G-structures and duality

Imperial Users onl

The initial value formulation of the λ\lambda-R model

We apply the conformal method to solve the initial value formulation of general relativity to the $\lambda$-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. We obtain a generalised Lichnerowicz-York equation for the conformal factor of the metric and derive its properties. We show that the behaviour of the equation depends on the value of the coupling $\lambda$. In the absence of a cosmological constant, we recover the existence and uniqueness properties of the original equation when $\lambda>1/3$ and the trace of the momentum of the metric, $\pi$, is non-vanishing. For $\pi=0$, we recover the original Lichnerowicz equation regardless of the value of $\lambda$ and must therefore restrict the metric to the positive Yamabe class. The same restriction holds for $\lambda<1/3$, a case in which we show that the spatial Ricci scalar must also be large enough to guarantee the existence of at least one solution. Taking the equations of motion into account, this allows us to prove that there is in general no way of matching both constraint solving data and time evolution of phase space variables between the $\lambda$-R model and general relativity, thereby proving the the non-equivalence between the theories outside of the previously known cases $\lambda=1$ and $\pi=0$.Comment: 29 pages, 6 figure

Perturbative QCD description of jet data from LHC Run-I and Tevatron Run-II

We present a systematic comparison of jet predictions at the LHC and the Tevatron, with accuracy up to next-to-next-to-leading order (NNLO). The exact computation at NNLO is completed for the gluons-only channel, so we compare the exact predictions for this channel with an approximate prediction based on threshold resummation, in order to determine the regions where this approximation is reliable at NNLO. The kinematic regions used in this study are identical to the experimental setup used by recently published jet data from the ATLAS and CMS experiments at the LHC, and CDF and D0 experiments at the Tevatron. We study the effect of choosing different renormalisation and factorisation scales for the NNLO exact prediction and as an exercise assess their impact on a PDF fit including these corrections. Finally we provide numerical values of the NNLO k-factors relevant for the LHC and Tevatron experiments.Comment: 51 pages, 13 figures, 35 tables. Final version, matches published version in JHE

More on "Little Lambda" in Ho\v{r}ava-Lifshitz Gravity

We analyze different claims on the role of the coupling constant lambda in so-called lambda-R models, a minimal generalization of general relativity inspired by Horava-Lifshitz gravity. The dimensionless parameter lambda appears in the kinetic term of the Einstein-Hilbert action, leading to a one-parameter family of classical theories. Performing a canonical constraint analysis for closed spatial hypersurfaces, we obtain a result analogous to that of Bellorin and Restuccia, who showed that all non-projectable lambda-R models are equivalent to general relativity in the asymptotically flat case. However, the tertiary constraint present for closed boundary conditions assumes a more general form. We juxtapose this with an earlier finding by Giulini and Kiefer, who ruled out a range of lambda-R models by a physical, cosmological argument. We show that their analysis can be interpreted consistently within the projectable sector of Horava-Lifshitz gravity, thus resolving the apparent contradiction.Comment: 21 pages, no figure

The use of the "Once-Upon-A-Time…" Test in treatment outcome assessment

In an era in which the advent of managed health care is questioning the value of traditional psychological assessment, we discuss the role of the "Once-upon-a-time…" Test in treatment outcome assessment. The "Once upon a time..." Test (Fagulha, 1992, 1997) is a storytelling projective technique whose purpose is to describe the way children deal with the emotions of anxiety and pleasure. In psychodynamic theories, these emotions have an important adaptive function for psychological development (Freud, 1926/1978; Klein, 1932/1969). The “Once upon a time..." Test task is to complete seven stories which are presented as pictures in a cartoon format. Each story depicts common situations in the life of any child that evoke emotions of anxiety and of pleasure. Five cards refer to anxiety provoking situations and two refer to pleasurable experiences. For each card there are nine scenes that represent different possible ways of dealing with the emotional experience evoked by the card. These scenes are grouped into three categories of three scenes each – the Anxiety category (A), the Fantasy category (F) and the Reality category (R). The child is asked to complete the story drawn on the card by selecting and then placing three of these nine scenes in sequence. The categories of the scenes chosen by the child and the sequences organized with these scenes reflect the way children deal with their emotions, anxiety and pleasure, in a transitional space (Winnicott, 1971/1975) between fantasy and reality. After selecting and placing the scenes in sequence, the child tells the story that he/she has just invented. Although the majority of the studies done on the "Once upon a time..." Test have been centered on the analysis of the chosen scenes, according to their category (Anxiety, Fantasy and Reality) and their placement in sequence (in the first, second or third position), a complementary coding system was developed afterwards. This system involves the study of the arranged sequences based on the nine scenes available for each card, and not only the three categories (Pires & Fagulha, 2001). According to this system, the arranged sequences based on the nine scenes available for each card correspond to four different possible ways of facing anxiety and confronting with it. There is a strategy that represents the non-recognition of the painful emotion – Denial –, and three strategies that involve the recognition of this disturbing affect, corresponding to two distinct ways of coping with it – Operational Adaptive Strategy and Emotional Equilibration Strategy – and to one other that proves to be inefficient in dealing with it – Impossibility. The studies done with both coding systems have come to the same conclusion: the patterns of answers reflect differences in ages. As children mature they are able to master anxiety in a more active and efficient manner. In the coding system category of the scenes chosen and their position in the sequence, this developmental achievement is seen through a tendency to respond to anxious situations by choosing scenes that show either anxiety or reality in the first position of the sequence. There is also a progressive decrease in choice of anxiety scenes for story endings corresponding to an increase in the choice of reality or fantasy scenes. As children mature, fantasy scenes in first position of the sequence are less chosen because they reflect the denial of the distress reflected in the card (Fagulha, 1992, 1997, 2000) Regarding the complementary coding system sequences of scenes, the higher degree of emotional stability allows children to deal with anxious situations through adaptive strategies, such us Operational Adaptive Strategy and Emotional Equilibration Strategy. Denial of the anxiety and Impossibility to deal with it are strategies less used by mature children (Pires & Fagulha, 2001) In view of these empirical data is our aim to analyze and discuss a child pattern of answers to the "Once upon a time..." Test at two different moments of her psychotherapeutic process, at treatment initiation and then again to make a decision about treatment termination. We expect to give an account of the "Once upon a time..." Test potentialities to the objective evaluation of the results of child psychotherapy