Graph coloring applied to secure computation in non-Abelian groups

We study the natural problem of secure n-party computation (in the computationally unbounded attack model) of circuits over an arbitrary finite non-Abelian group (G,⋅), which we call G-circuits. Besides its intrinsic interest, this problem is also motivating by a completeness result of Barrington, stating that such protocols can be applied for general secure computation of arbitrary functions. For flexibility, we are interested in protocols which only require black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our investigations focus on the passive adversarial model, where up to t of the n participating parties are corrupted.

Learning diaries to foster learner autonomy in mixed-ability groups. 'Los diarios de aprendizaje como herramientas para facilitar la autonomía en grupos de diferente capacidad'.

Resumen basado en el de la publicación. Resumen en español

Dealing with primary mixed ability groups : o qué hacer en clase. 'Tratando con grupos de habilidad mixtos de primaria'.

Un grupo de profesoras implicadas en experiencias de implantación del Inglés en el ciclo medio de Educación Primaria recoge en este documeto sus experiencias, reflexiones y materiales elaborados durante el proceso. La introducción aporta una serie de observaciones sobre las características del alumnado, la contextualización del Inglés como tercera lengua, los objetivos generales del área en esta etapa, el papel del profesorado y del alumnado y la organización del aula de inglés. Se incluyen una serie de actividades y materiales para cada uno de los cursos de 2õ y 3õ ciclo, asi como pautas para su utilización. Los contenidos de cada uno de los cursos se organizan en torno a una serie de temas (topics) seleccionados de acuerdo con la edad e intereses del alumnado.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Low-status monkeys “play dumb” when learning in mixed social groups

Many primates, including humans, live in complex hierarchical societies where social context and status affect daily life. Nevertheless, primate learning studies typically test single animals in limited laboratory settings where the important effects of social interactions and relationships cannot be studied. To investigate the impact of sociality on associative learning, we compared the individual performances of group-tested rhesus monkeys (Macaca mulatta) across various social contexts. We used a traditional discrimination paradigm that measures an animal’s ability to form associations between cues and the obtaining of food in choice situations; but we adapted the task for group testing. After training a 55-member colony to separate on command into two subgroups, composed of either high- or low-status families, we exposed animals to two color discrimination problems, one with all monkeys present (combined condition), the other in their “dominant” and “subordinate” cohorts (split condition). Next, we manipulated learning history by testing animals on the same problems, but with the social contexts reversed. Monkeys from dominant families excelled in all conditions, but subordinates performed well in the split condition only, regardless of learning history. Subordinate animals had learned the associations, but expressed their knowledge only when segregated from higher-ranking animals. Because aggressive behavior was rare, performance deficits probably reflected voluntary inhibition. This experimental evidence of rank-related, social modulation of performance calls for greater consideration of social factors when assessing learning and may also have relevance for the evaluation of human scholastic achievement.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

There is something about Mary… and Ted! : Training in mixed-sex groups makes you work harder. A study about the effort when training with the opposite sex.

In many sport associations, regardless of level, women and men rarely practice together. Previous studies indicate that work groups are generally more efficient when there is an even distribution between the sexes. Could that also be the case in sports? This study aims to investigate whether the sex composition of a training group affects the effort and performance of the participants. Eleven volunteers participated in the crossover study consisting of three different 150-meter sprint conditions; individually, single-sex group and mixed-sex group. Sprint times, heart rate and RPE were recorded during all three trials. The result of this study suggests that there might be practical benefits in regards to physical performance and effort to exercise in a training group consisting of both sexes instead of training only with the same-sex or individually. The understanding could be useful in areas such as; training optimisation for both athletes and in patient- and rehabilitation groups, increasing efficiency in work environments, in schools and sports clubs striving for both athletic success and gender equality.

Peer interaction in mixed age groups: a study in the computer area of an early childhood education center in Portugal

The study was developed as a teacher-research project during initial teacher education – Masters Degree of Early Childhood and Primary Education, in Portugal. It analysed the interactions between children of 3 to 6 years old, during the use of the computer as a free choice activity, confronting situations between peers of the same age and situations between peers of different ages. The focus of the analysis was the collaborative interactions. This was a qualitative study. Children could choose the computer, amongst other interest areas, and work for around an hour in pairs. In the computer, children used mainly educational games. During four weeks, the interactions between the pairs were audio recorded. Field notes and informal interviews to the children were also used to collect data. Eleven children were involved in the study with ages ranging from 3 to 6 years old. Baseline data on children’s basic computer proficiency was collected using the Individualized Computer Proficiency Checklist (ICPC) by Hyun. The recorded interactions were analysed using the types of talk offered by Scrimshaw and Perkins and Wegerif and Scrimshaw: cumulative talk, exploratory talk, disputational talk, and tutorial talk. This framework was already used in a study in an early childhood education context in Portugal by Amante. The results reveal differences in computer use and characterize the observed interactions. Seven different pairs of children's interactions were analysed. More than a third of the interactions were cumulative talk, followed by exploratory talk, tutorial talk and disputational talk. Comparing same and mixed age pairs, we observed that cumulative talk is the more present interaction, but in same age pairs this is followed by exploratory talk whereas in the mixed age pairs it is tutorial talk that has the second largest percentage. The pairs formed by the children were very asymmetrical in terms of age and computer proficiency. This lead to the more tutorial interactions, where one children showed the other or directed him/her on how to play. The results show that collaboration is present during the use of a computer area in early childhood education. The free choice of the children means the adults can only suggest pairing suited to specific interactions between the children. Another way to support children in more exploratory talk interactions could be by discussing the way the older children can help the younger ones beyond directing or correcting their work.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

The effect of increasing dietary fibre and the provision of straw racks on the welfare of sows housed in small static groups

This study assessed the effects of increasing dietary fibre levels in concentrate rations and providing access to straw in racks on the welfare of pregnant sows housed in small static groups. In a 2 x 2 factorial design experiment, 128 Large White x Landrace pregnant sows were offered one of two diets: (i) High fibre diet with 9% crude fibre, or (ii) Control diet with 4.5% CF, and one of two levels of access to a foraging substrate: (i) access to straw in racks or (ii) no straw. The study was replicated eight times using groups of four sows, and treatment periods lasted four weeks. Sows were housed in pens with voluntary cubicles and a slatted exercise area and were offered a wet diet twice a day. Back-fat levels were measured before sows were mixed into groups at 28 days post partum, and four weeks later. Aggressive interactions were recorded on the day of mixing, and injury scores were recorded one week post mixing. Scan sampling was used to collect data on general activity, posture and location of the sows, and on sham-chewing and bar-biting behaviours across the treatment period. In addition, detailed focal observations were carried out on all sows across the treatment period. Straw usage was also recorded. There were no treatment effects on changes in back-fat levels over the treatment period. Treatments had no effect on post-mixing aggression or on injury scores. However, focal observations showed that sows with access to straw were involved in fewer bouts of head-thrusting over the treatment period. Control diet sows spent more time inactive than sows on the high fibre diet, however high fibre diet sows spent more time lying with eyes closed than sows on the control diet. Sows on the high fibre diet with access to straw showed less sham-chewing and bar-biting behaviour than sows in other treatments. These results show that although a diet containing 9% crude fibre promoted resting behaviour, it was necessary to combine it with access to straw to reduce stereotypic behaviour of sows in small static groups.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.