Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form $\Theta(n^k)$, for some integer $k\leq d$, where $d$ is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal $k$. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a $k$ such that the termination complexity is $\Omega(n^k)$. Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925

Expression patterns of a circadian clock gene are associated with age-related polyethism in harvester ants, Pogonomyrmex occidentalis

<p>Abstract</p> <p>Background</p> <p>Recent advances in sociogenomics allow for comparative analyses of molecular mechanisms regulating the development of social behavior. In eusocial insects, one key aspect of their sociality, the division of labor, has received the most attention. Age-related polyethism, a derived form of division of labor in ants and bees where colony tasks are allocated among distinct behavioral phenotypes, has traditionally been assumed to be a product of convergent evolution. Previous work has shown that the circadian clock is associated with the development of behavior and division of labor in honeybee societies. We cloned the ortholog of the clock gene, <it>period</it>, from a harvester ant (<it>Pogonomyrmex occidentalis</it>) and examined circadian rhythms and daily activity patterns in a species that represents an evolutionary origin of eusociality independent of the honeybee.</p> <p>Results</p> <p>Using real time qPCR analyses, we determined that harvester ants have a daily cyclic expression of <it>period </it>and this rhythm is endogenous (free-running under dark-dark conditions). Cyclic expression of <it>period </it>is task-specific; foragers have strong daily fluctuations but nest workers inside the nest do not. These patterns correspond to differences in behavior as activity levels of foragers show a diurnal pattern while nest workers tend to exhibit continuous locomotor activity at lower levels. In addition, we found that foragers collected in the early fall (relative warm, long days) exhibit a delay in the nightly peak of <it>period </it>expression relative to foragers collected in the early spring (relative cold, short days).</p> <p>Conclusion</p> <p>The association of <it>period </it>mRNA expression levels with harvester ant task behaviors suggests that the development of circadian rhythms is associated with the behavioral development of ants. Thus, the circadian clock pathway may represent a conserved 'genetic toolkit' that has facilitated the parallel evolution of age-related polyethism and task allocation in social insects.</p

Revealing large-scale homogeneity and trace impurity sensitivity of GaAs nanoscale membranes

III-V nanostructures have the potential to revolutionize optoelectronics and energy harvesting. For this to become a reality, critical issues such as reproducibility and sensitivity to defects should be resolved. By discussing the optical properties of MBE grown GaAs nanomembranes we highlight several features that bring them closer to large scale applications. Uncapped membranes exhibit a very high optical quality, expressed by extremely narrow neutral exciton emission, allowing the resolution of the more complex excitonic structure for the first time. Capping of the membranes with an AlGaAs shell results in a strong increase of emission intensity but also to a shift and broadening of the exciton peak. This is attributed to the existence of impurities in the shell, beyond MBE-grade quality, showing the high sensitivity of these structures to the presence of impurities. Finally, emission properties are identical at the sub-micron and sub-millimeter scale, demonstrating the potential of these structures for large scale applications.Comment: just accepted in Nano Letters, http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b0025

A high flux source of cold strontium atoms

We describe an experimental apparatus capable of achieving a high loading rate of strontium atoms in a magneto-optical trap operating in a high vacuum environment. A key innovation of this setup is a two dimensional magneto-optical trap deflector located after a Zeeman slower. We find a loading rate of 6x10^9/s whereas the lifetime of the magnetically trapped atoms in the 3P2 state is 54s.Comment: 12 pages, 16 figure

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Three-dimensional imaging and detection efficiency performance of orthogonal coplanar CZT strip detectors

We report on recent three-dimensional imaging performance and detection efficiency measurements obtained with 5 mm thick prototype CdZnTe detectors fabricated with orthogonal coplanar anode strips. In previous work, we have shown that detectors fabricated using this design achieve both very good energy resolution and sub-millimeter spatial resolution with fewer electronic channels than are required for pixel detectors. As electron-only devices, like pixel detectors, coplanar anode strip detectors can be fabricated in the thickness required to be effective imagers for photons with energies in excess of 500 keV. Unlike conventional double-sided strip detectors, the coplanar anode strip detectors require segmented contacts and signal processing electronics on only one surface. The signals can be processed to measure the total energy deposit and the photon interaction location in three dimensions. The measurements reported here provide a quantitative assessment of the detection capabilities of orthogonal coplanar anode strip detectors

Strong light-matter coupling in bulk GaN-microcavities with double dielectric mirrors fabricated by two different methods

Two routes for the fabrication of bulk GaN microcavities embedded between two dielectric mirrors are described, and the optical properties of the microcavities thus obtained are compared. In both cases, the GaN active layer is grown by molecular beam epitaxy on (111) Si, allowing use of selective etching to remove the substrate. In the first case, a three period Al0.2Ga0.8N / AlN Bragg mirror followed by a lambda/2 GaN cavity are grown directly on the Si. In the second case, a crack-free 2,mu m thick GaN layer is grown, and progressively thinned to a final thickness of lambda. Both devices work in the strong coupling regime at low temperature, as evidenced by angle-dependent reflectivity or transmission experiments. However, strong light-matter coupling in emission at room temperature is observed only for the second one. This is related to the poor optoelectronic quality of the active layer of the first device, due to its growth only 250 nm above the Si substrate and its related high defect density. The reflectivity spectra of the microcavities are well accounted for by using transfer matrix calculations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3477450

Multiscale nature of hysteretic phenomena: Application to CoPt-type magnets

We suggest a workable approach for the description of multiscale magnetization reversal phenomena in nanoscale magnets and apply it to CoPt-type alloys. We show that their hysteretic properties are governed by two effects originating at different length scales: a peculiar splitting of domain walls and their strong pinning at antiphase boundaries. We emphasize that such multiscale nature of hysteretic phenomena is a generic feature of nanoscale magnetic materials.Comment: 4 pages (revtex 4), 2 color EPS figure