The Beylkin-Cramer Summation Rule and A New Fast Algorithm of Cosmic Statistics for Large Data Sets

Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and operators within the framework of multi-resolution analysis (MRA), and realize theirs discrete representations. Accordingly, a homogenous point process could be equivalently described by a operation of a Toeplitz matrix on a vector, which is accomplished by making use of fast Fourier transformation. The algorithm could be applied widely in the cosmic statistics to tackle large data sets. Especially, we demonstrate this novel technique using the spherical, cubic and cylinder counts in cells respectively. The numerical test shows that the algorithm produces an excellent agreement with the expected results. Moreover, the algorithm introduces naturally a sharp-filter, which is capable of suppressing shot noise in weak signals. In the numerical procedures, the algorithm is somewhat similar to particle-mesh (PM) methods in N-body simulations. As scaled with $O(N\log N)$, it is significantly faster than the current particle-based methods, and its computational cost does not relies on shape or size of sampling cells. In addition, based on this technique, we propose further a simple fast scheme to compute the second statistics for cosmic density fields and justify it using simulation samples. Hopefully, the technique developed here allows us to make a comprehensive study of non-Guassianity of the cosmic fields in high precision cosmology. A specific implementation of the algorithm is publicly available upon request to the author.Comment: 27 pages, 9 figures included. revised version, changes include (a) adding a new fast algorithm for 2nd statistics (b) more numerical tests including counts in asymmetric cells, the two-point correlation functions and 2nd variances (c) more discussions on technic

Convexity, translation invariance and subadditivity for gg-expectations and related risk measures

Under the continuous assumption on the generator $g$, Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] showed some connections between $g$ and the conditional $g$-expectation $({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$ and Rosazza Gianin [Insurance: Math. Econ. 39 (2006) 19--34] showed some connections between $g$ and the corresponding dynamic risk measure $(\rho^g_t)_{t\in[0,T]}$. In this paper we prove that, without the additional continuous assumption on $g$, a $g$-expectation ${\mathcal{E}}_g$ satisfies translation invariance if and only if $g$ is independent of $y$, and ${\mathcal{E}}_g$ satisfies convexity (resp. subadditivity) if and only if $g$ is independent of $y$ and $g$ is convex (resp. subadditive) with respect to $z$. By these conclusions we deduce that the static risk measure $\rho^g$ induced by a $g$-expectation ${\mathcal{E}}_g$ is a convex (resp. coherent) risk measure if and only if $g$ is independent of $y$ and $g$ is convex (resp. sublinear) with respect to $z$. Our results extend the results in Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] and Rosazza Gianin [Insurance: Math. Econ. 39 (2006) 19--34] on these subjects.Comment: Published in at http://dx.doi.org/10.1214/105051607000000294 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

editor’s introduction

The last issue of JNCHC (spring/summer 2019) included a Forum on “Current Challenges to Honors Education.” The essays focused on challenges to honors while this issue’s Forum addresses challenges within honors, especially the challenges we present to our students in courses that are designed to complicate, interrogate, and often defy accepted practices and beliefs. The introduction of risk-taking takes this topic beyond the unthreatening and inviting terrain of challenge into a different territory. Virtually all honors programs and colleges advertise themselves as presenting challenges to their students, but few if any boast that they are risky. Jumping hurdles is a challenge: jumping when you don’t know what is on the other side is risky. Risk involves some possibility of danger, and to varying degrees the essays in this issue’s Forum address not just the challenge but the risk for students, educators, and programs in honors

Edge Theorem for Multivariable Systems

This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented

Asian Roboticism: Connecting Mechanized Labor to the Automation of Work

Abstract This article reconsiders the present-day automation of work and its transformation of who we are as humans. What has been missing from this important conversation are the social meanings surrounding Asian roboticism or how Asians have already been rendered as “robotic” subjects and labor. Through this racial gendered trope, I assess whether industrial automation will lessen, complicate, or exacerbate this modern archetype. By looking at corporate organizational practices and public media discourse, I believe that Asian roboticism will not simply vanish, but potentially continue to affect the ways such subjects are rendered as exploitable alienated robots without human rights or status