5,964 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
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
Isotope reconstructions of East Asian Monsoon behaviour across Glacial Terminations I and II from Lake Suigetsu, Japan (IAP2â18â54)
Understanding the response of the East Asian Monsoon to rising temperatures is crucial in light of recent anthropogenic climate change and the vulnerability of East Asia to future climatic hazards. However, East Asian Monsoon dynamics during warming periods in the late Quaternary are poorly understood, particularly on decadal to millennial timescales. Significant sources of this uncertainty are the spatially and temporally heterogeneous responses of the East Asian Monsoon to submillennial temperature fluctuations. The conflicting patterns observed in available reconstructions of East Asian Monsoon strength suggest that the teleconnections acting during these intervals were complex. Understanding the behaviours of the East Asian Monsoon by accounting for links to remote climatic perturbations allows for a more holistic understanding of deglacial climate changes.
A means of tackling this ambiguity is by contributing wellâdated, highâresolution records of East Asian Monsoon evolution spanning Glacial Terminations I and II (which typify accessible, contrasting examples of rapid global warming) to the growing network of reconstructions from across the region. The aim of this thesis is to deconvolve East Asian Monsoon evolution during the last two glacial terminations by utilising the unique hydrological distribution of East Asian Monsoon precipitation over Japan to reconstruct both seasonal modes of the system (i.e., the East Asian Winter Monsoon and East Asian Summer Monsoon). This aim is met by the construction of isotopeâbased, seasonâspecific East Asian Monsoon records across Glacial Terminations I and II using materials from the Lake Suigetsu sediment cores.
This thesis is comprised of four interconnected research papers, preceded by an introduction and succeeded by a summary of findings, discussion of relevance, suggestions for future work and conclusions. In the first research paper, we utilise extended contemporary monitoring of the stable isotope composition of precipitation, river water and lake water in the Lake Suigetsu catchment to understand the factors affecting these variables and aid robust interpretation of isotopeâbased proxy reconstructions from the Lake Suigetsu sediment cores. Our results show that the composition of precipitation was influenced by the dual East Asian Monsoon system, and that these signals were then transferred to the lake system where they were combined with secondary local influences on lake water composition. Based on our knowledge of late Quaternary catchment dynamics, these observations suggest that the palaeoâisotope composition of Lake Suigetsu was closely related to the East Asian Monsoon.
In the second research paper, we examine the influence of remote climatic processes on the East Asian Winter Monsoon and East Asian Summer Monsoon in Japan during Glacial Termination I by reconstructing trends in the strength of each seasonal mode. This is achieved using oxygen isotope analysis of diatom silica and compoundâspecific hydrogen isotope analysis of nâalkanoic acids from the Lake Suigetsu sediment cores. Our results support distinctive seasonal behaviours of the East Asian Monsoon during Glacial Termination I, with evidence for East Asian Winter Monsoon weakening and East Asian Summer Monsoon strengthening. The East Asian Summer Monsoon also exhibited variations in strength which were synchronous with Antarctic temperature fluctuations after 16,000 years ago, which supports a temporally restricted climatic link between Japan and the Southern Hemisphere at this time.
In the third research paper, we reconstruct the East Asian Summer Monsoon in Japan during Glacial Termination II, and contrast the findings to those from Glacial Termination I. The reconstruction presented in this chapter, which is based on compoundâspecific hydrogen isotope analysis of nâalkanoic acids, provides evidence for early East Asian Summer Monsoon strengthening followed by a gradual weakening phase with submillennialâscale variability. Comparison of this record to others derived from mainland China supports the assertion that East Asian Summer Monsoon behaviours during Glacial Termination II were spatially heterogenous. Additionally, the different evolutions of the East Asian Summer Monsoon during Glacial Terminations I and II indicate that the system operated distinctively under contrasting boundary conditions, although the new reconstructions from Japan were consistently more closely linked with Southern Hemisphere (Antarctic) temperatures than Northern Hemisphere (Greenlandic) temperatures during both intervals.
The fourth research paper was motivated by a lack of an absolute chronology for the oldest (preâ50,000 years ago) parts of the Lake Suigetsu sediment cores (which includes Glacial Termination II). In this paper, we appraise the luminescence characteristics of the cores using rapid profiling techniques. These are employed across four key time periods in order to assess the application of these methods for the detection of local and environmental shifts, and to assess the suitability of the core materials for luminescence dating. We show that the luminescence characteristics of the cores were susceptible to a range of environmental perturbations, best illustrating local changes by using highâresolution contiguous sampling. The feasibility of future luminescence dating is supported by quantifiable luminescence signals, and first order approximate ages suggest that blue light optically stimulated luminescence dating of feldspar provides the most accurate and most practical assessment of burial age. This technique should be the subject of dating efforts in pursuit of refinements to the Suigetsu core chronology before 50,000 years ago.
The findings of this thesis contribute to our collective knowledge of East Asian Monsoon behaviours during glacial terminations. Critically, they represent a geographical expansion of the regional highâresolution record network to include Japan. The value of this process is demonstrated by the decoupled evolutions of each seasonal mode during Glacial Termination I, and a remote link between Antarctic temperatures and East Asian Summer Monsoon evolution in Japan during Glacial Terminations I and II, which were hitherto unconstrained by high resolution analysis. These findings acknowledge and begin to rationalise spatial and temporal heterogeneities in East Asian Monsoon behaviours by comparison to other records. This work highlights the complexity of the East Asian Monsoon, and the value of long records from contrasting deglacial periods for a better comprehension of this system in the context of anthropogenic climate change
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Algorithms and complexity for approximately counting hypergraph colourings and related problems
The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Î, this problem falls into the regime of LovĂĄsz local lemma when ΠⲠqáľ. In prior, however, fast approximate counting algorithms exist when ΠⲠqáľ/Âł, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows.
⢠When q, k ⼠4 are evens and Π⼠5¡qáľ/², approximating the number of hypergraph colourings is NP-hard.
⢠When the input hypergraph is linear and ΠⲠqáľ/², a fast approximate counting algorithm does exist
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
The Viability of Domain Constrained Coalition Formation for Robotic Collectives
Applications, such as military and disaster response, can benefit from
robotic collectives' ability to perform multiple cooperative tasks (e.g.,
surveillance, damage assessments) efficiently across a large spatial area.
Coalition formation algorithms can potentially facilitate collective robots'
assignment to appropriate task teams; however, most coalition formation
algorithms were designed for smaller multiple robot systems (i.e., 2-50
robots). Collectives' scale and domain-relevant constraints (i.e.,
distribution, near real-time, minimal communication) make coalition formation
more challenging. This manuscript identifies the challenges inherent to
designing coalition formation algorithms for very large collectives (e.g., 1000
robots). A survey of multiple robot coalition formation algorithms finds that
most are unable to transfer directly to collectives, due to the identified
system differences; however, auctions and hedonic games may be the most
transferable. A simulation-based evaluation of three auction and hedonic game
algorithms, applied to homogeneous and heterogeneous collectives, demonstrates
that there are collective compositions for which no existing algorithm is
viable; however, the experimental results and literature survey suggest paths
forward.Comment: 46 pages, 9 figures, Swarm Intelligence (under review
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