Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.Comment: 21 pages, To appear in Compositio Mathematic

Parametric Euler Sum Identities

We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables generate reduction formulae for these sums.Comment: 12 page

Abnormal flowers and pattern formation in floral

“From our acquaintance with this abnormal enabled to unveil the secrets that normal us, and to see distinctly what, from the regular we can only infer.” - J. W. von Goethe (1790

Genetic interactions among floral homeotic genes of Arabidopsis

We describe allelic series for three loci, mutations in which result in homeotic conversions in two adjacent whorls in the Arabidopsis thaliana flower. Both the structure of the mature flower and its development from the initial primordium are described by scanning electron microscopy. New mutations at the APETALA2 locus, ap2-2, ap2-8 and ap2-9, cause homeotic conversions in the outer two whorls: sepals to carpels (or leaves) and petals to stamens. Two new mutations of PISTILLATA, pi-2 and pi-3, cause second and third whorl organs to differentiate incorrectly. Homeotic conversions are petals to sepals and stamens to carpels, a pattern similar to that previously described for the apetala3-1 mutation. The AGAMOUS mutations, ag-2 and ag-3, affect the third and fourth whorls and cause petals to develop instead of stamens and another flower to arise in place of the gynoecium. In addition to homeotic changes, mutations at the APETALA2, APETALA3 and PISTILLATA loci may lead to reduced numbers of organs, or even their absence, in specific whorls. The bud and flower phenotypes of doubly and triply mutant strains, constructed with these and previously described alleles, are also described. Based on these results, a model is proposed that suggests that the products of these homeotic genes are each active in fields occupying two adjacent whorls, AP2 in the two outer whorls, PI and AP3 in whorls two and three, and AG in the two inner whorls. In combination, therefore, the gene products in these three concentric, overlapping fields specify the four types of organs in the wild-type flower. Further, the phenotypes of multiple mutant lines indicate that the wild-type products of the AGAMOUS and APETALA2 genes interact antagonistically. AP2 seems to keep the AG gene inactive in the two outer whorls while the converse is likely in the two inner whorls. This field model successfully predicts the phenotypes of all the singly, doubly and triply mutant flowers described

A Matter of Life and Death: Revising the Harmless Error Standard for Habeas Corpus Proceedings

Since 1967, federal courts have conducted harmless error analysis to determine whether to uphold a prisoner\u27s conviction notwithstanding a constitutional error committed at the prisoner\u27s trial. A review of the development of the harmless error doctrine reveals how the U.S. Supreme Court and federal courts have solidified a rational impact test to determine harmlessness. More recently, the U.S. Supreme Court has moved away from a clearly defined test with respect to errors alleged by habeas corpus petitioners. This Comment analyzes the obstacles faced by habeas petitioners in establishing a magnitude of error sufficient for reversal under the newer doctrine. It also reveals the difficulty lower courts have in applying the newer doctrine, as illustrated by a recent Ninth Circuit decision, Rice v. Wood. The Comment proposes a collateral-review harmless error standard that balances a defendant\u27s right to a fair trial with a state\u27s interests in finality of convictions

Duality for Finite Multiple Harmonic q-Series

We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients. Special cases of these identities--for example, with all parameters equal to 1--have occurred in the literature. The special case with only one parameter reduces to an identity for the divisor generating function, which has received some attention in connection with problems in sorting theory. The general case can be viewed as a duality result, reminiscent of the duality relation for the ordinary multiple zeta function.Comment: 12 pages AMSLaTeX. Submitted for publication October 26, 2003; revised September 14, 2004. New title reflects change in emphasis and new section devoted to connections with inverse pairs and Hoffman duality. References added and typos correcte

Control of flower development in Arabidopsis thaliana by APETALA1 and interacting genes

Mutations in the APETALA1 gene disturb two phases of flower development, flower meristem specification and floral organ specification. These effects become manifest as a partial conversion of flowers into inflorescence shoots and a disruption of sepal and petal development. We describe the changes in an allelic series of nine apetala1 mutants and show that the two functions of APETALA1 are separable. We have also studied the interaction between APETALA1 and other floral genes by examining the phenotypes of multiply mutant plants and by in situ hybridization using probes for several floral control genes. The results suggest that the products of APETALA1 and another gene, LEAFY, are required to ensure that primordia arising on the flanks of the inflorescence apex adopt a floral fate, as opposed to becoming an inflorescence shoot. APETALA1 and LEAFY have distinct as well as overlapping functions and they appear to reinforce each other's action. CAULIFLOWER is a newly discovered gene which positively regulates both APETALA1 and LEAFY expression. All functions of CAULIFLOWER are redundant with those of APETALA1. APETALA2 also has an early function in reinforcing the action of APETALA1 and LEAFY, especially if the activity of either is compromised by mutation. After the identity of a flower primordium is specified, APETALA1 interacts with APETALA2 in controlling the development of the outer two whorls of floral organs

A compact holographic optical tweezers instrument

Holographic optical tweezers have found many applications including the construction of complex micron-scale 3D structures and the control of tools and probes for position, force, and viscosity measurement. We have developed a compact, stable, holographic optical tweezers instrument which can be easily transported and is compatible with a wide range of microscopy techniques, making it a valuable tool for collaborative research. The instrument measures approximately 30×30×35 cm and is designed around a custom inverted microscope, incorporating a fibre laser operating at 1070 nm. We designed the control software to be easily accessible for the non-specialist, and have further improved its ease of use with a multi-touch iPad interface. A high-speed camera allows multiple trapped objects to be tracked simultaneously. We demonstrate that the compact instrument is stable to 0.5 nm for a 10 s measurement time by plotting the Allan variance of the measured position of a trapped 2 μm silica bead. We also present a range of objects that have been successfully manipulated

The Evolution of Life History Traits and Their Thermal Plasticity in Daphnia

Few studies have explored the relative strength of ecogeographic versus lineage-specific effects on a global scale, particularly for poikilotherms, those organisms whose internal temperature varies with their environment. Here, we compile a global dataset of life history traits in Daphnia, at the species-and population-level, and use those data to parse the relative influences of lineage-specific effects and climate. We also compare the thermal response (plasticity) of life history traits and their dependence on climate, temperature, precipitation, and latitude. We found that the mode of evolution for life history traits varies but that the thermal response of life history traits most often follows a random walk model of evolution. We conclude that life history trait evolution in Daphnia is not strongly species-specific but is ecogeographically distinct, suggesting that life history evolution should be understood at the population level for Daphnia and possibly for other poikilotherms