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We present two new algorithms for solving norm equations over global function fields with at least one infinite place of degree one. The first of these is a substantial improvement of a method due to Gaál and Pohst, while the second approach uses index calculus techniques and is significantly faster asymptotically and in practice. Both algorithms incorporate compact representations of field elements which results in a significant gain in performance compared to the Gaál–Pohst approach. We provide Magma implementations, analyze the complexity of all three algorithms under varying asymptotics on the field parameters, and provide empirical data on their performance. [ABSTRACT FROM AUTHOR]

This article examines how respondents understood items in the Spanish versions of the Short-Form 36 (SF-36v2). Cognitive interviews of the SF-36 were conducted in 2 phases with 46 Spanish speakers living in the United States. Roughly one-third (17/46) of respondents had difficulty understanding the Role Emotional items upon their initial reading, and almost half (21/46) provided examples that were inconsistent with the intended meaning of the items. The findings of this study underscore the importance of conducting cognitive testing to ensure conceptual equivalence of any instrument regardless of how well validated it appears to be. [ABSTRACT FROM AUTHOR]

We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-series to compute the group orders unconditionally for all Δ ≢ 1 (mod 8). The group structure is resolved using the factorization of the group order. The 1 mod 8 case was handled using the methods of Jacobson, Ramachandran, and Williams including the batch verification method based on the Eichler-Selberg trace formula to remove dependence on the Extended Riemann Hypothesis. Our new method enabled us to extend the previous bound of |Δ| < 2·1011 to 240. Statistical data in support of a variety of conjectures is presented, along with new examples of class groups with exotic structures. [ABSTRACT FROM AUTHOR]

We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-series to compute the group orders unconditionally for all Δ ≢ 1 (mod 8). The group structure is resolved using the factorization of the group order. The 1 mod 8 case was handled using the methods of Jacobson, Ramachandran, and Williams including the batch verification method based on the Eichler-Selberg trace formula to remove dependence on the Extended Riemann Hypothesis. Our new method enabled us to extend the previous bound of |Δ| < 2·1011 to 240. Statistical data in support of a variety of conjectures is presented, along with new examples of class groups with exotic structures. [ABSTRACT FROM AUTHOR]

We present an analysis of Bernstein's batch integer smoothness test when applied to the case of polynomials over a finite field Fq: We compare the performance of our algorithm with the standard method based on distinct degree factorization from both an analytical and a practical point of view. Our results show that although the batch test is asymptotically better as a function of the degree of the polynomials to test for smoothness, it is unlikely to offer significant practical improvements for cases of practical interest. [ABSTRACT FROM AUTHOR]

Real hyperelliptic curves admit two structures suitable for cryptography - the Jacobian (a finite abelian group) and the infrastructure. Mireles Morales described precisely the relationship between these two structures, and made the assertion that when implemented with balanced divisor arithmetic, the Jacobian generically yields more efficient arithmetic than the infrastructure for cryptographic applications. We confirm that this assertion holds for genus two curves, through rigorous analysis and the first detailed numerical performance comparisons, showing that cryptographic key agreement can be performed in the Jacobian without any extra operations beyond those required for basic scalar multiplication. We also present a modified version of Mireles Morales' map that more clearly reveals the algorithmic relationship between the two structures. [ABSTRACT FROM AUTHOR]

We describe improved versions of indeX-calculus algorithms for solving discrete logarithm problems in Jacobians of high-genus hyperelliptic curves defined over even characteristic fields. Our first improvement is to incorporate several ideas for the low-genus case by Gaudry and Theriault, including the large prime variant and using a smaller factor base, into the large-genus algorithm of Enge and Gaudry. We eXtend the analysis in a 2001 paper by Jacobson, Menzes, and Stein to our new algorithm, allowing us to predict accurately the number of random walk steps required to find all relations, and to select optimal degree bounds for the factor base. Our second improvement is the adaptation of sieving techniques from Flassenberg and Paulus, and Jacobson to our setting. The new algorithms are applied to concrete problem instances arising from the Weil descent attack methodology for solving the elliptic curve discrete logarithm problem, demonstrating significant improvements in practice. [ABSTRACT FROM AUTHOR]

A significant amount of effort has been devoted to improving divisor arithmetic on low-genus hyperelliptic curves via explicit versions of generic algorithms. Moderate and high genus curves also arise in cryptographic applications, for example, via the Weil descent attack on the elliptic curve discrete logarithm problem, but for these curves, the generic algorithms are to date the most efficient available. Nagao [22] described how some of the techniques used in deriving efficient explicit formulas can be used to speed up divisor arithmetic using Cantor's algorithm on curves of arbitrary genus. In this paper, we describe how Nagao's methods, together with a sub-quadratic complexity partial extended Euclidean algorithm using the half-gcd algorithm can be applied to improve arithmetic in the degree zero divisor class group. We present numerical results showing which combination of techniques is more efficient for hyperelliptic curves over F2n of various genera. [ABSTRACT FROM AUTHOR]

We present a method for tabulating all cubic function fields over Fq(t) whose discriminant D has either odd degree or even degree and the leading coefficient of -3D is a non-square in Fq* , up to a given bound B on deg(D). Our method is based on a generalization of Belabas' method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory for binary cubic forms that provides an efficient way to compute equivalence classes of binary cubic forms. The algorithm requires O(B4qB) field operations as B → ∞. The algorithm, examples and numerical data for q = 5, 7, 11, 13 are included. [ABSTRACT FROM AUTHOR]

The article presents a study which focuses on translating cognitive questionnaire items to create an effective research tool for English, Chinese, and Spanish-speaking workers in the U.S. The study found that response format is the common problem among languages, suggesting that translating a language to another would result to varying responses. It concludes that specific expertise and conceptual analysis is required to form a comprehensive and cognitive translated questionnaire.

We describe algorithms for point multiplication on Koblitz curves using multiple-base expansions of the form k = Σ ± τa( τ - 1)b and k = Σ ± τa (τ - μ )b(τ2 - μτ - 1)c. We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first provably sublinear point multiplication algorithm on Koblitz curves. For the first type, we conjecture that the number of terms is sublinear and provide numerical evidence demonstrating that the number of terms is significantly less than that of τ-adic nonadjacent form expansions. We present details of an innovative FPGA implementation of our algorithm and performance data demonstrating the efficiency of our method. We also show that implementations with very low computation latency are possible with the proposed method because parallel processing can be exploited efficiently. [ABSTRACT FROM AUTHOR]

Physical access to primary care is poorly understood in most remote and underserved populations, although technology exists that can quickly help bridge this information gap. To improve health care delivery in these regions, it is essential to understand the factors that enable or inhibit health care use. One key factor is that of distance from residence to health facility. Assessment of the effect distance has on health facility use provides a clearer picture of how access can be attained. This article focuses on understanding the geographic character of access to care and the expediency of data collection using global positioning system technology. It shows how to quantify geographic access for a given health facility. This procedure can be performed within a relatively short period of time with the assistance of modern technology and some knowledge of geographic techniques. [ABSTRACT FROM AUTHOR]

Little is known about how older women cope in long-term abusive intimate relationships. Understanding their coping strategies may give insight into how to further support their effective coping efforts. Interviews were conducted with 38 women older than age 55 years. Grounded theory analysis demonstrated that women who remained in their abusive relationships employed mainly cognitive (emotion-focused) strategies to find meaning in a situation that was perceived as unchangeable. By reappraising themselves, their spouses, and their relationships they refocused energies in certain roles, set limits with their abusers, and reached out to others (friends, family, and community organizations). Some women appeared to thrive, others merely survived, but all maintained the appearance of conjugal unity. [ABSTRACT FROM AUTHOR]

Recently, quality of life studies among patients with HIV/AIDS have shown high levels of life satisfaction. Spiritual and religious factors may contribute to these positive outcomes. We interviewed 19 patients with HIV/AIDS in order to understand better the role of religious-spiritual biographies and orientations in quality of life, and found four patterns to describe the ways in which past experiences with religion/spirituality and religious/spiritual meaning-making help to explain how patients are currently coping with HIV/AIDS. We illustrate each of these patterns with a prototypic patient: (1) the Deferring Believer (“God allows things to happen for a reason.”); (2) the Collaborating Believer (“This is where I'm supposed to be.”); (3) the Religious/Spiritual Seeker (“I'm trying to get my life together.”); and (4) the Self-Directing Believer (“What else is new?”). The findings support a previously described theoretical model of meaning-making in response to adversity, and they suggest the value of life course and narrative approaches to understanding religious coping. [ABSTRACT FROM AUTHOR]

Background: Intimate partner violence (IPV) is a problem in older women, but older victims of IPV are often unidentified in the medical setting because providers think of IPV as a problem of younger women. The experiences of older women with IPV are unknown. This study reports on the healthcare experiences and needs of older victims of IPV. Methods: Interviews were conducted with 38 women >55 years who responded to an advertisement recruiting "women who had been in an abusive relationship since age 55." Interviews were audiotaped, transcribed, and analyzed for themes. Results: The median age of participants was 58 years (range 55-90). The majority were Caucasian with annual incomes over $40,000. The median relationship length was 24 years (range 2-67), and 39% remained in their abusive relationships. About half had discussed IPV with a healthcare provider. The themes that were identified included disclosure about IPV and both negative and positive experiences with healthcare providers. Reasons for nondisclosure were similar to those of younger women but were compounded by the generational mores of privacy about domestic affairs and society's lack of understanding and resources for IPV. Some of the women who disclosed IPV to their providers felt discounted and unsupported. Others reported receiving valuable help, including empathy, referrals to resources, assistance in naming the abuse, linking the stress of IPV to health, and respect for their decisions to continue their abusive relationships. Conclusions: Older women victims have difficulty initiating discussions about IPV with their providers. Providers are encouraged to identify signals of potential abuse and to create privacy with all patients to discuss difficult issues, such as IPV, and to be knowledgeable about appropriate referrals. [ABSTRACT FROM AUTHOR]

To understand women's reasons for continuing long-term abusive relationships, interviews were conducted with 36 women who were over the age of 55. These women matured during times of sweeping social changes with the feminist, battered women's, and elder abuse movements. Reasons for remaining were organized into three categories: cohort, period, and aging effects. Cohort effects included reasons similar to those of younger women such as lacking education or job skills. Period effects related to efforts to seek help early in the abusive relationship and receiving little assistance from society's social institutions. Finally, aging effects dealt with how the health challenges of physical age limited options. [ABSTRACT FROM AUTHOR]

We present a new non-interactive public-key distribution system based on the class group of a non-maximal imaginary quadratic order Cl( Δp). The main advantage of our system over earlier proposals based on (Z}/nZ)* [25,27] is that embedding id information into group elements in a cyclic subgroup of the class group is easy (straight-forward embedding into prime ideals suffices) and secure, since the entire class group is cyclic with very high probability. Computational results demonstrate that a key generation center (KGC) with modest computational resources can set up a key distribution system using reasonably secure public system parameters.  In order to compute discrete logarithms in the class group, the KGC needs to know the prime factorization of Δp=Δ1 p2. We present an algorithm for computing discrete logarithms in Cl(Δp) by reducing the problem to computing discrete logarithms in Cl(Δ1) and either F*p or F*p2. Our algorithm is a specific case of the more general algorithm used in the setting of ray class groups [5]. We prove—for arbitrary non-maximal orders—that this reduction to discrete logarithms in the maximal order and a small number of finite fields has polynomial complexity if the factorization of the conductor is known. [ABSTRACT FROM AUTHOR]

Given the difficulty of separating the three Picea species—P. glauca, P. mariana, and P. rubens (white, black, and red spruce)—in the pollen record, little is known about their unique histories in eastern North America following deglaciation. Here we report the first use of a classification tree analysis (CART) to distinguish pollen grains of these species. It was successfully applied to fossil pollen from eight sites in Maine and one in Massachusetts. We focused on the late glacial/early Holocene (14,000 to 8000 cal yr B.P.) and the late Holocene (1400 cal yr B.P. to present)—the two key periods since deglaciation when Picea has been abundant in the region. The result shows a shift from a Picea forest of P. glauca and P. mariana in the late glacial to a forest of P. rubens and P. mariana in the late Holocene. The small number of P. rubens grains identified from the late glacial/early Holocene samples (<5%) suggests that that species was either absent or rare at most of the sites. The occurrence and distribution of the three species do not reveal any geographic or temporal trend during late glacial time, but the data suggest that they were distributed in local patches on the landscape. The results of this study indicate that the recent population expansion of Picea (1000 to 500 cal yr B.P.) was likely the first time since deglaciation that P. rubens was abundant in the region. [Copyright &y& Elsevier]

Examines the classification of Picea using morphometric analysis of pollen grains in North America. Use of quantitative analysis of grain attributes; Linkage of multiple binary trees for error detection using Hamming codes; Construction of the regression trees.

We present efficient algorithms for computing discrete logarithms in the class group of a quadratic order and for principality testing in a real quadratic order, based on the work of Düllmann and Abel. We show how the idea of generating relations with sieving can be applied to improve the performance of these algorithms. Computational results are presented which demonstrate that our new techniques yield a significant increase in the sizes of discriminants for which these discrete logarithm problems can be solved. [ABSTRACT FROM AUTHOR]

ABSTRACT. Multiple overlapping and replicate pollen stratigraphies from Canal de la Puntilla (40 Degrees 57'09"S, 72 Degrees 54'18"W, 120 m elevation) reveal that a Nothofagus dombeyi-type parkland occupied the Valle Central of the Chilean Lake District during the portion of the Last Glacial Maximum between 20,200 and about 14,600 [sup 14]C yr BP. Dominating this landscape was Nothofagus dombeyi-type and Gramineae, accompanied by taxa commonly found today in Subantarctic environments and above the Andean tree-line in the Lake District (Perezia-type, Valeriana, and Huperzia selago), along with cushion bog taxa characteristic of Magellanic Moorlands (Donatia fascicularis and Astelia pumila). Within this open landscape Nothofagus dombeyi-type expanded between 20,200 and 15,800 [sup 14]C yr BP, interrupted by a brief reversal between 19,200 and 18,800 [sup 14]C yr BP and followed by a prominent increase in Gramineae pollen between 15,800 and about 14,600 [sup 14]C yr BP. A major rise of Nothofagus dombeyi-type began at about 14,600 [sup 14]C yr BP, followed by decline in non-arboreal taxa and a remarkable expansion of North Patagonian Rain Forest taxa in pulses centered at 14,200 and 13,000 [sup 14]C yr BP. Podocarpus nubigena expanded between 12,200 and 9800 [sup 14]C yr BP, along with increases in Misodendrum and Maytenus disticha-type between 11,000 and 9800 [sup 14]C yr BP. Paleovegetation records suggest that mean annual temperature was 6-7 Degrees C colder than at present during the coldest episodes between 20,200 and about 14,600 [sup 14]C yr BP, with twice the modern annual precipitation between 20,200 and 13,000 [sup 14]C yr BP, suggesting a northward shift and intensification of westerly storm-tracks. Slight climate warming occurred between 20,200 and 15,800 [sup 14]C yr BP, interrupted by cooling events at 19,200 and 15,800 [sup 14]C yr BP. The initial warming of the last termination started at 14,600 [sup 14]C yr BP, followed by warming pulses at 14,20... [ABSTRACT FROM AUTHOR]

Investigates the influence of canopies on rates of dry deposition and nutrient influx to an acidic, sparsely wooded, poor fen in central Maine. Deposition rate of road-salt and nutrient-bearing aerosols; Concentrations and fluxes of chlorine and sodium in bulk precipitation; Peatland ecology.

(1) White pine (Pinus strobus L.), the last important tree species to reach Minnesota in the Holocene (Flandrian) period, entered from the east c. 7000 years ago, it was restricted to the north-eastern corner of the state for c. 2500 years, during the mid-postglacial period of warm dry climate, and then expanded its range to the west and south. (2) Witness-tree records from the U.S. Land Office Survey of the mid-1800s were examined to determine the nature of the natural vegetation in the study areas before logging. At the time of logging a century ago white pine was abundant in north central Minnesota, and was the major species cut for timber. (3) The immigration of white pine was studied in detail by pollen analysis of lake sediments at two paired sites in east-central and west-central Minnesota Small basins were selected, to differentiate local from regional components of the pollen rain. (4) In each case one member of the parr was on a jack-pine (Pinus banksiana) sand plain and the other on a white-pine till moraine, so that differences in the local vegetation related to soil and topography could be used to help determine how the pollen assemblage changed as white pine became important in the general area. (5) The matched pollen diagrams from each pair of sites were compared by subtracting the pollen influx for a taxon at one site from the corresponding influx at the other, and by calculating log-ratios of the pollen percentages of a taxon at the two sites. (6) White pine forests replaced oak-dominated hardwood forests in both study areas, despite the fact that the transition in north-east Minnesota occurred just prior to the maximum of the warm dry conditions of the mid-postglacial period about 7000 years ago, whereas in west-central Minnesota the change occurred only a few centuries ago. These conclusions are supported by pollen diagrams available for other areas in north-central Minnesota. The percentage profiles of oak pollen from a number of sites in... [ABSTRACT FROM AUTHOR]

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IN "My Student, the Purist: A Lament," Edgar F. Borgatta (1968) examines the issue of using parametric statistical measures with ordinal data, specifically using Pearson's r with ordinal-ordinal data. The concepts of a continuous distribution, interval data, ordinal data and ranking are compared. It is pointed out ( 1 ) that a set of ranks is incompatible with the concept of a continuous distribution, because a set of ranks cannot be obtained for the total set of continuous values, and (2) that within the context of a normal distribution and use of parametric measures, the concept of continuous distribution is not only congruent with a set of interval scale values but also with a set of ordinal scale values which are in the form of a normal curve. The second point is reinforced by the reasonable assumption that many sociological variables have populations that either approximate the normal curve or can be approximated by a transformation procedure. The issue of transforming a set of ordinal scale values into a set of ranks versus treating the set as a set of interval scale values is examined in terms of distorting reality. It is concluded that reality is distorted by assigning ranks and by performing arithmetic operations on a set of numbers that represents reality but is not isomorphic with the arithmetic system. Since bivariate normality, not scale level, is an underlying assumption for estimating Pearson's ρ, since reality represented by ordinal scale values is distorted by assigning ranks and by applying arithmetic operations, since the square of Pearson's product-moment correlation coefficient coincides with scientific goals, and since departures from the normality assumption produce an underestimation of ρ using r, the article ends with this motto: "Some parametric estimate is better than no parametric estimate" ( Borgatta, 1968: 34). [ABSTRACT FROM AUTHOR]