Testing Conditional Independence of Discrete Distributions

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with probability at least $2/3$, between the case that $X$ and $Y$ are conditionally independent given $Z$ from the case that $(X, Y, Z)$ is $\epsilon$-far, in $\ell_1$-distance, from every distribution that has this property. Conditional independence is a concept of central importance in probability and statistics with a range of applications in various scientific domains. As such, the statistical task of testing conditional independence has been extensively studied in various forms within the statistics and econometrics communities for nearly a century. Perhaps surprisingly, this problem has not been previously considered in the framework of distribution property testing and in particular no tester with sublinear sample complexity is known, even for the important special case that the domains of $X$ and $Y$ are binary. The main algorithmic result of this work is the first conditional independence tester with {\em sublinear} sample complexity for discrete distributions over $[\ell_1]\times[\ell_2] \times [n]$. To complement our upper bounds, we prove information-theoretic lower bounds establishing that the sample complexity of our algorithm is optimal, up to constant factors, for a number of settings. Specifically, for the prototypical setting when $\ell_1, \ell_2 = O(1)$, we show that the sample complexity of testing conditional independence (upper bound and matching lower bound) is \[ \Theta\left({\max\left(n^{1/2}/\epsilon^2,\min\left(n^{7/8}/\epsilon,n^{6/7}/\epsilon^{8/7}\right)\right)}\right)\,. \

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The oblique firehose instability in a bi-kappa magnetized plasma

In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfv\'en) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in the solar wind, some solutions of the dispersion equation, corresponding to the unstable mode, are presented. In order to implement the dispersion solver, several new mathematical properties of the special functions occurring in a kappa plasma are derived and included. The results presented here suggest that the superthermal characteristic of the distribution functions leads to reductions to both the maximum growth rate of the instability and of the spectral range of its occurrence

Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: from fluid to kinetic modeling

The nonlinear evolution of collisionless plasmas is typically a multi-scale process where the energy is injected at large, fluid scales and dissipated at small, kinetic scales. Accurately modelling the global evolution requires to take into account the main micro-scale physical processes of interest. This is why comparison of different plasma models is today an imperative task aiming at understanding cross-scale processes in plasmas. We report here the first comparative study of the evolution of a magnetized shear flow, through a variety of different plasma models by using magnetohydrodynamic, Hall-MHD, two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effects are discussed to emphasize the need for kinetic equilibriums to study the dynamics of collisionless plasmas in non trivial configurations. Discrepancies between models are studied both in the linear and in the nonlinear regime of the magnetized Kelvin-Helmholtz instability, to highlight the effects of small scale processes on the nonlinear evolution of collisionless plasmas. We illustrate how the evolution of a magnetized shear flow depends on the relative orientation of the fluid vorticity with respect to the magnetic field direction during the linear evolution when kinetic effects are taken into account. Even if we found that small scale processes differ between the different models, we show that the feedback from small, kinetic scales to large, fluid scales is negligable in the nonlinear regime. This study show that the kinetic modeling validates the use of a fluid approach at large scales, which encourages the development and use of fluid codes to study the nonlinear evolution of magnetized fluid flows, even in the colisionless regime

Power and spectral index anisotropy of the entire inertial range of turbulence in the fast solar wind

We measure the power and spectral index anisotropy of high speed solar wind turbulence from scales larger than the outer scale down to the ion gyroscale, thus covering the entire inertial range. We show that the power and spectral indices at the outer scale of turbulence are approximately isotropic. The turbulent cascade causes the power anisotropy at smaller scales manifested by anisotropic scalings of the spectrum: close to k^{-5/3} across and k^{-2} along the local magnetic field, consistent with a critically balanced Alfvenic turbulence. By using data at different radial distances from the Sun, we show that the width of the inertial range does not change with heliocentric distance and explain this by calculating the radial dependence of the ratio of the outer scale to the ion gyroscale. At the smallest scales of the inertial range, close to the ion gyroscale, we find an enhancement of power parallel to the magnetic field direction coincident with a decrease in the perpendicular power. This is most likely related to energy injection by ion kinetic modes such as the firehose instability and also marks the beginning of the dissipation range of solar wind turbulence.Comment: 5 pages, 4 figures, 1 table, submitted to MNRAS letter

How Cosmic Web Environment Affects Galaxy Quenching Across Cosmic Time

We investigate how cosmic web structures affect galaxy quenching in the IllustrisTNG (TNG-100) cosmological simulations by reconstructing the cosmic web in each snapshot using the DisPerSE framework. We measure the distance from each galaxy with stellar mass log(M*/Msun)>=8 to the nearest node (dnode) and the nearest filament spine (dfil) and study the dependence of both median specific star formation rate () and median gas fraction () on these distances. We find that of galaxies is only dependent on cosmic web environment at z<2, with the dependence increasing with time. At z<=0.5, 8<=log(M*/Msun)<9 galaxies are quenched at dnode<1 Mpc, and significantly star formation-suppressed at dfil<1 Mpc, trends which are driven mostly by satellite galaxies. At z of log(M*/Msun)=10 galaxies actually experience an upturn in at dnode<0.2 Mpc (this is caused by both satellites and centrals). Much of this cosmic web-dependence of star formation activity can be explained by the evolution in . Our results suggest that in the past ~10 Gyr, low-mass satellites are quenched by rapid gas stripping in dense environments near nodes and gradual gas starvation in intermediate-density environments near filaments, while at earlier times cosmic web structures efficiently channeled cold gas into most galaxies. State-of-the-art ongoing spectroscopic surveys such as SDSS and DESI, as well as those planned with JWST and Roman are required to test our predictions against observations.Comment: 5 Figures, 15 pages, submitted to ApJ Letter

Nonlinear theory of mirror instability near threshold

An asymptotic model based on a reductive perturbative expansion of the drift kinetic and the Maxwell equations is used to demonstrate that, near the instability threshold, the nonlinear dynamics of mirror modes in a magnetized plasma with anisotropic ion temperatures involves a subcritical bifurcation,leading to the formation of small-scale structures with amplitudes comparable with the ambient magnetic field

Filaments of The Slime Mold Cosmic Web And How They Affect Galaxy Evolution

We present a novel method for identifying cosmic web filaments using the IllustrisTNG (TNG100) cosmological simulations and investigate the impact of filaments on galaxies. We compare the use of cosmic density field estimates from the Delaunay Tessellation Field Estimator (DTFE) and the Monte Carlo Physarum Machine (MCPM), which is inspired by the slime mold organism, in the DisPerSE structure identification framework. The MCPM-based reconstruction identifies filaments with higher fidelity, finding more low-prominence/diffuse filaments and better tracing the true underlying matter distribution than the DTFE-based reconstruction. Using our new filament catalogs, we find that most galaxies are located within 1.5-2.5 Mpc of a filamentary spine, with little change in the median specific star formation rate and the median galactic gas fraction with distance to the nearest filament. Instead, we introduce the filament line density, {\Sigma}fil(MCPM), as the total MCPM overdensity per unit length of a local filament segment, and find that this parameter is a superior predictor of galactic gas supply and quenching. Our results indicate that most galaxies are quenched and gas-poor near high-line density filaments at z10.5 galaxies is mainly driven by mass, while lower-mass galaxies are significantly affected by the filament line density. In high-line density filaments, satellites are strongly quenched, whereas centrals have reduced star formation, but not gas fraction, at z<=0.5. We discuss the prospect of applying our new filament identification method to galaxy surveys with SDSS, DESI, Subaru PFS, etc. to elucidate the effect of large-scale structure on galaxy formation.Comment: Submitted to ApJ, comments welcome. Data available at https://github.com/farhantasy/CosmicWeb-Galaxies

A detailed analysis of a multi-agent diverse team

In an open system we can have many different kinds of agents. However, it is a challenge to decide which agents to pick when forming multi-agent teams. In some scenarios, agents coordinate by voting continuously. When forming such teams, should we focus on the diversity of the team or on the strength of each member? Can a team of diverse (and weak) agents outperform a uniform team of strong agents? We propose a new model to address these questions. Our key contributions include: (i) we show that a diverse team can overcome a uniform team and we give the necessary conditions for it to happen; (ii) we present optimal voting rules for a diverse team; (iii) we perform synthetic experiments that demonstrate that both diversity and strength contribute to the performance of a team; (iv) we show experiments that demonstrate the usefulness of our model in one of the most difficult challenges for Artificial Intelligence: Computer Go