Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Data integration is the problem of combining data residing at different sources, and providing the user with a unified view of these data. The problem of designing data integration systems is important in current real world applications, and is characterized by a number of issues that are interesting from a theoretical point of view. This document presents on overview of the material to be presented in a tutorial on data integration. The tutorial is focused on some of the theoretical issues that are relevant for data integration. Special attention will be devoted to the following aspects: modeling a data integration application, processing queries in data integration, dealing with inconsistent data sources, and reasoning on queries.

/pdf/data-integration-a-theoretical-perspective-58aesjvhuk.pdf

Data integration: a theoretical perspective

Optimization, approximation, and complexity classes

A frequent subgraph of a given collection of graphs is a graph that is isomorphic to a subgraph of at least as many graphs in the collection as a given threshold. Frequent subgraphs generalize frequent itemsets and arise in various contexts, from bioinformatics to the Web. Since the space of frequent subgraphs is typically extremely large, research in graph mining has focused on special types of frequent subgraphs that can be orders of magnitude smaller in number, yet encapsulate the space of all frequent subgraphs. Maximal frequent subgraphs (i.e., the ones not properly contained in any frequent subgraph) constitute the most useful such type.In this paper, we embark on a comprehensive investigation of the computational complexity of mining maximal frequent subgraphs. Our study is carried out by considering the effect of three different parameters: possible restrictions on the class of graphs; a fixed bound on the threshold; and a fixed bound on the number of desired answers. We focus on specific classes of connected graphs: general graphs, planar graphs, graphs of bounded degree, and graphs of bounded tree-width (trees being a special case). Moreover, each class has two variants: the one in which the nodes are unlabeled, and the one in which they are uniquely labeled. We delineate the complexity of the enumeration problem for each of these variants by determining when it is solvable in (total or incremental) polynomial time and when it is NP-hard. Specifically, for the labeled classes, we show that bounding the threshold yields tractability but, in most cases, bounding the number of answers does not, unless P=NP; an exception is the case of labeled trees, where bounding either of these two parameters yields tractability. The state of affairs turns out to be quite different for the unlabeled classes. The main (and most challenging to prove) result concerns unlabeled trees: we show NP-hardness, even if the input consists of two trees, and both the threshold and the number of desired answers are equal to just two. In other words, we establish that the following problem is NP-complete: given two unlabeled trees, do they have more than one maximal subtree in common?

https://researcher.watson.ibm.com/researcher/files/us-kimelfeld/papers-pods13-mining.pdf

The complexity of mining maximal frequent subgraphs

The probability of a property on the collection of all finite relational structures is the limit as n → ∞ of the fraction of structures with n elements satisfying the property, provided the limit exists. It is known that the 0-1 law holds for every property expressible in first-order logic, i.e., the probability of every such property exists and is either 0 or 1. Moreover, the associated decision problem for the probabilities is solvable.

In this survey, we consider fragments of existential second-order logic in which we restrict the patterns of first-order quantifiers. We focus on fragments in which the first-order part belongs to a prefix class. We show that the classifications of prefix classes of first-order logic with equality according to the solvability of the finite satisfiability problem and according to the 0-1 law for the corresponding +11 fragments are identical, but the classifications are different without equality.

0-1 Laws for Fragments of Existential Second-Order Logic: A Survey

A frequent subgraph of a given collection of graphs is a graph that is isomorphic to a subgraph of at least as many graphs in the collection as a given threshold. Frequent subgraphs generalize frequent itemsets and arise in various contexts, from bioinformatics to the Web. Since the space of frequent subgraphs is typically extremely large, research in graph mining has focused on special types of frequent subgraphs that can be orders of magnitude smaller in number, yet encapsulate the space of all frequent subgraphs. Maximal frequent subgraphs (i.e., the ones not properly contained in any frequent subgraph) constitute the most useful such type. In this article, we embark on a comprehensive investigation of the computational complexity of mining maximal frequent subgraphs. Our study is carried out by considering the effect of three different parameters: possible restrictions on the class of graphs; a fixed bound on the threshold; and a fixed bound on the number of desired answers. We focus on specific classes of connected graphs: general graphs, planar graphs, graphs of bounded degree, and graphs of bounded treewidth (trees being a special case). Moreover, each class has two variants: that in which the nodes are unlabeled, and that in which they are uniquely labeled. We delineate the complexity of the enumeration problem for each of these variants by determining when it is solvable in (total or incremental) polynomial time and when it is NP-hard. Specifically, for the labeled classes, we show that bounding the threshold yields tractability but, in most cases, bounding the number of answers does not, unless P=NP; an exception is the case of labeled trees, where bounding either of these two parameters yields tractability. The state of affairs turns out to be quite different for the unlabeled classes. The main (and most challenging to prove) result concerns unlabeled trees: we show NP-hardness, even if the input consists of two trees and both the threshold and the number of desired answers are equal to just two. In other words, we establish that the following problem is NP-complete: given two unlabeled trees, do they have more than one maximal subtree in commonq

The Complexity of Mining Maximal Frequent Subgraphs

A dichotomy theorem for a class of decision problems is a result asserting that certain problems in the class are solvable in polynomial time, while the rest are NP-complete. The first remarkable such dichotomy theorem was proved by T.J. Schaefer in 1978. It concerns the class of generalized satisfiability problems SAT(S), whose input is a CNF(S)-formula, i.e., a formula constructed from elements of a fixed set S of generalized connectives using conjunctions and substitutions by variables. Here, we investigate the complexity of minimal satisfiability problems MIN SAT(S), where S is a fixed set of generalized connectives. The input to such a problem is a CNF(S)-formula and a satisfying truth assignment; the question is to decide whether there is another satisfying truth assignment that is strictly smaller than the given truth assignment with respect to the coordinate-wise partial order on truth assignments. Minimal satisfiability problems were first studied by researchers in artificial intelligence while investigating the computational complexity of propositional circumscription. The question of whether dichotomy theorems can be proved for these problems was raised at that time, but was left open. In this paper, we settle this question affirmatively by establishing a dichotomy theorem for the class of all MIN SAT(S)-problems.

The Complexity of Minimal Satisfiability Problems

An inverse of a schema mapping M is intended to undo what M does, thus providing a way to perform reverse data exchange. In recent years, three different formalizations of this concept have been introduced and studied, namely the notions of an inverse of a schema mapping, a quasi-inverse of a schema mapping, and a maximum recovery of a schema mapping. The study of these notions has been carried out in the context in which source instances are restricted to consist entirely of constants, while target instances may contain both constants and labeled nulls. This restriction on source instances is crucial for obtaining some of the main technical results about these three notions, but, at the same time, limits their usefulness, since reverse data exchange naturally leads to source instances that may contain both constants and labeled nulls.We develop a new framework for reverse data exchange that supports source instances that may contain nulls, and we thereby overcome the semantic mismatch between source and target instances of the previous formalizations. The development of this new framework requires a careful reformulation of all the important notions, including the notions of the identity schema mapping, inverse, and maximum recovery. To this effect, we introduce the notions of extended identity schema mapping, extended inverse, and maximum extended recovery, by making systematic use of the homomorphism relation on instances. We give results concerning the existence of extended inverses and of maximum extended recoveries, and results concerning their applications to reverse data exchange and query answering. Moreover, we show that maximum extended recoveries can be used to capture in a quantitative way, the amount of information loss embodied in a schema mapping specified by source-to-target tuple-generating dependencies.

Phokion G. Kolaitis

Papers

The complexity of mining maximal frequent subgraphs

0-1 Laws for Fragments of Existential Second-Order Logic: A Survey

The Complexity of Mining Maximal Frequent Subgraphs

The Complexity of Minimal Satisfiability Problems

Reverse data exchange: Coping with nulls