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Dissipative Hamiltonian (DH) systems are an important concept in energy based modeling of dynamical
systems. One of the major advantages of the DH formulation is that the system encodes system
properties in an algebraic way in the system. Making use of the structure,
it is easy to see that DH systems are stable. In this paper
the question is discussed when a linear constant coefficient DH system is on the boundary
of the region of asymptotic stability, i.e., when it has purely imaginary eigenvalues,
or how much it has to be perturbed to be on this boundary. For unstructured systems this distance to instability (stability radius) is well-understood. In this paper,
explicit formulas for this distance under structure preserving perturbations are determined.
It is also shown (via numerical examples) that under structured perturbations the asymptotical
stability of a DH system is much more robust than for unstructured perturbations, since the
distance can be much larger.
Canonical forms for matrix triples $(A,G,\hat G)$, where
$A$ is arbitrary rectangular and $G$, $\hat G$ are either real symmetric
or skew symmetric, or complex Hermitian or skew Hermitian, are derived.
These forms generalize classical product Schur forms as well as
singular value decompositions.
An new proof for the complex case is given, where there is no need to
distinguish whether $G$ and $\hat G$ are Hermitian or skew Hermitian.
This proof is independent from the results in Bolschakov/Reichstein 1995, where
a similar canonical form has been obtained for the complex case,
and it allows generalization to the real case. Here,
the three cases, i.e., that
$G$ and $\hat G$ are both symmetric, both skew symmetric or one each,
are treated separately.
The long standing problem is discussed of how to deflate the part associated with the eigenvalue infinity in a structured matrix pencil using structure preserving unitary transformations. We derive such a deflation procedure and apply this new technique to symmetric, Hermitian or alternating pencils and in a modified form to (anti)-palindromic pencils. We present a detailed error and perturbation analysis of this and other deflation procedures and demonstrate the properties of the new algorithm with several numerical examples.
The paper provides a structural analysis of the feasible set defined by linear probabilistic constraints. Emphasis is laid on single (individual) probabilistic constraints. A classical convexity result by Van de Panne/Popp and Kataoka is extended to a broader class of distributions and to more general functions of the decision vector. The range of probability levels for which convexity can be expected is exactly identified. Apart from convexity, also nontriviality and compactness of the
feasible set are precisely characterized at the same time. The relation between feasible sets with negative and with nonnegative right-hand side is revealed. Finally, an existence result is formulated for the more difficult case of joint probabilistic constraints.
Actin is a major structural protein of the eukaryotic cytoskeleton and enables cell motility.
Here, we present a model of the actin filament (F-actin) that incorporates the global structure
of the recently published model by Oda et al. but also conserves internal stereochemistry. A
comparison is made using molecular dynamics simulation of the model with other recent F-
actin models. A number of structural determents such as the protomer propeller angle, the
number of hydrogen bonds and the structural variation among the protomers are analyzed.
The MD comparison is found to reflect the evolution in quality of actin models over the last
six years. In addition, simulations of the model are carried out in states with both ADP or
ATP bound and local hydrogen-bonding differences characterized. The results point to the
significance of a direct interaction of Gln137 with ATP for activation of ATPase activity after
the G-to-F-actin transition.
Diffusion Weighted Imaging has become and will certainly continue to be an important tool in medical research and diagnostics. Data obtained with Diffusion Weighted Imaging are characterized by a high noise level. Thus, estimation of quantities like anisotropy indices or the main diffusion direction may be significantly compromised by noise in clinical or neuroscience applications. Here, we present a new package dti for R, which provides functions for the analysis of diffusion weighted data within the diffusion tensor model. This includes smoothing by a recently proposed structural adaptive smoothing procedure based on the Propagation-Separation approach in the context of the widely used Diffusion Tensor Model. We extend the procedure and show, how a correction for Rician bias can be incorporated. We use a heteroscedastic nonlinear regression model to estimate the diffusion tensor. The smoothing procedure naturally adapts to different structures of different size and thus avoids oversmoothing edges and fine structures. We illustrate the usage and capabilities of the package through some examples.
Functional Magnetic Resonance Imaging inherently involves noisy measurements and a severe multiple test
problem. Smoothing is usually used to reduce the effective number of multiple
comparisons and to locally integrate the signal and hence increase the
signal-to-noise ratio. Here, we provide a new structural adaptive segmentation
algorithm (AS)
that naturally combines the signal detection with noise reduction in one procedure.
Moreover, the new method
is closely related to a recently proposed structural adaptive smoothing
algorithm and preserves shape and spatial extent of activation areas without
blurring the borders.
In this paper, we consider the characterization of strong stationary solutions to
equilibrium problems with equilibrium constraints (EPECs). Assuming that the underlying
generalized equation satisfies strong regularity in the sense of Robinson, an explicit
multiplier-based stationarity condition can be derived. This is applied then
to an equilibrium model arising from ISO-regulated electricity spot markets.
Research on flows over time has been conducted mainly in two separate and mainly independent approaches, namely \emph{discrete} and \emph{continuous} models, depending on whether a discrete or continuous representation of time is used. Recently, Borel flows have been introduced to build a bridge between these two models.
In this paper, we consider the maximum Borel flow problem formulated in a network where capacities on arcs are given as Borel measures and storage might be allowed at the nodes of the network. This problem is formulated as a linear program in a space of measures. We define a dual problem and prove a strong duality result. We show that strong duality is closely related to a MaxFlow-MinCut Theorem.
We present a novel algorithm for automatic parameterization of tube-like surfaces of arbitrary genus such as the surfaces of knots, trees, blood vessels, neurons, or any tubular graph with a globally consistent stripe texture. We use the principal curvature frame field of the underlying tube-like surface to guide the creation of a global, topologically consistent stripe parameterization of the surface. Our algorithm extends the QuadCover algorithm and is based, first, on the use of so-called projective vector fields instead of frame fields, and second, on different types of branch points. That does not only simplify the mathematical theory, but also reduces computation time by the decomposition of the underlying stiffness matrices.