Some examples of exponentially harmonic maps

The aim of this paper is to study some examples of exponentially harmonic maps. We study such maps firstly on flat euclidean and Minkowski spaces and secondly on Friedmann-Lema\^ itre universes. We also consider some new models of exponentially harmonic maps which are coupled with gravity which happen to be based on a generalization of the lagrangian for bosonic strings coupled with dilatonic field.Comment: 16 pages, 5 figure

A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO(n)

In this paper we consider an energy functional depending on the norm of the gradient and seek to extremise it over an admissible class of Sobolev maps defined on an annulus and taking values on the unit sphere whilst satisfying suitable boundary conditions. We establish the existence of an infinite family of solutions with certain symmetries to the associated nonlinear Euler-Lagrange system in even dimensions and discuss the stability of such extremisers by way of examining the positivity of the second variation of the energy at these solutions

NR4A Gene Expression Is Dynamically Regulated in the Ventral Tegmental Area Dopamine Neurons and Is Related to Expression of Dopamine Neurotransmission Genes

The NR4A transcription factors NR4A1, NR4A2, and NR4A3 (also known as Nur77, Nurr1, and Nor1, respectively) share similar DNA-binding properties and have been implicated in regulation of dopamine neurotransmission genes. Our current hypothesis is that NR4A gene expression is regulated by dopamine neuron activity and that induction of NR4A genes will increase expression of dopamine neurotransmission genes. Eticlopride and γ-butyrolactone (GBL) were used in wild-type (+/+) and Nurr1-null heterozygous (+/−) mice to determine the mechanism(s) regulating Nur77 and Nurr1 expression. Laser capture microdissection and real-time PCR was used to measure Nurr1 and Nur77 mRNA levels in the ventral tegmental area (VTA). Nur77 expression was significantly elevated 1 h after both GBL (twofold) and eticlopride (fourfold). In contrast, GBL significantly decreased Nurr1 expression in both genotypes, while eticlopride significantly increased Nurr1 expression only in the +/+ mice. In a separate group of mice, haloperidol injection significantly elevated Nur77 and Nor1, but not Nurr1 mRNA in the VTA within 1 h and significantly increased tyrosine hydroxylase (TH) and dopamine transporter (DAT) mRNA expression by 4 h. These data demonstrate that the NR4A genes are dynamically regulated in dopamine neurons with maintenance of Nurr1 expression requiring dopamine neuron activity while both attenuation of dopamine autoreceptors activation and dopamine neuronal activity combining to induce Nur77 expression. Additionally, these data suggest that induction of NR4A genes could regulate TH and DAT expression and ultimately regulate dopamine neurotransmission

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

Effect of Computer-Assisted Cognitive Behavior Therapy vs Usual Care on Depression Among Adults in Primary Care: A Randomized Clinical Trial

Importance Depression is a common disorder that may go untreated or receive suboptimal care in primary care settings. Computer-assisted cognitive behavior therapy (CCBT) has been proposed as a method for improving access to effective psychotherapy, reducing cost, and increasing the convenience and efficiency of treatment for depression. Objectives To evaluate whether clinician-supported CCBT is more effective than treatment as usual (TAU) in primary care patients with depression and to examine the feasibility and implementation of CCBT in a primary care population with substantial numbers of patients with low income, limited internet access, and low levels of educational attainment. Design, Setting, and Participants This randomized clinical trial included adult primary care patients from clinical practices at the University of Louisville who scored 10 or greater on the Patient Health Questionnaire–9 (PHQ-9) and were randomly assigned to CCBT or TAU for 12 weeks of active treatment. Follow-up assessments were conducted 3 and 6 months after treatment completion. Enrollment occurred from June 24, 2016, to May 13, 2019. The last follow-up assessment was conducted on January 30, 2020. Interventions CCBT included use of the 9-lesson computer program Good Days Ahead, along with as many as 12 weekly telephonic support sessions of approximately 20 minutes with a master’s level therapist, in addition to TAU, which consisted of the standard clinical management procedures at the primary care sites. TAU was uncontrolled, but use of antidepressants and psychotherapy other than CCBT was recorded. Main Outcomes and Measures The primary outcome measure (PHQ-9) and secondary outcome measures (Automatic Thoughts Questionnaire for negative cognitions, Generalized Anxiety Disorder–7, and the Satisfaction with Life Scale for quality of life) were administered at baseline, 12 weeks, and 3 and 6 months after treatment completion. Satisfaction with treatment was assessed with the Client Satisfaction Questionnaire–8. Results The sample of 175 patients was predominately female (147 of 174 [84.5%]) and had a high proportion of individuals who identified as racial and ethnic minority groups (African American, 44 of 162 patients who reported [27.2%]; American Indian or Alaska Native, 2 [1.2%]; Hispanic, 4 [2.5%]; multiracial, 14 [8.6%]). An annual income of less than $30 000 was reported by 88 of 143 patients (61.5%). Overall, 95 patients (54.3%) were randomly assigned to CCBT and 80 (45.7%) to TAU. Dropout rates were 22.1% for CCBT (21 patients) and 30.0% for TAU (24 patients). An intent-to-treat analysis found that CCBT led to significantly greater improvement in PHQ-9 scores than TAU at posttreatment (mean difference, −2.5; 95% CI, −4.5 to −0.8; P = .005) and 3 month (mean difference, −2.3; 95% CI, −4.5 to −0.8; P = .006) and 6 month (mean difference, −3.2; 95% CI, −4.5 to −0.8; P = .007) follow-up points. Posttreatment response and remission rates were also significantly higher for CCBT (response, 58.4% [95% CI, 46.4-70.4%]; remission, 27.3% [95% CI, 16.4%-38.2%]) than TAU (response, 33.1% [95% CI, 20.7%-45.5%]; remission, 12.0% [95% CI, 3.3%- 20.7%]). Conclusions and Relevance In this randomized clinical trial, CCBT was found to have significantly greater effects on depressive symptoms than TAU in primary care patients with depression. Because the study population included people with lower income and lack of internet access who typically have been underrepresented or not included in earlier investigations of CCBT, results suggest that this form of treatment can be acceptable and useful in diverse primary care settings. Additional studies with larger samples are needed to address implementation procedures that could enhance the effectiveness of CCBT and to examine potential factors associated with treatment outcome

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Perturbing gauge/gravity duals by a Romans mass

We show how to produce algorithmically gravity solutions in massive IIA (as infinitesimal first order perturbations in the Romans mass parameter) dual to assigned conformal field theories. We illustrate the procedure on a family of Chern--Simons--matter conformal field theories that we recently obtained from the N=6 theory by waiving the condition that the levels sum up to zero.Comment: 30 page

Remarks on symplectic twistor spaces

We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study \textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With these we define a moduli space of $\omega$-compatible complex structures. We recall the theory of flag manifolds in order to study the Siegel domain and other domains alike, which is the fibre of the referred twistor space. Finally the structure equations for the twistor of a Riemann surface with the canonical symplectic-metric connection are deduced, based on a given conformal coordinate on the surface. We then relate with the moduli space defined previously.Comment: 20 pages, title changed since v2, accepted in AMPA toda

On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure

Holographic Uniformization

We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the existence of solutions interpolating between an arbitrary metric in the UV and the constant-curvature metric in the IR. We confirm this conjecture with a rigorous global existence proof.Comment: 52 pages, 3 figure