Gradual sub-lattice reduction and a new complexity for factoring polynomials

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well

Generic properties in some classes of automaton groups

We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such as exponential growth

Algorithmic decidability of Engel's property for automaton groups

We consider decidability problems associated with Engel's identity ($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups generated by an automaton. We give a partial algorithm that decides, given $x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in proving that Grigorchuk's $2$-group is not Engel. We consider next the problem of recognizing Engel elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in general, we prove that it is decidable for Grigorchuk's group: Engel elements are precisely those of order at most $2$. Our computations were implemented using the package FR within the computer algebra system GAP

A characterization of those automata that structurally generate finite groups

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper

A new hierarchy for automaton semigroups

We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy extends that given by Sidki for automaton groups, and also gives new insights into the latter. Its exponential part coincides with a notion of entropy for some associated automata. We prove that the Order Problem is decidable when the state-activity is bounded. The Order Problem remains open for the next level of this hierarchy, that is, when the state-activity is linear. Gillibert showed that it is undecidable in the whole family. The former results are implemented and will be available in the GAP package FR developed by the first author.Comment: 12 pages, accepted and presented at CIAA 201

Obese and female adolescents skip breakfast more than their non-obese and male peers

We examined the association between overweight/gender and skipping breakfast among adolescent students in Tehran city using a cross-sectional study and a multistage random sampling method. All educational zones in Tehran city were covered during the educational year of 2000-01. In total, 2321 students aged 11-16 years (1068 male; 1263 female) participated in the study. Weight and height were measured and body mass index (BMI; kg/m2) was calculated. Overweight, pre-obesity and obesity were defined as BMI � 85 th , 85 th to 95 th , and � 95 th percentile of age-sex-specific BMI reference values, respectively. Self-reported frequency of breakfast consumption was categorized as usual/always, often, and rarely/never (5-7, 2-4 and 0-1 times/wk, respectively). Student's t and Chi-square tests were employed to analyze the data. Statistical inferences were made at α = 0.05. In boys and girls, the mean ± standard deviation of BMI was 19.8 ± 4.0 and 20.6 ± 4.1 kg/m2, the 18.8 and 23.1 were overweight, and 7.3 and 8.3 were obese, respectively. There was a significant difference in the frequency of breakfast consumption between obese and normal male students (P < 0.001). Differences between pre-obese and normal, and obese and normal female students were also significant (P < 0.002 and P < 0.001, respectively). A significant difference was found in the frequency of breakfast consumption between male and female adolescents in all three categories (P < 0.001). These results suggest that obese and female adolescents are more likely to skip breakfast than their normal and male peers and are therefore at higher risk for growth deficits and low educational performance. Preventive/educational programs are urgently needed in this age group. © 2007 Versita Warsaw and Springer-Verlag

Initial Commitment to Pre-Exposure Prophylaxis and Circumcision for HIV Prevention amongst Indian Truck Drivers

Studies of HIV prevention interventions such as pre-exposure prophylaxis (PREP) and circumcision in India are limited. The present study sought to investigate Indian truck-drivers initial commitment to PREP and circumcision utilizing the AIDS Risk Reduction Model. Ninety truck-drivers completed an in-depth qualitative interview and provided a blood sample for HIV and HSV-2 testing. Truck-drivers exhibited low levels of initial commitment towards PREP and even lower for circumcision. However, potential leverage points for increasing commitment were realized in fear of infecting family rather than self, self-perceptions of risk, and for PREP focusing on cultural beliefs towards medication and physicians. Cost was a major barrier to both HIV prevention interventions. Despite these barriers, our findings suggest that the ARRM may be useful in identifying several leverage points that may be used by peers, health care providers and public health field workers to enhance initial commitment to novel HIV prevention interventions in India