Miracle-dz/UniFAR-FTUs huggingface dataset:
Minimax Defense against Gradient-based Adversarial Attacks

State-of-the-art adversarial attacks are aimed at neural network classifiers. By default, neural networks use gradient descent to minimize their loss function. The gradient of a classifier's loss function is used by gradient-based adversarial attacks to generate adversarially perturbed images. We pose the question whether another type of optimization could give neural network classifiers an edge. Here, we introduce a novel approach that uses minimax optimization to foil gradient-based adversarial attacks. Our minimax classifier is the discriminator of a generative adversarial network (GAN) that plays a minimax game with the GAN generator. In addition, our GAN generator projects all points onto a manifold that is different from the original manifold since the original manifold might be the cause of adversarial attacks. To measure the performance of our minimax defense, we use adversarial attacks - Carlini Wagner (CW), DeepFool, Fast Gradient Sign Method (FGSM) - on three datasets: MNIST, CIFAR-10 and German Traffic Sign (TRAFFIC). Against CW attacks, our minimax defense achieves 98.07% (MNIST-default 98.93%), 73.90% (CIFAR-10-default 83.14%) and 94.54% (TRAFFIC-default 96.97%). Against DeepFool attacks, our minimax defense achieves 98.87% (MNIST), 76.61% (CIFAR-10) and 94.57% (TRAFFIC). Against FGSM attacks, we achieve 97.01% (MNIST), 76.79% (CIFAR-10) and 81.41% (TRAFFIC). Our Minimax adversarial approach presents a significant shift in defense strategy for neural network classifiers.
Reinhardt cardinals and non-definability

Work in $\mathsf{ZF}$ or $\mathsf{ZF}_2$ (second order $\mathsf{ZF}$), as appropriate. Recall that a Reinhardt cardinal is the critical point of a (non-trivial) elementary embedding $j:V\rightarrow V$. Beyond these, one has super-Reinhardt, total Reinhardt and Berkeley cardinals. We prove the following results. Let $X$ be a set and $A$ a class. Then (i) if there is a Reinhardt cardinal then $V\neq\mathrm{HOD}(X)$, and (ii) if $V$ is total Reinhardt or there is a Berkeley cardinal then $V\neq\mathrm{HOD}_A(X)$. Let $\delta$ be a limit ordinal and $j:V_\delta\to V_\delta$ be $\Sigma_1$-elementary. Then (i) $j$ is not definable from parameters over $V_\delta$, and (ii) there is $n<\omega$ such that the $n^{\mathrm{th}}$ iterate $j^n=j(j(\ldots (j))):V_\delta\to V_\delta$ is fully elementary; in fact, $j^n:(V_\delta,A)\to(V_\delta,j^n(A))$ is fully elementary for all $A\subseteq V_\delta$. Let $\delta$ be any ordinal and $j:V_{\delta+1}\to V_{\delta+1}$ be fully elementary. Then $j$ is not definable over $V_{\delta+1}$ from parameters in $V_\delta$. Suppose $V=L(V_\delta)$ and $\mathrm{cof}(\delta)>\omega$. Then there is no $\Sigma_1$-elementary $j:V_\delta\to V_\delta$. Let $G$ be $(V,\mathbb{P})$-generic for some $\mathbb{P}\in V$. Then (i) if $V[G]$ has a super-Reinhardt cardinal, then $V$ has a super-Reinhardt cardinal; (ii) if $\mathbb{P}\in V_\delta$ and $V[G]\models$``$V_\delta^{V[G]}$ is total Reinhardt'' then $V\models$``$V_\delta$ is total Reinhardt''; and (iii) if $V[G]$ has a set of ordinals which is not in $V$, then $V[G]$ has no elementary $j:V[G]\to M\subseteq V$. We also develop the theory of ultrapowers by extenders under $\mathsf{ZF}$, and show that if there is a proper class of L\"owenheim-Skolem cardinals, then being the critical point of an elementary $j:V\to M$ (with $M$ transitive) is first-order.
Optimal synchronization of partial deterministic finite automata

We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used. We compare our results with the ones obtained by the first author for exact synchronization, which is another version of synchronization studied in the literature, and draw some theoretical conclusions.
Study of the Cosmic Rays and Interstellar Medium in Local H i Clouds Using Fermi-LAT Gamma-Ray Observations

An accurate estimate of the interstellar gas density distribution is crucial to understanding the interstellar medium (ISM) and Galactic cosmic rays (CRs). To comprehend the ISM and CRs in a local environment, a study of the diffuse γ-ray emission in a midlatitude region of the third quadrant was performed. The γ-ray data in the 0.1–25.6 GeV energy range of the Fermi Large Area Telescope (LAT) and other interstellar gas tracers such as the HI4PI survey data and the Planck dust thermal emission model were used, and the northern and southern regions were analyzed separately. The variation of the dust emission with the total neutral gas column density was studied in high dust temperature areas, and the / ratio was calibrated using γ-ray data under the assumption of a uniform CR intensity in the studied regions. The measured integrated γ-ray emissivities above 100 MeV are and in the northern and southern regions, respectively, supporting the existence of a uniform CR intensity in the vicinity of the solar system. While most of the gas can be interpreted to be with a spin temperature of or higher, an area dominated by optically thick with was identified.
Polarization imaging of M 87 jets by general relativistic radiative transfer calculation based on GRMHD simulations

The spectacular images of the M 87 black hole taken by the Event Horizon Telescope (EHT) have opened a new era of black hole research. One of the next issues is to take polarization images around the central black hole (BH). Since radio emission is produced by synchrotron process, polarization properties should vividly reflect the magnetic field structures at the jet base and thus provide good information regarding the magnetic mechanism of jet formation. With this kept in mind we perform general relativistic (GR) radiative transfer calculations of polarized light based on the GR magnetohydrodynamic (MHD) simulation data of accretion flow and outflow in M 87, to obtain their linear and circular polarization images in the BH horizon-scale. We found that the linear polarization components originating from the jet base and inner accretion flow should experience Faraday rotation and depolarization when passing through magnetized plasmas around the BH, thus sensitively depending on the BH spin. Through the comparison with total intensity image at $1.3\:$mm by EHT and the polarization degree and the rotation measure (RM) measured at $1.3\:$mm with the Submillimeter Array, the model with the spin parameter of $a=0.9\, M_{\,\mathrm{BH}}$ (with $M_{\,\mathrm{BH}}$ being the BH mass) is favored over other models with $a = 0.5\, M_{\,\mathrm{BH}}$ or $0.99\, M_{\,\mathrm{BH}}$, though we need further systematic studies for confirmation. We also find in low-temperature models a clear ring-like image in the circular polarization map, which arises because of Faraday conversion of the linearly polarized synchrotron emission and is thus indicative of magnetic field direction. This occurs only when the emission region is threaded with well-ordered magnetic fields and hence no clear images are expected in high-temperature disk models, in which disk emission is appreciable. We will be able to elucidate the field configuration through the comparison between the simulated polarization images and future polarimetry with EHT and other VLBI observations.
Asymptotics of the principal eigenvalue for a linear time-periodic parabolic operator II: Small diffusion

We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as the diffusion coefficients tend to zero, are established for non-degenerate and degenerate spatial-temporally varying environments. A new finding is the dependence of these asymptotic behaviors on the periodic solutions of a specific ordinary differential equation induced by the drift. The proofs are based upon delicate constructions of super/sub-solutions and the applications of comparison principles.
Design-Based Ratio Estimators for Clustered, Blocked RCTs

This article develops design-based ratio estimators for clustered, blocked RCTs using the building blocks of experiments. We consider finite population regression estimators, allowing for weights and covariates. We prove consistency and asymptotic normality results and discuss simple variance estimators that share features with cluster-robust standard error (CRSE) estimators. Simulations show that with few clusters, the design-based estimator yields nominal rejection rates, while the standard CRSE estimator over-rejects. The key reason is that the randomization mechanism yields separate degrees of freedom adjustments for the treatment and control variances, rather than a single adjustment as for the CRSE estimator.
Birational geometry of the intermediate Jacobian fibration of a cubic fourfold

We show that the intermediate Jacobian fibration associated to any smooth cubic fourfold $X$ admits a hyper-K\"ahler compactification $J(X)$ with a regular Lagrangian fibration $J \to \mathbb P^5$. This builds upon arXiv:1602.05534, where the result is proved for general $X$, as well as on the degeneration techniques on arXiv:1704.02731 and techniques from the minimal model program. We then study some aspects of the birational geometry of $J(X)$: for very general $X$ we compute the movable and nef cones of $J(X)$, showing that $J(X)$ is not birational to the twisted version of the intermediate Jacobian fibration arXiv:1611.06679, nor to an OG$10$-type moduli space of objects in the Kuznetsov component of $X$; for any smooth $X$ we show, using normal functions, that the Mordell-Weil group $MW(\pi)$ of the abelian fibration $\pi: J \to \mathbb P^5$ is isomorphic to the integral degree $4$ primitive algebraic cohomology of $X$, i.e., $MW(\pi) = H^{2,2}(X, \mathbb Z)_0$.
Finite Time Analysis of Linear Two-timescale Stochastic Approximation with Markovian Noise

Linear two-timescale stochastic approximation (SA) scheme is an important class of algorithms which has become popular in reinforcement learning (RL), particularly for the policy evaluation problem. Recently, a number of works have been devoted to establishing the finite time analysis of the scheme, especially under the Markovian (non-i.i.d.) noise settings that are ubiquitous in practice. In this paper, we provide a finite-time analysis for linear two timescale SA. Our bounds show that there is no discrepancy in the convergence rate between Markovian and martingale noise, only the constants are affected by the mixing time of the Markov chain. With an appropriate step size schedule, the transient term in the expected error bound is $o(1/k^c)$ and the steady-state term is ${\cal O}(1/k)$, where $c>1$ and $k$ is the iteration number. Furthermore, we present an asymptotic expansion of the expected error with a matching lower bound of $\Omega(1/k)$. A simple numerical experiment is presented to support our theory.
Mesoscopic modeling of heptane: A surface tension calculation

Accurate and efficient flow models for hydrocarbons are important in the development of enhanced geotechnical engineering for energy source recovery and carbon capture & storage in low-porosity, low-permeability rock formations. This work reports an atomistically-validated, mesoscopic model for heptane based on a many-body dissipative particle dynamics (mDPD) method. In this model, each heptane molecule is coarse-grained in one mDPD bead and the mDPD model parameters are calibrated with a rigorous approach using reference data, including experimental measurements and/or molecular dynamics (MD) simulations. Results show that this mDPD model accurately predicts the bulk pressure-density relation of heptane and surface tension. Notice that our approach can be used to calibrate the mDPD model for other hydrocarbons as well, though heptane is chosen as a representative source fluid for its abundance in source rocks. Further, our timing test indicates that the mDPD model is three orders of magnitude faster than its MD counterpart for simulations of bulk heptane in equivalent volumes. Overall, this work serves as a key prerequisite for the development of accurate and efficient mesoscale models for the flow of hydrocarbons confined in mesoporous rock formations.
Updated parameter estimates for GW190425 using astrophysical arguments and implications for the electromagnetic counterpart

The progenitor system of the compact binary merger GW190425 had a total mass of $3.4^{+0.3}_{-0.1}$ M⊙ (90th-percentile confidence region) as measured from its gravitational wave signal. This mass is significantly different from the Milky Way (MW) population of binary neutron stars (BNSs) that are expected to merge in a Hubble time and from that of the first BNS merger, GW170817. Here, we explore the expected electromagnetic (EM) signatures of such a system. We make several astrophysically motivated assumptions to further constrain the parameters of GW190425. By simply assuming that both components were NSs, we reduce the possible component masses significantly, finding $m_{1}=1.85^{+0.27}_{-0.19}$ M⊙ and $m_{2}=1.47^{+0.16}_{-0.18}$ M⊙. However, if the GW190425 progenitor system was an NS–black hole (BH) merger, we find best-fitting parameters $m_{1}=2.19^{+0.21}_{-0.17}$ M⊙ and $m_{2}=1.26^{+0.10}_{-0.08}$ M⊙. For a well-motivated BNS system where the lighter NS has a mass similar to the mass of non-recycled NSs in MW BNS systems, we find $m_{1}=2.03^{+0.15}_{-0.14}$ M⊙ and m2 = 1.35 ± 0.09 M⊙, corresponding to only 7 per cent mass uncertainties. For all scenarios, we expect a prompt collapse of the resulting remnant to a BH. Examining detailed models with component masses similar to our best-fitting results, we find the EM counterpart to GW190425 is expected to be significantly redder and fainter than that of GW170817. We find that almost all reported search observations were too shallow to detect the expected counterpart to GW190425. If the LIGO–Virgo Collaboration promptly provides the chirp mass, the astronomical community can adapt their observations to improve the likelihood of detecting a counterpart for similarly ‘high-mass’ BNS systems.
All-in-one robust estimator of the Gaussian mean

The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time which is at most polynomial in dimension, sample size and the logarithm of the inverse of the contamination rate. Second, it is equivariant by translations, uniform scaling and orthogonal transformations. Third, it has a high breakdown point equal to $0.5$, and a nearly-minimax-rate-breakdown point approximately equal to $0.28$. Fourth, it is minimax rate optimal, up to a logarithmic factor, when data consists of independent observations corrupted by adversarially chosen outliers. Fifth, it is asymptotically efficient when the rate of contamination tends to zero. The estimator is obtained by an iterative reweighting approach. Each sample point is assigned a weight that is iteratively updated by solving a convex optimization problem. We also establish a dimension-free non-asymptotic risk bound for the expected error of the proposed estimator. It is the first result of this kind in the literature and involves only the effective rank of the covariance matrix. Finally, we show that the obtained results can be extended to sub-Gaussian distributions, as well as to the cases of unknown rate of contamination or unknown covariance matrix.
On the inference of applying Gaussian process modeling to a deterministic function

The Gaussian process modeling is a standard tool for building emulators for computer experiments, which is usually a deterministic function, for example, solution to a partial differential equations system. In this work, we investigate applying Gaussian process models to a deterministic function from prediction and uncertainty quantification perspectives. While the upper bounds and optimal convergence rates of prediction in Gaussian process modeling have been extensively studied in the literature, a thorough exploration of the convergence rate and theoretical study of uncertainty quantification is lacking. We prove that, if one uses maximum likelihood estimation to estimate the variance, under different choices of nugget parameters, the predictor is not optimal and/or the confidence interval is not reliable. In particular, lower bounds of the predictor under different choices of nugget parameters are obtained. The results suggest that, if one applies Gaussian process models to a deterministic function, the reliability of the confidence interval and the optimality of predictors cannot be achieved at the same time.
Galaxy mergers in eagle do not induce a significant amount of black hole growth yet do increase the rate of luminous AGN

We investigate the connection between galaxy–galaxy mergers and enhanced black hole (BH) growth using the cosmological hydrodynamical eagle simulation. We do this via three methods of analysis, investigating: the merger fraction of AGN, the AGN fraction of merging systems, and the AGN fraction of galaxies with close companions. In each case, we find an increased abundance of AGN within merging systems relative to control samples of inactive or isolated galaxies (by up to a factor of ≈3 depending on the analysis method used), confirming that mergers are enhancing BH accretion rates for at least a subset of the galaxy population. The greatest excess of AGN triggered via a merger are found in lower mass (M* ∼ 1010 M⊙) gas rich (fgas > 0.2) central galaxies with lower mass BHs (MBH ∼ 107 M⊙) at lower redshifts (z < 1). We find no enhancement of AGN triggered via mergers in more massive galaxies (M* ≳ 1011 M⊙). The enhancement of AGN is not uniform throughout the phases of a merger, and instead peaks within the early remnants of merging systems (typically lagging ≈300 Myr post-coalescence of the two galaxies at z = 0.5). We argue that neither major ($M_{\mathrm{*,1}} / M_{\mathrm{*,2}} \ge \frac{1}{4}$) nor minor mergers ($\frac{1}{10} \lt M_{\mathrm{*,1}} / M_{\mathrm{*,2}} \lt \frac{1}{4}$) are statistically relevant for enhancing BH masses globally. Whilst at all redshifts the galaxies experiencing a merger have accretion rates that are on average 2–3 times that of isolated galaxies, the majority of mass that is accreted on to BHs occurs outside the periods of a merger. We compute that on average no more than 15 per cent of a BHs final day mass comes from the enhanced accretion rates triggered via a merger.
Coalescing Eigenvalues and Crossing Eigencurves of 1-Parameter Matrix Flows

We investigate the eigenvalue curves of 1-parameter hermitean and general complex or real matrix flows $A(t)$ in light of their geometry and the uniform decomposability of $A(t)$ for all parameters $t$. The often misquoted and misapplied results by Hund and von Neumann and by Wigner for eigencurve crossings from the late 1920s are clarified for hermitean matrix flows $A(t) = (A(t))^*$. A conjecture on extending these results to general non-normal or non-hermitean 1-parameter matrix flows is formulated and investigated. An algorithm to compute the block dimensions of uniformly decomposable hermitean matrix flows is described and tested. The algorithm uses the ZNN method to compute the time-varying matrix eigenvalue curves of $A(t)$ for $t_o \leq t\leq t_f$. Similar efforts for general complex matrix flows are described. This extension leads to many new and open problems. Specifically, we point to the difficult relationship between the geometry of eigencurves for general complex matrix flows $A(t)$ and a general flow's decomposability into blockdiagonal form via one fixed unitary or general matrix similarity for all parameters $t$.
Locating the source field lines of Jovian decametric radio emissions

Decametric (DAM) radio emissions are one of the main windows through which one can reveal and understand the Jovian magnetospheric dynamics and its interaction with the moons. DAMs are generated by energetic electrons through cyclotron‐maser instability. For Io (the most active moon) related DAMs, the energetic electrons are sourced from Io volcanic activities, and quickly trapped by neighboring Jovian magnetic field. To properly interpret the physical processes behind DAMs, it is important to precisely locate the source field lines from which DAMs are emitted. Following the work by Hess et al. (2008, 2010), we develop a method to locate the source region as well as the associated field lines for any given DAM emission recorded in a radio dynamic spectrum by, e.g., Wind/WAVES or STEREO/WAVES. The field lines are calculated by the state‐of‐art analytical model, called JRM09 (Connerney et al., 2018). By using this method, we may also derive the emission cone angle and the energy of associated electrons. If multiple radio instruments at different perspectives observe the same DAM event, the evolution of its source region and associated field lines is able to be revealed. We apply the method to an Io‐DAM event, and find that the method is valid and reliable. Some physical processes behind the DAM event are also discussed.
Temporal Evolution of Spatially Resolved Individual Star Spots on a Planet-hosting Solar-type Star: Kepler-17

Star spot evolution is visible evidence of the emergence/decay of the magnetic field on a stellar surface, and it is therefore important for the understanding of the underlying stellar dynamo and consequential stellar flares. In this paper, we report the temporal evolution of individual star spot areas on the hot-Jupiter-hosting, active solar-type star Kepler-17, whose transits occur every 1.5 days. The spot longitude and area evolution are estimated (1) from the stellar rotational modulations of Kepler data and (2) from the brightness enhancements during the exoplanet transits caused by existence of large star spots. As a result of the comparison, the number of spots, spot locations, and the temporal evolution derived from the rotational modulations are largely different from those of in-transit spots. We confirm that, although only two light-curve minima appear per rotation, there are clearly many spots present on the star. We find that the observed differential intensity changes are sometimes consistent with the spot pattern detected by transits, but at other times they do not match with each other. Although the temporal evolution derived from the rotational modulation differs from those of in-transit spots to a certain degree, the emergence/decay rates of in-transit spots are within an order of magnitude of those derived for sunspots as well as our previous research based only on rotational modulations. This supports the hypothesis that the emergence/decay of sunspots and extremely large star spots on solar-type stars occur through the same underlying processes.