Coleman maps and the p-adic regulator

This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative Hodge-Tate weights. In this paper, we study these Coleman maps using Perrin-Riou's p-adic regulator L_V. Denote by H(\Gamma) the algebra of Qp-valued distributions on \Gamma = Gal(Qp(\mu (p^\infty) / Qp). Our first result determines the H(\Gamma)-elementary divisors of the quotient of D_{cris}(V) \otimes H(\Gamma) by the H(\Gamma)-submodule generated by (\phi * N(V))^{\psi = 0}, where N(V) is the Wach module of V. By comparing the determinant of this map with that of L_V (which can be computed via Perrin-Riou's explicit reciprocity law), we obtain a precise description of the images of the Coleman maps. In the case when V arises from a modular form, we get some stronger results about the integral Coleman maps, and we can remove many technical assumptions that were required in our previous work in order to reformulate Kato's main conjecture in terms of cotorsion Selmer groups and bounded p-adic L-functions.Comment: 27 page

Partial frequencies and Chladni’s law in church bells

The rim partials of a church bell (those with an antinode at the soundbow) generate the strike pitch or perceived note of the bell. The spacing in frequency of the higher rim partials has an important effect on the tonal quality of the bell. Investigations into the partial frequencies of 2752 bells, both bronze and steel, of a wide variety of dates, founders and sizes, show a simple and unexpected relationship between the frequencies of the rim partials. This relationship explains why attempts to tune the higher rim partials independently have failed. A modified version of Chladni’s law provides insight into the musical relationship of the partials, and predicts the partials of individual bells well, but fails to give a simple model of the spacing between the partials seen in bells with different profiles

Evaluation of methods for determining moisture in snap beans using microwave and conventional oven drying

The purpose of this study was to identify both a rapid method for determining moisture and a standard oven drying procedure for determining moisture in snap beans. Parameters of interest were sample size, sample preparation, sample condition (fresh vs. frozen), drying time. oven pressure, and a comparison of microwave, vacuum, and convection oven drying. The experiment was divided into four phases, each concentrating on selected parameters. The results of one phase determined parameter values used in later phases. Two convection ovens, two vacuum ovens, and one microwave oven were used. For the convection and vacuum oven drying, treatment effects were combinations of drying temperature and oven pressure. Treatment effects for microwave drying were combinations of sample size and power setting (energy level) coupled with drying time. Fresh and frozen samples were evaluated in all three types. For convection and vacuum oven drying, oven pressure, drying temperature and sample condition had little effect on indicated moisture content for the ranges tested. However, indicated moisture content was more sensitive to temperature than any other factor. Samples used in the microwave oven had to be ground in a food processor before drying. The indicated moisture contents given by the microwave oven were significantly affected by sample size, sample condition, and power setting. The larger samples and higher power settings produced higher indicated moisture contents. Frozen samples consistently gave higher Indicated moisture contents than fresh samples. For determination of moisture in snap beans, convection ovens at 100°C or vacuum ovens at 100°C with absolute pressures between 760 and 60 mm of mercury gave the same results. Both methods required a 24-hour drying period. Indicated moisture contents given by drying 10-gram samples in the microwave oven for 12 minutes were significantly different than convection or vacuum dried samples at the 95 percent level of probability. Even though they were statistically different, the moisture contents given by the three methods were within 1 percent of each other. Thus, the great time reduction from 24 hours to 12 minutes offered by microwave drying has potential for moisture determination in snap beans

Segmented field electron conformal therapy planning algorithm

Purpose: Segmented-field electron conformal therapy (SFECT) is rarely used, or if used, used sub optimally, primarily due to inadequate tools for its planning. The development of SFECT planning tools could help begin to bring electron therapy to the same level of sophistication as x-ray and proton therapy, resulting in greater consideration by radiation oncologists. The purpose of this work was to develop a forward planning algorithm that will improve segmentation of the SFECT treatment field. It was hypothesized that a forward planning algorithm can produce segmented-field ECT fields that improve dose conformity as the number of beam energies is increased from one to five using the Varian beam set (6, 9, 12, 16, and 20 MeV). Methods: A planning algorithm that allowed each field segment to have its own energy, shape, size, and weighting was developed. The planning algorithm developed an initial plan and then went through several iterations of re-planning based on the dose distributions of each previous plan in order to converge the 90% dose surface to the distal PTV surface. The planning algorithm was used to develop SFECT plans for six hypothetical PTVs and two head and neck patient PTVs. These plans were compared to single-energy plans developed by the same planning algorithm. Results: Conformity improved little beyond allowing three energies due to energy overlap and field-size restrictions. For the hypothetical PTVs, non-PTV treated to 90% of the prescribed dose was reduced compared to the single-energy plans, resulting in improved dose conformity, supporting the hypothesis. The improved conformity came at the expense of increased dose heterogeneity within the PTV. One of the patient plans improved in conformity, supporting the hypothesis and indicating the planning algorithm has the potential to plan patient cases. The other patient case did not improve in conformity and therefore did not support the hypothesis. Conclusion: The planning algorithm was successful in developing plans that improved conformity while still treating the PTV to prescription dose. The planning algorithm has the potential to plan patient SFECT treatments. Future improvements to the algorithm may improve its ability to plan patient cases

Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.Comment: 8 pages, 5 figure

Kolyvagin systems of Stark units

In this paper we construct, using Stark elements of Rubin [Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 33-62], Kolyvagin systems for certain modified Selmer structures (that are adjusted to have core rank one in the sense of [Mem. Amer. Math. Soc. 168 (2004), no. 799] and prove a Gras-type conjecture, relating these Kolyvagin systems to appropriate ideal class groups, refining the results of Rubin [J. Reine Angew. Math. 425 (1992), 141-154].Comment: 27 pages, revised version, accepted for publication in J. Reine Angew. Math. (Crelle's

The empirical accuracy of uncertain inference models

Uncertainty is a pervasive feature of the domains in which expert systems are designed to function. Research design to test uncertain inference methods for accuracy and robustness, in accordance with standard engineering practice is reviewed. Several studies were conducted to assess how well various methods perform on problems constructed so that correct answers are known, and to find out what underlying features of a problem cause strong or weak performance. For each method studied, situations were identified in which performance deteriorates dramatically. Over a broad range of problems, some well known methods do only about as well as a simple linear regression model, and often much worse than a simple independence probability model. The results indicate that some commercially available expert system shells should be used with caution, because the uncertain inference models that they implement can yield rather inaccurate results

Social Organization of the Eastern Rock Elephant-Shrew (\u3cem\u3eElephantulus myurus\u3c/em\u3e): The Evidence for Mate Guarding

Understanding the costs and benefits of defending solitary females, or mate guarding, may be the key to understanding the evolution of monogamy in most mammals. Elephant-shrews, or sengis, are a unique clade of small mammals that are particularly attractive for studies of mate guarding. We studied the spatial organization of Eastern Rock Sengis (Elephantulus myurus) in KwaZulu-Natal, South Africa, from August – December 2000. Our objectives were to describe the home ranges of males and females using radiotelemetry, noting the sizes and overlap of adjacent ranges and how the spatial organization changes through time. Males and females were spatially associated in monogamous pairs despite the fact that males contributed no obvious direct care to offspring. These monogamous associations persisted despite the fact that some males had home ranges large enough to encompass multiple females. Males also had more variable ranges, perhaps because they spent more time at the periphery of their ranges exploring for the presence of additional females. There was likely competition for females, as range shifts were observed when male territory holders died or disappeared. It seems likely that this species is a model study organism to investigate the costs and benefits of mate guarding

Patient-specific simulation of stent-graft deployment within an abdominal aortic aneurysm

In this study, finite element analysis is used to simulate the surgical deployment procedure of a bifurcated stent-graft on a real patient's arterial geometry. The stent-graft is modeled using realistic constitutive properties for both the stent and most importantly for the graft. The arterial geometry is obtained from pre-operative imaging exam. The obtained results are in good agreement with the post-operative imaging data. As the whole computational time was reduced to less than 2 hours, this study constitutes an essential step towards predictive planning simulations of aneurysmal endovascular surger