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The connection between galaxies and their host dark matter (DM) halos is critical to our understanding of cosmology, galaxy formation, and DM physics. To maximize the return of upcoming cosmological surveys, we need an accurate way to model this complex relationship. Many techniques have been developed to model this connection, from Halo Occupation Distribution (HOD) to empirical and semi-analytic models to hydrodynamic. Hydrodynamic simulations can incorporate more detailed astrophysical processes but are computationally expensive; HODs, on the other hand, are computationally cheap but have limited accuracy. In this work, we present NeHOD, a generative framework based on variational diffusion model and Transformer, for painting galaxies/subhalos on top of DM with an accuracy of hydrodynamic simulations but at a computational cost similar to HOD. By modeling galaxies/subhalos as point clouds, instead of binning or voxelization, we can resolve small spatial scales down to the resolution of the simulations. For each halo, NeHOD predicts the positions, velocities, masses, and concentrations of its central and satellite galaxies. We train NeHOD on the TNG-Warm DM suite of the DREAMS project, which consists of 1024 high-resolution zoom-in hydrodynamic simulations of Milky Way-mass halos with varying warm DM mass and astrophysical parameters. We show that our model captures the complex relationships between subhalo properties as a function of the simulation parameters, including the mass functions, stellar-halo mass relations, concentration-mass relations, and spatial clustering. Our method can be used for a large variety of downstream applications, from galaxy clustering to strong lensing studies., Comment: Submitted to ApJ; 30 + 6 pages; 11 + 4 figures; Comments welcomed

We present the first suite of cosmological hydrodynamical zoom-in simulations of isolated dwarf galaxies for a dark sector that consists of Cold Dark Matter and a strongly-dissipative sub-component. The simulations are implemented in GIZMO and include standard baryons following the FIRE-2 galaxy formation physics model. The dissipative dark matter is modeled as Atomic Dark Matter (aDM), which forms a dark hydrogen gas that cools in direct analogy to the Standard Model. Our suite includes seven different simulations of $\sim 10^{10} M_{\odot}$ systems that vary over the aDM microphysics and the dwarf's evolutionary history. We identify a region of aDM parameter space where the cooling rate is aggressive and the resulting halo density profile is universal. In this regime, the aDM gas cools rapidly at high redshifts and only a small fraction survives in the form of a central dark gas disk; the majority collapses centrally into collisionless dark "clumps", which are clusters of sub-resolution dark compact objects. These dark clumps rapidly equilibrate in the inner galaxy, resulting in an approximately isothermal distribution that can be modeled with a simple fitting function. Even when only a small fraction ($\sim 5\%$) of the total dark matter is strongly dissipative, the central densities of classical dwarf galaxies can be enhanced by over an order of magnitude, providing a sharp prediction for observations., Comment: 17 pages, 8 pages of appendices

Over the last few years, federated learning (FL) has emerged as a prominent method in machine learning, emphasizing privacy preservation by allowing multiple clients to collaboratively build a model while keeping their training data private. Despite this focus on privacy, FL models are susceptible to various attacks, including membership inference attacks (MIAs), posing a serious threat to data confidentiality. In a recent study, Rezaei \textit{et al.} revealed the existence of an accuracy-privacy trade-off in deep ensembles and proposed a few fusion strategies to overcome it. In this paper, we aim to explore the relationship between deep ensembles and FL. Specifically, we investigate whether confidence-based metrics derived from deep ensembles apply to FL and whether there is a trade-off between accuracy and privacy in FL with respect to MIA. Empirical investigations illustrate a lack of a non-monotonic correlation between the number of clients and the accuracy-privacy trade-off. By experimenting with different numbers of federated clients, datasets, and confidence-metric-based fusion strategies, we identify and analytically justify the clear existence of the accuracy-privacy trade-off.

We introduce the DREAMS project, an innovative approach to understanding the astrophysical implications of alternative dark matter models and their effects on galaxy formation and evolution. The DREAMS project will ultimately comprise thousands of cosmological hydrodynamic simulations that simultaneously vary over dark matter physics, astrophysics, and cosmology in modeling a range of systems -- from galaxy clusters to ultra-faint satellites. Such extensive simulation suites can provide adequate training sets for machine-learning-based analyses. This paper introduces two new cosmological hydrodynamical suites of Warm Dark Matter, each comprised of 1024 simulations generated using the Arepo code. One suite consists of uniform-box simulations covering a $(25~h^{-1}~{\rm M}_\odot)^3$ volume, while the other consists of Milky Way zoom-ins with sufficient resolution to capture the properties of classical satellites. For each simulation, the Warm Dark Matter particle mass is varied along with the initial density field and several parameters controlling the strength of baryonic feedback within the IllustrisTNG model. We provide two examples, separately utilizing emulators and Convolutional Neural Networks, to demonstrate how such simulation suites can be used to disentangle the effects of dark matter and baryonic physics on galactic properties. The DREAMS project can be extended further to include different dark matter models, galaxy formation physics, and astrophysical targets. In this way, it will provide an unparalleled opportunity to characterize uncertainties on predictions for small-scale observables, leading to robust predictions for testing the particle physics nature of dark matter on these scales., Comment: 28 pages, 8 figures, DREAMS website: https://www.dreams-project.org

A network-level small-signal model is developed for lossy microgrids, which considers coupled angle and voltage dynamics of inverter-based microgrids and uses a more general framework of droop controls in the inverter. It is shown that when relative resistances of the lines in the microgrid are reasonably consistent and differences of voltage angles across the lines are small at the operating point, the generalized droop controls can be designed to enforce decoupling between angle dynamics and voltage dynamics. Next, structural results for the asymptotic stability of small-signal angle and voltage dynamics are given for the case when generalized droop control achieves decoupling. Simulated transient responses of a modified IEEE 9-bus system are presented to validate the theoretical findings which show the effectiveness of generalized droop controls in independently shaping the settling times of the angle and voltage responses of the lossy microgrid system.

We study the impact of warm dark matter mass on the internal properties of individual galaxies using a large suite of 1,024 state-of-the-art cosmological hydrodynamic simulations from the DREAMS project. We take individual galaxies' properties from the simulations, which have different cosmologies, astrophysics, and warm dark matter masses, and train normalizing flows to learn the posterior of the parameters. We find that our models cannot infer the value of the warm dark matter mass, even when the values of the cosmological and astrophysical parameters are given explicitly. This result holds for galaxies with stellar mass larger than $2\times10^8 M_\odot/h$ at both low and high redshifts. We calculate the mutual information and find no significant dependence between the WDM mass and galaxy properties. On the other hand, our models can infer the value of $\Omega_{\rm m}$ with a $\sim10\%$ accuracy from the properties of individual galaxies while marginalizing astrophysics and warm dark matter masses., Comment: 13 pages, 8 figures

The membership inference attack (MIA) is a popular paradigm for compromising the privacy of a machine learning (ML) model. MIA exploits the natural inclination of ML models to overfit upon the training data. MIAs are trained to distinguish between training and testing prediction confidence to infer membership information. Federated Learning (FL) is a privacy-preserving ML paradigm that enables multiple clients to train a unified model without disclosing their private data. In this paper, we propose an enhanced Membership Inference Attack with the Batch-wise generated Attack Dataset (MIA-BAD), a modification to the MIA approach. We investigate that the MIA is more accurate when the attack dataset is generated batch-wise. This quantitatively decreases the attack dataset while qualitatively improving it. We show how training an ML model through FL, has some distinct advantages and investigate how the threat introduced with the proposed MIA-BAD approach can be mitigated with FL approaches. Finally, we demonstrate the qualitative effects of the proposed MIA-BAD methodology by conducting extensive experiments with various target datasets, variable numbers of federated clients, and training batch sizes., Comment: 6 pages, 5 figures, Accepted to be published in ICNC 23

The recently-launched James Webb Space Telescope (JWST) can resolve eV-scale emission lines arising from dark matter (DM) decay. We forecast the end-of-mission sensitivity to the decay of axions, a leading DM candidate, in the Milky Way using the blank-sky observations expected during standard operations. Searching for unassociated emission lines will constrain axions in the mass range $0.18$ eV to $2.6$ eV with axion-photon couplings $g_{a\gamma\gamma}\gtrsim 5.5 \times 10^{-12}$ GeV$^{-1}$. In particular, these results will constrain astrophobic QCD axions to masses $\lesssim$ 0.2 eV., Comment: 7 pages, 2 figures, 4 pages of Supplemental Material (6 figures)

Using cosmological hydrodynamical zoom-in simulations, we explore the properties of subhalos in Milky Way analogs that contain a sub-component of Atomic Dark Matter (ADM). ADM differs from Cold Dark Matter (CDM) due to the presence of self interactions that lead to energy dissipation and bound-state formation, analogous to Standard Model baryons. This model can arise in complex dark sectors that are natural and theoretically-motivated extensions to the Standard Model. The simulations used in this work were carried out using GIZMO and utilize the FIRE-2 galaxy formation physics in the Standard Model baryonic sector. For the parameter points we consider, the ADM gas cools efficiently, allowing it to collapse to the center of subhalos. This increases a subhalo's central density and affects its orbit, with more subhalos surviving small pericentric passages. The subset of subhalos that host visible satellite galaxies have cuspier density profiles and smaller stellar-half-mass radii relative to CDM. The entire population of dwarf galaxies produced in the ADM simulations is much more compact than those seen in CDM simulations, unable to reproduce the entire diversity of observed dwarf galaxy structures. Additionally, we also identify a population of highly compact subhalos that consist nearly entirely of ADM and form in the central region of the host, where they can leave distinctive imprints in the baryonic disk. This work presents the first detailed exploration of subhalo properties in a strongly dissipative dark matter scenario, providing intuition for how other regions of ADM parameter space, as well as other dark sector models, would impact galactic-scale observables., Comment: 18 pages, 10 figures, 8 pages of appendices

Dark sector theories naturally lead to multi-component scenarios for dark matter where a sub-component can dissipate energy through self-interactions, allowing it to efficiently cool inside galaxies. We present the first cosmological hydrodynamical simulations of Milky Way analogues where the majority of dark matter is collisionless Cold Dark Matter (CDM), but a sub-component (6%) is strongly dissipative minimal Atomic Dark Matter (ADM). The simulations, implemented in GIZMO and utilizing FIRE-2 galaxy formation physics to model the standard baryonic sector, demonstrate that the addition of even a small fraction of dissipative dark matter can significantly impact galactic evolution despite being consistent with current cosmological constraints. We show that ADM gas with roughly Standard-Model-like masses and couplings can cool to form a rotating "dark disk" with angular momentum closely aligned with the visible stellar disk. The morphology of the disk depends sensitively on the parameters of the ADM model, which affect the cooling rates in the dark sector. The majority of the ADM gas gravitationally collapses into dark "clumps" (regions of black hole or mirror star formation), which form a prominent bulge and a rotating thick disk in the central galaxy. These clumps form early and quickly sink to the inner ~kpc of the galaxy, affecting the galaxy's star-formation history and present-day baryonic and CDM distributions., Comment: 9 pages, 4 figures, 12 pages of appendices and supplementary figures

With the increase of uncertain and intermittent renewable energy supply on the grid, the power system has become more vulnerable to instability. In this paper, we develop a demand response strategy to improve power system small-signal stability. We pose the problem as an optimization problem wherein the total demand-responsive load is held constant at each time instance but shifted between different buses to improve small-signal stability, which is measured by small-signal stability metrics that are functions of subsets of the system's eigenvalues, such as the smallest damping ratio. To solve the problem, we use iterative linear programming and generalized eigenvalue sensitivities. We demonstrate the approach via a case study that uses the IEEE 14-bus system. Our results show that shifting the load between buses, can improve a small-signal stability margin. We explore the use of models of different fidelity and find that it is important to include models of the automatic voltage regulators and power system stabilizers. In addition, we show that load shifting can achieve similar improvements to generation shifting and better improvement than simply tuning power system stabilizers.

We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods, hypergraph cut algorithms, and power systems., Comment: 43 pages, 5 figures

A graph-theoretic analysis of the steady-state behavior of an open Jackson queueing network is developed. In particular, a number of queueing-network performance metrics are shown to exhibit a spatial dependence on local drivers (e.g. increments to local exogenous arrival rates), wherein the impacts fall off across graph cutsets away from a target queue. This graph-theoretic analysis is also used to motivate a structure-preserving model reduction algorithm, and an algorithm that exactly matches performance statistics of the original model is proposed. The graph-theoretic results and model-reduction method are evaluated via simulations of an example queueing-network model., Comment: 8 pages, 11 figures, this paper submitted to ACC2023

A notion of disturbance propagation stability is defined for dynamical network processes, in terms of decrescence of an input-output energy metric along cutsets away from the disturbance source. A characterization of the disturbance propagation notion is developed for a canonical model for synchronization of linearly-coupled homogeneous subsystems. Specifically, propagation stability is equivalenced with the frequency response of a certain local closed-loop model, which is defined from the subsystem model and local network connections, being sub-unity gain. For the case where the subsystem is single-input single-output (SISO), a further simplification in terms of the subsystem's open loop Nyquist plot is obtained. An extension of the disturbance propagation stability concept toward imperviousness of subnetworks to disturbances is briefly developed, and an example focused on networks with planar subsystems is considered.

A graph-theoretic analysis is undertaken for a compendium of input-output (transfer) metrics of a standard discrete-time linear synchronization model, including lp gains, frequency responses, frequency-band energy, and Markov parameters. We show that these transfer metrics exhibit a spatial degradation, such that they are monotonically nonincreasing along vertex cutsets away from an exogenous input. We use this spatial analysis to characterize signal-to-noise ratios (SNRs) in diffusive networks driven by process noise, and to develop a notion of propagation stability for dynamical networks. Finally, the formal results are illustrated through an example.

Terse representation of high-dimensional weather scene data is explored, in support of strategic air traffic flow management objectives. Specifically, we consider whether aviation-relevant weather scenes are compressible, in the sense that each scene admits a possibly-different sparse representation in a basis of interest. Here, compression of weather scenes extracted from METAR data (including temperature, flight categories, and visibility profiles for the contiguous United States) is examined, for the graph-spectral basis. The scenes are found to be compressible, with 75-95% of the scene content captured using 0.5-4% of the basis vectors. Further, the dominant basis vectors for each scene are seen to identify time-varying spatial characteristics of the weather, and reconstruction from the compressed representation is demonstrated. Finally, potential uses of the compressive representations in strategic TFM design are briefly scoped.

Motivated by security needs in unmanned aerial system (UAS) operations, an algorithm for identifying airspace intruders (e.g., birds vs. drones) is developed. The algorithm is structured to use sensed intruder velocity data from Internet-of-Things platforms together with limited knowledge of physical models. The identification problem is posed as a statistical hypothesis testing or detection problem, wherein inertial feedback-controlled objects subject to stochastic actuation must be distinguished by speed data. The maximum a posteriori probability detector is obtained, and then is simplified to an explicit computation based on two points in the sample autocorrelation of the data. The simplified form allows computationally-friendly implementation of the algorithm, and simplified learning from archived data. Also, the total probability of error of the detector is computed and characterized. Simulations based on synthesized data are presented to illustrate and supplement the formal analyses.

Opinion-evolution and spread processes on networks (e.g., infectious disease spread, opinion formation in social networks) are not only high dimensional but also volatile and multiscale in nature. In this study, we explore whether snapshot data from these processes can admit terse representations. Specifically, using three case studies, we explore whether the data are compressible in the Laplacian-eigenvector basis, in the sense that each snapshot can be approximated well using a (possibly different) small set of basis vectors. The first case study is concerned with a linear consensus model that is subject to a stochastic input at an unknown location; both empirical and formal analyses are used to characterize compressibility. Second, compressibility of state snapshots for a stochastic voter model is assessed via an empirical study. Finally, compressibility is studied for state-level daily COVID-19 positivity-rate data. The three case studies indicate that state snapshots from opinion-evolution and spread processes allow terse representations, which nevertheless capture their rich propagative dynamics., Comment: Submitted to the 2021 IEEE Conference on Decision and Control

The design of feedback control systems to block observability in a network synchronization model, i.e. to make the dynamics unobservable from measurements at a subset of the network's nodes, is studied. First, a general design algorithm is presented for blocking observability at any specified group of $m$ nodes, by applying state feedback controls at $m+2$ specified actuation nodes. The algorithm is based on a method for eigenstructure assignment, which allows surgical modification of particular eigenvectors to block observability while preserving the remaining open-loop eigenstructure. Next, the topological structure of the network is exploited to reduce the number of controllers required for blocking observability; the result is based on blocking observability on the nodes associated with a vertex-cutset separating the actuation and measurement locations. Also, the design is modified to encompass regional feedback controls, which only use data from a subset of accessible nodes. The regional feedback design does not maintain the open-loop eigenstructure, but can be guaranteed to preserve stability via a time-scale argument. The results are illustrated with numerical examples.

Queueing-network models are developed for enhanced and next-generation 911 (E911 and NG911) systems, which capture both their cyber-components (communications, data-processing) and physical-world-elements (call takers, vehicle dispatch). The models encompass both the call-processing and dispatch functions of 911, and can represent the interdependencies between multiple PSAPs enabled by NG911. An instantiation of the model for a future NG911 system for Charlotte, North Carolina, is developed and used to assess performance metrics. Representation of cyber-threats (e.g. Distributed Denial-of-Service attacks) within the queueing-network model is undertaken. Based on these representations, the model is used for analysis of holistic threat impacts, as a step toward risk and vulnerability assessment for future emergency response systems.

Assignability of all eigenvalues and a subset of key eigenvectors/generalized eigenvectors of a linear time-invariant system via state feedback is considered. We clarify that, if the key eigenvectors/generalized eigenvectors and their associated eigenvalues satisfy the classical conditions for full eigenstructure assignment, the remaining eigenvalues can be assigned at will.

Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design-time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. Next, we consider the problem of attacking (i.e., removing) the placed sensors under a sensor attack budget constraint in order to maximize the trace of the steady-state error covariance of the resulting Kalman filter. Using the insights obtained for the sensor placement problem, we provide an optimal strategy (computed in polynomial-time) to attack the placed sensors. Finally, we consider the scenario where a system designer places the sensors under a sensor placement budget constraint, and an adversary then attacks the placed sensors subject to a sensor attack budget constraint. The resilient sensor placement problem is to find a sensor placement strategy to minimize the trace of the steady-state error covariance of the Kalman filter corresponding to the sensors that survive the attack. We show that this problem is NP-hard, and provide a pseudo-polynomial-time algorithm to solve it.

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem, and show specifically that greedy algorithms can perform arbitrarily poorly., Comment: arXiv admin note: text overlap with arXiv:1711.01920

This paper considers maximum-a-posteriori (MAP) and linear discriminant based MAP detectors to detect changes in the mean and covariance of a stochastic input, driving specific network nodes, using noisy measurements from sensors non-collocated with the input nodes. We explicitly characterize both detectors' performance in terms of the network edge weights and input and sensor nodes' location. In the asymptotic measurement regime, when the input and measurement noise are jointly Gaussian, we show that the detectors' performance can be studied using the input to output gain of the system's transfer function matrix. Using this result, we obtain conditions for which the detection performance associated with the sensors on a given network cut is better (or worse) than that of the sensors associated with the subnetwork induced by the cut and not containing the input nodes. Our results also provide structural insights into the sensor placement from a detection-theoretic viewpoint. We validate our theoretical findings via multiple numerical examples., Comment: 14 pages; 6 figures; submitted to Automatica