An Orthogonal Test of the LL-functions Ratios Conjecture, II

Recently Conrey, Farmer, and Zirnbauer developed the L-functions Ratios conjecture, which gives a recipe that predicts a wealth of statistics, from moments to spacings between adjacent zeros and values of L-functions. The problem with this method is that several of its steps involve ignoring error terms of size comparable to the main term; amazingly, the errors seem to cancel and the resulting prediction is expected to be accurate up to square-root cancellation. We prove the accuracy of the Ratios Conjecture's prediction for the 1-level density of families of cuspidal newforms of constant sign (up to square-root agreement for support in (-1,1), and up to a power savings in (-2,2)), and discuss the arithmetic significance of the lower order terms. This is the most involved test of the Ratios Conjecture's predictions to date, as it is known that the error terms dropped in some of the steps do not cancel, but rather contribute a main term! Specifically, these are the non-diagonal terms in the Petersson formula, which lead to a Bessel-Kloosterman sum which contributes only when the support of the Fourier transform of the test function exceeds (-1, 1).Comment: 36 pages, first draf

Oropharyngeal bacteria, with respect to animal health classification, and viral serology of Montana bighorn sheep (Ovis canadensis) and domestic (Ovis aries) near to and distant from the wildlife/domestic animal interface

2010 Spring.Respiratory disease outbreaks attributed to pasteurellosis have lead to conflict at the wildlife/domestic interface, where domestic sheep have been hypothesized to be a reservoir of Pasteuerellaceae strains that cause disease in bighorn sheep. This dissertation compares bighorn sheep ( Ovis canadensis) and domestic sheep ( O. aries) oropharyngeal Pasteurellaceae biovariants from animals classified as diseased and healthy. It also compares bacteriology and viral serology of populations of these species near to and distant from the wildlife/domestic livestock interface. A retrospective study of clinical submissions (1990 - 2004) indicated that 94 Pasteurellaceae biovariants have been associated with domestic sheep classified as diseased. A second retrospective study (1989 - 2004) indicated that 37 Pasteurellaceae biovariants have been associated with bighorn sheep classified as diseased. A prospective study of domestic and bighorn sheep near to and distant from the wildlife/domestic interface indicated that Pasteurellaceae biovariants commonly associated with disease in the retrospective studies were also common in healthy animals, and that there was extensive interspecific sharing of biovariants. This suggests that a simple agent/disease relationship may not exist for Pasteurellaceae in these host species. In addition, it is not clear that either species serves as a reservoir for Pasteurellaceae that are pathogenic for the sympatric species. However, unstated assumptions that single samples represent an animal's Pasteurellaceae microflora are questionable, based on the minimal concordance of biovariants of individual domestic livestock (n = 118) sampled six months apart. Based on the populations in the prospective study, bighorn sheep populations were naive to Mycoplasma, and both Ovis species were largely naive to infectious bovine rhinotracheitis and bovine virus diarrhea 1 and 2. This suggests that these agents may cause outbreaks if introduced into these populations. Cluster analysis of Pasteurellaceae and viral serology results identified four different clusters (P < 0.0001), but these did not closely correspond to species and location categories. The results from this study suggest that emphasis on single determinants for causes of respiratory disease outbreaks in domestic and bighorn sheep, rather than determination of risk factors for multiple determinants, may not provide results that are useful for managing disease in these species

Sums and differences of correlated random sets

Many fundamental questions in additive number theory (such as Goldbach's conjecture, Fermat's last theorem, and the Twin Primes conjecture) can be expressed in the language of sum and difference sets. As a typical pair of elements contributes one sum and two differences, we expect that $|A-A| > |A+A|$ for a finite set $A$. However, in 2006 Martin and O'Bryant showed that a positive proportion of subsets of $\{0, \dots, n\}$ are sum-dominant, and Zhao later showed that this proportion converges to a positive limit as $n \to \infty$. Related problems, such as constructing explicit families of sum-dominant sets, computing the value of the limiting proportion, and investigating the behavior as the probability of including a given element in $A$ to go to zero, have been analyzed extensively. We consider many of these problems in a more general setting. Instead of just one set $A$, we study sums and differences of pairs of \emph{correlated} sets $(A,B)$. Specifically, we place each element $a \in \{0,\dots, n\}$ in $A$ with probability $p$, while $a$ goes in $B$ with probability $\rho_1$ if $a \in A$ and probability $\rho_2$ if $a \not \in A$. If $|A+B| > |(A-B) \cup (B-A)|$, we call the pair $(A,B)$ a \emph{sum-dominant $(p,\rho_1, \rho_2)$-pair}. We prove that for any fixed $\vec{\rho}=(p, \rho_1, \rho_2)$ in $(0,1)^3$, $(A,B)$ is a sum-dominant $(p,\rho_1, \rho_2)$-pair with positive probability, and show that this probability approaches a limit $P(\vec{\rho})$. Furthermore, we show that the limit function $P(\vec{\rho})$ is continuous. We also investigate what happens as $p$ decays with $n$, generalizing results of Hegarty-Miller on phase transitions. Finally, we find the smallest sizes of MSTD pairs.Comment: Version 1.0, 19 pages. Keywords: More Sum Than Difference sets, correlated random variables, phase transitio

Relationships between land use and nitrogen and phosphorus in New Zealand lakes

Developing policies to address lake eutrophication requires an understanding of the relative contribution of different nutrient sources and of how lake and catchment characteristics interact to mediate the source–receptor pathway. We analysed total nitrogen (TN) and total phosphorus (TP) data for 101 New Zealand lakes and related these to land use and edaphic sources of phosphorus (P). We then analysed a sub-sample of lakes in agricultural catchments to investigate how lake and catchment variables influence the relationship between land use and in-lake nutrients. Following correction for the effect of co-variation amongst predictor variables, high producing grassland (intensive pasture) was the best predictor of TN and TP, accounting for 38.6% and 41.0% of variation, respectively. Exotic forestry and urban area accounted for a further 18.8% and 3.6% of variation in TP and TN, respectively. Soil P (representing naturally-occurring edaphic P) was negatively correlated with TP, owing to the confounding effect of pastoral land use. Lake and catchment morphology (zmax and lake : catchment area) and catchment connectivity (lake order) mediated the relationship between intensive pasture and in-lake nutrients. Mitigating eutrophication in New Zealand lakes requires action to reduce nutrient export from intensive pasture and quantifying P export from plantation forestry requires further consideration

Constructing families of moderate-rank elliptic curves over number fields

We generalize a construction of families of moderate rank elliptic curves over $\mathbb{Q}$ to number fields $K/\mathbb{Q}$. The construction, originally due to Steven J. Miller, \'Alvaro Lozano-Robledo and Scott Arms, invokes a theorem of Rosen and Silverman to show that computing the rank of these curves can be done by controlling the average of the traces of Frobenius, the construction for number fields proceeds in essentially the same way. One novelty of this method is that we can construct families of moderate rank without having to explicitly determine points and calculating determinants of height matrices.Comment: Version 1.0, 4 pages, sequel to arXiv:math/040657

Sets Characterized by Missing Sums and Differences in Dilating Polytopes

A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of $\{0,\dots,n\}$ is bounded below by a positive constant as $n\to\infty$. Hegarty then extended their work and showed that for any prescribed $s,d\in\mathbb{N}_0$, the proportion $\rho^{s,d}_n$ of subsets of $\{0,\dots,n\}$ that are missing exactly $s$ sums in $\{0,\dots,2n\}$ and exactly $2d$ differences in $\{-n,\dots,n\}$ also remains positive in the limit. We consider the following question: are such sets, characterized by their sums and differences, similarly ubiquitous in higher dimensional spaces? We generalize the integers in a growing interval to the lattice points in a dilating polytope. Specifically, let $P$ be a polytope in $\mathbb{R}^D$ with vertices in $\mathbb{Z}^D$, and let $\rho_n^{s,d}$ now denote the proportion of subsets of $L(nP)$ that are missing exactly $s$ sums in $L(nP)+L(nP)$ and exactly $2d$ differences in $L(nP)-L(nP)$. As it turns out, the geometry of $P$ has a significant effect on the limiting behavior of $\rho_n^{s,d}$. We define a geometric characteristic of polytopes called local point symmetry, and show that $\rho_n^{s,d}$ is bounded below by a positive constant as $n\to\infty$ if and only if $P$ is locally point symmetric. We further show that the proportion of subsets in $L(nP)$ that are missing exactly $s$ sums and at least $2d$ differences remains positive in the limit, independent of the geometry of $P$. A direct corollary of these results is that if $P$ is additionally point symmetric, the proportion of sum-dominant subsets of $L(nP)$ also remains positive in the limit.Comment: Version 1.1, 23 pages, 7 pages, fixed some typo

Attendee-Sourcing: Exploring The Design Space of Community-Informed Conference Scheduling

Constructing a good conference schedule for a large multi-track conference needs to take into account the preferences and constraints of organizers, authors, and attendees. Creating a schedule which has fewer conflicts for authors and attendees, and thematically coherent sessions is a challenging task. Cobi introduced an alternative approach to conference scheduling by engaging the community to play an active role in the planning process. The current Cobi pipeline consists of committee-sourcing and author-sourcing to plan a conference schedule. We further explore the design space of community-sourcing by introducing attendee-sourcing -- a process that collects input from conference attendees and encodes them as preferences and constraints for creating sessions and schedule. For CHI 2014, a large multi-track conference in human-computer interaction with more than 3,000 attendees and 1,000 authors, we collected attendees' preferences by making available all the accepted papers at the conference on a paper recommendation tool we built called Confer, for a period of 45 days before announcing the conference program (sessions and schedule). We compare the preferences marked on Confer with the preferences collected from Cobi's author-sourcing approach. We show that attendee-sourcing can provide insights beyond what can be discovered by author-sourcing. For CHI 2014, the results show value in the method and attendees' participation. It produces data that provides more alternatives in scheduling and complements data collected from other methods for creating coherent sessions and reducing conflicts.Comment: HCOMP 201