The sign-real and the sign-complex spectral radius, also called the generalized spectral radius, proved to be an interesting generalization of the classical Perron-Frobenius theory (for nonnegative matrices) to general real and to general complex matrices, respectively. Especially the generalization of the well-known Collatz-Wielandt max-min characterization shows one of the many one-to-one cor...

We study the nonlinear eigenvalue problem f(x) = λx for a class of maps f : K → K which are homogeneous of degree one and order-preserving, where K ⊆ X is a closed convex cone in a Banach space X. Solutions are obtained, in part, using a theory of the “cone spectral radius” which we develop. Principal technical tools are the generalized measure of noncompactness and related degree-theoretic tec...

The next generation of instrumentation for nuclear astrophysics will have to achieve an improvement in sensitivity by a factor of 10-100 over present technologies. With the focusing gammaray telescope MAX we take up this challenge and propose to combine the required sensitivity with high spectral and angular resolution, and the capability to measure the polarization of the photons. MAX is a spa...

The dependence structure of a max-stable random vector is characterized by its spectral measure. Using only the spectral measure, we present a method for approximating the conditional density of an unobserved component of a max-stable random vector given the other components of the vector. The approximated conditional density can be used for prediction. Additionally, we present a new parametric...

The sign-real and the sign-complex spectral radius, also called the generalized spectral radius, proved to be an interesting generalization of the classical Perron-Frobenius theory (for nonnegative matrices) to general real and to general complex matrices, respectively. Especially the generalization of the well-known Collatz-Wielandt max-min characterization shows one of the many one-to-one cor...

Multiscale community detection can be viewed from a dynamical perspective within the Markov Stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed ...

Visual temporal resolution and scotopic spectral sensitivity of three coastal shark species (bonnethead Sphyrna tiburo, scalloped hammerhead Sphyrna lewini, and blacknose shark Carcharhinus acronotus) were investigated by electroretinogram. Temporal resolution was quantified under photopic and scotopic conditions using response waveform dynamics and maximum critical flicker-fusion frequency (CF...

Energy development of decaying isotropic turbulence in a 3-D periodic cube with non-rotating or rotating frames of reference is studied through direct numerical simulation using GPU accelerated lattice Boltzmann method. The initial turbulence is isotropic, generated in spectral space with prescribed energy spectrum E(κ)~κm in a range between κmin and ...

The eyes of the female small white butterfly, Pieris rapae crucivora, are furnished with three classes of short-wavelength photoreceptors, with sensitivity peaks in the ultraviolet (UV) (lambda(max) = 360 nm), violet (V) (lambda(max) = 425 nm), and blue (B) (lambda(max) = 453 nm) wavelength range. Analyzing the spectral origin of the photoreceptors, we isolated three novel mRNAs encoding opsins...

In the \(\textsc {Max} r\text {-}\textsc {SAT}{}\) problem, input is a CNF formula with n variables where each clause disjunction of at most r literals. The objective to compute an assignment which satisfies as many clauses possible. While there are polynomial-time approximation algorithms for this we take viewpoint space complexity following [Biswas et al., Algorithmica 2021] and design sublin...