Abstract:
We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Vaananen, and their compositional semantics due to Hodges. We show how Hodges' semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O'Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural role, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural r\^ole.

Abstract:
In earlier work of the second and third author the equivalence of a finite square principle square^fin_{lambda,D} with various model theoretic properties of structures of size lambda and regular ultrafilters was established. In this paper we investigate the principle square^fin_{lambda,D}, and thereby the above model theoretic properties, at a regular cardinal. By Chang's Two-Cardinal Theorem, square^fin_{lambda,D} holds at regular cardinals for all regular filters D if we assume GCH. In this paper we prove in ZFC that for certain regular filters that we call "doubly^+ regular", square^fin_{lambda,D} holds at regular cardinals, with no assumption about GCH. Thus we get new positive answers in ZFC to Open Problems 18 and 19 in the book "Model Theory" by Chang and Keisler.

Abstract:
Lindstr\"om theorems characterize logics in terms of model-theoretic conditions such as Compactness and the L\"owenheim-Skolem property. Most existing characterizations of this kind concern extensions of first-order logic. But on the other hand, many logics relevant to computer science are fragments or extensions of fragments of first-order logic, e.g., k-variable logics and various modal logics. Finding Lindstr\"om theorems for these languages can be challenging, as most known techniques rely on coding arguments that seem to require the full expressive power of first-order logic. In this paper, we provide Lindstr\"om theorems for several fragments of first-order logic, including the k-variable fragments for k>2, Tarski's relation algebra, graded modal logic, and the binary guarded fragment. We use two different proof techniques. One is a modification of the original Lindstr\"om proof. The other involves the modal concepts of bisimulation, tree unraveling, and finite depth. Our results also imply semantic preservation theorems.

Abstract:
Functional communication is a necessity to succeed in high technology product development where projects typically are multi-site, multi-cultural, multi-technical, and products are complex. The aim of this study is to clarify what kind of process is suitable for assessing the effectiveness of communication in high-tech product development. Based on the literature analysis, a communication audit process is constructed and tested in five product development projects of different information and communication technology (ICT) companies. Based on test case experiences and analyses, this study proposes a streamlined communication audit process. An outcome of this paper is a streamlined communi-cation audit process that provides benefits for companies, but does not burden the organisation unnecessarily. Man-agers of high-tech companies can utilise the developed process for enhancing communication in their product devel-opment.

Abstract:
Matter Neutrino Resonances (MNRs) can drastically modify neutrino flavor evolution in astrophysical environments and may significantly impact nucleosynthesis. Here we further investigate the underlying physics of MNR type flavor transitions. We provide generalized resonance conditions and make analytical predictions for the behavior of the system. We discuss the adiabatic evolution of these transitions, considering both Symmetric and Standard scenarios. Symmetric MNR transitions differ from Standard MNR transitions in that both neutrinos and antineutrinos can completely transform to other flavors simultaneously. We provide an example of the simplest system in which such transitions can occur with a neutrino and an antineutrino having a single energy and emission angle. We further apply linearized stability analysis to predict the location of self-induced nutation type (or bipolar) oscillations due to neutrino-neutrino interactions in the regions where MNR is ineffective. In all cases, we compare our analytical predictions to numerical calculations.

Abstract:
In arctic and sub-arctic regions semi-domestic reindeer management forms an important livelihood which should be able to provide enough income for herders. Reindeer management has natural limits of growth. Consequently it should be managed to optimise both the use of reindeer pastures and herder income. Reindeer pastures should be grazed at the economic carrying capabity level. This gives the maximum sustained harvest from reindeer stock and also the maximum sustained foraging from pastures. How is this to be accomplished? First, reliable knowledge about reindeer pastures in time and place is necessary: to estimate the quantity and quality of specific reindeer pastures within each management district, as well as the productive capacity and the changes in condition and productivity of those pastures. Secondly, data is needed on the accurate productivity of reindeer stock and the production costs for each management district. Thirdly, study the relationships between pasture resources and productivity of reindeer stock together with the effects of long-term reindeer densities on pasture condition and productivity. Finally, knowledge is needed about the effects of herd structure on reindeer stock productivity as well as the factors which restrict the use of reindeer pastures. Models based on adequate data could provide a useful tool for optimising the use of reindeer pastures and herder income. First the economic carrying capacity of reindeer pastures should be studied. Subsequently the economy of reindeer husbandry could be modelled with respect to reindeer stock density. Also the economy of reindeer husbandry based on different levels of feeding, and the effects of this husbandry practice on pastures, should be modelled. Models should be accurate and flexible enough to use when looking for solutions to practical questions and challenges in reindeer management.

Abstract:
In this talk I want to explain the operator substractions needed to renormalize gauge currents in a second quantized theory. The case of space-time dimensions $3+1$ is considered in detail. In presence of chiral fermions the renormalization effects a modification of the local commutation relations of the currents by local Schwinger terms. In $1+1$ dimensions on gets the usual central extension (Schwinger term does not depend on background gauge field) whereas in $3+1$ dimensions one gets an anomaly linear in the background potential. We extend our method to the spatial components of currents. Since the bose-fermi interaction hamiltonian is of the form $j^k A_k$ (in the temporal gauge) we get a new renormalization scheme for the interaction. The idea is to define a field dependent conjugation for the fermi hamiltonian in the one-particle space such that after the conjugation the hamiltonian can be quantized just by normal ordering prescription.

Abstract:
These notes explain recent developments concerning chiral anomalies and hamiltonian quantization, their relation to the theory of gerbes, and extensions of generalized loop algebras using the residue calculus of pseudodifferential operators. The renormalization of the Dirac field, leading to Schwinger terms in equal time commutation relations, is treated in a mathematically rigorous manner. The same renormalization can be used to prove the existence of S-operator in background field problems.

Abstract:
The commutator anomalies (Schwinger terms) of current algebras in $3+1$ dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra of PSDO's. The construction of the (second quantized) current algebra is closely related to a geometric renormalization of the interaction Hamiltonian $H_I=j_{\mu} A^{\mu}$ in gauge theory.

Abstract:
An algebraic rule is presented for computing expectation values of products of local nonabelian charge operators for fermions coupled to an external vector potential in $3+1$ space-time dimensions. The vacuum expectation value of a product of four operators is closely related to a cyclic cocycle in noncommutative geometry of Alain Connes. The relevant representation of the current is constructed using Kirillov's method of coadjoint orbits.