Characterization and Application of Educational Virtual Environments for Science Teaching in Secondary School

This work describes the characteristics of a representative set of seven different virtual laboratories (VLs) aimed for science teaching in secondary school. For this purpose, a 27-item evaluation model that facilitates the characterization of the VLs was prepared. The model takes into account the gaming features, the overall usability, and also the potential to induce scientific literacy. Five of the seven VLs were then tested with two larger and highly heterogenic groups of students, and in two different contexts – biotechnology and physics, respectively. It is described how the VLs were received by the students, taking into account both their motivation and their self-reported learning outcome. In some cases, students’ approach to work with the VLs was recorded digitally, and analyzed qualitatively. In general, the students enjoyed the VL activities, and claimed that they learned from them. Yet, more investigation is required to address the effectiveness of these tools for significant learning.

Orthogonal protecting groups in the synthesis of tryptophanyl-hexahydropyrroloindoles

The synthesis of various polycyclic systems containing a C3aNi bond between a hexahydropyrrolo[2,3-b]indole and an indole tryptophan is described here. A series of experiments were performed to determine the best combination of five orthogonal protecting groups and the best reaction conditions for formation of said bond, which is a common feature among many recently discovered marine natural products.

Orthogonal protecting groups in the synthesis of tryptophanyl-hexahydropyrroloindoles

The synthesis of various polycyclic systems containing a C3a-Ni bond between a hexahydropyrrolo[2,3-b]indole and an indole tryptophan is described here. A series of experiments were performed to determine the best combination of five orthogonal protecting groups and the best reaction conditions for formation of said bond, which is a common feature among many recently discovered marine natural products.

Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Metrics on diagram groups and uniform embeddings in a Hilbert space

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Pressure groups and experts in environmental regulation

We study a problem of adverse selection in the context of environmental regulation, where the firm may suffer from a certain degree of ignorance about its own type. In a framework like the construction of a certain infrastructure project, the presence of ignorance about its impact on the environment, can play an important role in the determination of the regulatory policy. First, an optimal contract is constructed for any exogenous level of ignorance. Second, the presence of potentially informed third-parties is studied from the perspective of the regulator, which allows us to analyze the impact on the efficiency of the contract, of the presence of environmentalists and of experts. Then, we obtain some insights on how the problem differs when the degree of ignorance is a choice variable for the firm. We finally use our results to derive policy implications concerning the existing envoronmental regulation, and the potential role of interested parties as information providers.

Pure braid subgroups of braided Thompson's groups

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Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

Distortion of wreath products in some finitely presented groups

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Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Minimal truncations of supersingular p-divisible groups

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