Index

Denna studies syfte är att med utgångspunkt i den allmänna diskursen om likvärdighet och dess pragmatiska innebörd, söka belysa spänningsfält mellan politiskt fattade beslut och skolans filosofiska, politiska och pedagogiska diskursser. Studien använder sig av kvalitativa teoretiska och metodologiska utgångspunkter. Studiens resultat uppvisar flera bilder av likvärdighetens pragmatiska innebörd. I skärningspunkten mellan pedagogik, politik och filosofi pågår olika diskurser om likvärdighet. Med stöd i diskursteorin visas att diskurser om ekonomi och politik står överordnatd andra moraletiska diskurser i skolan och att en gemensam norm för likvärdighet är en myt eftersom pragmatiska sammanhang förändrar diskursen om likvärdighet till många olika perspektiv och antaganden

High Energy Resummation of Jet Observables

In this paper we investigate the extension of high energy resummation at LLx accuracy to jet observables. In particular, we present the high energy resummed expression of the transverse momentum distribution of the outgoing parton in the general partonic process $g(q) + g(q) \to g(q) + X$. In order to reach this result, several new ideas are introduced and exploited. First we prove that LLx resummation is achieved by dressing with hard radiation an off-shell gluon initiated LO process even if its on-shell limit is vanishing or trivial. Then we present a gauge-invariant framework where these calculations can be performed by using the modern helicity techniques. Finally, we show a possible way to restore gluon indistinguishability in the final state, which is otherwise lost in the resummation procedure, at all orders in $\alpha_s$ at LLx. All partonic channels are then resummed and cross-checked against fixed-order calculations up to $\mathcal{O}(\alpha_s^3)$Comment: 31 pages, 6 figure

A New Algebra ic Approach to Representation Theorems for (Co)integrated Processes up to the Second Order

The paper establishes a unified representation theorem for (co)integrated processes up to the second order which provides a compact and informative insight into the solution of VAR models with unit roots, and sheds light on the cointegration features of the engendered processes. The theorem is primarily stated by taking a one-lag specification as a reference frame, and it is afterwards extended to cover the case of an arbitrary number of lags via a companion-form based approach. All proofs are obtained by resorting to an innovative and powerful algebraic apparatus tailored to the derivation of the intended results.Unified representation theorem, Cointegration, Orthogonal-complement algebra, Laurent expansion in matrix form

Counting statistics: a Feynman-Kac perspective

By building upon a Feynman-Kac formalism, we assess the distribution of the number of hits in a given region for a broad class of discrete-time random walks with scattering and absorption. We derive the evolution equation for the generating function of the number of hits, and complete our analysis by examining the moments of the distribution, and their relation to the walker equilibrium density. Some significant applications are discussed in detail: in particular, we revisit the gambler's ruin problem and generalize to random walks with absorption the arcsine law for the number of hits on the half-line.Comment: 10 pages, 6 figure

Universal properties of branching random walks in confined geometries

Characterizing the occupation statistics of a radiation flow through confined geometries is key to such technological issues as nuclear reactor design and medical diagnosis. This amounts to assessing the distribution of the travelled length $\ell$ and the number of collisions $n$ performed by the underlying stochastic transport process, for which remarkably simple Cauchy-like formulas were established in the case of branching Pearson random walks with exponentially distributed jumps. In this Letter, we show that such formulas strikingly carry over to the much broader class of branching processes with arbitrary jumps, provided that scattering is isotropic and the average jump size is finite.Comment: 5 pages, 3 figure

On a Partitioned Inversion Formula having Useful Applications in Econometrics

In this paper a novel partitioned inversion formula is obtained in terms of the orthogonal complements of off-diagonal blocks, with the emblematic matrix of unit-root econometrics springing up as the leading diagonal block of the inverse. On the one hand, the result paves the way to a stimulating reinterpretation of restricted least-squares estimation and, on the other, to a straightforward derivation of a key-result of time-series econometrics.Partitioned inversion; Restricted least-squares; VAR econometrics

A continuous time random walk model of transport in variably saturated heterogeneous porous media

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile (MIM) continuous time random walk framework, the heterogeneity will be characterized by algebraically decaying particle retention-times. We derive the corresponding (nonlinear) continuum limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories, for a variety of initial and boundary conditions.Comment: 12 pages, 9 figure