A new algorithm for fast generalized DFTs

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here $\omega$ is the exponent of matrix multiplication, so the exponent $\omega/2$ is optimal if $\omega = 2$. Previously, "exponent one" algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known (even under the assumption $\omega = 2$) for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for $SL_2(F_q)$ had exponent $4/3$ despite being the focus of significant effort. We unconditionally achieve exponent at most $1.19$ for this group, and exponent one if $\omega = 2$. Our algorithm also yields an improved exponent for computing the generalized DFT over general finite groups $G$, which beats the longstanding previous best upper bound, for any $\omega$. In particular, assuming $\omega = 2$, we achieve exponent $\sqrt{2}$, while the previous best was $3/2$

Vector modes generated by primordial density fluctuations

While vector modes are usually ignored in cosmology since they are not produced during inflation they are inevitably produced from the interaction of density fluctuations of differing wavelengths. This effect may be calculated via a second-order perturbative expansion. We investigate this effect during the radiation era. We discuss the generation mechanism by investigating two scalar modes interacting, and we calculate the power of vector modes generated by a power-law spectrum of density perturbations on all scales.Comment: 10 pages, 2 figures, minor changes in main text and new appendix added to match the accepted version for Physical Review D publicatio

On Multidimensional and Monotone k-SUM

The well-known k-SUM conjecture is that integer k-SUM requires time Omega(n^{ceil{k/2}-o(1)}). Recent work has studied multidimensional k-SUM in F_p^d, where the best known algorithm takes time tilde O(n^{ceil{k/2}}). Bhattacharyya et al. [ICS 2011] proved a min(2^{Omega(d)},n^{Omega(k)}) lower bound for k-SUM in F_p^d under the Exponential Time Hypothesis. We give a more refined lower bound under the standard k-SUM conjecture: for sufficiently large p, k-SUM in F_p^d requires time Omega(n^{k/2-o(1)}) if k is even, and Omega(n^{ceil{k/2}-2k(log k)/(log p)-o(1)}) if k is odd. For a special case of the multidimensional problem, bounded monotone d-dimensional 3SUM, Chan and Lewenstein [STOC 2015] gave a surprising tilde O(n^{2-2/(d+13)}) algorithm using additive combinatorics. We show this algorithm is essentially optimal. To be more precise, bounded monotone d-dimensional 3SUM requires time Omega(n^{2-frac{4}{d}-o(1)}) under the standard 3SUM conjecture, and time Omega(n^{2-frac{2}{d}-o(1)}) under the so-called strong 3SUM conjecture. Thus, even though one might hope to further exploit the structural advantage of monotonicity, no substantial improvements beyond those obtained by Chan and Lewenstein are possible for bounded monotone d-dimensional 3SUM

Associations Between Rest-Activity Rhythms and Liver Function Tests: the Us National Health and Nutrition Examination Survey, 2011-2014

Liver functions are regulated by the circadian rhythm; however, whether a weakened circadian rhythm is associated with impaired liver function is unclear. This study aims to investigate the association of characteristics of rest-activity rhythms with abnormal levels of biomarkers of liver function. Data were obtained from the National Health and Nutrition Examination Survey 2011-2014. Seven rest-activity rhythm parameters were derived from 24 h actigraphy data using the extended cosine model and non-parametric methods. Multiple logistic regression and multiple linear regression models were used to assess the associations between rest-activity rhythm parameters and alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP), gamma-glutamyl transaminase (GGT), albumin and bilirubin. Weakened overall rhythmicity characterized by a lower F statistic was associated with higher odds of abnormally elevated ALP (O

Foreground Subtraction in Intensity Mapping with the SKA

21cm intensity mapping experiments aim to observe the diffuse neutral hydrogen (HI) distribution on large scales which traces the Cosmic structure. The Square Kilometre Array (SKA) will have the capacity to measure the 21cm signal over a large fraction of the sky. However, the redshifted 21cm signal in the respective frequencies is faint compared to the Galactic foregrounds produced by synchrotron and free-free electron emission. In this article, we review selected foreground subtraction methods suggested to effectively separate the 21cm signal from the foregrounds with intensity mapping simulations or data. We simulate an intensity mapping experiment feasible with SKA phase 1 including extragalactic and Galactic foregrounds. We give an example of the residuals of the foreground subtraction with a independent component analysis and show that the angular power spectrum is recovered within the statistical errors on most scales. Additionally, the scale of the Baryon Acoustic Oscillations is shown to be unaffected by foreground subtraction.Comment: This article is part of the 'SKA Cosmology Chapter, Advancing Astrophysics with the SKA (AASKA14), Conference, Giardini Naxos (Italy), June 9th-13th 2014

Inspection and Evaluation of a Bridge Deck Partially Reinforced With GFRP Rebars

The corrosion of steel can be a significant problem in bridge decks in which the reinforcing and prestressing steel are accessible to deicing salts and combinations of moisture, temperature and chlorides through cracks, leading to concrete deterioration and loss of serviceability. Fiber Reinforced Polymer (FRP) rebars have emerged as one alternative to steel reinforcement in corrosive environments. The objective of this study is to evaluate the cracks formed on a bridge deck that is partially reinforced with glass fiber reinforced polymer (GFRP) rebars. The bridge constructed in 1997 is in Bourbon County, KY, on US460 over the Rogers\u27 Creek. Its deck is partially reinforced with GFRP rebars in place of epoxy coated steel rebars. The bridge has been monitored for cracks over a period of two years from June 1998 to July 2000. The maximum measured crack width of 0.013 in (0.3 mm) in the GFRP reinforced section meets the maximum allowed by ACI (Section 10.6) and AASHTO (Section 8.16.8.4) specifications in steel reinforced structures for exterior exposure

Us adolescent Rest-Activity Patterns: insights From Functional Principal Component analysis (Nhanes 2011-2014)

BACKGROUND: Suboptimal rest-activity patterns in adolescence are associated with worse health outcomes in adulthood. Understanding sociodemographic factors associated with rest-activity rhythms may help identify subgroups who may benefit from interventions. This study aimed to investigate the association of rest-activity rhythm with demographic and socioeconomic characteristics in adolescents. METHODS: Using cross-sectional data from the nationally representative National Health and Nutrition Examination Survey (NHANES) 2011-2014 adolescents (N = 1814), this study derived rest-activity profiles from 7-day 24-hour accelerometer data using functional principal component analysis. Multiple linear regression was used to assess the association between participant characteristics and rest-activity profiles. Weekday and weekend specific analyses were performed in addition to the overall analysis. RESULTS: Four rest-activity rhythm profiles were identified, which explained a total of 82.7% of variance in the study sample, including (1) High amplitude profile; (2) Early activity window profile; (3) Early activity peak profile; and (4) Prolonged activity/reduced rest window profile. The rest-activity profiles were associated with subgroups of age, sex, race/ethnicity, and household income. On average, older age was associated with a lower value for the high amplitude and early activity window profiles, but a higher value for the early activity peak and prolonged activity/reduced rest window profiles. Compared to boys, girls had a higher value for the prolonged activity/reduced rest window profiles. When compared to Non-Hispanic White adolescents, Asian showed a lower value for the high amplitude profile, Mexican American group showed a higher value for the early activity window profile, and the Non-Hispanic Black group showed a higher value for the prolonged activity/reduced rest window profiles. Adolescents reported the lowest household income had the lowest average value for the early activity window profile. CONCLUSIONS: This study characterized main rest-activity profiles among the US adolescents, and demonstrated that demographic and socioeconomic status factors may shape rest-activity behaviors in this population

A general test of the Copernican Principle

The recent discovery of apparent cosmic acceleration has highlighted the depth of our ignorance of the fundamental properties of nature. It is commonly assumed that the explanation for acceleration must come from a new form of energy dominating the cosmos - dark energy - or a modification of Einstein's theory of Relativity. It is often overlooked, however, that a currently viable alternative explanation of the data is radial inhomogeneity which alters the Hubble diagram without any acceleration. This explanation is often ignored for two reasons: radial inhomogeneity significantly complicates analysis and predictions, and so the full details have not been investigated; and it is a philosophically highly controversial idea, revoking as it does the long-held Copernican Principle. To date, there has not been a general way of determining the validity if the Copernican Principle -- that we live at a typical position in the universe -- significantly weakening the foundations of cosmology as a scientific endeavour. Here we present an observational test for the Copernican assumption which can be automatically implemented while we search for dark energy in the coming decade. Our test is entirely independent of any model for dark energy or theory of gravity and thereby represents a model-independent test of the Copernican Principle.Comment: 5 pages, no figure