Full State Space Research Articles

Formal Analysis of Reentrancy Vulnerabilities in Smart Contract Based on CPN

A smart contract is a special form of computer program that runs on a blockchain and provides a new way to implement financial and business transactions in a conflict-free and transparent environment. In blockchain systems such as Ethereum, smart contracts can handle and autonomously transfer assets of considerable value to other parties. Hence, it is particularly important to ensure that smart contracts function as intended since bugs or vulnerabilities may lead, and indeed have led, to substantial economic losses and erosion of trust for blockchain. While a number of approaches and tools have been developed to find vulnerabilities, formal methods present the highest level of confidence in the security of smart contracts. In this paper, we propose a formal solution to model a smart contract based on colored Petri nets (CPNs). Herein, we focus on the most common type of security bugs in smart contract, i.e., reentrancy bugs, which led to a serious financial loss of around USD 34 million for the Cream Finance project in 2021. We present a hierarchical CPN modelling method to analyze potential security vulnerabilities at the contract’s source code level. Then, modeling analysis methods such as correlation matrix, state space report and state space graph generated via CPN Tools simulation are exploited for formal analysis of smart contracts. The example shows the full state space and wrong path in accordance with our expected results. Finally, the conclusion was verified on the Ethereum network based on the Remix platform.

Equation-based and data-driven modeling strategies for industrial coating processes

Computational Fluid Dynamics (CFD) and Machine Learning (ML) approaches are implemented and compared in an industrial Chemical Vapor Deposition process for the production of cutting tools. In this work, the aim is to analyze the pros and cons of each method and propose a blend of the two approaches that is suitable in industrial applications, where the process is too complicated to address with first-principles models and the data do not allow the implementation of data-hungry methods. Both approaches accurately predict the coating thickness (Mean Absolute Percentage Error (MAPE) of 6.0% and 4.4% for CFD and ML respectively for the test case reactor). CFD, despite its increased computational cost, both in terms of developing and also calibrating for the application at hand, provides meaningful insight and illuminates the process. On the other hand, ML can provide predictions in a time-efficient manner, and is thus appropriate for inline and concurrent predictions. However, it is limited by the available data and has low extrapolation ability. Equation-based and data-driven methods are combined by exploiting a handful of CFD results for efficient interpolation in a reduced space defined by the principal components of the dataset, by implementing Gappy POD. This allows for the accurate reconstruction of the full state-space with limited data.

Data-driven low-dimensional dynamic model of Kolmogorov flow

Minimal dimensional models are desirable for reduced computational costs in simulations as well as for applications such as model-based control. Long-time dynamics of flows often evolve on a low-dimensional manifold M in the full state space. We use neural networks to estimate M and the dynamics on it for two-dimensional Kolmogorov flow in a chaotic bursting regime. Outcomes include: a minimal dimension estimate, good short-time tracking and long-time statistics, as well as accurate predictions of bursting events.

Sufficient Conditions for Global Integral Action via Incremental Forwarding for Input-Affine Nonlinear Systems

In this article, we study the problem of constant output regulation for a class of input-affine multi-input multi-output nonlinear systems, which do not necessarily admit a normal form. We allow the references and the disturbances to be arbitrarily large and the initial conditions of the system to range in the full-state space. We cast the problem in the contraction framework, and we rely on the common approach of extending the system with an integral action processing the regulation error. We then present sufficient conditions for the design of a state-feedback control law able to make the resulting closed-loop system incrementally stable, uniformly with respect to the references and the disturbances. Such a property ensures uniqueness and attractiveness of an equilibrium on which output regulation is obtained. To this end, we develop an incremental version of the forwarding (mod <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace L_gV\rbrace$</tex-math></inline-formula> ) approach. Finally, we provide a set of sufficient conditions for the design of a pure (small-gain) integral-feedback control. The proposed approach is also specialized for two classes of systems that are linear systems having a Lipschitz nonlinearity and a class of minimum-phase systems whose zero dynamics are incrementally stable.

Collaborative training of heterogeneous reinforcement learning agents in environments with sparse rewards: what and when to share?

In the early stages of human life, babies develop their skills by exploring different scenarios motivated by their inherent satisfaction rather than by extrinsic rewards from the environment. This behavior, referred to as intrinsic motivation, has emerged as one solution to address the exploration challenge derived from reinforcement learning environments with sparse rewards. Diverse exploration approaches have been proposed to accelerate the learning process over single- and multi-agent problems with homogeneous agents. However, scarce studies have elaborated on collaborative learning frameworks between heterogeneous agents deployed into the same environment, but interacting with different instances of the latter without any prior knowledge. Beyond the heterogeneity, each agent’s characteristics grant access only to a subset of the full state space, which may hide different exploration strategies and optimal solutions. In this work we combine ideas from intrinsic motivation and transfer learning. Specifically, we focus on sharing parameters in actor-critic model architectures and on combining information obtained through intrinsic motivation with the aim of having a more efficient exploration and faster learning. We test our strategies through experiments performed over a modified ViZDooM’s My Way Home scenario, which is more challenging than its original version and allows evaluating the heterogeneity between agents. Our results reveal different ways in which a collaborative framework with little additional computational cost can outperform an independent learning process without knowledge sharing. Additionally, we depict the need for modulating correctly the importance between the extrinsic and intrinsic rewards to avoid undesired agent behaviors.

Exploring the Tropical Pacific Manifold in Models and Observations

The threat of global warming and the demand for reliable climate predictions pose a formidable challenge because the climate system is multiscale, high-dimensional and nonlinear. Spatiotemporal recurrences of the system hint to the presence of a low-dimensional manifold containing the high-dimensional climate trajectory that could make the problem more tractable. Here we argue that reproducing the geometrical and topological properties of the low-dimensional attractor should be a key target for models used in climate projections. In doing so, we propose a general data-driven framework to characterize the climate attractor and showcase it in the tropical Pacific Ocean using a reanalysis as observational proxy and two state-of-the-art models. The analysis spans four variables simultaneously over the periods 1979–2019 and 2060–2100. At each time t, the system can be uniquely described by a state space vector parametrized by N variables and their spatial variability. The dynamics is confined on a manifold with dimension lower than the full state space that we characterize through manifold learning algorithms, both linear and nonlinear. Nonlinear algorithms describe the attractor through fewer components than linear ones by considering its curved geometry, allowing for visualizing the high-dimensional dynamics through low-dimensional projections. The local geometry and local stability of the high-dimensional, multivariable climate attractor are quantified through the local dimension and persistence metrics. Model biases that hamper climate predictability are identified and found to be similar in the multivariate attractor of the two models during the historical period while diverging under the warming scenario considered. Finally, the relationships between different subspaces (univariate fields), and therefore among climate variables, are evaluated. The proposed framework provides a comprehensive, physically based, test for assessing climate feedbacks and opens new avenues for improving their model representation.13 MoreReceived 8 October 2021Revised 14 March 2022Accepted 20 April 2022Corrected 15 July 2022DOI:https://doi.org/10.1103/PhysRevX.12.021054Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtmospheric fluid dynamicsPatterns in complex systemsSpatiotemporal chaosInterdisciplinary PhysicsNonlinear DynamicsFluid Dynamics

Digital Twin for Federated Analytics Using a Bayesian Approach

We are now in an information era and the volume of data is growing explosively. However, due to privacy issues, it is very common that data cannot be freely shared among the data generating. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Federated analytics</i> was recently proposed aiming at deriving analytical insights among data-generating devices without exposing the raw data, but the intermediate analytics results. Note that the computing resources at the data generating devices are limited, thus making on-device execution of computing-intensive tasks challenging. We thus propose to apply the digital twin technique, which emulates the resource-limited physical/end side, while utilizing the rich resource at the virtual/computing side. Nevertheless, how to use the digital twin technique to assist federated analytics while preserving distributed data privacy is challenging. To address such a challenge, this work first formulates a problem on digital twin-assisted federated distribution discovery. Then, we propose a federated Markov chain Monte Carlo with a delayed rejection (FMCMC-DR) method to estimate the representative parameters of the global distribution. We combine a rejection–acceptance sampling technique and a delayed rejection technique, allowing our method to be able to explore the full state space. Finally, we evaluate FMCMC-DR against the Metropolis–Hastings (MH) algorithm and random walk Markov chain Monte Carlo method (RW-MCMC) using numerical experiments. The results show our algorithm outperforms the other two methods by 50% and 95% contour accuracy, respectively, and has a better convergence rate.

Scalable inference of transcriptional kinetic parameters from MS2 time series data.

MotivationThe MS2-MCP (MS2 coat protein) live imaging system allows for visualization of transcription dynamics through the introduction of hairpin stem-loop sequences into a gene. A fluorescent signal at the site of nascent transcription in the nucleus quantifies mRNA production. Computational modelling can be used to infer the promoter states along with the kinetic parameters governing transcription, such as promoter switching frequency and polymerase loading rate. However, modelling of the fluorescent trace presents a challenge due its persistence; the observed fluorescence at a given time point depends on both current and previous promoter states. A compound state Hidden Markov Model (cpHMM) was recently introduced to allow inference of promoter activity from MS2-MCP data. However, the computational time for inference scales exponentially with gene length and the cpHMM is therefore not currently practical for application to many eukaryotic genes.ResultsWe present a scalable implementation of the cpHMM for fast inference of promoter activity and transcriptional kinetic parameters. This new method can model genes of arbitrary length through the use of a time-adaptive truncated compound state space. The truncated state space provides a good approximation to the full state space by retaining the most likely set of states at each time during the forward pass of the algorithm. Testing on MS2-MCP fluorescent data collected from early Drosophila melanogaster embryos indicates that the method provides accurate inference of kinetic parameters within a computationally feasible timeframe. The inferred promoter traces generated by the model can also be used to infer single-cell transcriptional parameters.Availability and implementationPython implementation is available at https://github.com/ManchesterBioinference/burstInfer, along with code to reproduce the examples presented here.Supplementary information Supplementary data are available at Bioinformatics online.

Dimension-reduction of dynamics on real-world networks with symmetry

We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a large-scale study of such symmetry-induced lumping in real-world networks, from which we identify specific networks for which lumping enables exact analysis that could not have been done on the full state-space. For most networks, lumping gives a state-space compression ratio of up to 10 7 , but the largest compression ratio identified is nearly 10 12 . Many of the highest compression ratios occur in animal social networks. We also present examples of types of symmetry found in real-world networks that have not been previously reported.

Default and determinacy under quantitative easing

We show that the path of inflation under quantitative easing policies that target interest rates, is determinate in the presence of default. We achieve this through different payoff profiles that a collateralised defaultable bond achieves in different states of nature with distinct default outcomes. In the model, heterogeneous households trade this bond and other shorter maturity risk-free bonds to maximize their intertemporal utility of consumption and labour. The differentiated payoffs of the collateralised bond, in an equilibrium with active default, span the full state space giving determinacy of prices and inflation as an outcome. This, implies that quantitative easing as implemented by the ECB in the recent years, can control the stochastic path of inflation.

Comparative Analysis of Lattice-based All-Pass Filter and Second Order Generalized Integrator as Orthogonal System Generator of a PLL

This paper presents a steady-state comparison of two methods that generate an orthogonal voltage system for a single-phase Phase-Locked Loop (PLL) structure: a widely accepted one based on a Second Order Generalized Integrator (SOGI) and a new one based on a All-Pass Filter (APF) with Lattice structure. Both methods are very attractive because of their simple digital implementation, low computational load and good performance under harmonically distorted grid conditions and variable frequency, so they are a good alternative to other known methods. The paper derives and analyzes the full state space models of the two methods.It is shown that these two methods are equivalent in the most common operation conditions of distributed energy resources, although the APF structure is clearly better than the SOGI one because it maintains its orthogonal generation ability for any higher notch frequencies and any lower sampling frequencies. The comparative analysis were validated by simulation with MATLAB/Simulink and experimental results using a fixed-point DSP.

Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model

Abstract We explore the possibility of combining a knowledge-based reduced order model (ROM) with a reservoir computing approach to learn and predict the dynamics of chaotic systems. The ROM is based on proper orthogonal decomposition (POD) with Galerkin projection to capture the essential dynamics of the chaotic system while the reservoir computing approach used is based on echo state networks (ESNs). Two different hybrid approaches are explored: one where the ESN corrects the modal coefficients of the ROM (hybrid-ESN-A) and one where the ESN uses and corrects the ROM prediction in full state space (hybrid-ESN-B). These approaches are applied on two chaotic systems: the Charney–DeVore system and the Kuramoto–Sivashinsky equation and are compared to the ROM obtained using POD/Galerkin projection and to the data-only approach based uniquely on the ESN. The hybrid-ESN-B approach is seen to provide the best prediction accuracy, outperforming the other hybrid approach, the POD/Galerkin projection ROM, and the data-only ESN, especially when using ESNs with a small number of neurons. In addition, the influence of the accuracy of the ROM on the overall prediction accuracy of the hybrid-ESN-B is assessed rigorously by considering ROMs composed of different numbers of POD modes. Further analysis on how hybrid-ESN-B blends the prediction from the ROM and the ESN to predict the evolution of the system is also provided.

The State Space of Artificial Intelligence

The goal of the paper is to develop and propose a general model of the state space of AI. Given the breathtaking progress in AI research and technologies in recent years, such conceptual work is of substantial theoretical interest. The present AI hype is mainly driven by the triumph of deep learning neural networks. As the distinguishing feature of such networks is the ability to self-learn, self-learning is identified as one important dimension of the AI state space. Another dimension is recognized as generalization, the possibility to go over from specific to more general types of problems. A third dimension is semantic grounding. Our overall analysis connects to a number of known foundational issues in the philosophy of mind and cognition: the blockhead objection, the Turing test, the symbol grounding problem, the Chinese room argument, and use theories of meaning. It shall finally be argued that the dimension of grounding decomposes into three sub-dimensions. And the dimension of self-learning turns out as only one of a whole range of “self-x-capacities” (based on ideas of organic computing) that span the self-x-subspace of the full AI state space.

Revealed reasoning

We model a decision maker (DM) making a choice under uncertainty who faces constraints on the set of contingencies she can consider, or reason about, when evaluating a given act (a mapping from states to outcomes). We model the DM's ability to reason about (coarse) contingencies when evaluating a given act using partitions of the state space. A key feature of the model is that the partition may vary with the act the DM is evaluating. This feature allows us to model a DM who, despite her inability to consider every individual state simultaneously, may completely understand the states of the world (in the sense that she may have a well defined prior on the full state space). We argue that this feature allows us to differentiate coarse reasoning from coarse contingencies (as it is typically modeled) and ambiguity aversion, both related phenomena, using only static choice of acts. Our main results axiomatically characterize this model, show how to uniquely identify beliefs in this setting, and uniquely identify the partitions that represent how the DM is able to reason. An application to reasoning about other agents' actions in a mechanism design setting is studied.

Deep learning to discover and predict dynamics on an inertial manifold.

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM) and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.

Improving swarming using genetic algorithms

The verification of temporal properties against a given system may require the exploration of its full state space. In explicit model checking, this exploration uses a depth-first search and can be achieved with multiple randomized threads to increase performance. Nonetheless, the topology of the state space and the exploration order can cap the speedup up to a certain number of threads. This paper proposes a new technique that aims to tackle this limitation by generating artificial initial states, using genetic algorithms. Threads are then launched from these states and thus explore different parts of the state space. Our prototype implementation is 10% faster than state-of-the-art algorithms on a general benchmark and 40% on a specialized benchmark. Even if we expected a decrease in an order of magnitude, these results are still encouraging since they suggest a new way to handle existing limitations. Empirically, our technique seems well suited for “linear” topology, i.e., the one we can obtain when combining model checking algorithms with partial-order reduction techniques.

Multiagent Fully Decentralized Value Function Learning With Linear Convergence Rates

This article develops a fully decentralized multiagent algorithm for policy evaluation. The proposed scheme can be applied to two distinct scenarios. In the first scenario, a collection of agents have distinct datasets gathered by following different behavior policies (none of which is required to explore the full state space) in different instances of the same environment and they all collaborate to evaluate a common target policy. The network approach allows for efficient exploration of the state space and allows all agents to converge to the optimal solution even in situations where neither agent can converge on its own without cooperation. The second scenario is that of multiagent games, in which the state is global and rewards are local. In this scenario, agents collaborate to estimate the value function of a target team policy. The proposed algorithm combines off-policy learning, eligibility traces, and linear function approximation. The proposed algorithm is of the variance-reduced kind and achieves linear convergence with O(1) memory requirements. The linear convergence of the algorithm is established analytically and simulations are used to illustrate the effectiveness of the method.

Is the Ott-Antonsen manifold attracting?

The Kuramoto model is a paradigm for studying oscillator networks with interplay between coupling tending towards synchronization, and heterogeneity in the oscillator population driving away from synchrony. In continuum versions of this model an oscillator population is represented by a probability density on the circle. Ott and Antonsen identified a special class of densities which is invariant under the dynamics and on which the dynamics are low-dimensional and analytically tractable. The reduction to the OA manifold has been used to analyze the dynamics of many variants of the Kuramoto model. To address the fundamental question of whether the OA manifold is attracting, we develop a systematic technique using weighted averages of Poisson measures for analyzing dynamics off the OA manifold. We show that for models with a finite number of populations, the OA manifold is {\it not} attracting in any sense; moreover, the dynamics off the OA manifold is often more complex than on the OA manifold, even at the level of macroscopic order parameters. The OA manifold consists of Poisson densities $\rho_\omega$. A simple extension of the OA manifold consists of averages of pairs of Poisson densities; then the hyperbolic distance between the centroids of each Poisson pair is a dynamical invariant (for each $\omega$). These conserved quantities, defined on the double Poisson manifold, are a measure of the distance to the OA manifold. This invariance implies that chimera states, which have some but not all populations in sync, can never be stable in the full state space, even if stable in the OA manifold. More broadly, our framework facilitates the analysis of multi-population continuum Kuramoto networks beyond the restrictions of the OA manifold, and has the potential to reveal more intricate dynamical behavior than has previously been observed for these networks.

A Hybrid Meta-heuristic Approach to Cope with State Space Explosion in Model Checking Technique for Deadlock Freeness

Model checking is an automatic technique for software verification through which all reachable states are generated from an initial state to finding errors and desirable patterns. In the model checking approach, the behavior and structure of system should be modeled. Graph transformation system is a graphical formal modeling language to specify and model the system. However, modeling of large systems with the graph transformation system suffers from the state space explosion problem which usually requires huge amounts of computational resources. In this paper, we propose a hybrid meta-heuristic approach to deal with this searching problem in the graph transformation system because meta-heuristic algorithms are efficient solutions to traverse the graph of large systems. Our approach, using Artificial Bee Colony and Simulated Annealing, replaces a full state space generation, only by producing part of it checking the safety, and finding errors (e.g., deadlock). The experimental results show that our proposed approach is more efficient and accurate compared to other approaches.

SEREP Integrated Control of Flexible Structures

Flexible structures are continuum modeled as infinite degrees of freedom. Most of the time finite element models are made with large number of degrees-of-freedom to analyse flexible structures. Continuous monitoring, analysis and control of dynamics of flexible structures need simulation of large degrees of freedom in real time. This is computationally expensive and realtime control fails. This study focuses on the development of a reduced order framework for dynamics of flexible structures and use the reduced order model for controlling the structure. Essentially, in the proposed framework, full order state space obtained from finite element modeling of the flexible structure has been reduced to lower subspace using a reduced order algorithm keeping the dynamical characteristic intact. The transformation matrix for reduction has been calculated using system equivalent reduction expansion process (SEREP). Traditionally, full order dynamical system is being used to find the gain matrix to suppress the uncontrolled dynamics associated with the dynamical system. Here in this methodology, the reduced dimension of state space of the system is used for estimating the gain matrix using optimal linear quadratic regulator (LQR). The gain obtained through the reduced system is subsequently used as a feedback to the attached actuators which produce the required force to control the system. A numerical example of a flexible cantilever beam has been shown to investigate the effectiveness of the algorithm.