Spectral faux trees

A spectral faux tree with respect to a given matrix is a graph which is not a tree but is cospectral with a tree for the given matrix. We consider the existence of spectral faux trees for several matrices, with emphasis on constructions. For the Laplacian matrix, there are no spectral faux trees. For the adjacency matrix, almost all trees are cospectral with a faux tree. For the signless Laplacian matrix, spectral faux trees can only exist when the number of vertices is of the form $n=4k$. For the normalized adjacency, spectral faux trees exist when the number of vertices $n\ge 4$, and we give an explicit construction for a family whose size grows exponentially with $k$ for $n=\alpha k+1$ where $\alpha$ is fixed.Comment: 17 page

Complements of coalescing sets

We consider matrices of the form $qD+A$, with $D$ being the diagonal matrix of degrees, $A$ being the adjacency matrix, and $q$ a fixed value. Given a graph $H$ and $B\subseteq V(G)$, which we call a coalescent pair $(H,B)$, we derive a formula for the characteristic polynomial where a copy of same rooted graph $G$ is attached by the root to \emph{each} vertex of $B$. Moreover, we establish if $(H_1,B_1)$ and $(H_2,B_2)$ are two coalescent pairs which are cospectral for any possible rooted graph $G$, then $(H_1,V(H_1)\setminus B_1)$ and $(H_2,V(H_2)\setminus B_2)$ will also always be cospectral for any possible rooted graph $G$.Comment: 16 page

X-rays from the Mira AB Binary System

We present the results of XMM-Newton X-ray observations of the Mira AB binary system, which consists of a pulsating, asymptotic giant branch primary and nearby (~0.6'' separation) secondary of uncertain nature. The EPIC CCD (MOS and pn) X-ray spectra of Mira AB are relatively soft, peaking at ~1 keV, with only very weak emission at energies > 3 keV; lines of Ne IX, Ne X, and O VIII are apparent. Spectral modeling indicates a characteristic temperature T_X ~ 10^7 K and intrinsic luminosity L_X ~ 5x10^29 erg s^{-1}, and suggests enhanced abundances of O and, possibly, Ne and Si in the X-ray-emitting plasma. Overall, the X-ray spectrum and luminosity of the Mira AB system more closely resemble those of late-type, pre-main sequence stars or late-type, magnetically active main sequence stars than those of accreting white dwarfs. We conclude that Mira B is most likely a late-type, magnetically active, main-sequence dwarf, and that X-rays from the Mira AB system arise either from magnetospheric accretion of wind material from Mira A onto Mira B, or from coronal activity associated with Mira B itself, as a consequence of accretion-driven spin-up. One (or both) of these mechanisms also could be responsible for the recently discovered, point-like X-ray sources within planetary nebulae.Comment: 14 pages, 3 figures; to appear in the Astrophysical Journa

Store-directed price promotions and communications strategies improve healthier food supply and demand: impact results from a randomized controlled, Baltimore City store-intervention trial

Abstract Objective Small food store interventions show promise to increase healthy food access in under-resourced areas. However, none have tested the impact of price discounts on healthy food supply and demand. We tested the impact of store-directed price discounts and communications strategies, separately and combined, on the stocking, sales and prices of healthier foods and on storeowner psychosocial factors. Design Factorial design randomized controlled trial. Setting Twenty-four corner stores in low-income neighbourhoods of Baltimore City, MD, USA. Subjects Stores were randomized to pricing intervention, communications intervention, combined pricing and communications intervention, or control. Stores that received the pricing intervention were given a 10–30 % price discount by wholesalers on selected healthier food items during the 6-month trial. Communications stores received visual and interactive materials to promote healthy items, including signage, taste tests and refrigerators. Results All interventions showed significantly increased stock of promoted foods v . control. There was a significant treatment effect for daily unit sales of healthy snacks ( β =6·4, 95 % CI 0·9, 11·9) and prices of healthy staple foods ( β =–0·49, 95 % CI –0·90, –0·03) for the combined group v . control, but not for other intervention groups. There were no significant intervention effects on storeowner psychosocial factors. Conclusions All interventions led to increased stock of healthier foods. The combined intervention was effective in increasing sales of healthier snacks, even though discounts on snacks were not passed to the consumer. Experimental research in small stores is needed to understand the mechanisms by which store-directed price promotions can increase healthy food supply and demand

On the Directional Derivative of Kemeny's Constant

In a connected graph, Kemeny's constant gives the expected time of a random walk from an arbitrary vertex $x$ to reach a randomly-chosen vertex $y$. Because of this, Kemeny's constant can be interpreted as a measure of how well a graph is connected. It is generally unknown how the addition or removal of edges affects Kemeny's constant. Inspired by the directional derivative of the normalized Laplacian, we derive the directional derivative of Kemeny's constant for several graph families. In addition, we find sharp bounds for the directional derivative of an eigenvalue of the normalized Laplacian and bounds for the directional derivative of Kemeny's constant

X-Ray Emission from Central Binary Systems of Planetary Nebulae

We study the conditions under which a main sequence binary companion to the central ionizing star of a planetary nebula (PN) might become magnetically active and thereby display strong X-ray luminosity. Since most PNe are older than few billion years, any main sequence companion will rotate too slowly to have magnetic activity and hence bright X-ray emission, unless it is spun-up. We demonstrate that if the orbital separation during the AGB phase of the PN progenitor is less than 30-60 AU, main sequence companions in the spectral type range F7 to M4 will accrete enough angular momentum from the AGB wind to rotate rapidly, become magnetically active, and exhibit strong X-ray luminosities. Lower mass M stars and brown dwarfs can also become magnetically active, but they should have small orbital separations and hence are less likely to survive the AGB phase of the progenitor. We estimate that 20-30 per cent of elliptical PNe and 30-50 per cent of bipolar PN are likely to have magnetically active companions which will reveal themselves in X-ray observations. Re-analysis of Chandra X-ray Observatory spectroscopy of the compact central source of NGC 7293 indicates that the emitting region of this object possesses abundance anomalies similar to those of coronally active main-sequence stars.Comment: 15 pages, Submitted to Ap

microRNA expression in the prefrontal cortex of individuals with schizophrenia and schizoaffective disorder

BACKGROUND: microRNAs (miRNAs) are small, noncoding RNA molecules that are now thought to regulate the expression of many mRNAs. They have been implicated in the etiology of a variety of complex diseases, including Tourette's syndrome, Fragile × syndrome, and several types of cancer. RESULTS: We hypothesized that schizophrenia might be associated with altered miRNA profiles. To investigate this possibility we compared the expression of 264 human miRNAs from postmortem prefrontal cortex tissue of individuals with schizophrenia (n = 13) or schizoaffective disorder (n = 2) to tissue of 21 psychiatrically unaffected individuals using a custom miRNA microarray. Allowing a 5% false discovery rate, we found that 16 miRNAs were differentially expressed in prefrontal cortex of patient subjects, with 15 expressed at lower levels (fold change 0.63 to 0.89) and 1 at a higher level (fold change 1.77) than in the psychiatrically unaffected comparison subjects. The expression levels of 12 selected miRNAs were also determined by quantitative RT-PCR in our lab. For the eight miRNAs distinguished by being expressed at lower microarray levels in schizophrenia samples versus comparison samples, seven were also expressed at lower levels with quantitative RT-PCR. CONCLUSION: This study is the first to find altered miRNA profiles in postmortem prefrontal cortex from schizophrenia patients

X-ray Emission from the Binary Central Stars of the Planetary Nebulae HFG 1, DS 1, and LoTr 5

Close binary systems undergoing mass transfer or common envelope interactions can account for the morphological properties of some planetary nebulae. The search for close binary companions in planetary nebulae is hindered by the difficulty of detecting cool, late-type, main sequence companions in binary systems with hot pre-white dwarf primaries. However, models of binary PN progenitor systems predict that mass accretion or tidal interactions can induce rapid rotation in the companion, leading to X-ray-emitting coronae. To test such models, we have searched for, and detected, X-ray emission from three binary central stars within planetary nebulae: the post-common envelope close binaries in HFG 1 and DS 1 consisting of O-type subdwarfs with late-type, main sequence companions, and the binary system in LoTr 5 consisting of O-type subdwarf and rapidly rotating, late-type giant companion. The X-ray emission in each case is best characterized by spectral models consisting of two optically-thin thermal plasma components with characteristic temperatures of about 10 MK and 15-40 MK, and total X-ray luminosities about 10^30 erg/s. We consider the possible origin of the X-ray emission from these binary systems and conclude that the most likely origin is, in each case, a corona around the late-type companion, as predicted by models of interacting binaries.Comment: tell your friend

B’More healthy: retail rewards - design of a multi-level communications and pricing intervention to improve the food environment in Baltimore City

BackgroundLow-income black residents of Baltimore City have disproportionately higher rates of obesity and chronic disease than other Maryland residents. Increasing the availability and affordability of healthy food are key strategies to improve the food environment and can lead to healthier diets. This paper describes B’More Healthy: Retail Rewards (BHRR), an intervention that tests the effectiveness of performance-based pricing discounts and health communications, separately and combined, on healthy food purchasing and consumption among low-income small store customers.Methods/designBHRR is 2x2 factorial design randomized controlled trial. Fifteen regular customers recruited from each of 24 participating corner stores in Baltimore City were enrolled. Food stores were randomized to 1) pricing intervention, 2) communications intervention, 3) combined intervention, or 4) control. Pricing stores were given a 10-30% price discount on selected healthier food items, such as fresh fruits, frozen vegetables, and baked chips, at the point of purchase from two food wholesale stores during the 6-month trial. Storeowners agreed to pass on the discount to the consumer to increase demand for healthy food. Communications stores received visual and interactive materials to promote healthy items, including signage, taste tests, and refrigerators. Primary outcome measures include consumer food purchasing and associated psychosocial variables. Secondary outcome measures include consumer food consumption, store sales, and associated storeowner psychosocial factors. Process evaluation was monitored throughout the trial at wholesaler, small store, and consumer levels.DiscussionThis is the first study to test the impact of performance-based pricing and communications incentives in small food stores, an innovative strategy to encourage local wholesalers and storeowners to share responsibility in creating a healthier food supply by stocking, promoting, and reducing costs of healthier foods in their stores. Local food wholesalers were involved in a top-down, participatory approach to develop and implement an effective and sustainable program. This study will provide evidence on the effectiveness of price incentives and health communications, separately and combined, among a low-income urban U.S. population.Trial registrationClinicalTrials.gov: NCT02279849 (2/18/2014)

A View of Tropical Cyclones from Above: The Tropical Cyclone Intensity Experiment

Tropical cyclone (TC) outflow and its relationship to TC intensity change and structure were investigated in the Office of Naval Research Tropical Cyclone Intensity (TCI) field program during 2015 using dropsondes deployed from the innovative new High-Definition Sounding System (HDSS) and remotely sensed observations from the Hurricane Imaging Radiometer (HIRAD), both on board the NASA WB-57 that flew in the lower stratosphere. Three noteworthy hurricanes were intensively observed with unprecedented horizontal resolution: Joaquin in the Atlantic and Marty and Patricia in the eastern North Pacific. Nearly 800 dropsondes were deployed from the WB-57 flight level of ∼60,000 ft (∼18 km), recording atmospheric conditions from the lower stratosphere to the surface, while HIRAD measured the surface winds in a 50-km-wide swath with a horizontal resolution of 2 km. Dropsonde transects with 4–10-km spacing through the inner cores of Hurricanes Patricia, Joaquin, and Marty depict the large horizontal and vertical gradients in winds and thermodynamic properties. An innovative technique utilizing GPS positions of the HDSS reveals the vortex tilt in detail not possible before. In four TCI flights over Joaquin, systematic measurements of a major hurricane’s outflow layer were made at high spatial resolution for the first time. Dropsondes deployed at 4-km intervals as the WB-57 flew over the center of Hurricane Patricia reveal in unprecedented detail the inner-core structure and upper-tropospheric outflow associated with this historic hurricane. Analyses and numerical modeling studies are in progress to understand and predict the complex factors that influenced Joaquin’s and Patricia’s unusual intensity changes