9,302 research outputs found
A Unifying Theory for Graph Transformation
The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO
On the non-efficient PAC learnability of conjunctive queries
This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.<p/
Cyclic proof systems for modal fixpoint logics
This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one
How to Turn Your Knowledge Graph Embeddings into Generative Models
Some of the most successful knowledge graph embedding (KGE) models for link
prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based
models. Under this perspective they are not amenable for exact
maximum-likelihood estimation (MLE), sampling and struggle to integrate logical
constraints. This work re-interprets the score functions of these KGEs as
circuits -- constrained computational graphs allowing efficient
marginalisation. Then, we design two recipes to obtain efficient generative
circuit models by either restricting their activations to be non-negative or
squaring their outputs. Our interpretation comes with little or no loss of
performance for link prediction, while the circuits framework unlocks exact
learning by MLE, efficient sampling of new triples, and guarantee that logical
constraints are satisfied by design. Furthermore, our models scale more
gracefully than the original KGEs on graphs with millions of entities
Dynamic Connectivity in Disk Graphs
Let S â R2 be a set of n sites in the plane, so that every site s â S has an associated
radius rs > 0. Let D(S) be the disk intersection graph defined by S, i.e., the graph
with vertex set S and an edge between two distinct sites s, t â S if and only if the
disks with centers s, t and radii rs , rt intersect. Our goal is to design data structures
that maintain the connectivity structure of D(S) as sites are inserted and/or deleted
in S. First, we consider unit disk graphs, i.e., we fix rs = 1, for all sites s â S.
For this case, we describe a data structure that has O(log2 n) amortized update time
and O(log n/ log log n) query time. Second, we look at disk graphs with bounded
radius ratio Ψ, i.e., for all s â S, we have 1 ⤠rs ⤠Ψ, for a parameter Ψ that is
known in advance. Here, we not only investigate the fully dynamic case, but also the
incremental and the decremental scenario, where only insertions or only deletions of
sites are allowed. In the fully dynamic case, we achieve amortized expected update
time O(Ψ log4 n) and query time O(log n/ log log n). This improves the currently
best update time by a factor of Ψ. In the incremental case, we achieve logarithmic
dependency on Ψ, with a data structure that has O(ι(n)) amortized query time and
O(log Ψ log4 n) amortized expected update time, where ι(n) denotes the inverse Ackermann
function. For the decremental setting, we first develop an efficient decremental
disk revealing data structure: given two sets R and B of disks in the plane, we can delete
disks from B, and upon each deletion, we receive a list of all disks in R that no longer
intersect the union of B. Using this data structure, we get decremental data structures
with a query time of O(log n/ log log n) that supports deletions in O(n log Ψ log4 n)
overall expected time for disk graphs with bounded radius ratio Ψ and O(n log5 n)
overall expected time for disk graphs with arbitrary radii, assuming that the deletion
sequence is oblivious of the internal random choices of the data structures
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On the homotopy type of multipath complexes
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph G is the simplicial complex whose faces are the multipaths of G. We compute Euler characteristics, and associated generating functions, of the multipath complexes of directed graphs from certain families, including transitive tournaments and complete bipartite graphs. We show that if G is a linear graph, polygon, small grid or transitive tournament, then the homotopy type of the multipath complex of G is always contractible or a wedge of spheres. We introduce a new technique for decomposing directed graphs into dynamical regions, which allows us to simplify the homotopy computations
Industrial relations, the New Right and the praxis of mismanagement
Purpose: The purpose of the article is to outline the insights provided by Alan Fox in Man Mismanagement in relation to the rise of the New Right political economy and the spread of unitarist managerialism. The article assesses the contemporary work and employment relations implications of mismanagement arising from a âsecond waveâ of the New Right ideology from 2010 in the UK. Design/methodology/approach: Responding to the Special Issue on Alan Fox, the article focuses on Alan Fox's book Man Mismanagement, considering industrial relations developments arising between the 1st (1974b) and 2nd (1985) editions relating to the political rise of the New Right. It reviews various literature that illustrates the contemporary IR relevance of the book and Fox's insights. Findings: The New Rightâs ideology has further fragmented work, disjointed labour rights and undermined collective industrial relations institutions, and macho mismanagement praxis is even more commonplace, compared to when Fox wrote Man Mismanagement. The stripping away of the institutional architecture of IR renders the renewal of pluralist praxis, like collective bargaining and other forms of joint regulation of work, a formidable task. Originality/value: The value of the article relates to the identification of dramatic historical industrial relations events and change in the UK in Alan Fox's book Man Mismanagement, most notably relating to the rise to power of the Thatcherite New Right in 1979. Originality is evidenced by the authorsâ drawing on Fox's ideas and assessing the implications of the âsecond waveâ of the New Right in the contemporary industrial relations (IR) context of the 2020s under the conceptual themes of fragmented work, disjointed labour rights and undermined collectivism.</p
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