Self-induced Banach algebras

A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a fertile framework for developing homological aspects of unital Banach algebras. Elementary results with applictions to computations of the bounded Hochschild cohomology groups H^1(A,A^*) with emphasis on A=A(X), the approximable operators on a Banach space X, are given.Comment: 14 pages, submitted to conference proceeding

Clear Visual Separation of Temporal Event Sequences

Extracting and visualizing informative insights from temporal event sequences becomes increasingly difficult when data volume and variety increase. Besides dealing with high event type cardinality and many distinct sequences, it can be difficult to tell whether it is appropriate to combine multiple events into one or utilize additional information about event attributes. Existing approaches often make use of frequent sequential patterns extracted from the dataset, however, these patterns are limited in terms of interpretability and utility. In addition, it is difficult to assess the role of absolute and relative time when using pattern mining techniques. In this paper, we present methods that addresses these challenges by automatically learning composite events which enables better aggregation of multiple event sequences. By leveraging event sequence outcomes, we present appropriate linked visualizations that allow domain experts to identify critical flows, to assess validity and to understand the role of time. Furthermore, we explore information gain and visual complexity metrics to identify the most relevant visual patterns. We compare composite event learning with two approaches for extracting event patterns using real world company event data from an ongoing project with the Danish Business Authority.Comment: In Proceedings of the 3rd IEEE Symposium on Visualization in Data Science (VDS), 201

The Dynamics of an Open Access: The case of the Baltic Sea Cod Fishery - A Strategic Approach -

The paper sets up a discrete-time, deterministic model of a single industry, in the light of the benchmark theory of Smith (1968). The model is used to de-scribe the dynamics of recovery from a replenishable resource such as the case of the eastern Baltic Cod fishery. The model advances from Smith’s (1968) theory since it includes a biological function dividing the change in the biomass into growth occurring during the year and recruits entering the spawning stock biomass and a dynamic entry/exit function applying a slightly more technical production function than the Schaefer production function. Theoretical possible types of steady state are discussed before the theory is applied to the eastern Baltic Sea cod fishery. The path the fishery has been following since 1982 is determined and it is discussed how it relates to the optimal path to steady state. The paper further throws light on questions as; Are we able to understand the dynamic behavior of fishermen in this fishery? Does a stable equilibrium exits and how is the path to this equilibrium described? When a fishery is regarded outside safe biological limits, could it be on the path to a positive steady state?

On Species Preservation and Non-Cooperative Exploiters

Game-theoretic fisheries models typically consider cases where some players harvest a single common fish stock. It is, however, the case that these types of models do not capture many real world mixed fisheries, where species are bio-logical independent or dependent. The present paper considers cases where several non-cooperative exploiters are involved in mixed fisheries. This paper is targeting biodiversity preservation by setting up a two species model with the aim of ensuring both species survive harvesting of exploiters adapting a non-cooperative behaviour. The model starts out as a multi-species model without biological dependency and is then modified to include also biological dependency. We contribute to the literature by analytically finding the limits on the number of players preserving both species including the conditions to be satisfied. For visual purposes we simulate a two species model with different kind of interrelationship.Biodiversity preservation, non-cooperative game, multi-species fisheries, bio-economic modelling

An Enforcement-Coalition Model: Fishermen and Authorities forming Coalitions

The paper sets up a four-stage enforcement model of fish quotas. The purpose of the paper is to show how the level of enforcement set by the authorities af-fects the way fishermen form coalitions. We show that a high level of control effort yields less cooperation among fishermen, while in the case of low control effort, coalitions are somewhat self-enforcing. The paper further discusses how the optimal enforcement level changes when the coalition formation among au-thorities changes: centralised, partly centralised and decentralised authorities. We show that decentralised authorities set a lower level of control effort com-pared to the centralised authorities. The theoretical results are illustrated by simulations of the Baltic Sea cod fishery.Coalition formation, Fisheries management, Quota enforcement, Self-enforcing policy

Smooth group representations on bornological vector spaces

We develop the basic theory of smooth representations of locally compact groups on bornological vector spaces. In this setup, we are able to formulate better general theorems than in the topological case. Still, smooth representations of totally disconnected groups on vector spaces and of Lie groups on Frechet spaces remain special cases of our theory. We identify smooth representations with essential modules over an appropriate convolution algebra. We examine smoothening functors on representations and modules and show that they agree if they are both defined. We establish the basic properties of induction and compact induction functors using adjoint functor techniques. We describe the center of the category of smooth representations.Comment: I corrected a mistake in the last section and added a french abstrac