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Catalan's formula, for the portion of the inheritance that a legitimate child of a 19th-century deceased French gentleman should receive, is given a new proof (using Difference Operators), and generalized. Another, more computationally efficient, formula is also derived.

Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach and find an impossibility theorem: any self-consistent ranking method, which satisfies a natural monotonicity property, should depend on the level of aggregation. Our result presents a trade-off between two axiomatic properties and reveals a dilemma of aggregation.

In this paper, we ask what properties makes a large corpus more or less useful. We suggest that size, by itself, should not be the ultimate goal of building a corpus. Large-scale corpora are considered desirable because they offer statistical stability and rich variation. But this rich variation means more factors to control and evaluate, which can limit the advantages of size. We discuss the use of multi-channel data to complement large-scale speech corpora. Even though multi-channel data may limit the scale of a corpus (due to the complex and labor-intensive nature of data collection) they can offer information that allows us to tease apart various factors related to speech production.

In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden variable realism. Effectively, the authors demand from the start that reality must be decided by mathematics, and not by measurements. If this unjustified assumption is dropped, the quantum formalism has a natural statistical interpretation that fully explains the paradox presented by the authors. It is therefore possible to conclude that the paradox actually supports the statistical interpretation, demonstrating once more that quantum mechanics should not be explained by measurement independent realities that are never observed and therefore lie beyond the reach of empirical tests.

Poor software quality can adversely affect application security by increasing the potential for a malicious breach of a system. Because computer security and cybersecurity are becoming such relevant topics for practicing software engineers, the need for educational opportunities in this area is steadily increasing. Universities and colleges have recognized this, and have started to offer programs in cybersecurity. At face value, these new programs may not appear controversial, but developing their curriculum requires answering a complex ethical question: Should programs teach hacking to their students? Even though there are different types of hackers, media reports of cybersecurity incidents tend to reserve the "hacker" label for cyber criminals, which overlooks the value in hacking (and, by extension, teaching students to hack). This article examines the full spectrum of hacking behavior, as well as arguments for and against including hacking in education programs, and recommends that hacking skills be considered an essential component of an education and practice in software quality assurance.

In a recent Letter [G. Chiribella et al., Phys. Rev. Lett. 98, 120501 (2007)], four protocols were proposed to secretly transmit a reference frame. Here We point out that in these protocols an eavesdropper can change the transmitted reference frame without being detected, which means the consistency of the shared reference frames should be reexamined. The way to check the above consistency is discussed. It is shown that this problem is quite different from that in previous protocols of quantum cryptography.

We consider a setting where in a known future time, a certain continuous random variable will be realized. There is a public prediction that gradually converges to its realized value, and an expert that has access to a more accurate prediction. Our goal is to study {\em when} should the expert reveal his information, assuming that his reward is based on a logarithmic market scoring rule (i.e., his reward is proportional to the gain in log-likelihood of the realized value). Our contributions are: (1) we characterize the expert's optimal policy and show that it is threshold based. (2) we analyze the expert's asymptotic expected optimal reward and show a tight connection to the Law of the Iterated Logarithm, and (3) we give an efficient dynamic programming algorithm to compute the optimal policy.

This paper argues that fully autonomous AI agents should not be developed. In support of this position, we build from prior scientific literature and current product marketing to delineate different AI agent levels and detail the ethical values at play in each, documenting trade-offs in potential benefits and risks. Our analysis reveals that risks to people increase with the autonomy of a system: The more control a user cedes to an AI agent, the more risks to people arise. Particularly concerning are safety risks, which affect human life and impact further values.

Shock/sound propagation from the quenched jets have well-defined front, separating the fireball into regions which are and are not affected. While even for the most robust jet quenching observed this increases local temperature and flow of ambient matter by only few percent at most, strong radial flow increases the contrast between the two regions so that the difference should be well seen in particle spectra at some $p_t$, perhaps even on event-by-event basis. We further show that the effect comes mostly from certain ellipse-shaped 1-d curve, the intercept of three 3-d surfaces, the Mach cone history, the timelike and spacelike freezeout surfaces. We further suggest that this "edge" is already seen in an event released by ATLAS collaboration.

Multi-view geometry-based methods dominate the last few decades in monocular Visual Odometry for their superior performance, while they have been vulnerable to dynamic and low-texture scenes. More importantly, monocular methods suffer from scale-drift issue, i.e., errors accumulate over time. Recent studies show that deep neural networks can learn scene depths and relative camera in a self-supervised manner without acquiring ground truth labels. More surprisingly, they show that the well-trained networks enable scale-consistent predictions over long videos, while the accuracy is still inferior to traditional methods because of ignoring geometric information. Building on top of recent progress in computer vision, we design a simple yet robust VO system by integrating multi-view geometry and deep learning on Depth and optical Flow, namely DF-VO. In this work, a) we propose a method to carefully sample high-quality correspondences from deep flows and recover accurate camera poses with a geometric module; b) we address the scale-drift issue by aligning geometrically triangulated depths to the scale-consistent deep depths, where the dynamic scenes are taken into account. Comprehensive a