4,299 research outputs found
Planetary Hinterlands:Extraction, Abandonment and Care
This open access book considers the concept of the hinterland as a crucial tool for understanding the global and planetary present as a time defined by the lasting legacies of colonialism, increasing labor precarity under late capitalist regimes, and looming climate disasters. Traditionally seen to serve a (colonial) port or market town, the hinterland here becomes a lens to attend to the times and spaces shaped and experienced across the received categories of the urban, rural, wilderness or nature. In straddling these categories, the concept of the hinterland foregrounds the human and more-than-human lively processes and forms of care that go on even in sites defined by capitalist extraction and political abandonment. Bringing together scholars from the humanities and social sciences, the book rethinks hinterland materialities, affectivities, and ecologies across places and cultural imaginations, Global North and South, urban and rural, and land and water
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
Piecewise Temperleyan dimers and a multiple SLE
We consider the dimer model on piecewise Temperleyan, simply connected
domains, on families of graphs which include the square lattice as well as
superposition graphs. We focus on the spanning tree
associated to this model via Temperley's bijection, which turns out to be a
Uniform Spanning Tree with singular alternating boundary conditions.
Generalising the work of the second author with Peltola and Wu
\cite{LiuPeltolaWuUST} we obtain a scaling limit result for
. For instance, in the simplest nontrivial case, the limit
of is described by a pair of trees whose Peano curves are
shown to converge jointly to a multiple SLE pair. The interface between the
trees is shown to be given by an SLE curve. More generally
we provide an equivalent description of the scaling limit in terms of imaginary
geometry. This allows us to make use of the results developed by the first
author and Laslier and Ray \cite{BLRdimers}. We deduce that, universally across
these classes of graphs, the corresponding height function converges to a
multiple of the Gaussian free field with boundary conditions that jump at each
non-Temperleyan corner. After centering, this generalises a result of Russkikh
\cite{RusskikhDimers} who proved it in the case of the square lattice. Along
the way, we obtain results of independent interest on chordal hypergeometric
SLE; for instance we show its law is equal to that of an SLE for a certain vector of force points, conditional on its hitting
distribution on a specified boundary arc.Comment: 42 page
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Quantum Alternating Operator Ansatz (QAOA) beyond low depth with gradually changing unitaries
The Quantum Approximate Optimization Algorithm and its generalization to
Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying
quantum computers to challenging problems such as combinatorial optimization
and computational chemistry. In this paper, we study the underlying mechanisms
governing the behavior of QAOA circuits beyond shallow depth in the practically
relevant setting of gradually varying unitaries. We use the discrete adiabatic
theorem, which complements and generalizes the insights obtained from the
continuous-time adiabatic theorem primarily considered in prior work. Our
analysis explains some general properties that are conspicuously depicted in
the recently introduced QAOA performance diagrams. For parameter sequences
derived from continuous schedules (e.g. linear ramps), these diagrams capture
the algorithm's performance over different parameter sizes and circuit depths.
Surprisingly, they have been observed to be qualitatively similar across
different performance metrics and application domains. Our analysis explains
this behavior as well as entails some unexpected results, such as connections
between the eigenstates of the cost and mixer QAOA Hamiltonians changing based
on parameter size and the possibility of reducing circuit depth without
sacrificing performance
Functional completeness of planar Rydberg blockade structures
The construction of Hilbert spaces that are characterized by local
constraints as the low-energy sectors of microscopic models is an important
step towards the realization of a wide range of quantum phases with long-range
entanglement and emergent gauge fields. Here we show that planar structures of
trapped atoms in the Rydberg blockade regime are functionally complete: Their
ground state manifold can realize any Hilbert space that can be characterized
by local constraints in the product basis. We introduce a versatile framework,
together with a set of provably minimal logic primitives as building blocks, to
implement these constraints. As examples, we present lattice realizations of
the string-net Hilbert spaces that underlie the surface code and the Fibonacci
anyon model. We discuss possible optimizations of planar Rydberg structures to
increase their geometrical robustness.Comment: 33 pages, 14 figures, v2: fixed typos, added additional references
and comment
Pairwise versus mutual independence: visualisation, actuarial applications and central limit theorems
Accurately capturing the dependence between risks, if it exists, is an increasingly relevant topic of actuarial research. In recent years, several authors have started to relax the traditional 'independence assumption', in a variety of actuarial settings. While it is known that 'mutual independence' between random variables is not equivalent to their 'pairwise independence', this thesis aims to provide a better understanding of the materiality of this difference. The distinction between mutual and pairwise independence matters because, in practice, dependence is often assessed via pairs only, e.g., through correlation matrices, rank-based measures of association, scatterplot matrices, heat-maps, etc. Using such pairwise methods, it is possible to miss some forms of dependence. In this thesis, we explore how material the difference between pairwise and mutual independence is, and from several angles.
We provide relevant background and motivation for this thesis in Chapter 1, then conduct a literature review in Chapter 2.
In Chapter 3, we focus on visualising the difference between pairwise and mutual independence. To do so, we propose a series of theoretical examples (some of them new) where random variables are pairwise independent but (mutually) dependent, in short, PIBD. We then develop new visualisation tools and use them to illustrate what PIBD variables can look like. We showcase that the dependence involved is possibly very strong. We also use our visualisation tools to identify subtle forms of dependence, which would otherwise be hard to detect.
In Chapter 4, we review common dependence models (such has elliptical distributions and Archimedean copulas) used in actuarial science and show that they do not allow for the possibility of PIBD data. We also investigate concrete consequences of the 'nonequivalence' between pairwise and mutual independence. We establish that many results which hold for mutually independent variables do not hold under sole pairwise independent. Those include results about finite sums of random variables, extreme value theory and bootstrap methods. This part thus illustrates what can potentially 'go wrong' if one assumes mutual independence where only pairwise independence holds.
Lastly, in Chapters 5 and 6, we investigate the question of what happens for PIBD variables 'in the limit', i.e., when the sample size goes to infi nity. We want to see if the 'problems' caused by dependence vanish for sufficiently large samples. This is a broad question, and we concentrate on the important classical Central Limit Theorem (CLT), for which we fi nd that the answer is largely negative. In particular, we construct new sequences of PIBD variables (with arbitrary margins) for which a CLT does not hold. We derive explicitly the asymptotic distribution of the standardised mean of our sequences, which allows us to illustrate the extent of the 'failure' of a CLT for PIBD variables. We also propose a general methodology to construct dependent K-tuplewise independent (K an arbitrary integer) sequences of random variables with arbitrary margins. In the case K = 3, we use this methodology to derive explicit examples of triplewise independent sequences for which no CLT hold. Those results illustrate that mutual independence is a crucial assumption within CLTs, and that having larger samples is not always a viable solution to the problem of non-independent data
Dynamic scene understanding: Pedestrian tracking from aerial devices.
Multiple Object Tracking (MOT) is the problem that involves following the trajectory of multiple objects in a sequence, generally a video. Pedestrians are among the most interesting subjects to track and recognize for many purposes such as surveillance, and safety. In the recent years, Unmanned Aerial Vehicles (UAV’s) have been viewed as a viable option for monitoring public areas, as they provide a low-cost method of data collection while covering large and difficult-to-reach areas. In this thesis, we present an online pedestrian tracking and re-identification from aerial devices framework. This framework is based on learning a compact directional statistic distribution (von-Mises-Fisher distribution) for each person ID using a deep convolutional neural network. The distribution characteristics are trained to be invariant to clothes appearances and to transformations. In real world scenarios, during deployment, new pedestrian and objects can appear in the scene and the model should detect them as Out Of Distribution (OOD). Thus, our frameworks also includes an OOD detection adopted from [16] called Virtual Outlier Synthetic (VOS), that detects OOD based on synthesising virtual outlier in the embedding space in an online manner. To validate, analyze and compare our approach, we use a large real benchmark data that contain detection tracking and identity annotations. These targets are captured at different viewing angles, different places, and different times by a ”DJI Phantom 4” drone. We validate the effectiveness of the proposed framework by evaluating their detection, tracking and long term identification performance as well as classification performance between In Distribution (ID) and OOD. We show that the the proposed methods in the framework can learn models that achieve their objectives
Mining Butterflies in Streaming Graphs
This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection.
sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals
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