Relaxed ISS Small-Gain Theorems for Discrete-Time Systems

In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of exponentially ISS systems we are able to prove that the proposed relaxed small-gain theorems are non-conservative in a sense to be made precise. The proofs of the small-gain theorems rely on the construction of a dissipative finite-step ISS Lyapunov function which is introduced in this work. Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of ISS Lyapunov functions, are shown to be sufficient and necessary to conclude ISS of the overall system.Comment: input-to-state stability, Lyapunov methods, small-gain conditions, discrete-time non-linear systems, large-scale interconnection

Analytic calculation of anomalous scaling in random shell models for a passive scalar

An exact non-perturbative calculation of the fourth-order anomalous correction to the scaling behaviour of a random shell-model for passive scalars is presented. Importance of ultraviolet (UV) and infrared (IR) boundary conditions on the inertial scaling properties are determined. We find that anomalous behaviour is given by the null-space of the inertial operator and we prove strong UV and IR independence of the anomalous exponent. A limiting case where diffusive behaviour can influence inertial properties is also presented.Comment: 3 pages, 1 figure, revised versio

The American species of the annulatipes group of the subgenus Lepidohelea, genus Forcipomyia (Diptera: Ceratopogonidae)

The annulatipes group of the genus Forcipomyia Meigen, subgenus Lepidohelea Kieffer, is represented in the Western Hemisphere by 12 species. Keys are presented for their identification, and to distinguish them from other groups of the subgenus Lepidohelea. The three previously known species, annulatipes Macfie, brasiliensis Macfie, and kuanoskeles Macfie, from southern Brazil, as well as the following nine new species, are described and illustrated: bahiensis, basifemoralis, bifida, convexipenis, euthystyla, gravesi, herediae, hobbsi, and weemsi

Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes

In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear $H_\infty$ estimate.Comment: 14 pages, several references added, remarks section added, clarified constructio

Origin and evolution of the Amazonian craton

The Amazonian craton appears to be formed and modifed by processes much like those of the better-known Precambrian cratons, but the major events did not always follow conventional sequences nor did they occur synchronously with those of other cratons. Much of the craton's Archean style continental crust formation, recorded in granite-greenstone and high-grade terranes, occurred in the Early Proterozoic: a period of relative quiescence in many other Precambrian regions. The common Archean to Proterozoic transition in geological style did not occur here, but an analogous change from abundant marine volcanism to dominantly continental sedimentary and eruptive styles occurred later. Amazonian geology is summarized, explaining the evolution of the craton

No-Core Shell Model for Nuclear Systems with Strangeness

We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique which we successfully applied in first calculations of lightest $\Lambda$ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon-nucleon and nucleon-hyperon interactions (such as those derived from EFT). We discuss formal aspects of the methodology, show first demonstrative results for ${}_{\Lambda}^3$H, ${}_{\Lambda}^4$H and ${}^4_\Lambda$He, and give outlook.Comment: 4 pages, 3 figures; Proceedings of the 22nd European Conference on Few Body Problems in Physics, 9 - 13 September, 2013, Cracow, Polan

Small gain theorems for large scale systems and construction of ISS Lyapunov functions

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a general formulation of ISS, the cases of summation, maximization and separation with respect to external gains are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio

Unconventional superfluid order in the FF-band of a bipartite optical square lattice

We report on the first observation of bosons condensed into the energy minima of an $F$-band of a bipartite square optical lattice. Momentum spectra indicate that a truly complex-valued staggered angular momentum superfluid order is established. The corresponding wave function is composed of alternating local $F_{2x^3-3x} + i F_{2y^3-3y}$-orbits and local $S$-orbits residing in the deep and shallow wells of the lattice, which are arranged as the black and white areas of a checkerboard. A pattern of staggered vortical currents arises, which breaks time reversal symmetry and the translational symmetry of the lattice potential. We have measured the populations of higher order Bragg peaks in the momentum spectra for varying relative depths of the shallow and deep lattice wells and find remarkable agreement with band calculations.Comment: 4 pages, 3 figure

Stability Criteria for SIS Epidemiological Models under Switching Policies

We study the spread of disease in an SIS model. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold parameter for this model in the spirit of the basic reproduction number for time-invariant models. We also present conditions for persistence and the existence of periodic orbits for the switched model and results for a stochastic switched model