Linearity defects of modules over commutative rings

This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its minimal resolution is acyclic. The results established track the change in this invariant under some standard operations in commutative algebra. As one of the applications, it is proved that a local ring is Koszul if and only if it admits a Koszul module that is Cohen-Macaulay of minimal degree. An injective analogue of the linearity defect is introduced and studied. The main results express this new invariant in terms of linearity defects of free resolutions, and relate it to other ring theoretic and homological invariants of the module.Comment: 23 pages, minor modification

Non-perturbative improvement of the vector current in Wilson lattice QCD

Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved in order to remove the leading discretization errors from the observables. Here we introduce and apply a new method to determine the improvement coefficient for the two most widely used discretizations of the current.Comment: 12 pages, 5 figure

Can environmental conditions experienced in early life influence future generations?

The consequences of early developmental conditions for performance in later life are now subjected to convergent interest from many different biological sub-disciplines. However, striking data, largely from the biomedical literature, show that environmental effects experienced even before conception can be transmissible to subsequent generations. Here, we review the growing evidence from natural systems for these cross-generational effects of early life conditions, showing that they can be generated by diverse environmental stressors, affect offspring in many ways and can be transmitted directly or indirectly by both parental lines for several generations. In doing so, we emphasize why early life might be so sensitive to the transmission of environmentally induced effects across generations. We also summarize recent theoretical advancements within the field of developmental plasticity, and discuss how parents might assemble different ‘internal’ and ‘external’ cues, even from the earliest stages of life, to instruct their investment decisions in offspring. In doing so, we provide a preliminary framework within the context of adaptive plasticity for understanding inter-generational phenomena that arise from early life conditions

An estimate for the thermal photon rate from lattice QCD

We estimate the production rate of photons by the quark-gluon plasma in lattice QCD. We propose a new correlation function which provides better control over the systematic uncertainty in estimating the photon production rate at photon momenta in the range {\pi}T/2 to 2{\pi}T. The relevant Euclidean vector current correlation functions are computed with $N_{\mathrm f}$ = 2 Wilson clover fermions in the chirally-symmetric phase. In order to estimate the photon rate, an ill-posed problem for the vector-channel spectral function must be regularized. We use both a direct model for the spectral function and a model-independent estimate from the Backus-Gilbert method to give an estimate for the photon rate.Comment: 15 pages, 11 figures, talk presented at 35th annual International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

A monopole antenna at optical frequencies: single-molecule near-field measurements

We present a monopole antenna for optical frequencies (~600 THz) and discuss near-field measurements with single fluorescent molecules as a technique to characterize such antennas. The similarities and differences between near-field antenna measurements at optical and radio frequencies are discussed in detail. Two typical antenna properties, polarization selectivity and resonances, are studied for the optical monopole by direct near-field measurements and finite integration technique calculations. The antenna is driven by the local field of a sub-wavelength aperture. This gives rise to a dependence of the antenna response on the orientation of the local field vector, in an analogous way to the polarization selectivity of linear wire antennas. The antenna resonances are studied by varying the antenna length. Typical monopole resonances are demonstrated. The finite conductivity of metals at optical frequencies (in combination with the antenna radius) causes the wavelength of the surface charge density oscillation (surface plasmon polariton) along the antenna to be shortened in comparison to the free space wavelength. As a result, resonances for the optical monopole antenna occur at much shorter relative lengths than for conventional radio monopole antennas\ud \u

Brown dwarf populations in open clusters

We present the results of multiple simulations of open clusters, modelling the dynamics of a population of brown dwarf members. We consider the effects of a large range of primordial binary populations, including the possibilities of having brown dwarf members contained within a binary system. We also examine the effects of various cluster diameters and masses. Our examination of a population of wide binary systems containing brown dwarfs, reveals evidence for exchange reactions whereby the brown dwarf is ejected from the system and replaced by a heavier main-sequence star. We find that there exists the possibility of hiding a large fraction of the brown dwarfs contained within the primordial binary population. We conclude that it is probable that the majority of brown dwarfs are contained within primordial binary systems which then hides a large proportion of them from detection.Comment: 16 pages, 8 figures; to appear in MNRA