1,916 research outputs found

    The End of the World and a Little Brown Dog

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    The End of the World and a Little Brown Dog

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    On the number of monochromatic solutions to multiplicative equations

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    Given an rr-colouring of the interval {2,‚Ķ,N}\{2, \dotsc, N \}, what is the minimum number of monochromatic solutions of the equation xy=zxy = z? For r=2r=2, we show that there are always asymptotically at least (1/22)N1/2log‚Ā°N(1/2\sqrt{2}) N^{1/2} \log N monochromatic solutions, and that the leading constant is sharp. We also establish a stability version of this result. For general rr, we show that there are at least CrN1/S(r‚ąí1)C_r N^{1/S(r-1)} monochromatic solutions, where S(r)S(r) is the Schur number for rr colours and CrC_r is a constant. This bound is sharp up to logarithmic factors when r‚ȧ4r \leq 4. We also obtain results for more general multiplicative equations of the form x1a1‚čĮxkak=yx_1^{a_1} \dotsb x_k^{a_k} = y, where a1,‚Ķ,aka_1, \dotsc, a_k are positive integers, at least one of which equals 11. Our corresponding upper bounds are given in terms of certain `interval Rado numbers' for additive equations. We pose a number of open problems concerning these numbers.Comment: 26 page

    Tephritid-microbial interactions to enhance fruit fly performance in sterile insect technique programs

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    Background: The Sterile Insect Technique (SIT) is being applied for the management of economically important pest fruit flies (Diptera: Tephritidae) in a number of countries worldwide. The success and cost effectiveness of SIT depends upon the ability of mass-reared sterilized male insects to successfully copulate with conspecific wild fertile females when released in the field. Methods: We conducted a critical analysis of the literature about the tephritid gut microbiome including the advancement of methods for the identification and characterization of microbiota, particularly next generation sequencing, the impacts of irradiation (to induce sterility of flies) and fruit fly rearing, and the use of probiotics to manipulate the fruit fly gut microbiota. Results: Domestication, mass-rearing, irradiation and handling, as required in SIT, may change the structure of the fruit flies’ gut microbial community compared to that of wild flies under field conditions. Gut microbiota of tephritids are important in their hosts’ development, performance and physiology. Knowledge of how mass-rearing and associated changes of the microbial community impact the functional role of the bacteria and host biology is limited. Probiotics offer potential to encourage a gut microbial community that limits pathogens, and improves the quality of fruit flies. Conclusions: Advances in technologies used to identify and characterize the gut microbiota will continue to expand our understanding of tephritid gut microbial diversity and community composition. Knowledge about the functions of gut microbes will increase through the use of gnotobiotic models, genome sequencing, metagenomics, metatranscriptomics, metabolomics and metaproteomics. The use of probiotics, or manipulation of the gut microbiota, offers significant opportunities to enhance the production of high quality, performing fruit flies in operational SIT programs

    The effectiveness of nutrition education programmes on improving dietary intake in athletes: A Systematic Review

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    Nutrition education programmes for athletes aim to enhance nutrition knowledge and more importantly support positive dietary change to enhance performance, health and well-being. This systematic review assessed changes in the dietary intakes of athletes in response to nutrition education programmes. A search was conducted which included studies providing quantitative dietary intake assessment of athletes of any calibre aged between 12 and 65 years in response to a nutrition education programme. Standardised differences (effect sizes) were calculated (when possible) for each dietary parameter. The search yielded 6285 papers with twenty-two studies (974 participants (71¬∑9 % female)) eligible for inclusion. Studies described athletes competing at high school (n 3) through to college level or higher (n 19). Study designs were either single arm with an intervention-only group (twelve studies; n 241) or double arm including an intervention and control group (ten studies; n 689). No control groups received an alternative or ‚Äėsham‚Äô intervention. Face-to-face lectures (9/22) and individual nutrition counselling (6/22) were the most common education interventions. Non-weighed, 3-d diet records (10/22) were the most frequently utilised dietary assessment method. Although 14/22 studies (n 5 single and n 9 double) reported significant change in at least one nutrition parameter, dietary changes were inconsistent. Poor study quality and heterogeneity of methods prohibit firm conclusions regarding overall intervention success or superior types of educational modalities. Of note, carbohydrate intakes ‚Äėpost-intervention‚Äô when assessed often failed to meet recommended guidelines (12/17 studies). Given the substantial investment made in nutrition education interventions with athletes, there is a need for well-designed and rigorous research to inform future best practice

    Complexity and entanglement for thermofield double states

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    Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t = 0, we show that the complexity of formation is proportional to the thermodynamic entropy, in qualitative agreement with holographic complexity proposals. For TFD states at t > 0, we demonstrate that the complexity evolves in time and saturates after a time of the order of the inverse temperature. The latter feature, which is in contrast with the results of holographic proposals, is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel technical aspect of our work is framing complexity calculations in the language of covariance matrices and the associated symplectic transformations, which provide a natural language for dealing with Gaussian states. Furthermore, for free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with the time dependence of the entanglement entropy for simple bipartitions of TFDs. We relate our results for the entanglement entropy to previous studies on non-equilibrium entanglement evolution following quenches. We also present a new analytic derivation of a logarithmic contribution due to the zero momentum mode in the limit of vanishing mass for a subsystem containing a single degree of freedom on each side of the TFD and argue why a similar logarithmic growth should be present for larger subsystems

    Distribution and kinematics of the HCN(3-2) emission down to the innermost region in the envelope of the O-rich star W Hya

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    We report high angular resolution observations of the HCN (3-2) line emission in the circumstellar envelope of the O-rich star W Hya with the Submillimeter Array. The proximity of this star allows us to image its molecular envelope with a spatial resolution of just ~40 AU, corresponding to about 10 times the stellar diameter. We resolve the HCN (3-2) emission and find that it is centrally peaked and has a roughly spherically symmetrical distribution. This shows that HCN is formed in the innermost region of the envelope (within ~10 stellar radii), which is consistent with predictions from pulsation-driven shock chemistry models, and rules out the scenario in which HCN forms through photochemical reactions in the outer envelope. Our model suggests that the envelope decreases steeply in temperature and increases smoothly in velocity with radius, inconsistent with the standard model for mass-loss driven by radiative pressure on dust grains. We detect a velocity gradient of ~5 km/s in the NW--SE direction over the central 40 AU. This velocity gradient is reminescent of that seen in OH maser lines, and could be caused by the rotation of the envelope or by a weak bipolar outflow.Comment: accepted for publication in ApJ

    The Spitzer Gould Belt Survey of Large Nearby Interstellar Clouds: Discovery of A Dense Embedded Cluster in the Serpens-Aquila Rift

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    We report the discovery of a nearby, embedded cluster of young stellar objects, associated filamentary infrared dark cloud, and 4.5 mu m shock emission knots from outflows detected in Spitzer IRAC mid-infrared imaging of the Serpens-Aquila Rift obtained as part of the Spitzer Gould Belt Legacy Survey. We also present radial velocity measurements of the region from molecular line observations obtained with the Submillimeter Array (SMA) that suggest the cluster is comoving with the Serpens Main embedded cluster to the north. We therefore assign it 3 degrees the same distance, 260 pc. The core of the new cluster, which we call Serpens South, is composed of an unusually large fraction of protostars (77%) at high mean surface density (> 430 pc(-2)) and short median nearest neighbor spacing (3700 AU). We perform basic cluster structure characterization using nearest neighbor surface density mapping of the YSOs and compare our findings to other known clusters with equivalent analyses available in the literature.Astronom
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