Lower bounds on the modified K-energy and complex deformations

Let (X,L) be a polarized K\"ahler manifold that admits an extremal K\"ahler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is bounded from below. This generalizes a result of Chen, Sz\'ekelyhidi and Tosatti to extremal metrics. Our proof also extends a convexity inequality on the space of K\"ahler potentials due to X.X. Chen to the extremal metric setup. As an application, we compute explicit polarized 4-points blow-ups of CP1\times CP1 that carry no extremal metric but with modified K-energy bounded from below.Comment: 22 pages; Last Version, to be published in Advances in Math

Quasilinear elliptic inclusions of hemivariational type: Extremality and compactness of the solution set

AbstractWe consider the Dirichlet boundary value problem for an elliptic inclusion governed by a quasilinear elliptic operator of Leray–Lions type and a multivalued term which is given by the difference of Clarke's generalized gradient of some locally Lipschitz function and the subdifferential of some convex function. Problems of this kind arise, e.g., in mechanical models described by nonconvex and nonsmooth energy functionals that result from nonmonotone, multivalued constitutive laws. Our main goal is to characterize the solution set of the problem under consideration. In particular we are going to prove that the solution set possesses extremal elements with respect to the underlying natural partial ordering of functions, and that the solution set is compact. The main tools used in the proofs are abstract results on pseudomonotone operators, truncation, and special test function techniques, Zorn's lemma as well as tools from nonsmooth analysis

Semi-stability and local wall-crossing for hermitian Yang-Mills connections

We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact K\"ahler manifold. Assuming the automorphism group of its graded object to be abelian, we provide a semialgebraic decomposition of a neighbourhood of the polarisation in the K\"ahler cone into chambers characterising (in)stability. For a path in a stable chamber converging to the initial polarisation, we show that the associated HYM connections converge to an HYM connection on the graded object.Comment: 15 pages, comments very welcome. arXiv admin note: substantial text overlap with arXiv:2301.0052

Development and validation of the e-Work Self-Efficacy Scale to assess digital competencies in remote working

The COVID-19 pandemic accelerated the adoption of remote working practices worldwide. This has focussed attention on the need to identify the competencies employers and employees should train and develop to build digital resilience, enabling the benefits of remote working to be realised while mitigating potential risks. This contribution presents a multifaceted e-Work Self-Efficacy Scale, which supports a recently developed Digital Resilience Competency Framework (DRCF), assessing e-skills, trust building, self-care, remote social skills, and remote emotional self-efficacy beliefs. Data from 670 non-managerial employees (54.0% males) from a telecommunications company based in the Czech Republic were analysed, providing support for a bi-factor model. Latent Profile Analysis identified three clusters, characterised by different profiles: the Well-adjusted (with a reasonably good balance in engagement, satisfaction, and productivity), the Unhealthily dedicated (suffering some difficulties in setting boundaries), and the Distrustful self-shielding (the most compromised) remote workers. The results reinforce the importance of focusing on digital resilience competencies to promote sustainable, productive, engaging and healthy remote working. The e-Work Self-Efficacy Scale is a practical and effective organisational tool for managers and employees to use to assess and build digital resilience and sits alongside the Digital Resilience Competency Framework

Toric sheaves and flips

Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this functor. On one hand, for a fixed toric sheaf, and natural polarisations that make the exceptional loci small, we provide a simple numerical criterion that characterizes when slope stability is preserved through the flip. On the other hand, for a given flip, we introduce full subcategories of logarithmic toric sheaves and characterize when polystability is preserved for all toric sheaves in those subcategories at once.Comment: 20 pages, 1 figur

Speech and language therapy versus placebo or no intervention for speech problems in Parkinson's disease

Parkinson's disease patients commonly suffer from speech and vocal problems including dysarthric speech, reduced loudness and loss of articulation. These symptoms increase in frequency and intensity with progression of the disease). Speech and language therapy (SLT) aims to improve the intelligibility of speech with behavioural treatment techniques or instrumental aids