arXiv subjects

Christopher King

Publications and source records attributed to Christopher King.

At least 19 recordsLinked to original sources

arXiv2025

Dynamic access pricing control for fair and stable resource sharing

We consider the co-existence of users with different price sensitivities under dynamic (or surge) pricing that regulates how they access a shared resource. To balance supply and demand in such settings, some dynamic pricing systems adopt a monotonically increasing price scheme which is well known to be socially regressive, driving out price-sensitive users in favor of price-insensitive ones. Here, we propose a new dynamic pricing scheme based on a non-monotonic price function that allows all user classes to coexist more fairly when price-insensitive users are present, but automatically reverts to conventional dynamic pricing when they leave the system, even though the exact price-sensitivity composition is unobservable. The resulting system consists of nonlinear ODEs, which we further investigate to characterize its equilibria and their domains of attraction, first for a single price-sensitive class competing with a price-insensitive one and then for the general $n$-class case. Numerical simulations demonstrate the effectiveness of the proposed design.

math.OC↗

arXiv2023

Fluid limit of a distributed ledger model with random delay

Distributed ledgers, including blockchain and other decentralized databases, are designed to store information online where all trusted network members can update the data with transparency. The dynamics of ledger's development can be mathematically represented by a directed acyclic graph (DAG). In this paper, we study a DAG model which considers batch arrivals and random delay of attachment. We analyze the asymptotic behavior of this model by letting the arrival rate go to infinity and the inter-arrival time go to zero. We establish that the number of leaves in the DAG and various random variables characterizing the vertices in the DAG can be approximated by its fluid limit, represented as the solution to a set of delayed partial differential equations. Furthermore, we establish the stable state of this fluid limit and validate our findings through simulations.

math.PR↗

arXiv2023

Almost sure one-endedness of a random graph model of distributed ledgers

Blockchain and other decentralized databases, known as distributed ledgers, are designed to store information online where all trusted network members can update the data with transparency. The dynamics of ledger's development can be mathematically represented by a directed acyclic graph (DAG). One essential property of a properly functioning shared ledger is that all network members holding a copy of the ledger agree on a sequence of information added to the ledger, which is referred to as consensus and is known to be related to a structural property of DAG called one-endedness. In this paper, we consider a model of distributed ledger with sequential stochastic arrivals that mimic attachment rules from the IOTA cryptocurrency. We first prove that the number of leaves in the random DAG is bounded by a constant infinitely often through the identification of a suitable martingale, and then prove that a sequence of specific events happens infinitely often. Combining those results we establish that, as time goes to infinity, the IOTA DAG is almost surely one-ended.

math.PR↗

arXiv2023

Time Associated Meta Learning for Clinical Prediction

Rich Electronic Health Records (EHR), have created opportunities to improve clinical processes using machine learning methods. Prediction of the same patient events at different time horizons can have very different applications and interpretations; however, limited number of events in each potential time window hurts the effectiveness of conventional machine learning algorithms. We propose a novel time associated meta learning (TAML) method to make effective predictions at multiple future time points. We view time-associated disease prediction as classification tasks at multiple time points. Such closely-related classification tasks are an excellent candidate for model-based meta learning. To address the sparsity problem after task splitting, TAML employs a temporal information sharing strategy to augment the number of positive samples and include the prediction of related phenotypes or events in the meta-training phase. We demonstrate the effectiveness of TAML on multiple clinical datasets, where it consistently outperforms a range of strong baselines. We also develop a MetaEHR package for implementing both time-associated and time-independent few-shot prediction on EHR data.

cs.LG↗

arXiv2023

A Multi-View Joint Learning Framework for Embedding Clinical Codes and Text Using Graph Neural Networks

Learning to represent free text is a core task in many clinical machine learning (ML) applications, as clinical text contains observations and plans not otherwise available for inference. State-of-the-art methods use large language models developed with immense computational resources and training data; however, applying these models is challenging because of the highly varying syntax and vocabulary in clinical free text. Structured information such as International Classification of Disease (ICD) codes often succinctly abstracts the most important facts of a clinical encounter and yields good performance, but is often not as available as clinical text in real-world scenarios. We propose a \textbf{multi-view learning framework} that jointly learns from codes and text to combine the availability and forward-looking nature of text and better performance of ICD codes. The learned text embeddings can be used as inputs to predictive algorithms independent of the ICD codes during inference. Our approach uses a Graph Neural Network (GNN) to process ICD codes, and Bi-LSTM to process text. We apply Deep Canonical Correlation Analysis (DCCA) to enforce the two views to learn a similar representation of each patient. In experiments using planned surgical procedure text, our model outperforms BERT models fine-tuned to clinical data, and in experiments using diverse text in MIMIC-III, our model is competitive to a fine-tuned BERT at a tiny fraction of its computational effort.

cs.CL↗

arXiv2022

Self-explaining Hierarchical Model for Intraoperative Time Series

Major postoperative complications are devastating to surgical patients. Some of these complications are potentially preventable via early predictions based on intraoperative data. However, intraoperative data comprise long and fine-grained multivariate time series, prohibiting the effective learning of accurate models. The large gaps associated with clinical events and protocols are usually ignored. Moreover, deep models generally lack transparency. Nevertheless, the interpretability is crucial to assist clinicians in planning for and delivering postoperative care and timely interventions. Towards this end, we propose a hierarchical model combining the strength of both attention and recurrent models for intraoperative time series. We further develop an explanation module for the hierarchical model to interpret the predictions by providing contributions of intraoperative data in a fine-grained manner. Experiments on a large dataset of 111,888 surgeries with multiple outcomes and an external high-resolution ICU dataset show that our model can achieve strong predictive performance (i.e., high accuracy) and offer robust interpretations (i.e., high transparency) for predicted outcomes based on intraoperative time series.

cs.LG↗

arXiv2022

Feedback control for distributed ledgers: An attack mitigation policy for DAG-based DLTs

In this paper we present a feedback approach to the design of an attack mitigation policy for DAG-based Distributed Ledgers. We develop a model to analyse the behaviour of the ledger under the so called Tips Inflation Attack and we design a control strategy to counteract this attack strategy. The efficacy of this approach is showcased through a theoretical analysis, in the form of two theorems about the stability properties of the ledger with and without the controller, and extensive Monte Carlo simulations of an agent-based model of the distributed ledger.

eess.SY↗

arXiv2022

Evaluation of Non-Invasive Thermal Imaging for detection of Viability of Onchocerciasis worms

Onchocerciasis is causing blindness in over half a million people in the world today. Drug development for the disease is crippled as there is no way of measuring effectiveness of the drug without an invasive procedure. Drug efficacy measurement through assessment of viability of onchocerca worms requires the patients to undergo nodulectomy which is invasive, expensive, time-consuming, skill-dependent, infrastructure dependent and lengthy process. In this paper, we discuss the first-ever study that proposes use of machine learning over thermal imaging to non-invasively and accurately predict the viability of worms. The key contributions of the paper are (i) a unique thermal imaging protocol along with pre-processing steps such as alignment, registration and segmentation to extract interpretable features (ii) extraction of relevant semantic features (iii) development of accurate classifiers for detecting the existence of viable worms in a nodule. When tested on a prospective test data of 30 participants with 48 palpable nodules, we achieved an Area Under the Curve (AUC) of 0.85.

eess.IV↗

arXiv2021

Reinforcement Learning with Algorithms from Probabilistic Structure Estimation

Reinforcement learning (RL) algorithms aim to learn optimal decisions in unknown environments through experience of taking actions and observing the rewards gained. In some cases, the environment is not influenced by the actions of the RL agent, in which case the problem can be modeled as a contextual multi-armed bandit and lightweight myopic algorithms can be employed. On the other hand, when the RL agent's actions affect the environment, the problem must be modeled as a Markov decision process and more complex RL algorithms are required which take the future effects of actions into account. Moreover, in practice, it is often unknown from the outset whether or not the agent's actions will impact the environment and it is therefore not possible to determine which RL algorithm is most fitting. In this work, we propose to avoid this difficult decision entirely and incorporate a choice mechanism into our RL framework. Rather than assuming a specific problem structure, we use a probabilistic structure estimation procedure based on a likelihood-ratio (LR) test to make a more informed selection of learning algorithm. We derive a sufficient condition under which myopic policies are optimal, present an LR test for this condition, and derive a bound on the regret of our framework. We provide examples of real-world scenarios where our framework is needed and provide extensive simulations to validate our approach.

cs.LG↗

arXiv2021

Personalised Feedback Control, Social Contracts, and Compliance Strategies for Ensembles

This paper describes the use of Distributed Ledger Technologies as a mean to enforce social contracts and to orchestrate the behaviour of agents in a smart city environment. Specifically, we present a scheme to price personalised risk in sharing economy applications. We provide proofs for the convergence of the proposed stochastic system and we validate our approach through the use of extensive Monte Carlo simulations.

math.OC↗

arXiv2019

Distributed Ledger Technology for Smart Mobility: Variable Delay Models

Recently, Directed Acyclic Graph (DAG) based Distributed Ledgers have been proposed for various applications in the smart mobility domain [1]. While many application studies have been described in the literature, an open problem in the DLT community concerns the lack of mathematical models describing their behaviour, and their validation. Building on a previous work in [1], we present, in this paper, a fluid based approximation for the IOTA Foundation DAG based DLT that incorporates varying transaction delays. This extension, namely the inclusion of varying delays, is important for feedback control applications (such as transactive control [2]). Extensive simulations are presented to illustrate the efficacy of our approach.

eess.SY↗

arXiv2019

Distributed Ledger Technology for IoT: Parasite Chain Attacks

Directed Acyclic Graph (DAG) based Distributed Ledgers can be useful in a number of applications in the IoT domain. A distributed ledger should serve as an immutable and irreversible record of transactions, however, a DAG structure is a more complicated mathematical object than its blockchain counterparts, and as a result, providing guarantees of immutability and irreversibility is more involved. In this paper, we analyse a commonly discussed attack scenario known as a parasite chain attack for the IOTA Foundation DAG based ledger. We analyse the efficacy of IOTA core MCMC algorithm using a matrix model and present an extension which improves the ledger resistance to these attacks.

cs.DC↗

arXiv2019

The fluid limit of a random graph model for a shared ledger

A shared ledger is a record of transactions that can be updated by any member of a group of users. The notion of independent and consistent record-keeping in a shared ledger is important for blockchain and more generally for distributed ledger technologies. In this paper we analyze the growth of a model for the tangle, which is the shared ledger protocol used as the basis for the IOTA cryptocurrency. The model is a random directed acyclic graph, and its growth is described by a non-Markovian stochastic process. We derive a delay differential equation for the fluid model which describes the tangle at high arrival rate. We prove convergence in probability of the tangle process to the fluid model, and also prove global stability of the fluid model. The convergence proof relies on martingale techniques.

math.PR↗

arXiv2018

IOTA-based Directed Acyclic Graphs without Orphans

Directed Acylic Graphs (DAGs) are emerging as an attractive alternative to traditional blockchain architectures for distributed ledger technology (DLT). In particular DAG ledgers with stochastic attachment mechanisms potentially offer many advantages over blockchain, including scalability and faster transaction speeds. However, the random nature of the attachment mechanism coupled with the requirement of protection against double-spend transactions leaves open the possibility that not all transactions will be eventually validated. Such transactions are said to be orphaned, and will never be validated. Our principal contribution is to propose a simple modification to the attachment mechanism for the Tangle (the IOTA DAG architecture). This modification ensures that all transactions are validated in finite time, and preserves essential features of the popular Monte-Carlo selection algorithm. In order to demonstrate these results we derive a fluid approximation for the Tangle (in the limit of infinite arrival rate) and prove that this fluid model exhibits the desired behavior. We also present simulations which validate the results for finite arrival rates.

cs.DC↗

arXiv2018

Distributed Ledger Technology, Cyber-Physical Systems, and Social Compliance

This paper describes how Distributed Ledger Technologies can be used to design a class of cyber-physical systems, as well as to enforce social contracts and to orchestrate the behaviour of agents trying to access a shared resource. The first part of the paper analyses the advantages and disadvantages of using Distributed Ledger Technologies architectures to implement certain control systems in an Internet of Things (IoT) setting, and then focuses on a specific type of DLT based on a Directed Acyclic Graph. In this setting we propose a set of delay differential equations to describe the dynamical behaviour of the Tangle, an IoT-inspired Directed Acyclic Graph designed for the cryptocurrency IOTA. The second part proposes an application of Distributed Ledger Technologies as a mechanism for dynamic deposit pricing, wherein the deposit of digital currency is used to orchestrate access to a network of shared resources. The pricing signal is used as a mechanism to enforce the desired level of compliance according to a predetermined set of rules. After presenting an illustrative example, we analyze the control system and provide sufficient conditions for the stability of the network.

eess.SY↗

arXiv2017

Potential output purity of completely positive maps

The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and Hadamard channels) it is shown that potential purity does not exceed the standard output purity. As an application the potential purity is used to bound the logarithmic Sobolev constant of a product of depolarizing channel semigroups.

quant-ph↗

arXiv2015

Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm

We develop the notions of hypercontractivity (HC) and the log-Sobolev (LS) inequality for completely bounded norms of one-parameter semigroups of super-operators acting on matrix algebras. We prove the equivalence of the completely bounded versions of HC and LS under suitable hypotheses. We also prove a version of the Gross Lemma which allows LS at general $q$ to be deduced from LS at $q=2$.

math-ph↗

arXiv2013

Alleviating a form of electric vehicle range anxiety through On-Demand vehicle access

On-demand vehicle access is a method that can be used to reduce types of range anxiety problems related to planned travel for electric vehicle owners. Using ideas from elementary queueing theory, basic QoS metrics are defined to dimension a shared fleet to ensure high levels of vehicle access. Using mobility data from Ireland, it is argued that the potential cost of such a system is very low.

math.OC↗