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Mark Bell

Publications and source records attributed to Mark Bell.

12 recordsLinked to original sources
arXiv2021

Diagonal flow detects topology of strata

We study the interplay between the diagonal flow on, and the topology of, a stratum component of a space of rooted quadratic differentials. We prove that the flow group -- the subgroup of the fundamental group generated by almost-flow loops -- equals the fundamental group. As a corollary, we show that the plus and minus modular Rauzy-Veech groups are finite-index subgroups of their ambient modular monodromy groups. This partially answers a question of Yoccoz. Using this, and recent advances on algebraic hulls and Zariski closures of symplectic monodromy groups, we prove that the Rauzy-Veech groups are Zariski dense in their ambient symplectic groups. Density, in turn, implies the simplicity of the plus and minus Lyapunov spectra of any component of any stratum of quadratic differentials. We thus establish the Kontsevich -- Zorich conjecture.

math.DS↗
arXiv2020

kD-STR: A Method for Spatio-Temporal Data Reduction and Modelling

Analysing and learning from spatio-temporal datasets is an important process in many domains, including transportation, healthcare and meteorology. In particular, data collected by sensors in the environment allows us to understand and model the processes acting within the environment. Recently, the volume of spatio-temporal data collected has increased significantly, presenting several challenges for data scientists. Methods are therefore needed to reduce the quantity of data that needs to be processed in order to analyse and learn from spatio-temporal datasets. In this paper, we present the k-Dimensional Spatio-Temporal Reduction method (kD-STR) for reducing the quantity of data used to store a dataset whilst enabling multiple types of analysis on the reduced dataset. kD-STR uses hierarchical partitioning to find spatio-temporal regions of similar instances and models the instances within each region to summarise the dataset. We demonstrate the generality of kD-STR with 3 datasets exhibiting different spatio-temporal characteristics and present results for a range of data modelling techniques. Finally, we compare kD-STR with other techniques for reducing the volume of spatio-temporal data. Our results demonstrate that kD-STR is effective in reducing spatio-temporal data and generalises to datasets that exhibit different properties.

cs.DB↗
arXiv2019

Coding Teichm\"uller flow using veering triangulations

We develop the theory of veering triangulations on oriented surfaces adapted to moduli spaces of half-translation surfaces. We use veering triangulations to give a coding of the Teichm\"uller flow on connected components of strata of quadratic differentials. We prove that this coding, given by a countable shift, has an approximate product structure and a roof function with exponential tails. This makes it conducive to the study of the dynamics of Teichm\"uller flow.

math.DS↗
arXiv2019

ARCHANGEL: Tamper-proofing Video Archives using Temporal Content Hashes on the Blockchain

We present ARCHANGEL; a novel distributed ledger based system for assuring the long-term integrity of digital video archives. First, we describe a novel deep network architecture for computing compact temporal content hashes (TCHs) from audio-visual streams with durations of minutes or hours. Our TCHs are sensitive to accidental or malicious content modification (tampering) but invariant to the codec used to encode the video. This is necessary due to the curatorial requirement for archives to format shift video over time to ensure future accessibility. Second, we describe how the TCHs (and the models used to derive them) are secured via a proof-of-authority blockchain distributed across multiple independent archives. We report on the efficacy of ARCHANGEL within the context of a trial deployment in which the national government archives of the United Kingdom, Estonia and Norway participated.

cs.CV↗
arXiv2018

A Low Complexity Detection Algorithm Based on Alternating Minimization

In this paper, we propose an algorithm based on the Alternating Minimization technique to solve the uplink massive MIMO detection problem. The proposed algorithm provides a lower complexity compared to the conventional MMSE detection technique, especially when the number of user equipment (UE) antennas is close to the number of base station (BS) antennas. This improvement is obtained without any matrix inversion. Moreover, the algorithm re-formulates the maximum likelihood (ML) detection problem as a sum of convex functions based on decomposing the received vector into multiple vectors. Each vector represents the contribution of one of the transmitted symbols in the received vector. Alternating Minimization is used to solve the new formulated problem in an iterative manner with a closed form solution update in every iteration. Simulation results demonstrate the efficacy of the proposed algorithm in the uplink massive MIMO setting for both coded and uncoded cases

cs.IT↗
arXiv2018

QoE-Aware Resource Allocation for Small Cells

In this paper, we study the problem of Quality of Experience (QoE) aware resource allocation in wireless systems. In particular, we consider application-aware joint Bandwidth-Power allocation for a small cell. We optimize a QoE metric for multi-user video streaming in a small cell that maintains a trade-off between maximizing the playback rate of each user and ensuring proportional fairness (PF) among users. We formulate the application-driven joint bandwidth-power allocation as a non-convex optimization problem. However, we develop a polynomial complexity algorithm, and we show that the proposed algorithm achieves the optimal solution of the proposed optimization problem. Simulation results show that the proposed QoE-aware algorithm significantly improves the average QoE. Moreover, it outperforms the weighted sum rate allocation which is the state-of-the-art physical resource allocation scheme.

cs.IT↗
arXiv2018

ARCHANGEL: Trusted Archives of Digital Public Documents

We present ARCHANGEL; a de-centralised platform for ensuring the long-term integrity of digital documents stored within public archives. Document integrity is fundamental to public trust in archives. Yet currently that trust is built upon institutional reputation --- trust at face value in a centralised authority, like a national government archive or University. ARCHANGEL proposes a shift to a technological underscoring of that trust, using distributed ledger technology (DLT) to cryptographically guarantee the provenance, immutability and so the integrity of archived documents. We describe the ARCHANGEL architecture, and report on a prototype of that architecture build over the Ethereum infrastructure. We report early evaluation and feedback of ARCHANGEL from stakeholders in the research data archives space.

cs.DL↗
arXiv2018

Two-Stage LASSO ADMM Signal Detection Algorithm For Large Scale MIMO

This paper explores the benefit of using some of the machine learning techniques and Big data optimization tools in approximating maximum likelihood (ML) detection of Large Scale MIMO systems. First, large scale MIMO detection problem is formulated as a LASSO (Least Absolute Shrinkage and Selection Operator) optimization problem. Then, Alternating Direction Method of Multipliers (ADMM) is considered in solving this problem. The choice of ADMM is motivated by its ability of solving convex optimization problems by breaking them into smaller sub-problems, each of which are then easier to handle. Further improvement is obtained using two stages of LASSO with interference cancellation from the first stage. The proposed algorithm is investigated at various modulation techniques with different number of antennas. It is also compared with widely used algorithms in this field. Simulation results demonstrate the efficacy of the proposed algorithm for both uncoded and coded cases.

cs.IT↗
arXiv2017

Computing trisections of 4-manifolds

Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to algorithmically construct a trisection, which describes a $4$-dimensional manifold as a union of three $4$-dimensional handlebodies. The complexity of the $4$-manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies. The algorithm begins with a description of a manifold as a union of pentachora, or $4$-dimensional simplices. It transforms this description into a trisection. This results in the first explicit complexity bounds for the trisection genus of a $4$-manifold in terms of the number of pentachora ($4$-simplices) in a triangulation.

math.GT↗
arXiv2017

Marginal sequential Monte Carlo for doubly intractable models

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (M{\o}ller et al., 2006; Murray et al., 2006) for tackling this problem; these approaches being members of the more general class of pseudo-marginal, or exact-approximate, Monte Carlo algorithms (Andrieu and Roberts, 2009), which make use of unbiased estimates of intractable posteriors. Everitt et al. (2017) investigated the use of exact-approximate importance sampling (IS) and sequential Monte Carlo (SMC) in doubly intractable problems, but focussed only on SMC algorithms that used data-point tempering. This paper describes SMC samplers that may use alternative sequences of distributions, and describes ways in which likelihood estimates may be improved adaptively as the algorithm progresses, building on ideas from Moores et al. (2015). This approach is compared with a number of alternative algorithms for doubly intractable problems, including approximate Bayesian computation (ABC), which we show is closely related to the method of M{\o}ller et al. (2006).

stat.CO↗
arXiv2012

The monodromies of homogeneous links

We show that there are only finitely many homogeneous links whose Conway polynomial has any given degree. Using this we give an example of an inhomogeneous, fibred knot. Secondly, we show how to compute the monodromy of a homogeneous link complement from a homogeneous braid word representative.

math.GT↗