On the density of the odd values of the partition function

The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2. Our main result will relate the densities, say $\delta_t$, of the odd values of the $t$-multipartition functions $p_t(n)$, for several integers $t$. In particular, we will show that if $\delta_t>0$ for some $t\in \{5,7,11,13,17,19,23,25\}$, then (assuming it exists) $\delta_1>0$; that is, $p(n)$ itself is odd with positive density. Notice that, currently, the best unconditional result does not even imply that $p(n)$ is odd for $\sqrt{x}$ values of $n\le x$. In general, we conjecture that $\delta_t=1/2$ for all $t$ odd, i.e., that similarly to the case of $p(n)$, all multipartition functions are in fact equidistributed modulo 2. Our arguments will employ a number of algebraic and analytic methods, ranging from an investigation modulo 2 of some classical Ramanujan identities and several other eta product results, to a unified approach that studies the parity of the Fourier coefficients of a broad class of modular form identities recently introduced by Radu.Comment: Several changes with respect to the 2015 version. 18 pages. To appear in the Annals of Combinatoric

Real-time observation of a coherent lattice transformation into a high-symmetry phase

Excursions far from their equilibrium structures can bring crystalline solids through collective transformations including transitions into new phases that may be transient or long-lived. Direct spectroscopic observation of far-from-equilibrium rearrangements provides fundamental mechanistic insight into chemical and structural transformations, and a potential route to practical applications, including ultrafast optical control over material structure and properties. However, in many cases photoinduced transitions are irreversible or only slowly reversible, or the light fluence required exceeds material damage thresholds. This precludes conventional ultrafast spectroscopy in which optical excitation and probe pulses irradiate the sample many times, each measurement providing information about the sample response at just one probe delay time following excitation, with each measurement at a high repetition rate and with the sample fully recovering its initial state in between measurements. Using a single-shot, real-time measurement method, we were able to observe the photoinduced phase transition from the semimetallic, low-symmetry phase of crystalline bismuth into a high-symmetry phase whose existence at high electronic excitation densities was predicted based on earlier measurements at moderate excitation densities below the damage threshold. Our observations indicate that coherent lattice vibrational motion launched upon photoexcitation with an incident fluence above 10 mJ/cm2 in bulk bismuth brings the lattice structure directly into the high-symmetry configuration for tens of picoseconds, after which carrier relaxation and diffusion restore the equilibrium lattice configuration.Comment: 22 pages, 4 figure

Low temperature solvent-free allylic oxidation of cyclohexene using graphitic oxide catalysts

A range of graphitic oxides have been utilised as metal free carbocatalysts for the low temperature oxidation of cyclohexene. The activity of the catalysts was correlated with the amount of surface oxygen on the graphitic oxide. In the case of cyclohexene oxidation, major selectivity is observed to allylic oxidation products. This is in contrast to the epoxide being the major product in linear alkene oxidation. This selectivity was maintained over long reaction times and at a conversion of above 50 %. Only small amounts of epoxide were observed, which eventually decreases at higher conversion due to hydrolysis to cyclohexane diol. The similarity between the non-catalysed and the catalysed product distribution suggests that these catalysts act as a solid initiator, and the role of the graphitic oxide is to decrease the lengthy induction period observed in the blank non-catalysed reaction

Simulating the Biogeochemical and Biogeophysical Impacts of Transient Land Cover Change and Wood Harvest in the Community Climate System Model (CCSM4) from 1850 to 2100

This is the publisher's version, also available electronically from http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-11-00256.1.To assess the climate impacts of historical and projected land cover change in the Community Climate System Model, version 4 (CCSM4), new time series of transient Community Land Model, version 4 (CLM4) plant functional type (PFT) and wood harvest parameters have been developed. The new parameters capture the dynamics of the Coupled Model Intercomparison Project phase 5 (CMIP5) land cover change and wood harvest trajectories for the historical period from 1850 to 2005 and for the four representative concentration pathway (RCP) scenarios from 2006 to 2100. Analysis of the biogeochemical impacts of land cover change in CCSM4 reveals that the model produced a historical cumulative land use flux of 127.7 PgC from 1850 to 2005, which is in general agreement with other global estimates of 156 PgC for the same period. The biogeophysical impacts of the transient land cover change parameters were cooling of the near-surface atmosphere over land by −0.1°C, through increased surface albedo and reduced shortwave radiation absorption. When combined with other transient climate forcings, the higher albedo from land cover change was counteracted by decreasing snow albedo from black carbon deposition and high-latitude warming. The future CCSM4 RCP simulations showed that the CLM4 transient PFT parameters can be used to represent a wide range of land cover change scenarios. In the reforestation scenario of RCP 4.5, CCSM4 simulated a drawdown of 67.3 PgC from the atmosphere into the terrestrial ecosystem and product pools. By contrast the RCP 8.5 scenario with deforestation and high wood harvest resulted in the release of 30.3 PgC currently stored in the ecosystem

Assembly and structure of α-helical peptide films on hydrophobic fluorocarbon surfaces

The structure, orientation and formation of amphiphilic α-helix model peptide films on fluorocarbon surfaces has been monitored with sum frequency generation (SFG) vibrational spectroscopy, near edge X-ray absorption fine structure (NEXAFS) spectroscopy and X-ray photoelectron spectroscopy (XPS). The α-helix peptide is a 14-mer of hydrophilic lysine and hydrophobic leucine residues with a hydrophobic periodicity of 3.5. This periodicity yields a rigid amphiphilic peptide with leucine and lysine side chains located on opposite sides. XPS composition analysis confirms the formation of a peptide film that covers about 75% of the surface. NEXAFS data are consistent with chemically intact adsorption of the peptides. A weak linear dichroism of the amide π* is likely due to the broad distribution of amide bond orientations inherent to the α-helical secondary structure. SFG spectra exhibit strong peaks near 2865 cm(−1) and 2935 cm(−1) related to aligned leucine side chains interacting with the hydrophobic surface. Water modes near 3200 cm(−1) and 3400 cm(−1) indicate ordering of water molecules in the adsorbed--peptide fluorocarbon surface interfacial region. Amide I peaks observed near 1655 cm(−1) confirm that the secondary structure is preserved in the adsorbed peptide. A kinetic study of the film formation process using XPS and SFG showed rapid adsorption of the peptides followed by a longer assembly process. Peptide SFG spectra taken at the air–buffer interface showed features related to well ordered peptide films. Moving samples through the buffer surface led to the transfer of ordered peptide films onto the substrates

An efficient basis set representation for calculating electrons in molecules

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.Comment: Submitted to JC

Prenatal development is linked to bronchial reactivity: epidemiological and animal model evidence

Chronic cardiorespiratory disease is associated with low birthweight suggesting the importance of the developmental environment. Prenatal factors affecting fetal growth are believed important, but the underlying mechanisms are unknown. The influence of developmental programming on bronchial hyperreactivity is investigated in an animal model and evidence for comparable associations is sought in humans. Pregnant Wistar rats were fed either control or protein-restricted diets throughout pregnancy. Bronchoconstrictor responses were recorded from offspring bronchial segments. Morphometric analysis of paraffin-embedded lung sections was conducted. In a human mother-child cohort ultrasound measurements of fetal growth were related to bronchial hyperreactivity, measured at age six years using methacholine. Protein-restricted rats' offspring demonstrated greater bronchoconstriction than controls. Airway structure was not altered. Children with lesser abdominal circumference growth during 11-19 weeks' gestation had greater bronchial hyperreactivity than those with more rapid abdominal growth. Imbalanced maternal nutrition during pregnancy results in offspring bronchial hyperreactivity. Prenatal environmental influences might play a comparable role in humans

An Exploration of Communities of Practice in the STEM Teacher Context: What Predicts Ties of Retention?

The STEM teacher workforce in the United States has faced a host of pressing challenges, including teacher shortages, pervasive job dissatisfaction, and high turnover, problems largely attributable to working conditions within schools and districts. These problems have been exacerbated in high-needs districts with fewer resources and more students from low-income communities. Since social network research has shown that workplace relationships are vital for retention, this study investigates the demographic and relational antecedents to what we dub ties of retention. We explore how demographic and relational properties affect the likelihood that teachers have “retention-friendly” networks, characterized by connections important for retention. Our analysis of data from a sample of 120 STEM teachers across five geographic regions identifies key demographics (i.e., site, gender, career changer, and prior teaching experience) and relational properties (network size, positive affect, and perceptions of bridging) associated with ties of retention. We discuss the implications of our findings for the STEM teacher workforce and for teacher education programs