413 research outputs found
Evolutionary robustness of differentiation in genetic regulatory networks
We investigate the ability of artificial Genetic Regulatory Networks (GRNs) to evolve differentiation. The proposed GRN model supports non-linear interaction between regulating factors, thereby facilitating the realization of complex regulatory logics. As a proof of concept we evolve GRNs of this kind to follow different pathways, producing two kinds of periodic dynamics in response to minimal differences in external input. Furthermore we find that successive increases in environmental pressure for differentiation, allowing a lineage to adapt gradually, compared to an immediate requirement for a switch between behaviors, yields better results on average. Apart from better success there is also less variability in performance, the latter indicating an increase in evolutionary robustness
Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation
A generalized approach to the quantization of a large class of maps on a
torus, i.e. quantization via the von Neumann Equation, is described and a
number of issues related to the quantization of model systems are discussed.
The approach yields well behaved mixed quantum states for tori for which the
corresponding Schrodinger equation has no solutions, as well as an extended
spectrum for tori where the Schrodinger equation can be solved.
Quantum-classical correspondence is demonstrated for the class of mappings
considered, with the Wigner-Weyl density going to the correct
classical limit. An application to the cat map yields, in a direct manner,
nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the
correspondence limit.Comment: 36 pages, RevTex preprint forma
Solitonic excitations in the Haldane phase of a S=1 chain
We study low-lying excitations in the 1D antiferromagnetic
valence-bond-solid (VBS) model. In a numerical calculation on finite systems
the lowest excitations are found to form a discrete triplet branch, separated
from the higher-lying continuum. The dispersion of these triplet excitations
can be satisfactorily reproduced by assuming approximate wave functions. These
wave functions are shown to correspond to moving hidden domain walls, i.e. to
one-soliton excitations.Comment: RevTex 3.0, 24 pages, 2 figures on request by fax or mai
Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms
We exhibit scarring for certain nonlinear ergodic toral automorphisms. There
are perturbed quantized hyperbolic toral automorphisms preserving certain
co-isotropic submanifolds. The classical dynamics is ergodic, hence in the
semiclassical limit almost all eigenstates converge to the volume measure of
the torus. Nevertheless, we show that for each of the invariant submanifolds,
there are also eigenstates which localize and converge to the volume measure of
the corresponding submanifold.Comment: 17 page
On the multiplicativity of quantum cat maps
The quantum mechanical propagators of the linear automorphisms of the
two-torus (cat maps) determine a projective unitary representation of the theta
group, known as Weil's representation. We prove that there exists an
appropriate choice of phases in the propagators that defines a proper
representation of the theta group. We also give explicit formulae for the
propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page
Proximal 21q deletion as a result of a <i>de novo </i>unbalanced t(12;21) translocation in a patient with dysmorphic features, hepatomegaly, thick myocardium and delayed psychomotor development
BACKGROUND: IInterstitial 21q deletions can cause a wide spectrum of symptoms depending on the size and the location of the deletion. It has previously been suggested that the long arm of chromosome 21 can be divided into three regions based on the clinical severity of the patients and deletion of the region from 32.3 Mb to 37.1 Mb was more crucial than the deletion of other regions. CASE PRESENTATION: In this study we describe a female patient with dysmorphic features, hepatomegaly, thick myocardium and psychomotor delay. Conventional karyotyping was initially interpreted as full monosomy 21, but subsequent chromosome microarray analysis suggested an approximately 18 Mb partial monosomy. Re-evaluation of the karyotype and fluorescence in situ hybridization revealed deletion of the proximal 21q11.2-q22.11 segment and insertion of 21q22.11-qter to 12qter. The deletion of the present case overlaps with two of the proposed regions including part of the proposed crucial region. CONCLUSIONS: This report emphasizes the relevance of investigating suspected full monosomies with high resolution methods and FISH in order to investigate the extent of the deletion and the presence of more complex rearrangements
Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map
We rationalize the somewhat surprising efficacy of the Hadamard transform in
simplifying the eigenstates of the quantum baker's map, a paradigmatic model of
quantum chaos. This allows us to construct closely related, but new, transforms
that do significantly better, thus nearly solving for many states of the
quantum baker's map. These new transforms, which combine the standard Fourier
and Hadamard transforms in an interesting manner, are constructed from
eigenvectors of the shift permutation operator that are also simultaneous
eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal)
symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title;
corrected minor error
Apoptosis and proliferation in the trigeminal placode
The neurogenic trigeminal placode develops from the crescent-shaped panplacodal primordium which delineates the neural plate anteriorly. We show that, in Tupaia belangeri, the trigeminal placode is represented by a field of focal ectodermal thickenings which over time changes positions from as far rostral as the level of the forebrain to as far caudal as opposite rhombomere 3. Delamination proceeds rostrocaudally from the ectoderm adjacent to the rostral midbrain, and contributes neurons to the trigeminal ganglion as well as to the ciliary ganglion/oculomotor complex. Proliferative events are centered on the field prior to the peak of delamination. They are preceded, paralleled and, finally, outnumbered by apoptotic events which proceed rostrocaudally from non-delaminating to delaminating parts of the field. Apoptosis persists upon regression of the placode, thereby exhibiting a massive “wedge” of apoptotic cells which includes the postulated position of the “ventrolateral postoptic placode” (Lee et al. in Dev Biol 263:176–190, 2003), merges with groups of lens-associated apoptotic cells, and disappears upon lens detachment. In conjunction with earlier work (Washausen et al. in Dev Biol 278:86–102, 2005) our findings suggest that apoptosis contributes repeatedly to the disintegration of the panplacodal primordium, to the elimination of subsets of premigratory placodal neuroblasts, and to the regression of placodes
Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions
A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on
a torus for general boundary conditions (BCs), whose number () is always
finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em
all} BCs is exactly equivalent to that of the renormalized QAM (with
Planck's constant ) at some {\em fixed} BCs that can
be of four types. The quantum cat maps are, up to time reversal, fixed points
of the renormalization transformation. Several results at fixed BCs, in
particular the existence of a complete basis of ``crystalline'' eigenstates in
a classical limit, can then be derived and understood in a simple and
transparent way in the general-BCs framework.Comment: REVTEX, 12 pages, 1 table. To appear in Physical Review Letter
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