Permutation patterns and statistics

Let S_n denote the symmetric group of all permutations of the set {1, 2, ...,n} and let S = \cup_{n\ge0} S_n. If Pi is a set of permutations, then we let Av_n(Pi) be the set of permutations in S_n which avoid every permutation of Pi in the sense of pattern avoidance. One of the celebrated notions in pattern theory is that of Wilf-equivalence, where Pi and Pi' are Wilf equivalent if #Av_n(Pi)=#Av_n(Pi') for all n\ge0. In a recent paper, Sagan and Savage proposed studying a q-analogue of this concept defined as follows. Suppose st:S->N is a permutation statistic where N represents the nonnegative integers. Consider the corresponding generating function, F_n^{st}(Pi;q) = sum_{sigma in Av_n(Pi)} q^{st sigma}, and call Pi,Pi' st-Wilf equivalent if F_n^{st}(Pi;q)=F_n^{st}(Pi';q) for all n\ge0. We present the first in-depth study of this concept for the inv and maj statistics. In particular, we determine all inv- and maj-Wilf equivalences for any Pi containd in S_3. This leads us to consider various q-analogues of the Catalan numbers, Fibonacci numbers, triangular numbers, and powers of two. Our proof techniques use lattice paths, integer partitions, and Foata's fundamental bijection. We also answer a question about Mahonian pairs raised in the Sagan-Savage article.Comment: 28 pages, 5 figures, tightened up the exposition, noted that some of the conjectures have been prove

Modeling Seven Years of Event Horizon Telescope Observations with Radiatively Inefficient Accretion Flow Models

An initial three-station version of the Event Horizon Telescope, a millimeter-wavelength very-long baseline interferometer, has observed Sagittarius A* (Sgr A*) repeatedly from 2007 to 2013, resulting in the measurement of a variety of interferometric quantities. Of particular importance, there is now a large set of closure phases, measured over a number of independent observing epochs. We analyze these observations within the context of a realization of semi-analytic radiatively inefficient disk models, implicated by the low luminosity of Sgr A*. We find a broad consistency among the various observing epochs and between different interferometric data types, with the latter providing significant support for this class of models of Sgr A*. The new data significantly tighten existing constraints on the spin magnitude and its orientation within this model context, finding a spin magnitude of $a=0.10^{+0.30+0.56}_{-0.10-0.10}$, an inclination with respect to the line of sight of $\theta={60^\circ}^{+5^\circ+10^\circ}_{-8^\circ-13^\circ}$, and a position angle of $\xi={156^\circ}^{+10^\circ+14^\circ}_{-17^\circ-27^\circ}$ east of north. These are in good agreement with previous analyses. Notably, the previous $180^\circ$ degeneracy in the position angle has now been conclusively broken by the inclusion of the closure phase measurements. A reflection degeneracy in the inclination remains, permitting two localizations of the spin vector orientation, one of which is in agreement with the orbital angular momentum of the infrared gas cloud G2 and the clockwise disk of young stars. This possibly supports a relationship between Sgr A*'s accretion flow and these larger-scale features.Comment: 16 pages, 11 figures, accepted to Ap

Borehole Radar Attenuation-Difference Tomography During the Tracer/Time-Lapse Test at the Boise Hydrogeophysical Research Site

A tracer test and time-lapse radar imaging experiment was conducted at the Boise Hydrogeophysical Research Site to investigate the utility of crosswell radar in imaging an electrically conductive tracer plume. A multilevel water sampling system down gradient from the tracer injection well and in the radar imaging plane was used to collect detailed, 1-dimensional, fluid electrical conductivity data during the tracer test. We compare the spatial and temporal position and concentration variations of the plume as indicated by the fluid conductivity data to those suggested by radar level run attenuation differences, shot-receiver attenuation difference crossplots, and an attenuation-difference tomogram. We find that attenuation differences generally correlate well with changes in fluid conductivity. Where correlations are not so strong, the discrepancies can be explained by the difference in support volumes for the radar and chemistry measurements, and also by regularization of the radar tomogram. Our results indicate that crosswell radar imaging coupled with hydrologic tracer testing can provide useful information about subsurface fluid flow and mass transport in complex fluvial aquifers

Rare Earth Element Distribution in the NE Atlantic: Evidence for Benthic Sources, Longevity of the Seawater Signal, and Biogeochemical Cycling

Seawater rare earth element (REE) concentrations are increasingly applied to reconstruct water mass histories by exploiting relative changes in the distinctive normalised patterns. However, the mechanisms by which water masses gain their patterns are yet to be fully explained. To examine this, we collected water samples along the Extended Ellett Line (EEL), an oceanographic transect between Iceland and Scotland, and measured dissolved REE by offline automated chromatography (SeaFAST) and ICP-MS. The proximity to two continental boundaries, the incipient spring bloom coincident with the timing of the cruise, and the importance of deep water circulation in this climatically sensitive gateway region make it an ideal location to investigate sources of REE to seawater and the effects of vertical cycling and lateral advection on their distribution. The deep waters have REE concentrations closest to typical North Atlantic seawater and are dominated by lateral advection. Comparison to published seawater REE concentrations of the same water masses in other locations provides a first measure of the temporal and spatial stability of the seawater REE signal. We demonstrate the REE pattern is replicated for Iceland-Scotland Overflow Water (ISOW) in the Iceland Basin from adjacent stations sampled 16 years previously. A recently published Labrador Sea Water (LSW) dissolved REE signal is reproduced in the Rockall Trough but shows greater light and mid REE alteration in the Iceland Basin, possibly due to the dominant effect of ISOW and/or continental inputs. An obvious concentration gradient from seafloor sediments to the overlying water column in the Rockall Trough, but not the Iceland Basin, highlights release of light and mid REE from resuspended sediments and pore waters, possibly a seasonal effect associated with the timing of the spring bloom in each basin. The EEL dissolved oxygen minimum at the permanent pycnocline corresponds to positive heavy REE enrichment, indicating maximum rates of organic matter remineralisation and associated REE release. We tentatively suggest a bacterial role to account for the observed heavy REE deviations. This study highlights the need for fully constrained REE sources and sinks, including the temporary nature of some sources, to achieve a balanced budget of seawater REE

Early visual foraging in relationship to familial risk for autism and hyperactivity/inattention

Objective. Information foraging is atypical in both autism spectrum disorders (ASDs) and ADHD; however, while ASD is associated with restricted exploration and preference for sameness, ADHD is characterized by hyperactivity and increased novelty seeking. Here, we ask whether similar biases are present in visual foraging in younger siblings of children with a diagnosis of ASD with or without additional high levels of hyperactivity and inattention. Method. Fifty-four low-risk controls (LR) and 50 high-risk siblings (HR) took part in an eye-tracking study at 8 and 14 months and at 3 years of age. Results. At 8 months, siblings of children with ASD and low levels of hyperactivity/inattention (HR/ASD-HI) were more likely to return to previously visited areas in the visual scene than were LR and siblings of children with ASD and high levels of hyperactivity/inattention (HR/ASD+HI). Conclusion. We show that visual foraging is atypical in infants at-risk for ASD. We also reveal a paradoxical effect, in that additional family risk for ADHD core symptoms mitigates the effect of ASD risk on visual information foraging

Descriptive Analysis of a Baseline Concussion Battery Among U.S. Service Academy Members: Results from the Concussion Assessment, Research, and Education (CARE) Consortium

Introduction The prevalence and possible long-term consequences of concussion remain an increasing concern to the U.S. military, particularly as it pertains to maintaining a medically ready force. Baseline testing is being used both in the civilian and military domains to assess concussion injury and recovery. Accurate interpretation of these baseline assessments requires one to consider other influencing factors not related to concussion. To date, there is limited understanding, especially within the military, of what factors influence normative test performance. Given the significant physical and mental demands placed on service academy members (SAM), and their relatively high risk for concussion, it is important to describe demographics and normative profile of SAMs. Furthermore, the absence of available baseline normative data on female and non-varsity SAMs makes interpretation of post-injury assessments challenging. Understanding how individuals perform at baseline, given their unique individual characteristics (e.g., concussion history, sex, competition level), will inform post-concussion assessment and management. Thus, the primary aim of this manuscript is to characterize the SAM population and determine normative values on a concussion baseline testing battery. Materials and Methods All data were collected as part of the Concussion Assessment, Research and Education (CARE) Consortium. The baseline test battery included a post-concussion symptom checklist (Sport Concussion Assessment Tool (SCAT), psychological health screening inventory (Brief Symptom Inventory (BSI-18) and neurocognitive evaluation (ImPACT), Balance Error Scoring System (BESS), and Standardized Assessment of Concussion (SAC). Linear regression models were used to examine differences across sexes, competition levels, and varsity contact levels while controlling for academy, freshman status, race, and previous concussion. Zero inflated negative binomial models estimated symptom scores due to the high frequency of zero scores. Results Significant, but small, sex effects were observed on the ImPACT visual memory task. While, females performed worse than males (p < 0.0001, pη2 = 0.01), these differences were small and not larger than the effects of the covariates. A similar pattern was observed for competition level on the SAC. There was a small, but significant difference across competition level. SAMs participating in varsity athletics did significantly worse on the SAC compared to SAMs participating in club or intramural athletics (all p’s < 0.001, η2 = 0.01). When examining symptom reporting, males were more than two times as likely to report zero symptoms on the SCAT or BSI-18. Intramural SAMs had the highest number of symptoms and severity compared to varsity SAMs (p < 0.0001, Cohen’s d < 0.2). Contact level was not associated with SCAT or BSI-18 symptoms among varsity SAMs. Notably, the significant differences across competition level on SCAT and BSI-18 were sub-clinical and had small effect sizes. Conclusion The current analyses provide the first baseline concussion battery normative data among SAMs. While statistically significant differences may be observed on baseline tests, the effect sizes for competition and contact levels are very small, indicating that differences are likely not clinically meaningful at baseline. Identifying baseline differences and significant covariates is important for future concussion-related analyses to inform concussion evaluations for all athlete levels

The Disunity of Consciousness

It is commonplace for both philosophers and cognitive scientists to express their allegiance to the "unity of consciousness". This is the claim that a subject’s phenomenal consciousness, at any one moment in time, is a single thing. This view has had a major influence on computational theories of consciousness. In particular, what we call single-track theories dominate the literature, theories which contend that our conscious experience is the result of a single consciousness-making process or mechanism in the brain. We argue that the orthodox view is quite wrong: phenomenal experience is not a unity, in the sense of being a single thing at each instant. It is a multiplicity, an aggregate of phenomenal elements, each of which is the product of a distinct consciousness-making mechanism in the brain. Consequently, cognitive science is in need of a multi-track theory of consciousness; a computational model that acknowledges both the manifold nature of experience, and its distributed neural basis