Probabilistic lower bounds on maximal determinants of binary matrices

Let ${\mathcal D}(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and $\mathcal R(n) = {\mathcal D}(n)/n^{n/2}$ be the ratio of ${\mathcal D}(n)$ to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on ${\mathcal D}(n)$ and $\mathcal R(n)$ in terms of $d = n-h$, where $h$ is the order of a Hadamard matrix and $h$ is maximal subject to $h \le n$. For example, $\mathcal R(n) > (\pi e/2)^{-d/2}$ if $1 \le d \le 3$, and $\mathcal R(n) > (\pi e/2)^{-d/2}(1 - d^2(\pi/(2h))^{1/2})$ if $d > 3$. By a recent result of Livinskyi, $d^2/h^{1/2} \to 0$ as $n \to \infty$, so the second bound is close to $(\pi e/2)^{-d/2}$ for large $n$. Previous lower bounds tended to zero as $n \to \infty$ with $d$ fixed, except in the cases $d \in \{0,1\}$. For $d \ge 2$, our bounds are better for all sufficiently large $n$. If the Hadamard conjecture is true, then $d \le 3$, so the first bound above shows that $\mathcal R(n)$ is bounded below by a positive constant $(\pi e/2)^{-3/2} > 0.1133$.Comment: 17 pages, 2 tables, 24 references. Shorter version of arXiv:1402.6817v4. Typos corrected in v2 and v3, new Lemma 7 in v4, updated references in v5, added Remark 2.8 and a reference in v6, updated references in v

Editors\u27 Dialogue: Reading the Continental Congress men\u27s Mail

For this feature, which is designed to promote that exchange of ideas for which the Association for Documentary Editing exists, the reviewer was instructed to focus his comments on two aspects of the work under examination--one thing done well and one thing that might have been done differently. Admittedly, when the perfect editor produces the perfect edition the flaw in this contrived format shall stand exposed. Yet, even when that perfect edition comes to hand we mortal editors are likely to benefit when one of our number, forced to write about something that might have been done differently, describes those lesser alternatives to which the perfect editor said No. The review, with its author\u27s name deleted, was sent to the editor of the reviewed work, who was asked to comment on the reviewer\u27s observations. Again, the intention is to foster constructive dialogue. Although the etiquette of some scholarly periodicals suggests that a reply to a review is evidence of ill grace, we stress here that Mr. Smith\u27s comments were invited. In the months before the arrival of that perfect edition exposes our contrivance to public ridicule, we trust that we may generate light, not heat. We are especially grateful to Messrs. Tarter and Smith for graciously accommodating the deadlines that circumstances imposed for this issue of the Newsletter

Frequency-Dependent Seed Dispersal by Ants of Two Deciduous Forest Herbs

Two co—occurring deciduous forest myrmecochores, Asarum canadense and Jeffersonia diphylla, release their seeds at approximately the same time, and therefore potentially compete for ants as dispersers. Within a single woodlot, we placed seeds of both species inside a dense Jeffersonia population away from Asarum plants, inside a dense Asarum population away from Jeffersonia plants, and in a site where plants of neither species occurred. No preference was exhibited by ants where natural populations were absent. Preference at the other two sites was frequency dependent: ants preferred seeds of the introduced species. Species preferred by ants have higher seed and seedling survival because by being carried into ant nests they escape predation and avoid nutrient deficiency. Implications of frequency—dependent dispersal are discussed

Thermodynamic stability and contributions to the Gibbs free energy of nanocrystalline Ni₃Fe

The heat capacities of nanocrystalline Ni₃Fe and control materials with larger crystallites were measured from 0.4–300 K. The heat capacities were integrated to obtain the enthalpy, entropy, and Gibbs free energy and to quantify how these thermodynamic functions are altered by nanocrystallinity. From the phonon density of states (DOS) measured by inelastic neutron scattering, we find that the Gibbs free energy is dominated by phonons and that the larger heat capacity of the nanomaterial below 100 K is attributable to its enhanced phonon DOS at low energies. Besides electronic and magnetic contributions, the nanocrystalline material has an additional contribution at higher temperatures, consistent with phonon anharmonicity. The nanocrystalline material shows a stronger increase with temperature of both the enthalpy and entropy compared to the bulk sample. Its entropy exceeds that of the bulk material by 0.4 k_B/atom at 300 K. This is insufficient to overcome the enthalpy of grain boundaries and defects in the nanocrystalline material, making it thermodynamically unstable with respect to the bulk control material

Investigating causality in the association between 25(OH)D and schizophrenia

Vitamin D deficiency is associated with increased risk of schizophrenia. However, it is not known whether this association is causal or what the direction of causality is. We performed two sample bidirectional Mendelian randomization analysis using single nucleotide polymorphisms (SNPs) robustly associated with serum 25(OH)D to investigate the causal effect of 25(OH)D on risk of schizophrenia, and SNPs robustly associated with schizophrenia to investigate the causal effect of schizophrenia on 25(OH)D. We used summary data from genome-wide association studies and meta-analyses of schizophrenia and 25(OH)D to obtain betas and standard errors for the SNP-exposure and SNP-outcome associations. These were combined using inverse variance weighted fixed effects meta-analyses. In 34,241 schizophrenia cases and 45,604 controls, there was no clear evidence for a causal effect of 25(OH)D on schizophrenia risk. The odds ratio for schizophrenia per 10% increase in 25(OH)D conferred by the four 25(OH)D increasing SNPs was 0.992 (95% CI: 0.969 to 1.015). In up to 16,125 individuals with measured serum 25(OH)D, there was no clear evidence that genetic risk for schizophrenia causally lowers serum 25(OH)D. These findings suggest that associations between schizophrenia and serum 25(OH)D may not be causal. Therefore, vitamin D supplementation may not prevent schizophrenia.</p

Castration remains despite decreasing definitive treatment of localized prostate cancer in the elderly: A case for de‐implementation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146605/1/cncr31665_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146605/2/cncr31665.pd

The Radial Distribution of the Interstellar Medium in Disk Galaxies: Evidence for Secular Evolution

One possible way for spiral galaxies to internally evolve would be for gas to flow to the center and form stars in a central disk (pseudo-bulge). If the inflow rate is faster than the rate of star formation, a central concentration of gas will form. In this paper we present radial profiles of stellar and 8 μm emission from polycyclic aromatic hydrocarbons (PAHs) for 11 spiral galaxies to investigate whether the interstellar medium in these galaxies contains a central concentration above that expected from the exponential disk. In general, we find that the two-dimensional CO and PAH emission morphologies are similar, and that they exhibit similar radial profiles. We find that in 6 of the 11 galaxies there is a central excess in the 8 μm and CO emission above the inward extrapolation of an exponential disk. In particular, all four barred galaxies in the sample have strong central excesses in both 8 μm and CO emission. These correlations suggest that the excess seen in the CO profiles is, in general, not simply due to a radial increase in the CO emissivity. In the inner disk, the ratio of the stellar to the 8 μm radial surface brightness is similar for 9 of the 11 galaxies, suggesting a physical connection between the average stellar surface brightness and the average gas surface brightness at a given radius. We also find that the ratio of the CO to 8 μm PAH surface brightness is consistent over the sample, implying that the 8 μm PAH surface brightness can be used as an approximate tracer of the interstellar medium