We discuss the forward and inverse problems between the potential V (x) measured in a heart chamber and its sources represented by a dipole density d(y) located on the heart wall. We show that the mapping from d(y) to V (x) is a compact integral operator. Its inverse is unbounded which makes the inverse problem ill-posed in the mathematical sense. We investigate methods to solve the inverse pro...

The mouse heart is a popular model for cardiovascular studies due to the existence of low cost technology for genetic engineering in this species. Cardiovascular physiological phenotyping of the mouse heart can be easily done using fluorescence imaging employing various probes for transmembrane potential (V(m;)), calcium transients (CaT), and other parameters. Excitation-contraction coupling is...

1.1. Independence Sampler for Topic Activations V The posterior of v:i does not have a closed analytical form due to the nonlinearity associated with the logistic mapping of our stick-breaking weights π:i. We instead perform a Metropolis-Hastings update with an independence proposal q(v∗ :i | v:i, η, φ:i, λV ) = N(v∗ :i | ηφ:i, λ −1 V IK), which represents a sample from our prior. Since our pro...

The dynamical inverse problem of representation theory (the Wigner problem) 1] is solved for a certain class of interactions of Hamiltonian systems. The constructed quantum dynamics describes transition processes and stationary regimes on an equal footing. Among other numerous applications the results may be useful for the description of the simultaneous quantum dynamics of the open and closed ...

In this paper we show that any Fréchet holomorphic function mapping the open unit ball of one normed linear space into the closed unit ball of another must be a linear mapping if the Fréchet derivative of the function at zero is a surjective isometry. From this fact we deduce a Banach-Stone theorem for operator algebras which generalizes that of R. V. Kadison.

Let T : K → H be a mapping from a nonempty closed convex subset K of a finitedimensional Hilbert space H into H . Let f : K → R be proper, convex, and lower semicontinuous on K and let h : K → R be continuously Frećhet-differentiable on K with h′ (gradient of h), α-strongly monotone, and β-Lipschitz continuous on K . Then the sequence {xk} generated by the general auxiliary problem principle co...

An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f , or the edge vw equals e or f . The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In...

In this study, we deal with the conjecture given in [R. Keskin, Suborbital graph for the normalizer of Γ0(m), European Journal of Combinatorics 27 (2006) 193206.], that when the normalizer of Γ0(N) acts transitively on Q ∪ {∞}, any circuit in the suborbital graph G(∞, u/n) for the normalizer of Γ0(N), is of the form v → T (v) → T (v) → · · · → T (v) → v, where n > 1, v ∈ Q ∪ {∞} and T is an ell...