Sum of Two Squares - Pair Correlation and Distribution in Short Intervals

In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is consistent with a Poissonian distribution, where "short" means of length comparable to the mean spacing between sums of two squares. In addition we present a method for producing such conjectures through calculations in prime power residue rings and describe how these conjectures, as well as the above stated result, may by generalized to other binary quadratic forms. While producing these pair correlation conjectures we arrive at a surprising result regarding Mertens' formula for primes in arithmetic progressions, and in order to test the validity of the conjectures, we present numericalz computations which support our approach.Comment: 3 figure

Search for methylamine in high mass hot cores

We aim to detect methylamine, CH$_{3}$NH$_{2}$, in a variety of hot cores and use it as a test for the importance of photon-induced chemistry in ice mantles and mobility of radicals. Specifically, CH$_3$NH$_2$ cannot be formed from atom addition to CO whereas other NH$_2$-containing molecules such as formamide, NH$_2$CHO, can. Submillimeter spectra of several massive hot core regions were taken with the James Clerk Maxwell Telescope. Abundances are determined with the rotational diagram method where possible. Methylamine is not detected, giving upper limit column densities between 1.9 $-$ 6.4 $\times$ 10$^{16}$ cm$^{-2}$ for source sizes corresponding to the 100 K envelope radius. Combined with previously obtained JCMT data analyzed in the same way, abundance ratios of CH$_{3}$NH$_{2}$, NH$_{2}$CHO and CH$_{3}$CN with respect to each other and to CH$_{3}$OH are determined. These ratios are compared with Sagittarius B2 observations, where all species are detected, and to hot core models. The observed ratios suggest that both methylamine and formamide are overproduced by up to an order of magnitude in hot core models. Acetonitrile is however underproduced. The proposed chemical schemes leading to these molecules are discussed and reactions that need further laboratory studies are identified. The upper limits obtained in this paper can be used to guide future observations, especially with ALMA.Comment: 14 pages, 5 figures, accepted for publication in A&

Earthquake networks based on similar activity patterns

Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network, a node represents a spatial location while a link between two nodes represents similar activity patterns in the two different locations. The strength of a link is proportional to the strength of the cross-correlation in activities of two nodes joined by the link. We apply our network approach to a Japanese earthquake catalog spanning the 14-year period 1985-1998. We find strong links representing large correlations between patterns in locations separated by more than 1000 km, corroborating prior observations that earthquake interactions have no characteristic length scale. We find network characteristics not attributable to chance alone, including a large number of network links, high node assortativity, and strong stability over time.Comment: 8 pages text, 9 figures. Updated from previous versio

Raising argument strength using negative evidence: A constraint on models of induction

Both intuitively, and according to similarity-based theories of induction, relevant evidence raises argument strength when it is positive and lowers it when it is negative. In three experiments, we tested the hypothesis that argument strength can actually increase when negative evidence is introduced. Two kinds of argument were compared through forced choice or sequential evaluation: single positive arguments (e.g., “Shostakovich’s music causes alpha waves in the brain; therefore, Bach’s music causes alpha waves in the brain”) and double mixed arguments (e.g., “Shostakovich’s music causes alpha waves in the brain, X’s music DOES NOT; therefore, Bach’s music causes alpha waves in the brain”). Negative evidence in the second premise lowered credence when it applied to an item X from the same subcategory (e.g., Haydn) and raised it when it applied to a different subcategory (e.g., AC/DC). The results constitute a new constraint on models of induction

Community Classification and Distribution Patterns of Freshwater Mussels of Strawberry River, Arkansas

The purpose of this study is to determine if there are distinct communities of freshwater mussels in the Strawberry River, Arkansas, and if environmental variables influenced these communities. The Strawberry River watershed is located in the Ozark Mountains in northcentral Arkansas. Based on previous studies of interior highland mussels, we expected distinct low, mid, and high order stream mussel communities. Mussels were surveyed from headwaters to mouth and resulted in 38 species from 57 sites. Environmental variables of land cover, geology, soiltype, and drainage area were calculated at local and subwatershed scale using GIS. Mussel presence/absence and environmental variables were analyzed using Principle Components Analysis (PCA). Amblima plicata was the most abundant species, representing 17% of all individuals collected. The cumulative percent of variation explained for PCA axes 1 -3 for mussels and environmental variables were approximately 40% and 48%, respectively. Contrary to expectations, we did not observe distinct mussel communities. However, some environmental variables (developed open space, cultivated crops and alluvial soil at subwatershed scale and dolostone and alluvium at local scale) were correlated with the mussel PCA pattern. Sujata Poudel. University of Massachusetts Boston, Biology Department, 100 Morrissey Boulevard, Boston, Massachusetts 02125 David E. Tenenbaum. University of Massachusetts Boston, Department of Environmental, Earth, and Ocean Sciences, 100 Morrissey Boulevard, Boston, Massachusetts 02125 John L. Harris. Arkansas State University, Department of Biological Sciences, P.O. Box 599, State University, Arkansas 72767. [email protected] Alan D. Christian. University of Massachusetts Boston, Biology Department, 100 Morrissey Boulevard, Boston, Massachusetts 0212

Cohesion, team mental models, and collective efficacy: Towards an integrated framework of team dynamics in sport

A nomological network on team dynamics in sports consisting of a multi-framework perspective is introduced and tested. The aim was to explore the interrelationship among cohesion, team mental models (TMM), collective-efficacy (CE), and perceived performance potential (PPP). Three hundred and forty college-aged soccer players representing 17 different teams (8 female and 9 male) participated in the study. They responded to surveys on team cohesion, TMM, CE and PPP. Results are congruent with the theoretical conceptualization of a parsimonious view of team dynamics in sports. Specifically, cohesion was found to be an exogenous variable predicting both TMM and CE beliefs. TMM and CE were correlated and predicted PPP, which in turn accounted for 59% of the variance of objective performance scores as measured by teams’ season record. From a theoretical standpoint, findings resulted in a parsimonious view of team dynamics, which may represent an initial step towards clarifying the epistemological roots and nomological network of various team-level properties. From an applied standpoint, results suggest that team expertise starts with the establishment of team cohesion. Following the establishment of cohesiveness, teammates are able to advance team-related schemas and a collective sense of confidence. Limitations and key directions for future research are outlined

Kepler Presearch Data Conditioning I - Architecture and Algorithms for Error Correction in Kepler Light Curves

Kepler provides light curves of 156,000 stars with unprecedented precision. However, the raw data as they come from the spacecraft contain significant systematic and stochastic errors. These errors, which include discontinuities, systematic trends, and outliers, obscure the astrophysical signals in the light curves. To correct these errors is the task of the Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline. The original version of PDC in Kepler did not meet the extremely high performance requirements for the detection of miniscule planet transits or highly accurate analysis of stellar activity and rotation. One particular deficiency was that astrophysical features were often removed as a side-effect to removal of errors. In this paper we introduce the completely new and significantly improved version of PDC which was implemented in Kepler SOC 8.0. This new PDC version, which utilizes a Bayesian approach for removal of systematics, reliably corrects errors in the light curves while at the same time preserving planet transits and other astrophysically interesting signals. We describe the architecture and the algorithms of this new PDC module, show typical errors encountered in Kepler data, and illustrate the corrections using real light curve examples.Comment: Submitted to PASP. Also see companion paper "Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction" by Jeff C. Smith et a

Detection of C3O in IRC+10216: Oxygen-Carbon chain chemistry in the outer envelope

The oxygen-bearing species C3O has been identified in the circumstellar envelope of the carbon star IRC +10216. The J = 8-->7, 9-->8, 10-->9, 14-->13, and 15-->14 transitions were detected at 2 and 3 mm using the Arizona Radio Observatory’s 12 m telescope. Measurements of the J = 9-->8, 10-->9, and 12-->11 lines were simultaneously conducted at the IRAM 30 m telescope. The line profiles of C3O are roughly U-shaped, indicating an extended shell distribution for this molecule in IRC +10216. The total column density derived for C3O is 1.2x10^12 cm^-2, at least an order of magnitude higher than that predicted by current chemical models. However, a revised model that includes reactions of atomic oxygen with carbon-chain radicals, such as l-C3H and C4, can reproduce the observed abundance. This model also predicts that C3O arises from a shell source with an outer radius near r ∼ 30", consistent with the observations. These results suggest that gas phase neutral-neutral chemistry may be producing the oxygen-bearing molecules present in the outer envelope of IRC +10216.This material is based on work supported by the National Aeronautics and Space Administration through the NASA Astrobiology Institute under Cooperative Agreement CAN-02-OSS-02 issued through the Office of Space Science. We also acknowledge support from Spanish MEC under project AYA2003-2785 and from "Comunidad de Madrid" under PRICIT project S-0505/ESP-0237 (ASTROCAM). E. D. T. thanks NSF for a graduate research fellowship, and M. A. acknowledges Spanish MEC for a predoctoral grant AP2003-4619.Peer reviewe

Compositional inductive biases in function learning.

How do people recognize and learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is achieved by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian regression using a grammar over Gaussian process kernels, and compare this approach with other structure learning approaches. Participants consistently chose compositional (over non-compositional) extrapolations and interpolations of functions. Experiments designed to elicit priors over functional patterns revealed an inductive bias for compositional structure. Compositional functions were perceived as subjectively more predictable than non-compositional functions, and exhibited other signatures of predictability, such as enhanced memorability and reduced numerosity. Taken together, these results support the view that the human intuitive theory of functions is inherently compositional