The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only i...

Gauged linear sigma-models at critical coupling on Riemann surfaces yield self-dual field theories, their classical vacua being described by the vortex equations. For local models with structure group U(r), we give a description of the vortex moduli spaces in terms of a fibration over symmetric products of the base surface Σ, which we assume to be compact. Then we show that all these fibrations...

Redox-regulated effector systems that counteract oxidative stress are essential for all forms of life. Here we uncover a new paradigm for sensing oxidative stress centred on the hydrophobic core of a sensor protein. RsrA is an archetypal zinc-binding anti-sigma factor that responds to disulfide stress in the cytoplasm of Actinobacteria. We show that RsrA utilizes its hydrophobic core to bind th...

For a continuous map on a topological graph containing a unique loop S it is possible to define the degree and, for a map of degree 1, rotation numbers. It is known that the set of rotation numbers of points in S is a compact interval and for every rational r in this interval there exists a periodic point of rotation number r. The whole rotation set (i.e. the set of all rotation numbers) may no...

Let $S(G^{sigma})$ be the skew-adjacency matrix of the oriented graph $G^{sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $sigma$ to each of its edges. The skew energy of an oriented graph $G^{sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{sigma})$. Two oriented graphs are said to be skew equienergetic iftheir skew energies...

In reinforcement learning, least-squares temporal difference methods (e.g., LSTD and LSPI) are effective, data-efficient techniques for policy evaluation and control with linear value function approximation. These algorithms rely on policy-dependent expectations of the transition and reward functions, which require all experience to be remembered and iterated over for each new policy evaluated....

We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we an extension metrics, which states that if $X$ is space, $A$ closed subset $X$, and $d$ metric generates the same topology $A$, then there exists such $D$ $D|_{A^{2}}=d$. Moreover, retraction, ca...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...