Information-theoretic Analysis of Unsteady Data

The temporal evolution of scientific data is of high relevance in many fields of application. Understanding the dynamics over time is a crucial step in understanding the underlying system. The availability of large scale parallel computers has led to a finer and finer resolution of simulation data, which makes it difficult to detect all relevant changes of the system by watching a video or a set of snapshots. In recent years, algorithms for the automatic detection of coherent temporal structures have been developed that allow for an identification of interesting areas and time steps in unsteady data. With such techniques, the user can be guided to interesting subsets of the data or a video can be automatically created that does not occlude relevant aspects of the simulation. In this paper, we give an overview over the different techniques, show how their combination helps to gain deeper insight and look at different directions for further improvement. Two CFD simulations are used to illustrate the different techniques

Linear combination of one-step predictive information with an external reward in an episodic policy gradient setting: a critical analysis

One of the main challenges in the field of embodied artificial intelligence is the open-ended autonomous learning of complex behaviours. Our approach is to use task-independent, information-driven intrinsic motivation(s) to support task-dependent learning. The work presented here is a preliminary step in which we investigate the predictive information (the mutual information of the past and future of the sensor stream) as an intrinsic drive, ideally supporting any kind of task acquisition. Previous experiments have shown that the predictive information (PI) is a good candidate to support autonomous, open-ended learning of complex behaviours, because a maximisation of the PI corresponds to an exploration of morphology- and environment-dependent behavioural regularities. The idea is that these regularities can then be exploited in order to solve any given task. Three different experiments are presented and their results lead to the conclusion that the linear combination of the one-step PI with an external reward function is not generally recommended in an episodic policy gradient setting. Only for hard tasks a great speed-up can be achieved at the cost of an asymptotic performance lost

On mathematical modelling of insect flight dynamics in the context of micro air vehicles

This paper discusses several aspects of mathematical modelling relevant to the flight dynamics of insect flight in the context of insect-like flapping wing micro air vehicles (MAVs). MAVs are defined as flying vehicles ca six inch in size (hand-held) and are developed to reconnoitre in confined spaces (inside buildings, tunnels etc). This requires power-efficient, highly-manoeuvrable, low-speed flight with stable hover. All of these attributes are present in insect flight and hence the focus of reproducing the functionality of insect flight by engineering means. This can only be achieved if qualitative insight is accompanied by appropriate quantitative analysis, especially in the context of flight dynamics, as flight dynamics underpin the desirable manoeuvrability. We consider two aspects of mathematical modelling for insect flight dynamics. The first one is theoretical (computational), as opposed to empirical, generation of the aerodynamic data required for the six-degrees-of-freedom equations of motion. For these purposes we first explain insect wing kinematics and the salient features of the corresponding flow. In this context, we show that aerodynamic modelling is a feasible option for certain flight regimes, focussing on a successful example of modelling hover. Such modelling progresses from first principles of fluid mechanics, but relies on simplifications justified by the known flow phenomenology and/or geometric and kinematic symmetries. In particular, this is relevant to six types of fundamental manoeuvres, which we define as those steady flight conditions for which only one component of both the translational and rotational body velocities is non-zero (and constant). The second aspect of mathematical modelling for insect flight dynamics addressed here deals with the periodic character of the aerodynamic force and moment production. This leads to consideration of the types of solutions of nonlinear equations forced by nonlinear oscillations. In particular, the existence of non-periodic solutions of equations of motion is of practical interest, since this allows steady recitilinear flight. Progress in both aspects of mathematical modelling for insect flight will require further advances in aerodynamics of insect-like flapping. Improved aerodynamic modelling and computational fluid dynamics (CFD) calculations are required. These theoretical advances must be accompanied by further flow visualisation and measurement to validate both the aerodynamic modelling and CFD predictions

Long time behavior of unsteady flow computations

This paper addresses a specific issue of time accuracy in the calculation of external aerodynamic problems. The class of problems discussed consists of inviscid compressible subsonic flows. These problems are governed by a convective equation. A key issue that is not understood is the long time behavior of the solution. This is important if one desires transient calculations of problems governed by the Euler equations or its derivatives such as the small disturbance equations or the potential formulations for the gust problem. Difficulties arise for two dimensional problems where the time rate decay solutions of the wave equation is slow. In concert with the above mentioned problem, exterior flows require proper modeling of the boundary conditions. In particular, this requires the truncation of infinite regions into finite regions with the aid of artificial boundaries. These boundary conditions must be consistent with the physics of the unbounded problem as well as consistent in time and space. Our treatment of the problem is discussed in detail and examples are given to verify the results

The information-theoretic meaning of Gagliardo--Nirenberg type inequalities

Gagliardo--Nirenberg inequalities are interpolation inequalities which were proved independently by Gagliardo and Nirenberg in the late fifties. In recent years, their connections with theoretic aspects of information theory and nonlinear diffusion equations allowed to obtain some of them in optimal form, by recovering both the sharp constants and the explicit form of the optimizers. In this note, at the light of these recent researches, we review the main connections between Shannon-type entropies, diffusion equations and a class of these inequalities

Direct Acyclic Graph based Ledger for Internet of Things: Performance and Security Analysis

Direct Acyclic Graph (DAG)-based ledger and the corresponding consensus algorithm has been identified as a promising technology for Internet of Things (IoT). Compared with Proof-of-Work (PoW) and Proof-of-Stake (PoS) that have been widely used in blockchain, the consensus mechanism designed on DAG structure (simply called as DAG consensus) can overcome some shortcomings such as high resource consumption, high transaction fee, low transaction throughput and long confirmation delay. However, the theoretic analysis on the DAG consensus is an untapped venue to be explored. To this end, based on one of the most typical DAG consensuses, Tangle, we investigate the impact of network load on the performance and security of the DAG-based ledger. Considering unsteady network load, we first propose a Markov chain model to capture the behavior of DAG consensus process under dynamic load conditions. The key performance metrics, i.e., cumulative weight and confirmation delay are analysed based on the proposed model. Then, we leverage a stochastic model to analyse the probability of a successful double-spending attack in different network load regimes. The results can provide an insightful understanding of DAG consensus process, e.g., how the network load affects the confirmation delay and the probability of a successful attack. Meanwhile, we also demonstrate the trade-off between security level and confirmation delay, which can act as a guidance for practical deployment of DAG-based ledgers.Comment: accepted by IEEE Transactions on Networkin