The paper investigates the problem of fitting protein complexes into electron density maps. They are represented by high-resolution cryoEM density maps converted into overlapping matrices and partly show a structure of a complex. The general purpose is to define positions of all proteins inside it. This problem is known to be NP-hard, since it lays in the field of combinatorial optimization ove...

Linear least squares problems with box constraints are commonly solved to find model parameters within bounds based on physical considerations. Common algorithms include Bounded Variable Least Squares (BVLS) and the Matlab function lsqlin. Here, we formulate the box constraints as quadratic constraints, and solve the corresponding unconstrained regularized least squares problem. Box constraints...

We consider certain families of quadratic polynomials which admit pa-rameterisations in a neighbourhood of the boundary of the Mandelbrot set. We show that the associated Julia sets are of Hausdorr dimension arbitrarily close to 2. Our construction clariies related work by Shishikura. 0 Introduction During the last decade much attention has been paid to the fractal aspects of degeneration proce...

This paper is a sequel to [6], in which we introduced quadratic forms on a module over a supertropical semiring R and analyzed the set of bilinear companions of a single quadratic form V → R in case the module V is free. Any (semi)module over a semiring gives rise to what we call its minimal ordering, which is a partial order iff the semiring is “upper bound.” Any polynomial map q (or quadratic...

We consider an inverse problem of recovering a potential associated to semi-linear wave equation with quadratic nonlinearity in $ 1+1 dimensions. develop numerical scheme determine the from noisy Dirichlet-to-Neumann map on lateral boundary. The is based recent higher order linearization method employed [23]. also present approach numerically estimating two-dimensional derivatives data via Tikh...

We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. rst return) map. We apply this to show exponential return time statistics in i) smooth interval maps with nowhere{dense critical orbits and ii) certain interval maps with neutral xed points. The method also applies to iii) certain quadratic maps of the complex plane.

We determined the exact location of the shearless KAM curve in the quadratic map and numerically investigate the breakup thresholds of those curves in the entire parameter space. The breakup diagram reveals many sharp singularities like fractals on the reconnection thresholds of the twin-chains with rational rotation numbers.

The linear quadratic regulator problem for the second order evolution system with boundary controls is studied. Case that the input-to-state map is non-admissible is treated assuming that the system is exponentially stabilizable by the passive feedback. It is shown that the optimal control is of feedback form in terms of solution to the operator Riccati equation.

We present conditions for the local and global synchronization in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the pote...