Navigating in the Cayley graph of SL2(Fp)SL_2(F_p) and applications to hashing

Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, $A$ and $B$, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with $2 \times 2$ matrices over $F_p$. Since there are many known pairs of $2 \times 2$ matrices over $Z$ that generate a free monoid, this yields numerous pairs of matrices over $F_p$, for a sufficiently large prime $p$, that are candidates for collision-resistant hashing. However, this trick can "backfire", and lifting matrix entries to $Z$ may facilitate finding a collision. This "lifting attack" was successfully used by Tillich and Z\'emor in the special case where two matrices $A$ and $B$ generate (as a monoid) the whole monoid $SL_2(Z_+)$. However, in this paper we show that the situation with other, "similar", pairs of matrices from $SL_2(Z)$ is different, and the "lifting attack" can (in some cases) produce collisions in the group generated by $A$ and $B$, but not in the positive monoid. Therefore, we argue that for these pairs of matrices, there are no known attacks at this time that would affect security of the corresponding hash functions. We also give explicit lower bounds on the length of collisions for hash functions corresponding to some particular pairs of matrices from $SL_2(F_p)$.Comment: 10 page

Some applications of noncommutative groups and semigroups to information security

We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL2(Fp), and compute bounds on the girth of the Cayley graph of the subgroup of SL2(Fp) for specific generators A, B. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family

Reflection on Oral Quizzes

In this article we reflect on an instructional technique piloted in our discrete mathematics course this past semester. Motivated by a desire for students to better prepare for class and for them to receive adaptive feedback, we introduced oral quizzes as a check on preparation. We observed oral quizzes to be a good inspiration for out of class reading and practice, they forced students to practice oral and written communication of mathematics, and allowed us to tailor feedback to be appropriate for each student. We will discuss our motivation in more depth and detail oral quizzes as we implemented them. Finally we reflect on the instructional method and consider how oral quizzes can be improved and modified for other classes. We found oral quizzes to be very successful, and we believe they can be adapted to suit nearly any college math class

Teoria quântica: estudos históricos e implicações culturais

A obra, produzida a três mãos, pelos professores e pesquisadores Olival Freire Jr., Osvaldo Pessoa Jr. e Joan Lisa Bromberg, aborda vários aspectos da revolucinária teoria científica, desde sua criação aos desenvolvimentos ulteriores, incluindo a controvérsia sobre os seus fundamentos e sobre suas implicações filosóficas e culturais. A obra discute também problemas relacionados à pesquisa sobre o ensino e a difusão cultural dessa teoria, bem como os usos, e abusos, que aí podem aparecer

Ambient Particulate Matter Induces Interleukin-8 Expression through an Alternative NF-κB (Nuclear Factor-Kappa B) Mechanism in Human Airway Epithelial Cells

Background: Exposure to ambient air particulate matter (PM) has been shown to increase rates of cardiopulmonary morbidity and mortality, but the underlying mechanisms are still not well understood

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure

An integrated approach to the interpretation of Single Amino Acid Polymorphisms within the framework of CATH and Gene3D

Background The phenotypic effects of sequence variations in protein-coding regions come about primarily via their effects on the resulting structures, for example by disrupting active sites or affecting structural stability. In order better to understand the mechanisms behind known mutant phenotypes, and predict the effects of novel variations, biologists need tools to gauge the impacts of DNA mutations in terms of their structural manifestation. Although many mutations occur within domains whose structure has been solved, many more occur within genes whose protein products have not been structurally characterized.<p></p> Results Here we present 3DSim (3D Structural Implication of Mutations), a database and web application facilitating the localization and visualization of single amino acid polymorphisms (SAAPs) mapped to protein structures even where the structure of the protein of interest is unknown. The server displays information on 6514 point mutations, 4865 of them known to be associated with disease. These polymorphisms are drawn from SAAPdb, which aggregates data from various sources including dbSNP and several pathogenic mutation databases. While the SAAPdb interface displays mutations on known structures, 3DSim projects mutations onto known sequence domains in Gene3D. This resource contains sequences annotated with domains predicted to belong to structural families in the CATH database. Mappings between domain sequences in Gene3D and known structures in CATH are obtained using a MUSCLE alignment. 1210 three-dimensional structures corresponding to CATH structural domains are currently included in 3DSim; these domains are distributed across 396 CATH superfamilies, and provide a comprehensive overview of the distribution of mutations in structural space.<p></p> Conclusion The server is publicly available at http://3DSim.bioinfo.cnio.es/ webcite. In addition, the database containing the mapping between SAAPdb, Gene3D and CATH is available on request and most of the functionality is available through programmatic web service access.<p></p&gt

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

Neuropsychosocial profiles of current and future adolescent alcohol misusers

A comprehensive account of the causes of alcohol misuse must accommodate individual differences in biology, psychology and environment, and must disentangle cause and effect. Animal models1 can demonstrate the effects of neurotoxic substances; however, they provide limited insight into the psycho-social and higher cognitive factors involved in the initiation of substance use and progression to misuse. One can search for pre-existing risk factors by testing for endophenotypic biomarkers2 in non-using relatives; however, these relatives may have personality or neural resilience factors that protect them from developing dependence3. A longitudinal study has potential to identify predictors of adolescent substance misuse, particularly if it can incorporate a wide range of potential causal factors, both proximal and distal, and their influence on numerous social, psychological and biological mechanisms4. Here we apply machine learning to a wide range of data from a large sample of adolescents (n = 692) to generate models of current and future adolescent alcohol misuse that incorporate brain structure and function, individual personality and cognitive differences, environmental factors (including gestational cigarette and alcohol exposure), life experiences, and candidate genes. These models were accurate and generalized to novel data, and point to life experiences, neurobiological differences and personality as important antecedents of binge drinking. By identifying the vulnerability factors underlying individual differences in alcohol misuse, these models shed light on the aetiology of alcohol misuse and suggest targets for prevention