Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Comments on Holographic Entanglement Entropy and RG Flows

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a 'phase transition' as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.Comment: References adde

Universality and exactness of Schrodinger geometries in string and M-theory

We propose an organizing principle for classifying and constructing Schrodinger-invariant solutions within string theory and M-theory, based on the idea that such solutions represent nonlinear completions of linearized vector and graviton Kaluza-Klein excitations of AdS compactifications. A crucial simplification, derived from the symmetry of AdS, is that the nonlinearities appear only quadratically. Accordingly, every AdS vacuum admits infinite families of Schrodinger deformations parameterized by the dynamical exponent z. We exhibit the ease of finding these solutions by presenting three new constructions: two from M5 branes, both wrapped and extended, and one from the D1-D5 (and S-dual F1-NS5) system. From the boundary perspective, perturbing a CFT by a null vector operator can lead to nonzero beta-functions for spin-2 operators; however, symmetry restricts them to be at most quadratic in couplings. This point of view also allows us to easily prove nonrenormalization theorems: for any Sch(z) solution of two-derivative supergravity constructed in the above manner, z is uncorrected to all orders in higher derivative corrections if the deforming KK mode lies in a short multiplet of an AdS supergroup. Furthermore, we find infinite classes of 1/4 BPS solutions with 4-,5- and 7-dimensional Schrodinger symmetry that are exact.Comment: 31 pages, plus appendices; v2, minor corrections, added refs, slight change in interpretation in section 2.3, new Schrodinger and Lifshitz solutions included; v3, clarifications in sections 2 and 3 regarding existence of solutions and multi-trace operator

Holographic GB gravity in arbitrary dimensions

We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general $D \ge 5$ dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.Comment: 48 pages, 9 figures. v2: New discussion on free fields in subsection 3.3 and new appendix B on conformal tensor fields. Added comments on the relation between the central charge appearing in the two-point function and the "central charge" characterizing the entropy density in the discussion. References adde

Holographic studies of quasi-topological gravity

Quasi-topological gravity is a new gravitational theory including curvature-cubed interactions and for which exact black hole solutions were constructed. In a holographic framework, classical quasi-topological gravity can be thought to be dual to the large $N_c$ limit of some non-supersymmetric but conformal gauge theory. We establish various elements of the AdS/CFT dictionary for this duality. This allows us to infer physical constraints on the couplings in the gravitational theory. Further we use holography to investigate hydrodynamic aspects of the dual gauge theory. In particular, we find that the minimum value of the shear-viscosity-to-entropy-density ratio for this model is $\eta/s \simeq 0.4140/(4\pi)$.Comment: 45 pages, 6 figures. v2: References adde

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte

Implementing a guideline for the treatment of type 2 diabetics: results of a Cluster- Randomized Controlled Trial (C-RCT)

<p>Abstract</p> <p>Background</p> <p>In Italy many diabetics still lack adequate care in general practice. We assessed the effectiveness of different strategies for the implementation of an evidence-based guideline for the management of non-complicated type 2 diabetes among General Practitioners (GPs) of Lazio region.</p> <p>Methods</p> <p>Three-arm cluster-randomised controlled trial with GPs as units of randomisation (clusters). 252 GPs were randomised either to an active strategy (training module with administration of the guideline), or to a passive dissemination (administration of the guideline only), or to usual care (control). Data on prescriptions of tests and drugs were collected by existing information systems, whereas patients' data came from GPs' databases. Process outcomes were measured at the cluster level one year after the intervention. Primary outcomes concerned the measurement of glycosilated haemoglobin and the commissioning of micro- and macrovascular complications assessment tests. In order to assess the physicians' drug prescribing behaviour secondary outcomes were also calculated.</p> <p>Results</p> <p>GPs identified 6395 uncomplicated type 2 patients with a high prevalence of cardiovascular risk factors. Data on GPs baseline performance show low proportions of glycosilated haemoglobin assessments. Results of the C-RCT analysis indicate that the active implementation strategy was ineffective relating to all primary outcomes (respectively, OR 1.06 [95% IC: 0.76–1.46]; OR 1.07 [95% IC: 0.80–1.43]; OR 1.4 [95% IC:0.91–2.16]. Similarly, passive dissemination of the guideline showed no effect.</p> <p>Conclusion</p> <p>In our region compliance of GPs with guidelines was not enhanced by a structured learning programme. Implementation through organizational measures appears to be essential to induce behavioural changes.</p> <p>Trial registration</p> <p>ISRCTN80116232</p

Characterization of a Large Group of Individuals with Huntington Disease and Their Relatives Enrolled in the COHORT Study

Careful characterization of the phenotype and genotype of Huntington disease (HD) can foster better understanding of the condition.We conducted a cohort study in the United States, Canada, and Australia of members of families affected by HD. We collected demographic and clinical data, conducted the Unified Huntington's Disease Rating Scale and Mini-Mental State Examination, and determined Huntingtin trinucleotide CAG repeat length. We report primarily on cross-sectional baseline data from this recently completed prospective, longitudinal, observational study.As of December 31, 2009, 2,318 individuals enrolled; of these, 1,985 (85.6%) were classified into six analysis groups. Three groups had expanded CAG alleles (36 repeats or more): individuals with clinically diagnosed HD [n = 930], and clinically unaffected first-degree relatives who had previously pursued [n = 248] or not pursued [n = 112] predictive DNA testing. Three groups lacked expanded alleles: first-degree relatives who had previously pursued [n = 41] or not pursued [n = 224] genetic testing, and spouses and caregivers [n = 430]. Baseline mean performance differed across groups in all motor, behavioral, cognitive, and functional measures (p<0.001). Clinically unaffected individuals with expanded alleles weighed less (76.0 vs. 79.6 kg; p = 0.01) and had lower cognitive scores (28.5 vs. 29.1 on the Mini Mental State Examination; p = 0.008) than individuals without expanded alleles. The frequency of "high normal" repeat lengths (27 to 35) was 2.5% and repeat lengths associated with reduced penetrance (36 to 39) was 2.7%.Baseline analysis of COHORT study participants revealed differences that emerge prior to clinical diagnosis. Longitudinal investigation of this cohort will further characterize the natural history of HD and genetic and biological modifiers.Clinicaltrials.gov NCT00313495

Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

We evaluate the one loop determinant of matter multiplet fields of N=4 supergravity in the near horizon geometry of quarter BPS black holes, and use it to calculate logarithmic corrections to the entropy of these black holes using the quantum entropy function formalism. We show that even though individual fields give non-vanishing logarithmic contribution to the entropy, the net contribution from all the fields in the matter multiplet vanishes. Thus logarithmic corrections to the entropy of quarter BPS black holes, if present, must be independent of the number of matter multiplet fields in the theory. This is consistent with the microscopic results. During our analysis we also determine the complete spectrum of small fluctuations of matter multiplet fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references adde

Effect of a mixed reality-based intervention on arm, hand, and finger function on chronic stroke

[EN] Background: Virtual and mixed reality systems have been suggested to promote motor recovery after stroke. Basing on the existing evidence on motor learning, we have developed a portable and low-cost mixed reality tabletop system that transforms a conventional table in a virtual environment for upper limb rehabilitation. The system allows intensive and customized training of a wide range of arm, hand, and finger movements and enables interaction with tangible objects, while providing audiovisual feedback of the participants' performance in gamified tasks. This study evaluates the clinical effectiveness and the acceptance of an experimental intervention with the system in chronic stroke survivors. Methods: Thirty individuals with stroke were included in a reversal (A-B-A) study. Phase A consisted of 30 sessions of conventional physical therapy. Phase B consisted of 30 training sessions with the experimental system. Both interventions involved flexion and extension of the elbow, wrist, and fingers, and grasping of different objects. Sessions were 45-min long and were administered three to five days a week. The body structures (Modified Ashworth Scale), functions (Motricity Index, Fugl-Meyer Assessment Scale), activities (Manual Function Test, Wolf Motor Function Test, Box and Blocks Test, Nine Hole Peg Test), and participation (Motor Activity Log) were assessed before and after each phase. Acceptance of the system was also assessed after phase B (System Usability Scale, Intrinsic Motivation Inventory). Results: Significant improvement was detected after the intervention with the system in the activity, both in arm function measured by the Wolf Motor Function Test (p < 0.01) and finger dexterity measured by the Box and Blocks Test (p < 0.01) and the Nine Hole Peg Test (p < 0.01); and participation (p < 0.01), which was maintained to the end of the study. The experimental system was reported as highly usable, enjoyable, and motivating. Conclusions: Our results support the clinical effectiveness of mixed reality interventions that satisfy the motor learning principles for upper limb rehabilitation in chronic stroke survivors. This characteristic, together with the low cost of the system, its portability, and its acceptance could promote the integration of these systems in the clinical practice as an alternative to more expensive systems, such as robotic instruments.The authors wish to thank the staff and patients of the Servicio de Neurorrehabilitación y Daño Cerebral de los Hospitales NISA for their involvement in the study. The authors also wish to thank the staff of LabHuman for their support in this project, especially Francisco Toledo and José Roda for their assistance. 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