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We use a modified version of the Peak Patch excursion set formalism to compute the mass and size distribution of QCD axion miniclusters from a fully non-Gaussian initial density field obtained from numerical simulations of axion string decay. We find strong agreement with N-Body simulations at a significantly lower computational cost. We employ a spherical collapse model and provide fitting functions for the modified barrier in the radiation era. The halo mass function at $z=629$ has a power-law distribution $M^{-0.6}$ for masses within the range $10^{-15}lesssim Mlesssim 10^{-10}M_{odot}$, with all masses scaling as $(m_a/50mumathrm{eV})^{-0.5}$. We construct merger trees to estimate the collapse redshift and concentration mass relation, $C(M)$, which is well described using analytical results from the initial power spectrum and linear growth. Using the calibrated analytic results to extrapolate to $z=0$, our method predicts a mean concentration $Csim mathcal{O}(text{few})times10^4$. The low computational cost of our method makes future investigation of the statistics of rare, dense miniclusters easy to achieve.
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We give a short proof of Gaos Quantum Union Bound and Gentle Sequential Measurement theorems.
We develop taggers for multi-pronged jets that are simple functions of jet substructure (so-called `subjettiness) variables. These taggers can be approximately decorrelated from the jet mass in a quite simple way. Specifically, we use a Logistic Regression Design (LoRD) which, even being one of the simplest machine learning classifiers, shows a performance which surpasses that of simple variables used by the ATLAS and CMS Collaborations and is not far from more complex models based on neural networks. Contrary to the latter, our method allows for an easy implementation of tagging tasks by providing a simple and interpretable analytical formula with already optimised parameters.
Visual imitation learning provides a framework for learning complex manipulation behaviors by leveraging human demonstrations. However, current interfaces for imitation such as kinesthetic teaching or teleoperation prohibitively restrict our ability to efficiently collect large-scale data in the wild. Obtaining such diverse demonstration data is paramount for the generalization of learned skills to novel scenarios. In this work, we present an alternate interface for imitation that simplifies the data collection process while allowing for easy transfer to robots. We use commercially available reacher-grabber assistive tools both as a data collection device and as the robots end-effector. To extract action information from these visual demonstrations, we use off-the-shelf Structure from Motion (SfM) techniques in addition to training a finger detection network. We experimentally evaluate on two challenging tasks: non-prehensile pushing and prehensile stacking, with 1000 diverse demonstrations for each task. For both tasks, we use standard behavior cloning to learn executable policies from the previously collected offline demonstrations. To improve learning performance, we employ a variety of data augmentations and provide an extensive analysis of its effects. Finally, we demonstrate the utility of our interface by evaluating on real robotic scenarios with previously unseen objects and achieve a 87% success rate on pushing and a 62% success rate on stacking. Robot videos are available at https://dhiraj100892.github.io/Visual-Imitation-Made-Easy.
Linials seminal result shows that any deterministic distributed algorithm that finds a $3$-colouring of an $n$-cycle requires at least $log^*(n)/2 - 1$ communication rounds. We give a new simpler proof of this theorem.
In this paper we present a deterministic CONGEST algorithm to compute an $O(kDelta)$-vertex coloring in $O(Delta/k)+log^* n$ rounds, where $Delta$ is the maximum degree of the network graph and $1leq kleq O(Delta)$ can be freely chosen. The algorithm is extremely simple: Each node locally computes a sequence of colors and then it tries colors from the sequence in batches of size $k$. Our algorithm subsumes many important results in the history of distributed graph coloring as special cases, including Linials color reduction [Linial, FOCS87], the celebrated locally iterative algorithm from [Barenboim, Elkin, Goldenberg, PODC18], and various algorithms to compute defective and arbdefective colorings. Our algorithm can smoothly scale between these and also simplifies the state of the art $(Delta+1)$-coloring algorithm. At the cost of losing the full algorithms simplicity we also provide a $O(kDelta)$-coloring algorithm in $O(sqrt{Delta/k})+log^* n$ rounds. We also provide improved deterministic algorithms for ruling sets, and, additionally, we provide a tight characterization for one-round color reduction algorithms.
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