Copula Correlation: An Equitable Dependence Measure and Extension of Pearson's Correlation

In Science, Reshef et al. (2011) proposed the concept of equitability for measures of dependence between two random variables. To this end, they proposed a novel measure, the maximal information coefficient (MIC). Recently a PNAS paper (Kinney and Atwal, 2014) gave a mathematical definition for equitability. They proved that MIC in fact is not equitable, while a fundamental information theoretic measure, the mutual information (MI), is self-equitable. In this paper, we show that MI also does not correctly reflect the proportion of deterministic signals hidden in noisy data. We propose a new equitability definition based on this scenario. The copula correlation (Ccor), based on the L1-distance of copula density, is shown to be equitable under both definitions. We also prove theoretically that Ccor is much easier to estimate than MI. Numerical studies illustrate the properties of the measures

Alternative Justifications for Academic Support III: An Empirical Analysis of the Impact of Academic Support on Perceived Autonomy Support and Humanizing Law Schools

This article details the findings of a two-year empirical study on the impact of a law school academic support program (ASP) on law students. The hypothesis of the study was that as students\u27 participation in a well-resourced, open-access ASP increases, students\u27 perception of autonomy support and humanizing grows as well. The study concludes, based upon statistically significant data, that law school ASPs impact students in positive ways and therefore are worth the investment. This article is the third in a series designed to show that law school academic support measures positively impact students\u27 well-being and lead to a more robust educational experience

Granger causality and transfer entropy are equivalent for Gaussian variables

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.Comment: In review, Phys. Rev. Lett., Nov. 200

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

Simpler, Faster, and More Robust T-test Based Leakage Detection

The TVLA procedure using the t-test has become a popular leakage detection method. To protect against environmental fluctuation in laboratory measurements, we propose a paired t-test to improve the standard procedure. We take advantage of statistical matched-pairs design to remove the environmental noise effect in leakage detection. Higher order leakage detection is further improved with a moving average method. We compare the proposed test with standard t-test on synthetic data and physical measurements. Our results show that the proposed tests are robust to environmental noise

High pressure evolution of Fe2_{2}O3_{3} electronic structure revealed by X-ray absorption

We report the first high pressure measurement of the Fe K-edge in hematite (Fe$_2$O$_3$) by X-ray absorption spectroscopy in partial fluorescence yield geometry. The pressure-induced evolution of the electronic structure as Fe$_2$O$_3$ transforms from a high-spin insulator to a low-spin metal is reflected in the x-ray absorption pre-edge. The crystal field splitting energy was found to increase monotonically with pressure up to 48 GPa, above which a series of phase transitions occur. Atomic multiplet, cluster diagonalization, and density-functional calculations were performed to simulate the pre-edge absorption spectra, showing good qualitative agreement with the measurements. The mechanism for the pressure-induced phase transitions of Fe$_2$O$_3$ is discussed and it is shown that ligand hybridization significantly reduces the critical high-spin/low-spin pressure.Comment: 5 pages, 4 figures and 1 tabl

Towards Secure Cryptographic Software Implementation Against Side-Channel Power Analysis Attacks

Side-channel attacks have been a real threat against many critical embedded systems that rely on cryptographic algorithms as their security engine. A commonly used algorithmic countermeasure, random masking, incurs large execution delay and resource overhead. The other countermeasure, operation shuffling or permutation, can mitigate side-channel leakage effectively with minimal overhead. In this paper, we target utilizing the independence among operations in cryptographic algorithms and randomizing their execution order. We design a tool to automatically detect such independence between statements at the source code level and devise an algorithm for automatic operation shuffling. We test our algorithm on the new SHA3 standard, Keccak. Results show that the tool has effectively implemented operation-shuffling to reduce the side-channel leakage significantly, and therefore can guide automatic secure cryptographic software implementations against differential power analysis attacks

Differential Fault Analysis of SHA3-224 and SHA3-256

The security of SHA-3 against different kinds of attacks are of vital importance for crypto systems with SHA-3 as the security engine. In this paper, we look into the differential fault analysis of SHA-3, and this is the first work to conquer SHA3-224 and SHA3-256 using differential fault analysis. Comparing with one existing related work, we relax the fault models and make them realistic for different implementation architectures. We analyze fault propagation in SHA-3 under such single-byte fault models, and propose to use fault signatures at the observed output for analysis and secret retrieval. Results show that the proposed method can effectively identify the injected single-byte faults, and then recover the whole internal state of the input of last round $\chi$ operation ($\chi^{22}_i$) for both SHA3-224 and SHA3-256

An Improvement of Both Security and Reliability for Keccak Implementations on Smart Card

As the new SHA-3 standard, the security and reliability of Keccak have attracted a lot of attentions. Previous works already show that both software and hardware implementations of Keccak have strong side-channel power (electromagnetic) leakages, and these leakages can be easily used by attackers to recover secret key bits. Meanwhile, Keccak is vulnerable to random errors and injected faults, which will cause errors in the computation results. In this paper, we introduce a scheme based on the round rotation invariance property of Keccak to reduce the side-channel leakages while improve its reliability. The proposed scheme is resource friendly. Side-channel analysis results show that this method can efficiently reduce the side-channel leakages of Keccak implementations. Meanwhile, fault injection simulation results show that the proposed scheme can effectively improve the reliability of Keccak implementation, with error coverage almost 100%