Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Norm attaining operators and pseudospectrum

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Automated nonlinear system modelling with multiple neural networks

This article discusses the identification of nonlinear dynamic systems using multi-layer perceptrons (MLPs). It focuses on both structure uncertainty and parameter uncertainty, which have been widely explored in the literature of nonlinear system identification. The main contribution is that an integrated analytic framework is proposed for automated neural network structure selection, parameter identification and hysteresis network switching with guaranteed neural identification performance. First, an automated network structure selection procedure is proposed within a fixed time interval for a given network construction criterion. Then, the network parameter updating algorithm is proposed with guaranteed bounded identification error. To cope with structure uncertainty, a hysteresis strategy is proposed to enable neural identifier switching with guaranteed network performance along the switching process. Both theoretic analysis and a simulation example show the efficacy of the proposed method.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Approximating the Set of Local Minima in Partial RNA Folding Landscapes

Motivation: We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004).

Results: The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n2D?ln?), where n is the sequence length, ? is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.

Spectral isometries on non-simple C*-algebras

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

Environmental pricing of externalities from different sources of electricity generation in Chile

The rapid increase in electricity demand in Chile means a choice must be made between major investments in renewable or non-renewable sources for additional production. Current projects to develop large dams for hydropower in Chilean Patagonia impose an environmental price by damaging the natural environment. On the other hand, the increased use of fossil fuels entails an environmental price in terms of air pollution and greenhouse gas emissions contributing to climate change. This paper studies the debate on future electricity supply in Chile by investigating the preferences of households for a variety of different sources of electricity generation such as fossil fuels, large hydropower in Chilean Patagonia and other renewable energy sources. Using Double Bounded Dichotomous Choice Contingent Valuation, a novel advanced disclosure method and internal consistency test are used to elicit the willingness to pay for less environmentally damaging sources. Policy results suggest a strong preference for renewable energy sources with higher environmental prices imposed by consumers on electricity generated from fossil fuels than from large dams in Chilean Patagonia. Policy results further suggest the possibility of introducing incentives for renewable energy developments that would be supported by consumers through green tariffs or environmental premiums. Methodological findings suggest that advanced disclosure learning overcomes the problem of internal inconsistency in SB-DB estimates.

Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons

We discuss the quantum-circuit realization of the state of a nucleon in the scope of simple simmetry groups. Explicit algorithms are presented for the preparation of the state of a neutron or a proton as resulting from the composition of their quark constituents. We estimate the computational resources required for such a simulation and design a photonic network for its implementation. Moreover, we highlight that current work on three-body interactions in lattices of interacting qubits, combined with the measurement-based paradigm for quantum information processing, may also be suitable for the implementation of these nucleonic spin states.

Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

Late Quaternary glaciations in Far NE Russia; combining moraines, topography and chronology to assess regional and global glaciation synchrony

During various periods of Late Quaternary glaciation, small ice-sheets, -caps, -fields and valley glaciers, occupied the mountains and uplands of Far NE Russia (including the Verkhoyansk, Suntar-Khayata, and Chersky Mountains; the KolymaeAnyuy and Koryak Highlands; and much of the Kamchatka and Chukchi
Peninsulas). Here, the margins of former glaciers across this region are constrained through the comprehensive mapping of moraines from remote sensing data (Landsat 7 ETM+ satellite images; ASTER Global Digital Elevation Model (GDEM2); and Viewfinder Panorama DEM data). A total of 8414 moraines
are mapped, and this record is integrated with a series of published age-estimates (n = 25), considered to chronologically-constrain former ice-margin positions. Geomorphological and chronological data are compiled in a Geographic Information System (GIS) to produce ‘best estimate’ reconstructions of ice extent during the global Last Glacial Maximum (gLGM) and, to a lesser degree, during earlier phases of glaciation. The data reveal that much of Far NE Russia (~1,092,427 km2) preserves a glaciated landscape (i.e. is bounded by moraines), but there is no evidence of former ice masses having extended more than 270 km beyond mountain centres (suggesting that, during the Late Quaternary, the region has not been occupied by extensive ice sheets). During the gLGM, specifically, glaciers occupied ~253,000 km2, and rarely extended more than 50 km in length. During earlier (pre-gLGM) periods, glaciers were more extensive, though the timing of former glaciation, and the maximum Quaternary extent, appears to have been asynchronous across the region, and out-of-phase with ice-extent maxima elsewhere in the Northern Hemisphere. This glacial history is partly explained through consideration of climatic-forcing
(particularly moisture-availability, solar insolation and albedo), though topographic-controls upon the former extent and dynamics of glaciers are also considered, as are topographic-controls upon moraine deposition and preservation. Ultimately, our ability to understand the glacial and climatic history of this region is restricted when the geomorphological-record alone is considered, particularly as directly-dated glacial deposits are few, and topographic and climatic controls upon the moraine record are difficult to
distinguish.

The 'Europeanization' of Reference Groups

In this paper we address the question of the relative importance of within and between country differences in income and material deprivation in the European Union in the context of recent suggestions that insufficient attention has been paid to the latter. In particular, we respond to the argument that the 'state bounded' relative income approach obscures the significance of EU-wide reference groups. Making use of EU-SILC 2004, we have sought to quantify the magnitude of relevant within and between country differences and their relative impact. Overall, our analysis supports the view that the predominant frame of reference is a national one. The limited impact of European reference groups observed in our analysis does not require explanation in terms of the emergence of a European social stratification system. Furthermore, the significance of such comparisons depends not only on the expectations of those affected by European inequalities but on the degree of legitimacy afforded to ensuing demands. While an EU-wide income-threshold can provide information regarding progress of the Union towards greater social cohesion, its usage for this purpose does not require a strong sense of European identity. Given the current status of the European Social Model, it would seem unwise to attribute an undue degree of policy relevance to the relatively modest impact of EU-wide reference groups revealed in our analysis.

Lorentz TEM investigation of the switching behavior in artificial spin ice building blocks

Frustration – the inability to simultaneously satisfy all interactions – occurs in a wide range of systems including neural networks, water ice and magnetic systems. An example of the latter is the so called spin-ice in pyrochlore materials [1] which have attracted a lot of interest not least due to the emergence of magnetic monopole defects when the ‘ice rules’ governing the local ordering breaks down [2]. However it is not possible to directly measure the frustrated property – the direction of the magnetic moments – in such spin ice systems with current experimental techniques. This problem can be solved by instead studying artificial spin-ice systems where the molecular magnetic moments are replaced by nanoscale ferromagnetic islands [3-8]. Two different arrangements of the ferromagnetic islands have been shown to exhibit spin ice behaviour: a square lattice maintaining four moments at each vertex [3,8] and the Kagome lattice which has only three moments per vertex but equivalent interactions between them [4-7]. Magnetic monopole defects have been observed in both types of lattices [7-8]. One of the challenges when studying these artificial spin-ice systems is that it is difficult to arrive at the fully demagnetised ground-state [6-8].
Here we present a study of the switching behaviour of building blocks of the Kagome lattice influenced by the termination of the lattice. Ferromagnetic islands of nominal size 1000 nm by 100 nm were fabricated in five island blocks using electron-beam lithography and lift-off techniques of evaporated 18 nm Permalloy (Ni80Fe20) films. Each block consists of a central island with four arms terminated by a different number and placement of ‘injection pads’, see Figure 1. The islands are single domain and magnetised along their long axis. The structures were grown on a 50 nm thick electron transparent silicon nitride membrane to allow TEM observation, which was back-coated with a 5 nm film of Au to prevent charge build-up during the TEM experiments.
To study the switching behaviour the sample was subjected to a magnetic field strong enough to magnetise all the blocks in one direction, see Figure 1. Each block obeys the Kagome lattice ‘ice-rules’ of “2-in, 1-out” or “1-in, 2-out” in this fully magnetised state. Fresnel mode Lorentz TEM images of the sample were then recorded as a magnetic field of increasing magnitude was applied in the opposite direction. While the Fresnel mode is normally used to image magnetic domain structures [9] for these types of samples it is possible to deduce the direction of the magnetisation from the Lorentz contrast [5]. All images were recorded at the same over-focus judged to give good Lorentz contrast.
The magnetisation was found to switch at different magnitudes of the applied field for nominally identical blocks. However, trends could still be identified: all the blocks with any injection pads, regardless of placement and number, switched the direction of the magnetisation of their central island at significantly smaller magnitudes of the applied magnetic field than the blocks without injection pads. It can therefore be concluded that the addition of an injection pad lowers the energy barrier to switching the connected island, acting as a nucleation site for monopole defects. In these five island blocks the defects immediately propagate through to the other side, but in a larger lattice the monopoles could potentially become trapped at a vertex and observed [10].
References

[1] M J Harris et al, Phys Rev Lett 79 (1997) p.2554.
[2] C Castelnovo, R Moessner and S L Sondhi, Nature 451 (2008) p. 42.
[3] R F Wang et al, Nature 439 (2006) 303.
[4] M Tanaka et al, Phys Rev B 73 (2006) 052411.
[5] Y Qi, T Brintlinger and J Cumings, Phys Rev B 77 (2008) 094418.
[6] E Mengotti et al, Phys Rev B 78 (2008) 144402.
[7] S Ladak et al, Nature Phys 6 (2010) 359.
[8] C Phatak et al, Phys Rev B 83 (2011) 174431.
[9] J N Chapman, J Phys D 17 (1984) 623.
[10] The authors gratefully acknowledge funding from the EPSRC under grant number EP/D063329/1.