On iterated minimization in nonconvex optimization

In dynamic programming and decomposition methods one often applies an iterated minimization procedure. The problem variables are partitioned into several blocks, say x and y. Treating y as a parameter, the first phase consists of minimization with respect to the variable x. In a second phase the minimization of the resulting optimal value function depending on y is considered. In this paper we treat this basic idea on a local level. It turns out that strong stability (in the sense of Kojima) in the first phase is a natural assumption. In order to show that the iterated local minima of the parametric problem lead to a local minimum for the whole problem, we use a generalized version of a positive definiteness criterion of Fujiwara-Han-Mangasarian

A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation

We study the coupled dynamics of primary and secondary structure formation (i.e. slow genetic sequence selection and fast folding) in the context of a solvable microscopic model that includes both short-range steric forces and and long-range polarity-driven forces. Our solution is based on the diagonalization of replicated transfer matrices, and leads in the thermodynamic limit to explicit predictions regarding phase transitions and phase diagrams at genetic equilibrium. The predicted phenomenology allows for natural physical interpretations, and finds satisfactory support in numerical simulations.Comment: 51 pages, 13 figures, submitted to J. Phys.

Zero-field incommensurate spin-Peierls phase with interchain frustration in TiOCl

We report on the magnetic, thermodynamic and optical properties of the quasi-one-dimensional quantum antiferromagnets TiOCl and TiOBr, which have been discussed as spin-Peierls compounds. The observed deviations from canonical spin-Peierls behavior, e.g. the existence of two distinct phase transitions, have been attributed previously to strong orbital fluctuations. This can be ruled out by our optical data of the orbital excitations. We show that the frustration of the interchain interactions in the bilayer structure gives rise to incommensurate order with a subsequent lock-in transition to a commensurate dimerized state. In this way, a single driving force, the spin-Peierls mechanism, induces two separate transitions.Comment: 4 pages, 4 figure

Hierarchical Self-Programming in Recurrent Neural Networks

We study self-programming in recurrent neural networks where both neurons (the `processors') and synaptic interactions (`the programme') evolve in time simultaneously, according to specific coupled stochastic equations. The interactions are divided into a hierarchy of $L$ groups with adiabatically separated and monotonically increasing time-scales, representing sub-routines of the system programme of decreasing volatility. We solve this model in equilibrium, assuming ergodicity at every level, and find as our replica-symmetric solution a formalism with a structure similar but not identical to Parisi's $L$-step replica symmetry breaking scheme. Apart from differences in details of the equations (due to the fact that here interactions, rather than spins, are grouped into clusters with different time-scales), in the present model the block sizes $m_i$ of the emerging ultrametric solution are not restricted to the interval $[0,1]$, but are independent control parameters, defined in terms of the noise strengths of the various levels in the hierarchy, which can take any value in [0,\infty\ket. This is shown to lead to extremely rich phase diagrams, with an abundance of first-order transitions especially when the level of stochasticity in the interaction dynamics is chosen to be low.Comment: 53 pages, 19 figures. Submitted to J. Phys.

Collective learning in schools described: building collective learning capacity

Processes of collective learning are expected to increase the professionalism of teachers and school leaders. Little is known about the processes of collective learning which take place in schools and about the way in which those processes may be improved. This paper describes a research into processes of collective learning at three primary schools. Processes of collective learning are described which took place in small teams in these schools. It is also pointed out which attempts can be made in order to reinforce these processes in the schools mentioned

The effects of the increase in the retirement age in the Netherlands.

Hervorming Sociale Regelgevin

Diagonalization of replicated transfer matrices for disordered Ising spin systems

We present an alternative procedure for solving the eigenvalue problem of replicated transfer matrices describing disordered spin systems with (random) 1D nearest neighbor bonds and/or random fields, possibly in combination with (random) long range bonds. Our method is based on transforming the original eigenvalue problem for a $2^n\times 2^n$ matrix (where $n\to 0$) into an eigenvalue problem for integral operators. We first develop our formalism for the Ising chain with random bonds and fields, where we recover known results. We then apply our methods to models of spins which interact simultaneously via a one-dimensional ring and via more complex long-range connectivity structures, e.g. $1+\infty$ dimensional neural networks and `small world' magnets. Numerical simulations confirm our predictions satisfactorily.Comment: 24 pages, LaTex, IOP macro

Plant-litter-soil feedbacks in common grass species are slightly negative and only marginally modified by litter exposed to insect herbivory

Purpose Insect herbivory affects plant growth, nutrient and secondary metabolite concentrations and litter quality. Changes to litter quality due to insect herbivory can alter decomposition, with knock on effects for plant growth mediated through the plant-litter-soil feedback pathway. Methods Using a multi-phase glasshouse experiment, we tested how changes in shoot and root litter quality of fast- and slow-growing grass caused by insect herbivores affect the performance of response plants in the soil in which the litter decomposed. Results We found that insect herbivory resulted in marginal changes to litter quality and did not affect growth when plants were grown with fast- versus slow-growing litter. Overall, presence of litter resulted in reduced root and shoot growth and this effect was significantly more negative in shoots versus roots. However, this effect was minimal, with a loss of c. 1.4% and 3.1% dry weight biomass in roots versus shoots, respectively. Further, shoot litter exposed to insect herbivory interacted with response plant identity to affect root growth. Conclusions Our results suggest that whether litter originates from plant tissues exposed to insect herbivory or not and its interaction with fast- versus slow-growing grasses is of little importance, but species-specific responses to herbivory-conditioned litter can occur. Taken collectively, the overall role of the plant-litter-soil feedback pathway, as well as its interaction with insect herbivory, is unlikely to affect broader ecosystem processes in this system

Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural network (Hopfield) models and we show that due to the minimisation of the frustration effects the retrieval region of the phase diagram can be significantly enlarged. Moreover, the fraction of misaligned spins is reduced by this effect, and is smaller than in the infinite connectivity regime. The main cause of this difference is found to be the non-zero fraction of sites with vanishing local field when the connectivity is finite.Comment: 17 pages, 8 figure

Persistence of plant-mediated microbial soil legacy effects in soil and inside roots

Plant-soil feedbacks are shaped by microbial legacies that plants leave in the soil. We tested the persistence of these legacies after subsequent colonization by the same or other plant species using 6 typical grassland plant species. Soil fungal legacies were detectable for months, but the current plant effect on fungi amplified in time. By contrast, in bacterial communities, legacies faded away rapidly and bacteria communities were influenced strongly by the current plant. However, both fungal and bacterial legacies were conserved inside the roots of the current plant species and their composition significantly correlated with plant growth. Hence, microbial soil legacies present at the time of plant establishment play a vital role in shaping plant growth even when these legacies have faded away in the soil due the growth of the current plant species. We conclude that soil microbiome legacies are reversible and versatile, but that they can create plant-soil feedbacks via altering the endophytic community acquired during early ontogeny