Using a Parameterization of a Radiative Transfer Model to Build High-Resolution Maps of Typical Clear-Sky UV Index in Catalonia, Spain

To perform a climatic analysis of the annual UV index (UVI) variations in Catalonia, Spain (northeast of the Iberian Peninsula), a new simple parameterization scheme is presented based on a multilayer radiative transfer model. The parameterization performs fast UVI calculations for a wide range of cloudless and snow-free situations and can be applied anywhere. The following parameters are considered: solar zenith angle, total ozone column, altitude, aerosol optical depth, and single-scattering albedo. A sensitivity analysis is presented to justify this choice with special attention to aerosol information. Comparisons with the base model show good agreement, most of all for the most common cases, giving an absolute error within 0.2 in the UVI for a wide range of cases considered. Two tests are done to show the performance of the parameterization against UVI measurements. One uses data from a high-quality spectroradiometer from Lauder, New Zealand [45.04°S, 169.684°E, 370 m above mean sea level (MSL)], where there is a low presence of aerosols. The other uses data from a Robertson–Berger-type meter from Girona, Spain (41.97°N, 2.82°E, 100 m MSL), where there is more aerosol load and where it has been possible to study the effect of aerosol information on the model versus measurement comparison. The parameterization is applied to a climatic analysis of the annual UVI variation in Catalonia, showing the contributions of solar zenith angle, ozone, and aerosols. High-resolution seasonal maps of typical UV index values in Catalonia are presented

Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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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.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

Free triples, large indifference classes and the majority rule

We present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.

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.

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

The density of injective endomorphisms of a free group

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On the number of K3,3-minor-free and maximal K3,3-minor-free graphs

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The Benefits of building barrier-free: a contingent valuation of accessibilty as an attribute of housing

Estimating the social benefits of barrier-free building has always required indirect solutions, such as calculating the savings in social services, hospitalisation or adaptations made possible by the increase in accessibility. This research uses the Contingent Valuation Method to gain a direct appraisal of the benefits from barrier-free housing. When comparing two similar dwellings, with the only difference being their accessibility conditions, the 1,007 randomly chosen households that answered the direct survey would pay, on average 12.5 per cent more for being barrier-free. None of the different appraisals made on accessibility costs reaches 5 per cent. This confirms the social profitability of building without barriers and shows the potential size of the private market for those housing developers that meet the demand. Accessibility is a general concern, an economic good or attribute that most households value, irrespective of the physical conditions of their members.

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

The Spread of free-riding behavior in a social network

We study a model where agents, located in a social network, decide whether to exert effort or not in experimenting with a new technology (or acquiring a new skill, innovating, etc.). We assume that agents have strong incentives to free ride on their neighbors' effort decisions. In the static version of the model efforts are chosen simultaneously. In equilibrium, agents exerting effort are never connected with each other and all other agents are connected with at least one agent exerting effort. We propose a mean-field dynamics in which agents choose in each period the best response to the last period's decisions of their neighbors. We characterize the equilibrium of such a dynamics and show how the pattern of free riders in the network depends on properties of the connectivity distribution.