1,047 research outputs found
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 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 -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 of the emerging
ultrametric solution are not restricted to the interval , 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.
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.
The XY Spin-Glass with Slow Dynamic Couplings
We investigate an XY spin-glass model in which both spins and couplings
evolve in time: the spins change rapidly according to Glauber-type rules,
whereas the couplings evolve slowly with a dynamics involving spin correlations
and Gaussian disorder. For large times the model can be solved using replica
theory. In contrast to the XY-model with static disordered couplings, solving
the present model requires two levels of replicas, one for the spins and one
for the couplings. Relevant order parameters are defined and a phase diagram is
obtained upon making the replica-symmetric Ansatz. The system exhibits two
different spin-glass phases, with distinct de Almeida-Thouless lines, marking
continuous replica-symmetry breaking: one describing freezing of the spins
only, and one describing freezing of both spins and couplings.Comment: 7 pages, Latex, 3 eps figure
Deeltijdwerkers hebben meestal al een lage marginale druk
Het kabinet wil dat mensen meer uren gaan werken, om de krapte op de arbeidsmarkt tegen te gaan. Maar loont het voor deeltijders wel om meer te werken? En in hoeverre spelen belastingen een rol in hun keuze. De marginale belastingdruk van meer uren werken is over het algemeen veel lager voor deeltijdwerknemers dan voltijders. Voor huishoudens die gebruikmaken van kinderopvang is de marginale druk wel hoger, en de kabinetsplannen gaan die verlagen. Werkenden reageren echter slechts beperkt op financiële prikkels – zoals belastingen – in het aantal gewerkte uren per week.Hervorming Sociale Regelgevin
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
Income differences across migrant groups in the Netherlands: an intergenerational perspective.
Hervorming Sociale Regelgevin
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