Unexpected local extrema for the Sendov conjecture

Let S(n) be the set of all polynomials of degree n with all roots in the unit disk, and define d(P) to be the maximum of the distances from each of the roots of a polynomial P to that root's nearest critical point. In this notation, Sendov's conjecture asserts that d(P)<=1 for every P in S(n). Define P in S(n) to be locally extremal if d(P)>=d(Q) for all nearby Q in S(n), and note that maximizing d(P) over all locally extremal polynomials P would settle the Sendov conjecture. Prior to now, the only polynomials known to be locally extremal were of the form P(z)=c(z^n+a) with |a|=1. In this paper, we determine sufficient conditions for real polynomials of a different form to be locally extremal, and we use these conditions to find locally extremal polynomials of this form of degrees 8, 9, 12, 13, 14, 15, 19, 20, and 26.Comment: 10 pages, AMS-LaTeX, no figures. The Maple code and results used in this paper are included in the source files. We constructed an unexpected locally extremal polynomial of degree 8 in version 1, then added degrees 12, 14, 20 and 26 in version 2, and degrees 9, 13, 15 and 19 in version

Design of a Recreational Fishing Survey and Mark-Recapture Study for the Blue Crab, Callinectes sapidus, in Chesapeake Bay

The development of bay wide estimates of recreational harvest has been identified as a high priority by the Chesapeake Bay Scientific Advisory Committee (CBSAC) and by the Chesapeake Bay Program as reflected in the Chesapeake Bay Blue Crab Fishery Management Plan (Chesapeake Bay Program 1996). In addition, the BiState Blue Crab Commission (BBCAC), formed in 1996 by mandate from the legislatures of Maryland and Virginia to advise on crab management, has also recognized the importance of estimating the levels and trends in catches in the recreational fishery. Recently, the BBCAC has adopted limit and target biological reference points. These analyses have been predicated on assumptions regarding the relative magnitude of the recreational and commercial catch. The reference points depend on determination of the total number of crabs removed from the population. In essence, the number removed by the various fishery sectors, represents a minimum estimate of the population size. If a major fishery sector is not represented, the total population will be accordingly underestimated. If the relative contribution of the unrepresented sector is constant over time and harvests the same components of the population as the other sectors, it may be argued that the population estimate derived from the other sectors is biased but still adequately represents trends in population size over time. If either of the two constraints mentioned above is not met, the validity of relative trends over time is suspect. With the recent increases in the human population in the Chesapeake Bay watershed, there is reason to be concerned that the recreational catch may not have been a constant proportion of the total harvest over time. It is important to assess the catch characteristics and the magnitude of the recreational fishery to evaluate this potential bias. (PDF contains 70 pages

Nearctic \u3ci\u3eAcleris\u3c/i\u3e: Resurrection of \u3ci\u3eA. Stadiana\u3c/i\u3e and a Revised Identity for \u3ci\u3eA. Semiannula\u3c/i\u3e (Lepidoptera: Tortricidae)

Type study showed that Acleris stadiana (Barnes & Busck), currently considered a junior synonym of A. semiannula (Robinson), is in fact a distinct taxon. Although superficially similar, these taxa differ markedly in genital structure. In males of A. semiannula, the aedeagus is short, broad, and virtually straight, whereas in those of A. stadiana, it is long, thin, and sharply bent. What was known in literature as A. semiannula proved to be A. stadi­ana. We redefine both A. semiannula and the resurrected A. stadiana

Does electronic coherence enhance anticorrelated pigment vibrations under realistic conditions?

The light-harvesting efficiency of a photoactive molecular complex is largely determined by the properties of its electronic quantum states. Those, in turn, are influenced by molecular vibrational states of the nuclear degrees of freedom. Here, we reexamine two recently formulated concepts that a coherent vibronic coupling between molecular states would either extend the electronic coherence lifetime or enhance the amplitude of the anticorrelated vibrational mode at longer times. For this, we study a vibronically coupled dimer and calculate the nonlinear two-dimensional (2D) electronic spectra which directly reveal electronic coherence. The timescale of electronic coherence is initially extracted by measuring the anti-diagonal bandwidth of the central peak in the 2D spectrum at zero waiting time. Based on the residual analysis, we identify small-amplitude long-lived oscillations in the cross-peaks, which, however, are solely due to groundstate vibrational coherence, regardless of having resonant or off-resonant conditions. Our studies neither show an enhancement of the electronic quantum coherence nor an enhancement of the anticorrelated vibrational mode by the vibronic coupling under ambient conditions

Dynamics of Co-translational Membrane Protein Integration and Translocation via the Sec Translocon

An important aspect of cellular function is the correct targeting and delivery of newly synthesized proteins. Central to this task is the machinery of the Sec translocon, a transmembrane channel that is involved in both the translocation of nascent proteins across cell membranes and the integration of proteins into the membrane. Considerable experimental and computational effort has focused on the Sec translocon and its role in nascent protein biosynthesis, including the correct folding and expression of integral membrane proteins. However, the use of molecular simulation methods to explore Sec-facilitated protein biosynthesis is hindered by the large system sizes and long (i.e., minute) timescales involved. In this work, we describe the development and application of a coarse-grained simulation approach that addresses these challenges and allows for direct comparison with both in vivo and in vitro experiments. The method reproduces a wide range of experimental observations, providing new insights into the underlying molecular mechanisms, predictions for new experiments, and a strategy for the rational enhancement of membrane protein expression levels

Vocal learning promotes patterned inhibitory connectivity.

Skill learning is instantiated by changes to functional connectivity within premotor circuits, but whether the specificity of learning depends on structured changes to inhibitory circuitry remains unclear. We used slice electrophysiology to measure connectivity changes associated with song learning in the avian analog of primary motor cortex (robust nucleus of the arcopallium, RA) in Bengalese Finches. Before song learning, fast-spiking interneurons (FSIs) densely innervated glutamatergic projection neurons (PNs) with apparently random connectivity. After learning, there was a profound reduction in the overall strength and number of inhibitory connections, but this was accompanied by a more than two-fold enrichment in reciprocal FSI-PN connections. Moreover, in singing birds, we found that pharmacological manipulations of RA's inhibitory circuitry drove large shifts in learned vocal features, such as pitch and amplitude, without grossly disrupting the song. Our results indicate that skill learning establishes nonrandom inhibitory connectivity, and implicates this patterning in encoding specific features of learned movements

VALUING WATER QUALITY MONITORING: A CONTINGENT VALUATION EXPERIMENT INVOLVING HYPOTHETICAL AND REAL PAYMENTS

This paper studies the preferences and willingness-to-pay for individuals for volunteer water quality monitoring programs. The study involves supporting water quality monitoring at two ponds in the state of Rhode Island. The paper uses both a hypothetical and a real-payment contingent valuation survey to directly measure individual preferences and willingness-to-pay (WTP) for volunteer water quality monitoring at the two ponds. The overall results of the study suggest that hypothetical WTP is not statistically greater than real WTP, and that the average survey respondent is willing to support water quality monitoring on one of the two ponds. The study also finds that the specified purpose of water quality monitoring and certain socioeconomic characteristics of a respondent significantly affect the respondent's decision to support volunteer water quality monitoring.Environmental Economics and Policy,