Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound d 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Continued use of process modeling grammars : the impact of individual difference factors

Process modeling grammars are used by analysts to describe information systems domains in terms of the business operations an organization is conducting. While prior research has examined the factors that lead to continued usage behavior, little knowledge has been established as to what extent characteristics of the users of process modeling grammars inform usage behavior. In this study, a theoretical model is advanced that incorporates determinants of continued usage behavior as well as key antecedent individual difference factors of the grammar users, such as modeling experience, modeling background and perceived grammar familiarity. Findings from a global survey of 529 grammar users support the hypothesized relationships of the model. The study offers three central contributions. First, it provides a validated theoretical model of post-adoptive modeling grammar usage intentions. Second, it discusses the effects of individual difference factors of grammar users in the context of modeling grammar usage. Third, it provides implications for research and practice.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Soil management effects on organic carbon in isolated fractions of a Gray Luvisol

Agricultural management affects soil organic matter, which is important for sustainable crop production and as a greenhouse gas sink. Our objective was to determine how tillage, residue management and N fertilization affect organic C in unprotected, and physically, chemically and biochemically protected soil C pools. Samples from Breton, Alberta were fractionated and analysed for organic C content. As in previous report, N fertilization had a positive effect, tillage had a minimal effect, and straw management had no effect on whole-soil organic C. Tillage and straw management did not alter organic C concentrations in the isolated C pools, while N fertilization increased C concentrations in all pools. Compared with a woodlot soil, the cultivated plots had lower total organic C, and the C was redistributed among isolated pools. The free light fraction and coarse particulate organic matter responded positively to C inputs, suggesting that much of the accumulated organic C occurred in an unprotected pool. The easily dispersed silt-sized fraction was the mineral-associated pool most responsive to changes in C inputs, whereas the microaggregate-derived silt-sized fraction best preserved C upon cultivation. These findings suggest that the silt-sized fraction is important for the long-term stabilization of organic matter through both physical occlusion in microaggregates and chemical protection by mineral association.

Acid hydrolysis of easily dispersed and microaggregate-derived silt- and clay-sized fractions to isolate resistant soil organic matter

The current paradigm in soil organic matter (SOM) dynamics is that the proportion of biologically resistant SOM will increase when total SOM decreases. Recently, several studies have focused on identifying functional pools of resistant SOM consistent with expected behaviours. Our objective was to combine physical and chemical approaches to isolate and quantify biologically resistant SOM by applying acid hydrolysis treatments to physically isolated silt- and clay-sized soil fractions. Microaggegrate-derived and easily dispersed silt- and clay-sized fractions were isolated from surface soil samples collected from six long-term agricultural experiment sites across North America. These fractions were hydrolysed to quantify the non-hydrolysable fraction, which was hypothesized to represent a functional pool of resistant SOM. Organic C and total N concentrations in the four isolated fractions decreased in the order: native > no-till > conventional-till at all sites. Concentrations of non-hydrolysable C (NHC) and N (NHN) were strongly correlated with initial concentrations, and C hydrolysability was found to be invariant with management treatment. Organic C was less hydrolysable than N, and overall, resistance to acid hydrolysis was greater in the silt-sized fractions compared with the clay-sized fractions. The acid hydrolysis results are inconsistent with the current behaviour of increasing recalcitrance with decreasing SOM content: while %NHN was greater in cultivated soils compared with their native analogues, %NHC did not increase with decreasing total organic C concentrations. The analyses revealed an interaction between biochemical and physical protection mechanisms that acts to preserve SOM in fine mineral fractions, but the inconsistency of the pool size with expected behaviour remains to be fully explained.

Impact of soil texture on the distribution of soil organic matter in physical and chemical fractions

Previous research on the protection of soil organic C from decomposition suggests that soil texture affects soil C stocks. However, different pools of soil organic matter (SOM) might be differently related to soil texture. Our objective was to examine how soil texture differentially alters the distribution of organic C within physically and chemically defined pools of unprotected and protected SOM. We collected samples from two soil texture gradients where other variables influencing soil organic C content were held constant. One texture gradient (16-60% clay) was located near Stewart Valley, Saskatchewan, Canada and the other (25-50% clay) near Cygnet, OH. Soils were physically fractionated into coarse- and fine-particulate organic matter (POM), silt- and clay-sized particles within microaggregates, and easily dispersed silt-and clay-sized particles outside of microaggregates. Whole-soil organic C concentration was positively related to silt plus clay content at both sites. We found no relationship between soil texture and unprotected C (coarse- and fine-POM C). Biochemically protected C (nonhydrolyzable C) increased with increasing clay content in whole-soil samples, but the proportion of nonhydrolyzable C within silt- and clay-sized fractions was unchanged. As the amount of silt or clay increased, the amount of C stabilized within easily dispersed and microaggregate-associated silt or clay fractions decreased. Our results suggest that for a given level of C inputs, the relationship between mineral surface area and soil organic matter varies with soil texture for physically and biochemically protected C fractions. Because soil texture acts directly and indirectly on various protection mechanisms, it may not be a universal predictor of whole-soil C content.

Land use effects on soil carbon fractions in the southeastern United States. II. changes in soil carbon fractions along a forest to pasture chronosequence

Since land use change can have significant impacts on regional biogeochemistry, we investigated how conversion of forest and cultivation to pasture impact soil C and N cycling. In addition to examining total soil C, we isolated soil physiochemical C fractions in order to understand the mechanisms by which soil C is sequestered or lost. Total soil C did not change significantly over time following conversion from forest, though coarse (250-2,000 mum) particulate organic matter C increased by a factor of 6 immediately after conversion. Aggregate mean weight diameter was reduced by about 50% after conversion, but values were like those under forest after 8 years under pasture. Samples collected from a long-term pasture that was converted from annual cultivation more than 50 years ago revealed that some soil physical properties negatively impacted by cultivation were very slow to recover. Finally, our results indicate that soil macroaggregates turn over more rapidly under pasture than under forest and are less efficient at stabilizing soil C, whereas microaggregates from pasture soils stabilize a larger concentration of C than forest microaggregates. Since conversion from forest to pasture has a minimal impact on total soil C content in the Piedmont region of Virginia, United States, a simple C stock accounting system could use the same base soil C stock value for either type of land use. However, since the effects of forest to pasture conversion are a function of grassland management following conversion, assessments of C sequestration rates require activity data on the extent of various grassland management practices.

Land use effects on soil carbon fractions in the southeastern United States. I. Management-intensive versus extensive grazing

Changes in grassland management intended to increase productivity can lead to sequestration of substantial amounts of atmospheric C in soils. Management-intensive grazing (MiG) can increase forage production in mesic pastures, but potential impacts on soil C have not been evaluated. We sampled four pastures (to 50 cm depth) in Virginia, USA, under MiG and neighboring pastures that were extensively grazed or bayed to evaluate impacts of grazing management on total soil organic C and N pools, and soil C fractions. Total organic soil C averaged 8.4 Mg C ha(-1) (22%) greater under MiG; differences were significant at three of the four sites examined while total soil N was greater for two sites. Surface (0-10 cm) particulate organic matter (POM) C increased at two sites; POM C for the entire depth increment (0-50 cm) did not differ significantly between grazing treatments at any of the sites. Mineral-associated C was related to silt plus clay content and tended to be greater under MiG. Neither soil C:N ratios, POM C, or POM C:total C ratios were accurate indicators of differences in total soil C between grazing treatments, though differences in total soil C between treatments attributable to changes in POM C (43%) were larger than expected based on POM C as a percentage of total C (24.5%). Soil C sequestration rates, estimated by calculating total organic soil C differences between treatments (assuming they arose from changing grazing management and can be achieved elsewhere) and dividing by duration of treatment, averaged 0.41 Mg C ha(-1) year(-1) across the four sites.

Cell density alters matrix accumulation in two distinct fractions and the mechanical integrity of alginate-chondrocyte constructs

Chondrocyte density in articular cartilage is known to change with the development and growth of the tissue and may play an important role in the formation of a functional extracellular matrix (ECM). The objective of this study was to determine how initial chondrocyte density in an alginate hydrogel affects the matrix composition, its distribution between the cell-associated (CM) and further removed matrix (FRM) fractions, and the tensile mechanical properties of the developing engineered cartilage. Alginate constructs containing primary bovine chondrocytes at densities of 0, 4, 16, and 64 million cells/ml were fabricated and cultured for 1 or 2 weeks, at which time structural, biochemical, and mechanical properties were analyzed. Both matrix content and distribution varied with the initial cell density. Increasing cell density resulted in an increasing content of collagen and sulfated-glycosaminoglycan (GAG) and an increasing proportion of these molecules localized in the CM. While the equilibrium tensile modulus of cell-free alginate did not change with time in culture, the constructs with highest cell density were 116% stiffer than cell-free controls after 2 weeks of culture. The equilibrium tensile modulus was positively correlated with total collagen (r2 = 0.47, p < 0.001) and GAG content (r2 = 0.68, p < 0.001), and these relationships were enhanced when analyzing only those matrix molecules in the CM fraction (r2 = 0.60 and 0.72 for collagen and GAG, respectively, each p < 0.001). Overall, the results of this study indicate that initial cell density has a considerable effect on the developing composition, structure, and function of alginate–chondrocyte constructs.

To be continued... fan fiction and the constructing of identity

This chapter contributes to the existing body of knowledge on fan fiction by reporting the findings from a quantitative and qualitative study on fan fiction in a Swedish context. The authors contextualize the fan fiction phenomenon as a part of a larger transformation of the media sphere and the society in general where media consumers’ role as collaborative cultural producers grows ever stronger. They explore what kind of stories inspire the writers and conclude that as in many other parts of the entertainment industry, fan fiction is dominated by a small number of international media brands. The authors show how fan fiction can play an important role in the development of adolescents’ literacies and identities and how their pastime works as a vehicle for personal growth.