Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Beam Energy Dependence of the Third Harmonic of Azimuthal Correlations in Au+Au Collisions at RHIC

We present results from a harmonic decomposition of two-particle azimuthal correlations measured with the STAR detector in Au+Au collisions for energies ranging from $\sqrt{s_{NN}}=7.7$ GeV to 200 GeV. The third harmonic $v_3^2\{2\}=\langle \cos3(\phi_1-\phi_2)\rangle$, where $\phi_1-\phi_2$ is the angular difference in azimuth, is studied as a function of the pseudorapidity difference between particle pairs $\Delta\eta = \eta_1-\eta_2$. Non-zero {\vthree} is directly related to the previously observed large-$\Delta\eta$ narrow-$\Delta\phi$ ridge correlations and has been shown in models to be sensitive to the existence of a low viscosity Quark Gluon Plasma (QGP) phase. For sufficiently central collisions, $v_3^2\{2\}$ persist down to an energy of 7.7 GeV suggesting that QGP may be created even in these low energy collisions. In peripheral collisions at these low energies however, $v_3^2\{2\}$ is consistent with zero. When scaled by pseudorapidity density of charged particle multiplicity per participating nucleon pair, $v_3^2\{2\}$ for central collisions shows a minimum near {\snn}$=20$ GeV.Comment: 7 pages, 4 figures, for submission to Phys. Rev. Let

J/ψ\rm{J}/\psi production at low transverse momentum in p+p and d+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We report on the measurement of $\rm{J}/\psi$ production in the dielectron channel at mid-rapidity (|y|<1) in p+p and d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider. The transverse momentum $p_{T}$ spectra in p+p for $p_{T}$ < 4 GeV/c and d+Au collisions for $p_{T}$ < 3 GeV/c are presented. These measurements extend the STAR coverage for $\rm{J}/\psi$ production in p+p collisions to low $p_{T}$. The $$ from the measured $\rm{J}/\psi$ invariant cross section in p+p and d+Au collisions are evaluated and compared to similar measurements at other collision energies. The nuclear modification factor for $\rm{J}/\psi$ is extracted as a function of $p_{T}$ and collision centrality in d+Au and compared to model calculations using the modified nuclear Parton Distribution Function and a final-state $\rm{J}/\psi$ nuclear absorption cross section

A standardisation framework for bio‐logging data to advance ecological research and conservation

Bio‐logging data obtained by tagging animals are key to addressing global conservation challenges. However, the many thousands of existing bio‐logging datasets are not easily discoverable, universally comparable, nor readily accessible through existing repositories and across platforms, slowing down ecological research and effective management. A set of universal standards is needed to ensure discoverability, interoperability and effective translation of bio‐logging data into research and management recommendations. We propose a standardisation framework adhering to existing data principles (FAIR: Findable, Accessible, Interoperable and Reusable; and TRUST: Transparency, Responsibility, User focus, Sustainability and Technology) and involving the use of simple templates to create a data flow from manufacturers and researchers to compliant repositories, where automated procedures should be in place to prepare data availability into four standardised levels: (a) decoded raw data, (b) curated data, (c) interpolated data and (d) gridded data. Our framework allows for integration of simple tabular arrays (e.g. csv files) and creation of sharable and interoperable network Common Data Form (netCDF) files containing all the needed information for accuracy‐of‐use, rightful attribution (ensuring data providers keep ownership through the entire process) and data preservation security. We show the standardisation benefits for all stakeholders involved, and illustrate the application of our framework by focusing on marine animals and by providing examples of the workflow across all data levels, including filled templates and code to process data between levels, as well as templates to prepare netCDF files ready for sharing. Adoption of our framework will facilitate collection of Essential Ocean Variables (EOVs) in support of the Global Ocean Observing System (GOOS) and inter‐governmental assessments (e.g. the World Ocean Assessment), and will provide a starting point for broader efforts to establish interoperable bio‐logging data formats across all fields in animal ecology

Effects of Alcohol on the Acquisition and Expression of Fear Potentiated Startle in Mouse Lines Selectively Bred for High and Low Alcohol Preference

Rationale: Anxiety disorders and alcohol-use disorders frequently co-occur in humans perhaps because alcohol relieves anxiety. Studies in humans and rats indicate that alcohol may have greater anxiolytic effects in organisms with increased genetic propensity for high alcohol consumption. Objectives and Methods: The purpose of this study was to investigate the effects of moderate doses of alcohol (0.5, 1.0, 1.5 g/kg) on the acquisition and expression of anxiety-related behavior using a fear-potentiated startle (FPS) procedure. Experiments were conducted in two replicate pairs of mouse lines selectively bred for high- (HAP1 and HAP2) and low- (LAP1 and LAP2) alcohol preference; these lines have previously shown a genetic correlation between alcohol preference and FPS (HAP\u3eLAP; Barrenha and Chester 2007). In a control experiment, the effect of diazepam (4.0 mg/kg) on the expression of FPS was tested in HAP2 and LAP2 mice. Results: The 1.5 g/kg alcohol dose moderately decreased the expression of FPS in both HAP lines but not LAP lines. Alcohol had no effect on the acquisition of FPS in any line. Diazepam reduced FPS to a similar extent in both HAP2 and LAP2 mice. Conclusions: HAP mice may be more sensitive to the anxiolytic effects of alcohol than LAP mice when alcohol is given prior to the expression of FPS. These data collected in two pairs of HAP/LAP mouse lines suggest that the anxiolytic response to alcohol in HAP mice may be genetically correlated with their propensity toward high alcohol preference and robust FPS

Brain architecture in the terrestrial hermit crab Coenobita clypeatus (Anomura, Coenobitidae), a crustacean with a good aerial sense of smell

<p>Abstract</p> <p>Background</p> <p>During the evolutionary radiation of Crustacea, several lineages in this taxon convergently succeeded in meeting the physiological challenges connected to establishing a fully terrestrial life style. These physiological adaptations include the need for sensory organs of terrestrial species to function in air rather than in water. Previous behavioral and neuroethological studies have provided solid evidence that the land hermit crabs (Coenobitidae, Anomura) are a group of crustaceans that have evolved a good sense of aerial olfaction during the conquest of land. We wanted to study the central olfactory processing areas in the brains of these organisms and to that end analyzed the brain of <it>Coenobita clypeatus </it>(Herbst, 1791; Anomura, Coenobitidae), a fully terrestrial tropical hermit crab, by immunohistochemistry against synaptic proteins, serotonin, FMRFamide-related peptides, and glutamine synthetase.</p> <p>Results</p> <p>The primary olfactory centers in this species dominate the brain and are composed of many elongate olfactory glomeruli. The secondary olfactory centers that receive an input from olfactory projection neurons are almost equally large as the olfactory lobes and are organized into parallel neuropil lamellae. The architecture of the optic neuropils and those areas associated with antenna two suggest that <it>C. clypeatus </it>has visual and mechanosensory skills that are comparable to those of marine Crustacea.</p> <p>Conclusion</p> <p>In parallel to previous behavioral findings of a good sense of aerial olfaction in C. clypeatus, our results indicate that in fact their central olfactory pathway is most prominent, indicating that olfaction is a major sensory modality that these brains process. Interestingly, the secondary olfactory neuropils of insects, the mushroom bodies, also display a layered structure (vertical and medial lobes), superficially similar to the lamellae in the secondary olfactory centers of <it>C. clypeatus</it>. More detailed analyses with additional markers will be necessary to explore the question if these similarities have evolved convergently with the establishment of superb aerial olfactory abilities or if this design goes back to a shared principle in the common ancestor of Crustacea and Hexapoda.</p