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We apply Game Theory to a mathematical representation of two competing teams of agents connected within a complex network, where the ability of each side to manoeuvre their resource and degrade that of the other depends on their ability to internally synchronise decision-making while out-pacing the other. Such a representation of an adversarial socio-physical system has application in a range of business, sporting, and military contexts. Specifically, we unite here two physics-based models, that of Kuramoto to represent decision-making cycles, and an adaptation of a multi-species Lotka-Volterra system for the resource competition. For complex networks we employ variations of the Barab\'asi-Alberts scale-free graph, varying how resources are initially distributed between graph hub and periphery. We adapt as equilibrium solution Nash Dominant Game Pruning as a means of efficiently exploring the dynamical decision tree. Across various scenarios we find Nash solutions where the side initially concentrating resources in the periphery can sustain competition to achieve victory except when asymmetries exist between the two. When structural advantage is limited we find that agility in how the victor stays ahead of decision-state of the other becomes critical., Comment: 11 pages, 27 figures

Certified robustness circumvents the fragility of defences against adversarial attacks, by endowing model predictions with guarantees of class invariance for attacks up to a calculated size. While there is value in these certifications, the techniques through which we assess their performance do not present a proper accounting of their strengths and weaknesses, as their analysis has eschewed consideration of performance over individual samples in favour of aggregated measures. By considering the potential output space of certified models, this work presents two distinct approaches to improve the analysis of certification mechanisms, that allow for both dataset-independent and dataset-dependent measures of certification performance. Embracing such a perspective uncovers new certification approaches, which have the potential to more than double the achievable radius of certification, relative to current state-of-the-art. Empirical evaluation verifies that our new approach can certify $9\%$ more samples at noise scale $\sigma = 1$, with greater relative improvements observed as the difficulty of the predictive task increases., Comment: IEEE S&P 2024, IEEE Security & Privacy 2024, 14 pages

Poisoning attacks can disproportionately influence model behaviour by making small changes to the training corpus. While defences against specific poisoning attacks do exist, they in general do not provide any guarantees, leaving them potentially countered by novel attacks. In contrast, by examining worst-case behaviours Certified Defences make it possible to provide guarantees of the robustness of a sample against adversarial attacks modifying a finite number of training samples, known as pointwise certification. We achieve this by exploiting both Differential Privacy and the Sampled Gaussian Mechanism to ensure the invariance of prediction for each testing instance against finite numbers of poisoned examples. In doing so, our model provides guarantees of adversarial robustness that are more than twice as large as those provided by prior certifications.

A significant portion of research on distributed ledgers has focused on circumventing the limitations of leader-based blockchains mainly in terms of scalability, decentralization and power consumption. Leaderless architectures based on directed acyclic graphs (DAGs) avoid many of these limitations altogether, but their increased flexibility and performance comes at the cost of increased design complexity, so their potential has remained largely unexplored. Management of write access to these ledgers presents a major challenge because ledger updates may be made in parallel, hence transactions cannot simply be serialised and prioritised according to token fees paid to validators. In this work, we propose an access control scheme for leaderless DAG-based ledgers which is based on consuming credits rather than paying fees in the base token. We outline a general model for this new approach and provide some simulation results showing promising performance boosts., Comment: Short version awarded with the Best Paper Award at BLOCKCHAIN Congress 2023

The forced Korteweg-de Vries (fKdV) equation describes incompressible inviscid free surface flows over some arbitrary topography. We investigate solitary and hydraulic fall solutions to the fKdV equation. Numerical results show that the calculation of exponentially decaying solitary waves at the critical Froude number is a nonlinear eigenvalue problem. Furthermore we show how exponential decaying solitary waves evolve into the continuous spectrum of algebraic decaying solitary waves. A novel and stable numerical approach using the wave-resistance coefficient and tabletop solutions is used to generate the hydraulic fall parametric space. We show how hydraulic fall solutions periodically evolve into exponential decaying solitary waves., Comment: 22 pages, 5 figures

This paper discusses congestion control and inconsistency problems in DAG-based distributed ledgers and proposes an additional filter to mitigate these issues. Unlike traditional blockchains, DAG-based DLTs use a directed acyclic graph structure to organize transactions, allowing higher scalability and efficiency. However, this also introduces challenges in controlling the rate at which blocks are added to the network and preventing the influence of spam attacks. To address these challenges, we propose a filter to limit the tip pool size and to avoid referencing old blocks. Furthermore, we present experimental results to demonstrate the effectiveness of this filter in reducing the negative impacts of various attacks. Our approach offers a lightweight and efficient solution for managing the flow of blocks in DAG-based DLTs, which can enhance the consistency and reliability of these systems. Index

The analysis of distributed techniques is often focused upon their efficiency, without considering their robustness (or lack thereof). Such a consideration is particularly important when devices or central servers can fail, which can potentially cripple distributed systems. When such failures arise in wireless communications networks, important services that they use/provide (like anomaly detection) can be left inoperable and can result in a cascade of security problems. In this paper, we present a novel method to address these risks by combining both flat- and star-topologies, combining the performance and reliability benefits of both. We refer to this method as "Tol-FL", due to its increased failure-tolerance as compared to the technique of Federated Learning. Our approach both limits device failure risks while outperforming prior methods by up to 8% in terms of anomaly detection AUROC in a range of realistic settings that consider client as well as server failure, all while reducing communication costs. This performance demonstrates that Tol-FL is a highly suitable method for distributed model training for anomaly detection, especially in the domain of wireless networks.

In guaranteeing the absence of adversarial examples in an instance's neighbourhood, certification mechanisms play an important role in demonstrating neural net robustness. In this paper, we ask if these certifications can compromise the very models they help to protect? Our new \emph{Certification Aware Attack} exploits certifications to produce computationally efficient norm-minimising adversarial examples $74 \%$ more often than comparable attacks, while reducing the median perturbation norm by more than $10\%$. While these attacks can be used to assess the tightness of certification bounds, they also highlight that releasing certifications can paradoxically reduce security., Comment: 17 pages, 8 figures

In response to subtle adversarial examples flipping classifications of neural network models, recent research has promoted certified robustness as a solution. There, invariance of predictions to all norm-bounded attacks is achieved through randomised smoothing of network inputs. Today's state-of-the-art certifications make optimal use of the class output scores at the input instance under test: no better radius of certification (under the $L_2$ norm) is possible given only these score. However, it is an open question as to whether such lower bounds can be improved using local information around the instance under test. In this work, we demonstrate how today's "optimal" certificates can be improved by exploiting both the transitivity of certifications, and the geometry of the input space, giving rise to what we term Geometrically-Informed Certified Robustness. By considering the smallest distance to points on the boundary of a set of certifications this approach improves certifications for more than $80\%$ of Tiny-Imagenet instances, yielding an on average $5 \%$ increase in the associated certification. When incorporating training time processes that enhance the certified radius, our technique shows even more promising results, with a uniform $4$ percentage point increase in the achieved certified radius., Comment: Accepted for Neurips`22, 19 pages, 14 figures, for associated code see https://github.com/andrew-cullen/DoubleBubble

An outstanding problem in the design of distributed ledgers concerns policies that govern the manner in which users interact with the network. Network usability is crucial to the mainstream adoption of distributed ledgers, particularly for enterprise applications in which most users do not wish to operate full node. For DAG-based ledgers such as IOTA, we propose a user-node interaction mechanism that is designed to ensure the risk of a user experiencing a poor quality of service is low. Our mechanism involves users selecting nodes to issue their transactions to the ledger based on quality of service indicators advertised by the nodes. Simulation results are presented to illustrate the efficacy of the proposed policies.

We apply computational Game Theory to a unification of physics-based models that represent decision-making across a number of agents within both cooperative and competitive processes. Here the competitors try to both positively influence their own returns, while negatively affecting those of their competitors. Modelling these interactions with the so-called Boyd-Kuramoto-Lanchester (BKL) complex dynamical system model yields results that can be applied to business, gaming and security contexts. This paper studies a class of decision problems on the BKL model, where a large set of coupled, switching dynamical systems are analysed using game-theoretic methods. Due to their size, the computational cost of solving these BKL games becomes the dominant factor in the solution process. To resolve this, we introduce a novel Nash Dominant solver, which is both numerically efficient and exact. The performance of this new solution technique is compared to traditional exact solvers, which traverse the entire game tree, as well as to approximate solvers such as Myopic and Monte Carlo Tree Search (MCTS). These techniques are assessed, and used to gain insights into both nonlinear dynamical systems and strategic decision making in adversarial environments.

Access control is a fundamental component of the design of distributed ledgers, influencing many aspects of their design, such as fairness, efficiency, traditional notions of network security, and adversarial attacks such as Denial-of-Service (DoS) attacks. In this work, we consider the security of a recently proposed access control protocol for Directed Acyclic Graph-based distributed ledgers. We present a number of attack scenarios and potential vulnerabilities of the protocol and introduce a number of additional features which enhance its resilience. Specifically, a blacklisting algorithm, which is based on a reputation-weighted threshold, is introduced to handle both spamming and multi-rate malicious attackers. The introduction of a solidification request component is also introduced to ensure the fairness and consistency of network in the presence of attacks. Finally, a timestamp component is also introduced to maintain the consistency of the network in the presence of multi-rate attackers. Simulations to illustrate the efficacy and robustness of the revised protocol are also described., Comment: Submitted for consideration for publication in IEEE IoT Journal

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.

In the Internet of Things (IoT) domain, devices need a platform to transact seamlessly without a trusted intermediary. Although Distributed Ledger Technologies (DLTs) could provide such a platform, blockchains, such as Bitcoin, were not designed with IoT networks in mind, hence are often unsuitable for such applications: they offer poor transaction throughput and confirmation times, put stress on constrained computing and storage resources, and require high transaction fees. In this work, we consider a class of IoT-friendly DLTs based on directed acyclic graphs, rather than a blockchain, and with a reputation system in the place of Proof of Work (PoW). However, without PoW, implementation of these DLTs requires an access control algorithm to manage the rate at which nodes can add new transactions to the ledger. We model the access control problem and present an algorithm that is fair, efficient and secure. Our algorithm represents a new design paradigm for DLTs in which concepts from networking are applied to the DLT setting for the first time. For example, our algorithm uses distributed rate setting which is similar in nature to transmission control used in the Internet. However, our solution features novel adaptations to cope with the adversarial environment of DLTs in which no individual agent can be trusted. Our algorithm guarantees utilisation of resources, consistency, fairness, and resilience against attackers. All of this is achieved efficiently and with regard for the limitations of IoT devices. We perform extensive simulations to validate these claims.

We introduce a permissioned distributed ledger technology (DLT) design for crowdsourced smart mobility applications. This architecture is based on a directed acyclic graph architecture (similar to the IOTA tangle) and uses both Proof-of-Work and Proof-of-Position mechanisms to provide protection against spam attacks and malevolent actors. In addition to enabling individuals to retain ownership of their data and to monetize it, the architecture also is suitable for distributed privacy-preserving machine learning algorithms, is lightweight, and can be implemented in simple internet-of-things (IoT) devices. To demonstrate its efficacy, we apply this framework to reinforcement learning settings where a third party is interested in acquiring information from agents. In particular, one may be interested in sampling an unknown vehicular traffic flow in a city, using a DLT-type architecture and without perturbing the density, with the idea of realizing a set of virtual tokens as surrogates of real vehicles to explore geographical areas of interest. These tokens, whose authenticated position determines write access to the ledger, are thus used to emulate the probing actions of commanded (real) vehicles on a given planned route by "jumping" from a passing-by vehicle to another to complete the planned trajectory. Consequently, the environment stays unaffected (i.e., the autonomy of participating vehicles is not influenced by the algorithm), regardless of the number of emitted tokens. The design of such a DLT architecture is presented, and numerical results from large-scale simulations are provided to validate the proposed approach., Comment: A short version of this paper was submitted to ICCVE 2019: The 8th IEEE International Conference on Connected Vehicles and Expo

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.

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., Comment: 8 pages, submitted to the IEEE 2019 Control and Decision Conference (CDC). arXiv admin note: text overlap with arXiv:1901.07302, arXiv:1807.00649

We present an algorithm for constructing numerical solutions to one--dimensional nonlinear, variable coefficient boundary value problems. This scheme is based upon applying the Homotopy Analysis Method (HAM) to decompose a nonlinear differential equation into a series of linear differential equations that can be solved using a sparse, spectrally accurate Gegenbauer discretisation. Uniquely for nonlinear methods, our scheme involves constructing a single, sparse matrix operator that is repeatedly solved in order to solve the full nonlinear problem. As such, the resulting scheme scales quasi-linearly with respect to the grid resolution. We demonstrate the accuracy, and computational scaling of this method by examining a fourth-order nonlinear variable coefficient boundary value problem by comparing the scheme to Newton-Iteration and the Spectral Homotopy Analysis Method, which is the most commonly used implementation of the HAM.

This report discusses the possibility of expanding the resource and finance data to be collected as part of the 1999-2000 Schools and Staffing Survey (SASS) of the National Center for Education Statistics (NCES). The proposal under consideration, which is being field tested in the fall of 1998 and winter of 1999, has two major components. The first is to collect more detailed information about staffing resources in the schools included in the SASS sample. This information would improve understanding of how schools allocate personnel resources, which account for more than 85% of expenditures at most school sites. A review of the options suggests that the data needed to conduct Resource Cost Model analyses of U.S. schools can be collected through the SASS without much increase in the burden on respondents. The second component is to gather expenditure data for individual schools in the SASS sample to permit analysis of expenditures at the school level. The analysis shows that it is possible to collect information by NCES function and object categories and to collect school-level data across a diverse array of districts. A drawback is that an instrument of the complexity needed to meet these two purposes is difficult and time consuming for the respondent. The final section of the paper discusses linking the staffing and expenditure data. Appendixes contain information about the development of the surveys and copies of the public school and private school surveys. (Contains 19 exhibits.) (SLD)

Data are not available to inform education policy discussion regarding how resources are allocated both within and among schools. This study was conducted to develop and pilot test a questionnaire that would collect school-level expenditure data. This report describes the three site visits and focus group conducted for this project, findings from pilot tests of two versions of questionnaires (one in seven districts and one in eight school districts), and the revised instrument, the "Public School Expenditure Survey." Both pilot instruments were developed as mailed questionnaires linked to the Schools and Staffing Survey. Collecting data by the functional categories defined by the National Center for Education Statistics was the challenge that was most clearly met by the developed instrument. The instrument also shows that it is possible to collect school-level data, but the drawback is that the instrument must be fairly complex and thus creates a burden for the respondent. One appendix contains the instrument, and the other explains common errors that cause data inconsistency. (SLD)