Оценка времени на прогнозирование технического состояния средств аппаратного контроля

Предлагается метод повышения достоверности функционирования ЭВМ АСУ в условиях воздействия мощных электромагнитных помех (МЭМП), приводятся оценки допустимого времени на прогнозирование технического состояния средств аппаратного контроля (АК) после воздействия мощных электромагнитных помех

An algorithm for a super-stable roommates problem

In this paper, we describe an efficient algorithm that decides if a stable matching exists for a generalized stable roommates problem, where, instead of linear preferences, agents have partial preference orders on potential partners. Furthermore, we may forbid certain partnerships, that is, we are looking for a matching such that none of the matched pairs is forbidden, and yet, no blocking pair (forbidden or not) exists. To solve the above problem, we generalize the first algorithm for the ordinary stable roommates problem

The stable marriage problem with master preference lists

We study variants of the classical stable marriage problem in which the preferences of the men or the women, or both, are derived from a master preference list. This models real-world matching problems in which participants are ranked according to some objective criteria. The master list(s) may be strictly ordered, or may include ties, and the lists of individuals may involve ties and may include all, or just some, of the members of the opposite sex. In fact, ties are almost inevitable in the master list if the ranking is done on the basis of a scoring scheme with a relatively small range of distinct values. We show that many of the interesting variants of stable marriage that are NP-hard remain so under very severe restrictions involving the presence of master lists, but a number of special cases can be solved in polynomial time. Under this master list model, versions of the stable marriage problem that are already solvable in polynomial time typically yield to faster and/or simpler algorithms, giving rise to simple new structural characterisations of the solutions in these cases

Stable marriage with ties and bounded length preference lists

We consider variants of the classical stable marriage problem in which preference lists may contain ties, and may be of bounded length. Such restrictions arise naturally in practical applications, such as centralised matching schemes that assign graduating medical students to their first hospital posts. In such a setting, weak stability is the most common solution concept, and it is known that weakly stable matchings can have different sizes. This motivates the problem of finding a maximum cardinality weakly stable matching, which is known to be NP-hard in general. We show that this problem is solvable in polynomial time if each man's list is of length at most 2 (even for women's lists that are of unbounded length). However if each man's list is of length at most 3, we show that the problem becomes NP-hard (even if each women's list is of length at most 3) and not approximable within some δ>1 (even if each woman's list is of length at most 4)

Hard variants of stable marriage

The Stable Marriage Problem and its many variants have been widely studied in the literature (Gusfield and Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, Cambridge, MA, 1989; Roth and Sotomayor, Two-sided matching: a study in game-theoretic modeling and analysis, Econometric Society Monographs, vol. 18, Cambridge University Press, Cambridge, 1990; Knuth, Stable Marriage and its Relation to Other Combinatorial Problems, CRM Proceedings and Lecture Notes, vol. 10, American Mathematical Society, Providence, RI, 1997), partly because of the inherent appeal of the problem, partly because of the elegance of the associated structures and algorithms, and partly because of important practical applications, such as the National Resident Matching Program (Roth, J. Political Economy 92(6) (1984) 991) and similar large-scale matching schemes. Here, we present the first comprehensive study of variants of the problem in which the preference lists of the participants are not necessarily complete and not necessarily totally ordered. We show that, under surprisingly restrictive assumptions, a number of these variants are hard, and hard to approximate. The key observation is that, in contrast to the case where preference lists are complete or strictly ordered (or both), a given problem instance may admit stable matchings of different sizes. In this setting, examples of problems that are hard are: finding a stable matching of maximum or minimum size, determining whether a given pair is stable––even if the indifference takes the form of ties on one side only, the ties are at the tails of lists, there is at most one tie per list, and each tie is of length 2; and finding, or approximating, both an `egalitarian' and a `minimum regret' stable matching. However, we give a 2-approximation algorithm for the problems of finding a stable matching of maximum or minimum size. We also discuss the significant implications of our results for practical matching schemes

The College Admissions problem with lower and common quotas

We study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in Hungary. The first problem is an extension of the College Admissions problem in which the colleges have lower quotas as well as the normal upper quotas. Here, we show that a stable matching may not exist and we prove that the problem of determining whether one does is NP-complete in general. The second problem is a different extension in which, as usual, individual colleges have upper quotas, but, in addition, certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas. Again, we show that a stable matching may not exist and the related decision problem is NP-complete. On the other hand, we prove that, when the bounded sets form a nested set system, a stable matching can be found by generalising, in non-trivial ways, both the applicant-oriented and college-oriented versions of the classical Gale–Shapley algorithm. Finally, we present an alternative view of this nested case using the concept of choice functions, and with the aid of a matroid model we establish some interesting structural results for this case

Two algorithms for the student-project allocation problem

We study the Student-Project Allocation problem (SPA), a generalisation of the classical Hospitals / Residents problem (HR). An instance of SPA involves a set of students, projects and lecturers. Each project is offered by a unique lecturer, and both projects and lecturers have capacity constraints. Students have preferences over projects, whilst lecturers have preferences over students. We present two optimal linear-time algorithms for allocating students to projects, subject to the preference and capacity constraints. In particular, each algorithm finds a stable matching of students to projects. Here, the concept of stability generalises the stability definition in the HR context. The stable matching produced by the first algorithm is simultaneously best-possible for all students, whilst the one produced by the second algorithm is simultaneously best-possible for all lecturers. We also prove some structural results concerning the set of stable matchings in a given instance of SPA. The SPA problem model that we consider is very general and has applications to a range of different contexts besides student-project allocation

Marcellus Shale BEG Natural Fracture Project Final Report

Operators in the Marcellus Shale gas play are aware of the importance of natural fractures, and there has been substantial work on the fracture systems in core and outcrop in the large region covered by this play (Eastern Shale Gas Project reports; Evans, 1980, 1994, 1995; Engelder et al., 2009 and references therein; Lash and Engelder, 2005, 2007, 2009). The most common fractures documented by these authors in core and outcrop are subvertical opening-mode fractures that are broadly strike parallel (J1) or cross-fold joints (J2). Evans (1995) also found strike-parallel veins that post-date the J2 set, and Lash and Engelder (2005) describe bitumen-filled microcracks developed during catagenesis. Gale and Holder (2010) found in a study of several gas-shales that narrow, sealed, subvertical fractures are typically present in most shale cores. In shale-gas plays that are produced using hydraulic fracturing stimulation, these fractures are nevertheless important because of their interaction with hydraulic treatment fractures (Gale et al., 2007). At the scale of hydraulic fracture stimulation, natural fracture patterns and in situ stress can be highly variable, even though a broad tectonic pattern may be consistent over hundreds of miles. Thus, site-specific evaluation of the natural fractures and in situ stress is necessary. Open fractures are observed in a few cases in core. Fracture-size scaling, coupled with a fracture-size control over sealing cementation and a subcritical growth mechanism that favors clustering, suggests that open fractures are likely to be concentrated in clusters spaced hundreds of feet apart (Gale, 2002; Gale et al., 2007). Our goal for this project is to characterize the fractures and identify the characteristic spatial arrangement of fractures, including potential clusters of large fractures. Our emphasis is on characterizing, quantifying, and modeling fractures that have grown in the subsurface in a chemically reactive environment through a combination of observation at a range of scales, detailed petrographic and microstructural observation of cement fills, and geomechanical modeling (cf. Marrett et al., 1999; Gale, 2002; Laubach 1997, 2003; Olson, 2004). Large natural fractures, open or sealed, are typically sparsely sampled in core or image logs. Yet these are the fractures that would have the most effect in augmenting gas flow or influencing the growth of hydraulic fractures. Our approach overcomes the sampling problem by use of fracture size and spatial scaling analysis coupled with geomechanical modeling. That is, we may make predictions about their attributes without sampling them. Fracture morphology, orientation, spatial organization, and cementation were analyzed using datasets from the project well-experiment area in SW Pennsylvania. We added a dataset from a field area to evaluate the use of outcrop fracture data in reservoir characterization in the Marcellus, thus expanding the relevance of the study beyond the well-experiment area in SW Pennsylvania.Bureau of Economic Geolog

The stable roommates problem with ties

We study the variant of the well-known stable roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear–time algorithm for finding a super-stable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NP-hardness of the analogous problem under weak stability. We also extend our algorithm to cope with preference lists that are incomplete and/or partially ordered. On the other hand, for a given stable roommates instance with ties and incomplete lists, we show that the weakly stable matchings may be of different sizes and the problem of finding a maximum cardinality weakly stable matching is NP-hard, though approximable within a factor of 2