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The occurrence of high frequency (>1000 Hz) thermoacoustic instability (TAI) sustained by mutual feedback among the acoustic field, heat release rate oscillations, and hydrodynamic oscillations poses severe challenges to the operation and structural integrity of rocket engines. Hence, quantifying the differing levels of feedback between these variables can help uncover the underlying mechanisms behind such high frequency TAI, enabling redesign of combustors to mitigate TAI. However, so far, no concrete method exists to decipher the varying levels of mutual feedback during high-frequency TAI. In the present study, we holistically investigate the mutual influence based on the spatiotemporal directionality among acoustic pressure, heat release rate, hydrodynamic and thermal oscillations during TAI of a single-element rocket engine combustor. Using symbolic transfer entropy (STE), we identify the spatiotemporal direction of feedback interactions between those primary variables when acoustic waves significantly emerge during TAI. We unveil the influence of vorticity dynamics at the fuel collar (or the propellant splitter plate) as the primary stimulant over the heat release rate fluctuations to rapidly amplify the amplitude of the acoustic field. Further, depending on the quantification of the degree of the mutual information (i.e., the net direction of information), we identify the switches in dominating the thermoacoustic driving between the variables during TAI, each representing a distinct mechanism of a thermoacoustic state. Additionally, from this quantification, we analyze the relative dominance of the variables and rank-order the mutual feedback according to their impact on driving TAI., Comment: 48 pages, 16 figures

Turbulent flow physics regulates the aerodynamic properties of lifting surfaces, the thermodynamic efficiency of vapor power systems, and exchanges of natural and anthropogenic quantities between the atmosphere and ocean, to name just a few applications. The dynamics of turbulent flows are described via numerical integration of the non-linear Navier-Stokes equation -- a procedure known as computational fluid dynamics (CFD). At the dawn of scientific computing in the late 1950s, it would be many decades before terms such as ``carbon footprint'' or ``sustainability'' entered the lexicon, and longer still before these themes attained national priority throughout advanced economies. This paper introduces a framework designed to calculate the carbon footprint of CFD and its contribution to carbon emission reduction strategies. We will distinguish between "hero" and "routine" calculations, noting that the carbon footprint of hero calculations is largely determined by the energy source mix utilized. We will also review CFD of flows where turbulence effects are modeled, thus reducing the degrees of freedom. Estimates of the carbon footprint are presented for such fully- and partially-resolved simulations as functions of turbulence activity and calculation year, demonstrating a reduction in carbon emissions by two to five orders of magnitude at practical conditions. Beyond analyzing CO2 emissions, we quantify the benefits of applying CFD towards overall carbon emission reduction. The community's effort to avoid redundant calculations via turbulence databases merits particular attention, with estimates indicating that a single database could potentially reduce CO2 emissions by approximately O(1) million metric tons. Additionally, implementing CFD in the fluids industry has markedly decreased dependence on wind tunnel testing, which is anticipated to lead to CO2 emission reduction., Comment: 18 pages, 6 figures

The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this partial differential equation (PDE) using conventional numerical methods becomes computationally prohibitive. Here, we introduce a fast, scalable, and interpretable method for solving the Fokker-Planck equation which is applicable in higher dimensions. This method approximates the solution as a linear combination of shape-morphing Gaussians with time-dependent means and covariances. These parameters evolve according to the method of reduced-order nonlinear solutions (RONS) which ensures that the approximate solution stays close to the true solution of the PDE for all times. As such, the proposed method approximates the transient dynamics as well as the equilibrium density, when the latter exists. Our approximate solutions can be viewed as an evolution on a finite-dimensional statistical manifold embedded in the space of probability densities. We show that the metric tensor in RONS coincides with the Fisher information matrix on this manifold. We also discuss the interpretation of our method as a shallow neural network with Gaussian activation functions and time-varying parameters. In contrast to existing deep learning methods, our method is interpretable, requires no training, and automatically ensures that the approximate solution satisfies all properties of a probability density.

Automated Intelligent Cyberdefense Agents (AICAs) that are part Intrusion Detection Systems (IDS) and part Intrusion Response Systems (IRS) are being designed to protect against sophisticated and automated cyber-attacks. An AICA based on the ideas of Self-Adaptive Autonomic Computing Systems (SA-ACS) can be considered as a managing system that protects a managed system like a personal computer, web application, critical infrastructure, etc. An AICA, specifically the IRS components, can compute a wide range of potential responses to meet its security goals and objectives, such as taking actions to prevent the attack from completing, restoring the system to comply with the organizational security policy, containing or confining an attack, attack eradication, deploying forensics measures to enable future attack analysis, counterattack, and so on. To restrict its activities in order to minimize collateral/organizational damage, such an automated system must have set Rules of Engagement (RoE). Automated systems must determine which operations can be completely automated (and when), which actions require human operator confirmation, and which actions must never be undertaken. In this paper, to enable this control functionality over an IRS, we create Rules of EngaGement for Automated cybeR Defense (REGARD) system which holds a set of Rules of Engagement (RoE) to protect the managed system according to the instructions provided by the human operator. These rules help limit the action of the IRS on the managed system in compliance with the recommendations of the domain expert. We provide details of execution, management, operation, and conflict resolution for Rules of Engagement (RoE) to constrain the actions of an automated IRS. We also describe REGARD system implementation, security case studies for cyber defense, and RoE demonstrations.

The current state of the art systems in Artificial Intelligence (AI) enabled intrusion detection use a variety of black box methods. These black box methods are generally trained using Error Based Learning (EBL) techniques with a focus on creating accurate models. These models have high performative costs and are not easily explainable. A white box Competitive Learning (CL) based eXplainable Intrusion Detection System (X-IDS) offers a potential solution to these problem. CL models utilize an entirely different learning paradigm than EBL approaches. This different learning process makes the CL family of algorithms innately explainable and less resource intensive. In this paper, we create an X-IDS architecture that is based on DARPA's recommendation for explainable systems. In our architecture we leverage CL algorithms like, Self Organizing Maps (SOM), Growing Self Organizing Maps (GSOM), and Growing Hierarchical Self Organizing Map (GHSOM). The resulting models can be data-mined to create statistical and visual explanations. Our architecture is tested using NSL-KDD and CIC-IDS-2017 benchmark datasets, and produces accuracies that are 1% - 3% less than EBL models. However, CL models are much more explainable than EBL models. Additionally, we use a pruning process that is able to significantly reduce the size of these CL based models. By pruning our models, we are able to increase prediction speeds. Lastly, we analyze the statistical and visual explanations generated by our architecture, and we give a strategy that users could use to help navigate the set of explanations. These explanations will help users build trust with an Intrusion Detection System (IDS), and allow users to discover ways to increase the IDS's potency.

The Human Immune System (HIS) works to protect a body from infection, illness, and disease. This system can inspire cybersecurity professionals to design an Artificial Immune System (AIS) based Intrusion Detection System (IDS). These biologically inspired algorithms using Self/Nonself and Danger Theory can directly augmentIDS designs and implementations. In this paper, we include an examination into the elements of design necessary for building an AIS-IDS framework and present an architecture to create such systems.

We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent partial differential equations (PDEs), where the modes depend nonlinearly on a set of time-varying parameters. RONS uses a set of ordinary differential equations (ODEs) for the parameters to optimally evolve the shape of the modes to adapt to the PDE's solution. This method has already proven extremely effective in tackling challenging problems such as advection-dominated flows and high-dimensional PDEs. However, as the number of parameters grow, integrating the RONS equation and even its formation become computationally prohibitive. Here, we develop three separate methods to address these computational bottlenecks: symbolic RONS, collocation RONS and regularized RONS. We demonstrate the efficacy of these methods on two examples: Fokker-Planck equation in high dimensions and the Kuramoto-Sivashinsky equation. In both cases, we observe that the proposed methods lead to several orders of magnitude in speedup and accuracy. Our proposed methods extend the applicability of RONS beyond reduced-order modeling by making it possible to use RONS for accurate numerical solution of linear and nonlinear PDEs. Finally, as a special case of RONS, we discuss its application to problems where the PDE's solution is approximated by a neural network, with the time-dependent parameters being the weights and biases of the network. The RONS equations dictate the optimal evolution of the network's parameters without requiring any training., Comment: Minor revisions

Modern Artificial Intelligence (AI) enabled Intrusion Detection Systems (IDS) are complex black boxes. This means that a security analyst will have little to no explanation or clarification on why an IDS model made a particular prediction. A potential solution to this problem is to research and develop Explainable Intrusion Detection Systems (X-IDS) based on current capabilities in Explainable Artificial Intelligence (XAI). In this paper, we create a Self Organizing Maps (SOMs) based X-IDS system that is capable of producing explanatory visualizations. We leverage SOM's explainability to create both global and local explanations. An analyst can use global explanations to get a general idea of how a particular IDS model computes predictions. Local explanations are generated for individual datapoints to explain why a certain prediction value was computed. Furthermore, our SOM based X-IDS was evaluated on both explanation generation and traditional accuracy tests using the NSL-KDD and the CIC-IDS-2017 datasets.

The application of Artificial Intelligence (AI) and Machine Learning (ML) to cybersecurity challenges has gained traction in industry and academia, partially as a result of widespread malware attacks on critical systems such as cloud infrastructures and government institutions. Intrusion Detection Systems (IDS), using some forms of AI, have received widespread adoption due to their ability to handle vast amounts of data with a high prediction accuracy. These systems are hosted in the organizational Cyber Security Operation Center (CSoC) as a defense tool to monitor and detect malicious network flow that would otherwise impact the Confidentiality, Integrity, and Availability (CIA). CSoC analysts rely on these systems to make decisions about the detected threats. However, IDSs designed using Deep Learning (DL) techniques are often treated as black box models and do not provide a justification for their predictions. This creates a barrier for CSoC analysts, as they are unable to improve their decisions based on the model's predictions. One solution to this problem is to design explainable IDS (X-IDS). This survey reviews the state-of-the-art in explainable AI (XAI) for IDS, its current challenges, and discusses how these challenges span to the design of an X-IDS. In particular, we discuss black box and white box approaches comprehensively. We also present the tradeoff between these approaches in terms of their performance and ability to produce explanations. Furthermore, we propose a generic architecture that considers human-in-the-loop which can be used as a guideline when designing an X-IDS. Research recommendations are given from three critical viewpoints: the need to define explainability for IDS, the need to create explanations tailored to various stakeholders, and the need to design metrics to evaluate explanations.

The Farrington-Manning method is a common method for evaluating equivalence and non-inferiority of independent proportions. It is implemented in various software, in particular SAS$^\circledR$ PROC FREQ, and the R$^\circledR$ function farrington.manning(), which is part of the DescrTab2 package. The equations for the estimated proportions can create numerical issues in case both sample proportions equal 1, and neither of these packages will yield an acceptable solution in this special case. In this note we demonstrate a closed form solution for the situation in this and other extreme cases.

Free-space communications at optical wavelengths offers the potential for orders-of-magnitude improvement in data rates over conventional radio wavelengths, and this will be needed to meet the demand of future space-to-ground applications. Supporting this new paradigm necessitates a global network of optical ground stations. This paper describes the architecture and commissioning of the Western Australian Optical Ground Station, to be installed on the roof of the physics building at the University of Western Australia. This ground station will incorporate amplitude- and phase-stabilisation technology, previously demonstrated over horizontal free-space links, into the ground station's optical telescope. Trialling this advanced amplitude- and phase-stabilisation technology, the ground station will overcome turbulence-induced noise to establish stable, coherent free-space links between ground-to-air and ground-to-space. These links will enable significant advances in high-speed and quantum-secured communications; positioning, navigation, and timing; and fundamental physics., Comment: To be published in the Proceedings of the International Communications Satellite Systems Conference (ICSSC), 26th-29th September 2021, Arlington, Virginia, USA

We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the variational formulation of NLS and (ii) The recently developed method of reduced-order nonlinear solutions (RONS). First, we prove the surprising result that, although the two methods are seemingly quite different, they can be obtained from the real and imaginary parts of a single complex-valued master equation. Furthermore, for the NLS equation in a stationary frame, we show that the reduced Lagrangian method fails to predict the correct group velocity of the waves whereas RONS predicts the correct group velocity. Finally, for the modified NLS equation, where the reduced Lagrangian approach is inapplicable, the RONS reduced-order model accurately approximates the true solutions., Comment: Accepted for publication in Nonlinear Dynamics

Rocket engine combustors are prone to transverse instabilities that are characterized by large amplitude high frequency oscillations in the acoustic pressure and the heat release rate. We study the coupled interaction between the acoustic pressure and the CH* intensity oscillations in a 2D multi-element self-excited model rocket combustor during the transition from a stable state to thermoacoustic instability through intermittency. We show the emergence of synchronization between these oscillations from desynchronization through intermittent phase synchronization during the onset of thermoacoustic instability. We find substantial evidence that the intensities of the jet flames close to the end wall is higher than that observed near the center of the combustor as a result of its strong coupling to the local acoustic field. Using concepts from recurrence theory, we distinguish the type of synchronization between the acoustic pressure and the CH* intensity oscillations at the end wall and the center of the combustor during thermoacoustic instability. Analyzing the local CH* intensity oscillations, we observe that the longitudinally propagating jet flames experience substantial transverse displacement with flame merging effects during thermoacoustic instability. Furthermore, we differentiate the interaction of the jet flames with the shock wave during intermittency and thermoacoustic instability at both the end wall and the center of the combustor. We also discerned the change from stochastic to deterministic nature in the local CH* intensity oscillations during the transition to thermoacoustic instability. Our results demonstrate that only the first few transverse modes contribute to the generation of acoustic power from the reacting flow, in spite of the pressure oscillations featuring several harmonics.

Contrast resolution beyond the limits of conventional cone-beam CT (CBCT) systems is essential to high-quality imaging of the brain. We present a deep learning reconstruction method (dubbed DL-Recon) that integrates physically principled reconstruction models with DL-based image synthesis based on the statistical uncertainty in the synthesis image. A synthesis network was developed to generate a synthesized CBCT image (DL-Synthesis) from an uncorrected filtered back-projection (FBP) image. To improve generalizability (including accurate representation of lesions not seen in training), voxel-wise epistemic uncertainty of DL-Synthesis was computed using a Bayesian inference technique (Monte-Carlo dropout). In regions of high uncertainty, the DL-Recon method incorporates information from a physics-based reconstruction model and artifact-corrected projection data. Two forms of the DL-Recon method are proposed: (i) image-domain fusion of DL-Synthesis and FBP (DL-FBP) weighted by DL uncertainty; and (ii) a model-based iterative image reconstruction (MBIR) optimization using DL-Synthesis to compute a spatially varying regularization term based on DL uncertainty (DL-MBIR). The error in DL-Synthesis images was correlated with the uncertainty in the synthesis estimate. Compared to FBP and PWLS, the DL-Recon methods (both DL-FBP and DL-MBIR) showed ~50% reduction in noise (at matched spatial resolution) and ~40-70% improvement in image uniformity. Conventional DL-Synthesis alone exhibited ~10-60% under-estimation of lesion contrast and ~5-40% reduction in lesion segmentation accuracy (Dice coefficient) in simulated and real brain lesions, suggesting a lack of reliability / generalizability for structures unseen in the training data. DL-FBP and DL-MBIR improved the accuracy of reconstruction by directly incorporating information from the measurements in regions of high uncertainty., Comment: This work was presented at the 16th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Fully3D), July 19-23, 2021, Leuven, Belgium

Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced solutions depend nonlinearly on time varying parameters have thus far been derived in an ad hoc manner. Here, we introduce Reduced-order Nonlinear Solutions (RONS): a unified framework for deriving reduced-order models that depend nonlinearly on a set of time-dependent parameters. The set of all possible reduced-order solutions are viewed as a manifold immersed in the function space of the PDE. The parameters are evolved such that the instantaneous discrepancy between reduced dynamics and the full PDE dynamics is minimized. This results in a set of explicit ordinary differential equations on the tangent bundle of the manifold. In the special case of linear parameter dependence, our reduced equations coincide with the standard Galerkin projection. Furthermore, any number of conserved quantities of the PDE can readily be enforced in our framework. Since RONS does not assume an underlying variational formulation for the PDE, it is applicable to a broad class of problems. We demonstrate the efficacy of RONS on three examples: an advection-diffusion equation, the nonlinear Schrodinger equation and Euler's equation for ideal fluids.

High precision measurements of isospin $T=1/2$ decays in the neutron and nuclei provide strong model-independent constraints on extensions to the standard model of particle physics. A measurement of the $\beta$-asymmetry in $^{19}$Ne decay between the initial nuclear spin and the direction of the emitted positron is presented which establishes this decay as the most precisely characterized nuclear mirror and fixes the Fermi-to-Gamow-Teller mixing ratio to $\rho = 1.6014(+21/-28)_{sys}(8)_{stat}$. This is consistent with the previous, most precise measurement, produces a value of the CKM unitarity parameter $V_{ud}$ in agreement with the nuclear mirror, neutron and superallowed $\beta$-decay data sets, shows no evidence for second class currents, and can be effectively used with neutron decay data to place a limits on exotic tensor couplings., Comment: addressed typographical errors in Eq. (4) - (9) and in Table 1, made minor adjustments to input data for Ft_0 values for 19Ne and the neutron, and updated the analysis of the limits for left-handed tensor couplings