Remarkable analytic relations among greybody parameters

In this paper we derive and discuss several implications of the analytic form of a modified blackbody, also called greybody, which is widely used in Astrophysics, and in particular in the study of star formation in the far-infrared/sub-millimeter domain. The research in this area has been greatly improved thanks to recent observations taken with the Herschel satellite, so that it became important to clarify the sense of the greybody approximation, to suggest possible further uses, and to delimi its intervals of validity. First, we discuss the position of the greybody peak, making difference between the optically thin and thick regimes. Second, we analyze the behavior of bolometric quantities as a function of the different greybody parameters. The ratio between the bolometric luminosity and the mass of a source, the ratio between the so-called "sub-millimeter luminosity" and the bolometric one, and the bolometric temperature are observables used to characterize the evolutionary stage of a source, and it is of primary importance to have analytic equations describing the dependence of such quantities on the greybody parameters. Here we discuss all these aspects, providing analytic relations, illustrating particular cases and providing graphical examples. Some equations reported here are well-known in Astrophysics, but are often spread over different publications. Some of them, instead, are brand new and represent a novelty in Astrophysics literature. Finally we indicate an alternative way to obtain, under some conditions, the greybody temperature and dust emissivity directly from an observing spectral energy distribution, avoiding a best-fit procedure.Comment: accepted by MNRA

On the Decoding Complexity of Cyclic Codes Up to the BCH Bound

The standard algebraic decoding algorithm of cyclic codes $[n,k,d]$ up to the BCH bound $t$ is very efficient and practical for relatively small $n$ while it becomes unpractical for large $n$ as its computational complexity is $O(nt)$. Aim of this paper is to show how to make this algebraic decoding computationally more efficient: in the case of binary codes, for example, the complexity of the syndrome computation drops from $O(nt)$ to $O(t\sqrt n)$, and that of the error location from $O(nt)$ to at most $\max \{O(t\sqrt n), O(t^2\log(t)\log(n))\}$.Comment: accepted for publication in Proceedings ISIT 2011. IEEE copyrigh

Efficient evaluation of polynomials over finite fields

A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large with respect to the base field. Applications to the syndrome computation in the decoding of cyclic codes, Reed-Solomon codes in particular, are highlighted.Comment: presented at AusCTW 201

The Rabin cryptosystem revisited

The Rabin public-key cryptosystem is revisited with a focus on the problem of identifying the encrypted message unambiguously for any pair of primes. In particular, a deterministic scheme using quartic reciprocity is described that works for primes congruent 5 modulo 8, a case that was still open. Both theoretical and practical solutions are presented. The Rabin signature is also reconsidered and a deterministic padding mechanism is proposed.Comment: minor review + introduction of a deterministic scheme using quartic reciprocity that works for primes congruent 5 modulo

Improvements on Cantor-Zassenhaus Factorization Algorithm

After revisiting Cantor-Zassenhaus polynomial factorization algorithm, we describe a new simplified version of it, which requires less computational cost. Moreover we show that it is able to find a factor of a fully splitting polynomial of degree $t$ over $\mathbb F_{2^m}$ with $O(\frac{2^m}{3^{t}})$ attempts and over $\mathbb F_{p^m}$ for odd $p$ with $O(\frac{p^m}{2^{t}})$ attempts.Comment: extended and revised version; case s>1 adde

Learning Agile, Vision-based Drone Flight: from Simulation to Reality

We present our latest research in learning deep sensorimotor policies for agile, vision-based quadrotor flight. We show methodologies for the successful transfer of such policies from simulation to the real world. In addition, we discuss the open research questions that still need to be answered to improve the agility and robustness of autonomous drones toward human-pilot performance

Calibration of evolutionary diagnostics in high-mass star formation

The evolutionary classification of massive clumps that are candidate progenitors of high-mass young stars and clusters relies on a variety of independent diagnostics based on observables from the near-infrared to the radio. A promising evolutionary indicator for massive and dense cluster-progenitor clumps is the L/M ratio between the bolometric luminosity and the mass of the clumps. With the aim of providing a quantitative calibration for this indicator we used SEPIA/APEX to obtain CH3C2H(12-11) observations, that is an excellent thermometer molecule probing densities > 10^5 cm^-3 , toward 51 dense clumps with M>1000 solar masses, and uniformly spanning -2 < Log(L/M) < 2.3. We identify three distinct ranges of L/M that can be associated to three distinct phases of star formation in massive clumps. For L/M <1 no clump is detected in CH3C2H , suggesting an inner envelope temperature below 30K. For 1< L/M < 10 we detect 58% of the clumps, with a temperature between 30 and 35 K independently from the exact value of L/M; such clumps are building up luminosity due to the formation of stars, but no star is yet able to significantly heat the inner clump regions. For L/M> 10 we detect all the clumps, with a gas temperature rising with Log(L/M), marking the appearance of a qualitatively different heating source within the clumps; such values are found towards clumps with UCHII counterparts, suggesting that the quantitative difference in T - L/M behaviour above L/M >10 is due to the first appearance of ZAMS stars in the clumps.Comment: Astrophysical Journal Letters, Accepte

Deep Drone Racing: From Simulation to Reality with Domain Randomization

Dynamically changing environments, unreliable state estimation, and operation under severe resource constraints are fundamental challenges that limit the deployment of small autonomous drones. We address these challenges in the context of autonomous, vision-based drone racing in dynamic environments. A racing drone must traverse a track with possibly moving gates at high speed. We enable this functionality by combining the performance of a state-of-the-art planning and control system with the perceptual awareness of a convolutional neural network (CNN). The resulting modular system is both platform- and domain-independent: it is trained in simulation and deployed on a physical quadrotor without any fine-tuning. The abundance of simulated data, generated via domain randomization, makes our system robust to changes of illumination and gate appearance. To the best of our knowledge, our approach is the first to demonstrate zero-shot sim-to-real transfer on the task of agile drone flight. We extensively test the precision and robustness of our system, both in simulation and on a physical platform, and show significant improvements over the state of the art.Comment: Accepted as a Regular Paper to the IEEE Transactions on Robotics Journal. arXiv admin note: substantial text overlap with arXiv:1806.0854

Polynomial evaluation over finite fields: new algorithms and complexity bounds

An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques, when the degree of the polynomial is large enough compared to the field characteristic. Specifically, if n is the degree of the polynomiaI, the asymptotic complexity is shown to be $${O(\sqrt{n})}$$ , versus O(n) of classical algorithms. Applications to the syndrome computation in the decoding of Reed-Solomon codes are highlighte