A renormalization procedure for tensor models and scalar-tensor theories of gravity

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.Comment: 20 pages, 3 figures, references added, minor correction

Case complexity as a guide for psychological treatment selection

Objective: Some cases are thought to be more complex and difficult to treat, although there is little consensus on how to define complexity in psychological care. This study proposes an actuarial, data-driven method of identifying complex cases based on their individual characteristics. Method: Clinical records for 1512 patients accessing low and high intensity psychological treatments were partitioned in 2 random subsamples. Prognostic indices (PI) predicting post-treatment reliable and clinically significant improvement (RCSI) in depression (PHQ-9) and anxiety (GAD-7) symptoms were estimated in one subsample using penalized (Lasso) regressions with optimal scaling. A PI-based algorithm was used to classify patients as standard (St) or complex (Cx) cases in the second (cross-validation) subsample. RCSI rates were compared between Cx cases that accessed treatments of different intensities using logistic regression. Results: St cases had significantly higher RCSI rates compared to Cx cases (OR = 1.81 to 2.81). Cx cases tended to attain better depression outcomes if they were initially assigned to high intensity (vs. low intensity) interventions (OR = 2.23); a similar pattern was observed for anxiety but the odds ratio (1.74) was not statistically significant. Conclusions: Complex cases could be detected early and matched to high intensity interventions to improve outcomes

Transdermal Delivery of Cytochrome C—A 12.4kDa Protein—Across Intact Skin by Constant-Current Iontophoresis

Purpose: To demonstrate the transdermal iontophoretic delivery of a small (12.4kDa) protein across intact skin. Materials and Methods: The iontophoretic transport of Cytochrome c (Cyt c) across porcine ear skin in vitro was investigated and quantified by HPLC. The effect of protein concentration (0.35 and 0.7mM), current density (0.15, 0.3 or 0.5mA.cm−2 applied for 8h) and competing ions was evaluated. Co-iontophoresis of acetaminophen was employed to quantify the respective contributions of electromigration (EM) and electroosmosis (EO). Results: The data confirmed the transdermal iontophoretic delivery of intact Cyt c. Electromigration was the principal transport mechanism, accounting for ∼90% of delivery; correlation between EM flux and electrophoretic mobility was consistent with earlier results using small molecules. Modest EO inhibition was observed at 0.5mA.cm−2. Cumulative permeation at 0.3 and 0.5mA.cm−2 was significantly greater than that at 0.15mA.cm−2; fluxes using 0.35 and 0.7mM Cyt c in the absence of competing ions (J tot  = 182.8 ± 56.8 and 265.2 ± 149.1μg.cm−2.h−1, respectively) were statistically equivalent. Formulation in PBS (pH8.2) confirmed the impact of competing charge carriers; inclusion of ∼170mM Na+ resulted in a 3.9-fold decrease in total flux. Conclusions: Significant amounts (∼0.9mg.cm−2 over 8h) of Cyt c were delivered non-invasively across intact skin by transdermal electrotranspor

Matrix geometries and Matrix Models

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.Comment: 20 page

Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure

Heterogeneity in patient-reported outcomes following low-intensity mental health interventions: a multilevel analysis.

BACKGROUND: Variability in patient-reported outcomes of psychological treatments has been partly attributed to therapists--a phenomenon commonly known as therapist effects. Meta-analytic reviews reveal wide variation in therapist-attributable variability in psychotherapy outcomes, with most studies reporting therapist effects in the region of 5% to 10% and some finding minimal to no therapist effects. However, all except one study to date have been conducted in high-intensity or mixed intervention groups; therefore, there is scarcity of evidence on therapist effects in brief low-intensity psychological interventions. OBJECTIVE: To examine therapist effects in low-intensity interventions for depression and anxiety in a naturalistic setting. DATA AND ANALYSIS: Session-by-session data on patient-reported outcome measures were available for a cohort of 1,376 primary care psychotherapy patients treated by 38 therapists. Outcome measures included PHQ-9 (sensitive to depression) and GAD-7 (sensitive to general anxiety disorder) measures. Three-level hierarchical linear modelling was employed to estimate therapist-attributable proportion of variance in clinical outcomes. Therapist effects were evaluated using the intra-cluster correlation coefficient (ICC) and Bayesian empirical predictions of therapist random effects. Three sensitivity analyses were conducted: 1) using both treatment completers and non-completers; 2) a sub-sample of cases with baseline scores above the conventional clinical thresholds for PHQ-9 and GAD-7; and 3) a two-level model (using patient-level pre- and post-treatment scores nested within therapists). RESULTS: The ICC estimates for all outcome measures were very small, ranging between 0% and 1.3%, although most were statistically significant. The Bayesian empirical predictions showed that therapist random effects were not statistically significantly different from each other. Between patient variability explained most of the variance in outcomes. CONCLUSION: Consistent with the only other study to date in low intensity interventions, evidence was found to suggest minimal to no therapist effects in patient-reported outcomes. This draws attention to the more prominent source of variability which is found at the between-patient level

Quantum effective potential for U(1) fields on S^2_L X S^2_L

We compute the one-loop effective potential for noncommutative U(1) gauge fields on S^2_L X S^2_L. We show the existence of a novel phase transition in the model from the 4-dimensional space S^2_L X S^2_L to a matrix phase where the spheres collapse under the effect of quantum fluctuations. It is also shown that the transition to the matrix phase occurs at infinite value of the gauge coupling constant when the mass of the two normal components of the gauge field on S^2_L X S^2_L is sent to infinity.Comment: 13 pages. one figur

A projective Dirac operator on CP^2 within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos correcte

Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere

We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the role they play in the ``striped phase'', pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. Next, we test a quantitative, non-trivial theoretical prediction for this model, which has been formulated in the literature: The existence of an eigenvalue sector characterised by a precise probability density, and the emergence of the phase transition associated with the opening of a gap around the origin in the eigenvalue distribution. The theoretical predictions are confirmed by our numerical results. Finally, we propose a possible method to detect numerically the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study of the eigenvalue distribution, added figures, tables and references, typos corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references added, technical details about the tests at small matrix size skipped, version published in JHE

Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.Comment: 31 pages. V2: minor corrections, references adde