation of subdirect embeddings, subdirect irreducibility and to the dualization of those. In w 4 we applicate the results developed before for rings, groups, module ~ and abelian groups. Most of the applications are concerned with rings.

I-patches represent a family of implicit multi-sided surfaces. Similarly to functional splines, each boundary curve of the patch is defined as the intersection of a primary and a bounding surface, both given in implicit form, and the patch can connect to the primaries with arbitrary geometric continuity. Following the publication of Várady et al. [1], this paper elaborates the basic formulation in more detail, and introduces several interesting features, including a distance-based surface interpretation, consistent orientation of the primaries, setting shape parameters, and handling various special cases. Implicit multi-sided patches are primarily used for connecting simple implicit surfaces, such as planes, cylinders, spheres etc., however, I-patches are also capable of modeling complex free-form shapes. We show constructions for producing setback vertex blends with conic boundaries and patchworks defined by control polyhedra. We discuss the benefits and limitations of the representation through several examples.

Introduction: Many scholars have argued for already more than two decades that integration between health and social care services would be needed to enhance system efficiency, quality of care and users’ quality of life. This has been emphasised worldwide by the implementation and evaluation of countless models, initiatives and innovative practice examples across the health and social care continuum. As the advance of integrated care took place in the context of a pronounced shift towards market-oriented governance – also in health and social care – increasing fragmentation has often been identified as a major barrier to integrated care. While the latter calls for cooperation and partnership working, ‘New Public Management’ is promoting user-choice and competition. Our contribution will address this most puzzling dilemma: How compatible (if at all) is integrated health and long-term care delivery with increasingly fragmented provider markets stimulating user choice in a competitive environment?Theory and Methods: The contribution is based on a mixed-methods study commissioned by the Swedish Ministry of Health and Social Affairs. In 2014/15, a literature review and three case studies in Germany (Dortmund, Leipzig) and Sweden (Norrtälje, Stockholm County) were carried out, involving 19 key-stakeholders that were interviewed following a semi-structured questionnaire.The two countries were chosen for comparison to contrast the most pronounced open market for care services in Europe (Germany) with Sweden, where the market share of private providers is growing and where the ‘customer choice’ model has only been introduced since 2008.The innovative feature of this research consists in bringing together the two strands of theoretical discourse that are dealing with market-oriented governance and with integrated care, and to provide empirical evidence how integrated care initiatives are coping with the challenges of choice and competition.Theoretical considerations range from reflections on introducing elements of user choice in integrated care to contributions that put trust in integration as a response to a competitive environment and/or competition as an incentive for integrated care, in particular if new types of integrated funding are implemented.Results: Each of the three sites are ‘special cases’ within their respective national context. The municipality of Norrtälje (Stockholm County) had realised a defined model of integrated care, including joint health and social care budgets, before introducing a regulated extension of providers and ‘user choice’. Regulation and strong leadership were thus used as key-instruments to reconcile integrated care provision and user choice. Stakeholders in the German sites reacted to the open market by searching for strategies to promote coordination and networking. This implied developing mechanisms to re-create trust between public, non-profit and for-profit providers, e.g. ‘Round Tables’, as well as instruments to empower users’ choice in the neighbourhood (coordination and consultancy centres, case management). In some cases, thematic and/or provider networks were established to coordinate stakeholders and to moderate competition, e.g. by defining operational areas.Discussion: The findings showed a nuanced picture related to the conciliation of integrated care, choice and competition. The majority of key-stakeholders underlined opportunities to achieve integrated, or at least coordinated care in a context of user choice and competition. Especially in Germany user choice has been internalised as a de facto right of users. Integrated care initiatives are therefore forced to cope with it, in some cases they even were a reaction to this framework condition. In Norrtälje, competition and user choice became a new challenge for an already established integrated care model, but regulatory interventions were partly able to mitigate uprising fragmentation. Interestingly, instruments to better support and empower users to make choices have not (yet) been on the agenda in Sweden, while financial integration of health and long-term care budgets remains foreign to German stakeholders.Conclusion: The study showed that it is possible to build common values and to enhance trust and joint working through quite dissimilar approaches to integrated care. Full integration such as in Norrtälje is not the only way to achieve (better) collaboration. While there is no ‘one-size-fits-all’ solution, sufficient time and space are necessary to find common grounds. In all sites it took several years to develop ways of cooperation and mutual understanding. Short-term projects of integrated care can thus hardly be successful, though competition and customer choice may accelerate the search for solutions.

The wave transmission from seaside to lee of break waters depends on structural parameters as well as on the initial wave climate. Transmission coefficients for special boundary: conditions are known, but information about wave parameters are often not available or they cover often only special cases. Again a case study, undertaken for the break water at the proposed deep water harbour at Scharhoern/Neuwerk, Germany, documented this lack. The results of the case study using conservative wave parameters did not answer the important questions of energy transmission sufficiently, thus we investigated the characteristics of the initial and transmitted wave spectra. A special case was treated initially and subsequently more general situations were examined. These tests were carried out using a physical model of a length scale of 1:10 under conditions described by Froude's law.

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox--which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation--including classical preference aggregation. As a case study we present a logical study of, including a formal proof of, the neutrality lemma, the main ingredient in a well-known proof of Arrow's theorem.

The Resource-Constrained Project Scheduling Problem (RCPSP) is a general problem class of scheduling problems. It even contains the well-known job shop scheduling problem as a special case. In these problems, jobs demand different amounts from multiple resources at once. The goal is to minimize completion time while satisfying resource capacity constraints throughout the schedule. The RCPSP has several variations and generalizations, one of which is the multi-mode problem. Multiple operation modes are given for jobs, differing in resource usages and execution times. Another generalization is where resources have time-varying capacities instead of a constant limit. The S-graph framework was developed for batch process scheduling and used successfully in various applications. The advantages of this approach motivate research to extend its capabilities to more general problem classes and apply it in various specialized case studies. The authors have previously presented an extension of the S-graph framework for RCPSP and its multi-mode generalization. In this work, a further extension is proposed for handling time-varying capacities. The method relies on a model transformation technique and recent algorithmic developments of the framework.

In non-life insurance pricing we determine how one or more key ratios Y vary with a number of rating factors. This is reminiscent of analyzing how the dependent variable Y varies with the covariates x in a multiple linear regression. In this chapter we introduce the class of Generalized Linear Models (GLMs), which generalizes the linear regression model in two directions: (i) instead of the normal distribution, GLMs work with a general class of distributions, the Exponential Dispersion Models, which as special cases contains distributions suitable for non-life insurance pricing, such as the Poisson distribution; (ii) instead of a linear relationship between the mean and the covariates, a GLM uses a link function to connect the mean to a linear function of the x’s, having the multiplicative model that we need as a special case. We derive estimators of the regression parameters and apply them to the moped example. The chapter ends by a case study (a larger exercise that requires computer assistance) on motor cycle insurance.

Motion during PET data acquisition is either introduced by design (e.g., couch wobble to enrich data sampling) or through unintentional motion of the object under study (e.g., subject head motion). Prior to this present work, such effects have been considered within distinctly different frameworks in PET imaging, with a rather basic approach having been devised for the cases of intentional motion (such as couch wobble or bed translation) in contrast to the relatively advanced modeling approaches devised for object motion. This article unifies the treatment of these different types of acquisition motion within a generalized framework through the use of the PET supersets data format. From this general framework, a range of conventional motion-compensation methods can be examined as special cases, permitting a revealing investigation into both the suboptimality of commonly adopted approximations, as well as the beneficial impact of known acquisition motion on image quality. The PET superset data format is a data representation ideally suited for the (potentially lossless) combination of conventional PET data with complementary motion information. Different practical implementations for the reconstruction from PET superset data involving varying levels of approximation to facilitate computation are identified and their impact on the final reconstructed image quality is assessed. Three main simulated case studies are investigated: (i) Motion compensation for subject head motion for 18F-FDG imaging, (ii) motion exploitation using either couch wobble or random motion, and (iii) motion exploitation using involuntary object motion both with and without couch wobble occurring. The motion exploitation case study goes beyond merely correcting for motion: The motion is directly modeled by the iterative reconstruction to exploit the increased sampling which is available to the benefit of reconstructed image quality. Reconstruction from superset data was successfully demonstrated for the case of motion correction for a 18F-FDG brain phantom simulation. Building on this success, the methodology was then applied to the case of motion exploitation. The case study resulted in three important findings. First, only reconstruction implementations which model the motion directly within the iterative reconstruction can succeed in significantly improving image resolution and contrast recovery for a given reconstructed noise level. Therefore, the commonly adopted approximation of binning the motion-adjusted data (which is the only method reported to date in the literature) is suboptimal and underestimates the beneficial impact of methods such as wobble during acquisition. Second, similar improvements were found for both types of motion patterns: Periodic wobble motion as well as random motion. Finally, for the case of simulated realistic involuntary object motion, similar resolution improvements were found (both with and without couch wobble). The proposed superset framework allows comprehensive analysis of the commonly adopted approximations when considering motion in PET reconstruction. The findings demonstrate that the supersets data format successfully unify reconstruction in the presence of different sources of known acquisition motion into one framework, and as a result leads to hitherto unreported image quality improvements for all the cases tested where the object motion is accurately known.

PurposeThe traditional view of the process of value creation suggests that it occurs inside the firm through its activities or resources. However, there are special cases where firms create value using external shared resources, e.g. a territorial brand. The purpose of this study is to demonstrate how the combination of both internal and external resources co-create value in wine regions.Design/methodology/approachAn in-depth case study of nine firms covering different co-creation processes in Champagne, France. The selection of interviews was designed to cover the diversity of firms within the area with different market positioning. Most firms in the region have been selling champagne for more than 50 years, so they have established long-standing relationships with their markets.FindingsWhile there is only one value, Champagne, firms create many different values based on owners’ perceptions with diverse effects on the process of value co-creation in the territorial brand. Some firms have strategies which could deteriorate the value of shared resource. This threat needs institutional changes with unknown consequences on the territorial brand.Research limitations/implicationsThe research only involved one case study with a highly developed territorial brand system. There are multiple wine regions that have considered managing either implicitly or explicitly their shared strategic resources (e.g. a territorial brand). Consequently, the findings may not be applicable to all wine regions but it can provide a “gold standard” for regions and wineries that do not realize the impact that their value creation actions can have on the wine region.Practical implicationsCollective management of shared strategic resources, such as a territorial brand, can be a powerful action to sustain competitive advantage rather than individual actions to develop individual brands. However, it can work only with an institutional organization managing the collective process.Originality/valueThe paper offers lessons from a comprehensive and well-known case study where resource bundles co-create value with a territorial brand.

BackgroundBiomarkers are considered the method of choice for determining exposure to environmental contaminants and relating such exposures to health outcomes. However, the association between many biomarkers and outcome is not direct because of variability in sensitivity and susceptibility in the individual.ObjectivesWe explore the relationship between environmental exposures and health outcomes as mitigated by differential susceptibility in individuals or populations and address the question “Can biomarkers enable us to understand and quantify better the population burden of disease and health effects attributable to environmental exposures?”MethodsWe use a case–study approach to develop the thesis that biomarkers offer a pathway to disaggregation of health effects into specific, if multiple, risk factors. We offer the point of view that a series or array of biomarkers, including biomarkers of exposure, biomarkers of susceptibility, and biomarkers of effect, used in concert offer the best means by which to effect this disaggregation. We commence our discussion by developing the characteristics of an ideal biomarker, then give some examples of commonly used biomarkers to show the strengths and weaknesses of current usage. We follow this by more detailed case-study assessment outlining the state-of-the-science in specific cases. We complete our work with recommendations regarding the future use of biomarkers and areas for continued development.ConclusionsThe case studies provide examples of when and how biomarkers can be used to infer the source and magnitude of exposure among a set of competing sources and pathways. The answer to this question is chemical specific and relates to how well the biomarker matches the characteristics of an “ideal” biomarker–in particular ease of collection and persistence. The use of biomarkers in combination provides a better opportunity to disaggregate both source and pathway contributions.