Hammersley\u27s Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers

The analogue of Hammersley\u27s theorem on the length of the longest monotonic subsequence of independent, identically, and continuously distributed random variables is obtained for the pseudorandom van der Corput sequence. In this case there is no limit but the precise limits superior and inferior are determined. The constants obtained are closely related to those established in the independent case by Logan and Shepp, and Vershik and Kerov

Environmental Factors Influencing Reproduction in a Temperate Marine Reef Goby, Rhinogobiops nicholsii, and Associated Behaviors

The blackeye goby is a protogynous reef fish common to the northeastern Pacific Ocean. While this ubiquitous species has been the focus of numerous studies, there are several aspects of its reproductive ecology that are unknown. By directly quantifying reproduction from digital photographs of blackeye goby nests in the field, this study aimed to determine whether reproductive patterns were linked to 1) lunar phase or 2) ambient water temperature; and 3) whether the behavior of gobies changed when a nearby conspecific had eggs in his nest. At Santa Catalina Island, California, twenty 2.25-m2 artificial reefs were established and stocked with similar numbers and size-distributions of blackeye gobies during the summers of 2012 and 2013. Photographs of nests were taken weekly for ~3 months each summer. Through analysis of photographs, incubation time was found to be more than 7 days but less than 14 days. Nests, each guarded by one male, contained an average of 8664 eggs, in an area of 43.8 cm2, with 215 eggs cm-2. Blackeye gobies laid eggs during all lunar phases and the number of eggs produced was not related to lunar phase. Reproductive output, however, was negatively correlated with water temperature, with populations on reefs that experienced cooler temperatures producing more eggs. The presence of eggs in a nest had little effect on behavior of blackeye gobies on that reef. Additional observations made outside of summer months indicated that blackeye gobies can reproduce year-round in southern California. These results suggest a reproductive strategy aimed at maximizing total reproductive output by spreading the risk of reproductive failure throughout the year rather than optimizing the timing of reproduction

Exact Expectations of Minimal Spanning Trees for Graphs With Random Edge Weights

Two methods are used to compute the expected value of the length of the minimal spanning tree (MST) of a graph whose edges are assigned lengths which are independent and uniformly distributed. The first method yields an exact formula in terms of the Tutte polynomial. As an illustration, the expected length of the MST of the Petersen graph is found to be 34877/12012 = 2.9035 .... A second, more elementary, method for computing the expected length of the MST is then derived by conditioning on the length of the shortest edge. Both methods in principle apply to any finite graph. To illustrate the method we compute the expected lengths of the MSTs for complete graphs

Searching for Organics Preserved in 4.5 Billion Year Old Salt

Our understanding of early solar system fluids took a dramatic turn a decade ago with the discovery of fluid inclusion-bearing halite (NaCl) crystals in the matrix of two freshly fallen brecciated H chondrite falls, Monahans and Zag. Both meteorites are regolith breccias, and contain xenolithic halite (and minor admixed sylvite -- KCl, crystals in their regolith lithologies. The halites are purple to dark blue, due to the presence of color centers (electrons in anion vacancies) which slowly accumulated as 40K (in sylvite) decayed over billions of years. The halites were dated by K-Ar, Rb-Sr and I-Xe systematics to be 4.5 billion years old. The "blue" halites were a fantastic discovery for the following reasons: (1) Halite+sylvite can be dated (K is in sylvite and will substitute for Na in halite, Rb substitutes in halite for Na, and I substitutes for Cl). (2) The blue color is lost if the halite dissolves on Earth and reprecipitates (because the newly-formed halite has no color centers), so the color serves as a "freshness" or pristinity indicator. (3) Halite frequently contains aqueous fluid inclusions. (4) Halite contains no structural oxygen, carbon or hydrogen, making them ideal materials to measure these isotopic systems in any fluid inclusions. (5) It is possible to directly measure fluid inclusion formation temperatures, and thus directly measure the temperature of the mineralizing aqueous fluid. In addition to these two ordinary chondrites halite grains have been reliably reported in several ureilites, an additional ordinary chondrite (Jilin), and in the carbonaceous chondrite (Murchison), although these reports were unfortunately not taken seriously. We have lately found additional fluid inclusions in carbonates in several additional carbonaceous chondrites. Meteoritic aqueous fluid inclusions are apparently relatively widespread in meteorites, though very small and thus difficult to analyze

The large‐scale freshwater cycle of the Arctic

This paper synthesizes our understanding of the Arctic\u27s large‐scale freshwater cycle. It combines terrestrial and oceanic observations with insights gained from the ERA‐40 reanalysis and land surface and ice‐ocean models. Annual mean freshwater input to the Arctic Ocean is dominated by river discharge (38%), inflow through Bering Strait (30%), and net precipitation (24%). Total freshwater export from the Arctic Ocean to the North Atlantic is dominated by transports through the Canadian Arctic Archipelago (35%) and via Fram Strait as liquid (26%) and sea ice (25%). All terms are computed relative to a reference salinity of 34.8. Compared to earlier estimates, our budget features larger import of freshwater through Bering Strait and larger liquid phase export through Fram Strait. While there is no reason to expect a steady state, error analysis indicates that the difference between annual mean oceanic inflows and outflows (∼8% of the total inflow) is indistinguishable from zero. Freshwater in the Arctic Ocean has a mean residence time of about a decade. This is understood in that annual freshwater input, while large (∼8500 km3), is an order of magnitude smaller than oceanic freshwater storage of ∼84,000 km3. Freshwater in the atmosphere, as water vapor, has a residence time of about a week. Seasonality in Arctic Ocean freshwater storage is nevertheless highly uncertain, reflecting both sparse hydrographic data and insufficient information on sea ice volume. Uncertainties mask seasonal storage changes forced by freshwater fluxes. Of flux terms with sufficient data for analysis, Fram Strait ice outflow shows the largest interannual variability

Cholinergic Modulation of Locomotion and Striatal Dopamine Release Is Mediated by α6α4* Nicotinic Acetylcholine Receptors

Dopamine (DA) release in striatum is governed by firing rates of midbrain DA neurons, striatal cholinergic tone, and nicotinic ACh receptors (nAChRs) on DA presynaptic terminals. DA neurons selectively express α6* nAChRs, which show high ACh and nicotine sensitivity. To help identify nAChR subtypes that control DA transmission, we studied transgenic mice expressing hypersensitive α6^(L9’S*) receptors. α6^(L9’S) mice are hyperactive, travel greater distance, exhibit increased ambulatory behaviors such as walking, turning, and rearing, and show decreased pausing, hanging, drinking, and grooming. These effects were mediated by α6 α4* pentamers, as α6^(L9’S) mice lacking α4 subunits displayed essentially normal behavior. In α6^(L9’S) mice, receptor numbers are normal, but loss of α4 subunits leads to fewer and less sensitive α6* receptors. Gain-of-function nicotine-stimulated DA release from striatal synaptosomes requires α4 subunits, implicating α6α4β2* nAChRs in α6^(L9’S) mouse behaviors. In brain slices, we applied electrochemical measurements to study control of DA release by α6^(L9’S) nAChRs. Burst stimulation of DA fibers elicited increased DA release relative to single action potentials selectively in α6^(L9’S), but not WT or α4KO/ α6^(L9’S), mice. Thus, increased nAChR activity, like decreased activity, leads to enhanced extracellular DA release during phasic firing. Bursts may directly enhance DA release from α6^(L9’S) presynaptic terminals, as there was no difference in striatal DA receptor numbers or DA transporter levels or function in vitro. These results implicate α6α4β2* nAChRs in cholinergic control of DA transmission, and strongly suggest that these receptors are candidate drug targets for disorders involving the DA system

A Macrophysiological Analysis of Energetic Constraints on Geographic Range Size in Mammals

Physiological processes are essential for understanding the distribution and abundance of organisms, and recently, with widespread attention to climate change, physiology has been ushered back to the forefront of ecological thinking. We present a macrophysiological analysis of the energetics of geographic range size using combined data on body size, basal metabolic rate (BMR), phylogeny and range properties for 574 species of mammals. We propose three mechanisms by which interspecific variation in BMR should relate positively to geographic range size: (i) Thermal Plasticity Hypothesis, (ii) Activity Levels/Dispersal Hypothesis, and (iii) Energy Constraint Hypothesis. Although each mechanism predicts a positive correlation between BMR and range size, they can be further distinguished based on the shape of the relationship they predict. We found evidence for the predicted positive relationship in two dimensions of energetics: (i) the absolute, mass-dependent dimension (BMR) and (ii) the relative, mass-independent dimension (MIBMR). The shapes of both relationships were similar and most consistent with that expected from the Energy Constraint Hypothesis, which was proposed previously to explain the classic macroecological relationship between range size and body size in mammals and birds. The fact that this pattern holds in the MIBMR dimension indicates that species with supra-allometric metabolic rates require among the largest ranges, above and beyond the increasing energy demands that accrue as an allometric consequence of large body size. The relationship is most evident at high latitudes north of the Tropics, where large ranges and elevated MIBMR are most common. Our results suggest that species that are most vulnerable to extinction from range size reductions are both large-bodied and have elevated MIBMR, but also, that smaller species with elevated MIBMR are at heightened risk. We also provide insights into the global latitudinal trends in range size and MIBMR and more general issues of phylogenetic and geographic scale

Relative kerf and sawing variation values for some hardwood sawing machines

Information on the conversion efficiency of sawing machines is important to those involved in the management, maintenance, and design of sawmills. Little information on the conversion characteristics of hardwood sawing machines has been available. This study, based on 266 studies of 6 machine types, provides an analysis of the machine characteristics of kerf width, within-board, between-board, and total sawing variations and wood loss per sawline. Machine conversion efficiency was found to be explained by feedworks and setworks type, and sawblade thickness and type. This analysis of machine characteristics provides information for a rational choice of sawing machines for hardwood sawmills

Estimating hardwood sawmill conversion efficiency based on sawing machine and log characteristics

Increased problems of hardwood timber availability have caused many sawmiller, industry analysts, and planners to recognize the importance of sawmill conversion efficiency. Conversion efficiency not only affects sawmill profits, but is also important on a much broader level. Timber supply issues have caused resource planners and policy makers to consider the effects of conversion efficiency on the utilization and depletion of the timber resource. Improvements in sawmill conversion efficiency would favorably impact sawmill profits, and would be equivalent in effect to extending existing supplies of standing timber. An equation was developed to estimate lumber recovery factor for hardwood sawmills based on the characteristics of sawing machines and log resources. Variables included in the model were headrig type, headrig kerf, average log diameter and length, and the influence of total sawing variation. The estimated coefficients significantly influenced lumber recovery factor. The model should be helpful in assessing conversion efficiency trends and potential benefits from gains in sawmill efficiency

Online Selection of Alternating Subsequences from a Random Sample

We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12 percent worse than a person who can make selections with full knowledge of the random sequence