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 $\rho(p,q,t)$ 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 $S=1$ 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 ($k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em all} $k$ BCs is exactly equivalent to that of the renormalized QAM (with Planck's constant $\hbar ^{\prime}=\hbar /k$) 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