Collection of Mutually Synchronized Chaotic Systems

A general explicit coupling for mutual synchronization of two arbitrary identical continuous systems is proposed. The synchronization is proved analytically. The coupling is given for all 19 systems from Sprott's collection. For one of the systems the numerical results are shown in detail. The method could be adopted for the teaching of the topic.Comment: Published in Physics Letters A 352 (2006) 222-22

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

Reciprocal t(9;22) ABL/BCR fusion proteins: leukemogenic potential and effects on B cell commitment

Background: t(9;22) is a balanced translocation, and the chromosome 22 breakpoints (Philadelphia chromosome – Ph+) determine formation of different fusion genes that are associated with either Ph+ acute lymphatic leukemia (Ph+ ALL) or chronic myeloid leukemia (CML). The "minor" breakpoint in Ph+ ALL encodes p185BCR/ABL from der22 and p96ABL/BCR from der9. The "major" breakpoint in CML encodes p210BCR/ABL and p40ABL/BCR. Herein, we investigated the leukemogenic potential of the der9-associated p96ABL/BCR and p40ABL/BCR fusion proteins and their roles in the lineage commitment of hematopoietic stem cells in comparison to BCR/ABL. Methodology: All t(9;22) derived proteins were retrovirally expressed in murine hematopoietic stem cells (SL cells) and human umbilical cord blood cells (UCBC). Stem cell potential was determined by replating efficiency, colony forming - spleen and competitive repopulating assays. The leukemic potential of the ABL/BCR fusion proteins was assessed by in a transduction/transplantation model. Effects on the lineage commitment and differentiation were investigated by culturing the cells under conditions driving either myeloid or lymphoid commitment. Expression of key factors of the B-cell differentiation and components of the preB-cell receptor were determined by qRT-PCR. Principal Findings: Both p96ABL/BCR and p40ABL/BCR increased proliferation of early progenitors and the short term stem cell capacity of SL-cells and exhibited own leukemogenic potential. Interestingly, BCR/ABL gave origin exclusively to a myeloid phenotype independently from the culture conditions whereas p96ABL/BCR and to a minor extent p40ABL/BCR forced the B-cell commitment of SL-cells and UCBC. Conclusions/Significance: Our here presented data establish the reciprocal ABL/BCR fusion proteins as second oncogenes encoded by the t(9;22) in addition to BCR/ABL and suggest that ABL/BCR contribute to the determination of the leukemic phenotype through their influence on the lineage commitment

Semiclassical analysis of Dirac fields on curved spacetime

We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat both massive and massless Dirac fields and show how a covariantly defined Berry connection and the associated Berry curvature govern the semiclassical dynamics. The gravitational spin Hall equations are shown to be particular cases of the Mathisson-Papapetrou equations for spinning objects

Weyl geometric effects on the propagation of light in gravitational fields

We consider the effects of Weyl geometry on the propagation of electromagnetic waves and on the gravitational spin Hall effect of light. It is usually assumed that in vacuum the electromagnetic waves propagate along null geodesics, a result which follows from the geometrical optics approximation. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, the ray dynamics is affected by the wave polarization. Therefore, the propagation of the electromagnetic waves can deviate from null geodesics, and this phenomenon is known as the gravitational spin Hall effect of light. On the other hand, Maxwell's equations have the remarkable property of conformal invariance. This property is a cornerstone of Weyl geometry and the corresponding gravitational theories. As a first step in our study, we obtain the polarization-dependent ray equations in Weyl geometry, describing the gravitational spin Hall effect of light in the presence of nonmetricity. As a specific example of the spin Hall effect of light in Weyl geometry, we consider the case of the simplest conformally invariant action, constructed from the square of the Weyl scalar, and the strength of the Weyl vector only. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. In static spherical symmetry, this theory admits an exact black hole solution, which generalizes the standard Schwarzschild solution through the presence of two new terms in the metric, having a linear and a quadratic dependence on the radial coordinate. We numerically study the polarization-dependent propagation of light rays in this exact Weyl geometric metric, and the effects of the presence of the Weyl vector on the magnitude of the spin Hall effect are estimated

Polarization transport in optical fibers beyond Rytov's law

We consider the propagation of light in arbitrarily curved step-index optical fibers. Using a multiple-scales approximation scheme, set-up in Fermi normal coordinates, the full vectorial Maxwell equations are solved in a perturbative manner. At leading order, this provides a rigorous derivation of Rytov's law. At next order, we obtain non-trivial dynamics of the electromagnetic field, characterized by two coupling constants, the phase and the polarization curvature moments, which describe the curvature response of the light's phase and its polarization vector, respectively. The latter can be viewed as an inverse spin Hall effect of light, where the direction of propagation is constrained along the optical fiber and the polarization evolves in a frequency-dependent way.Comment: 13 pages, 5 figure

Spin Hall effects in the sky

In many areas of physics, the propagation of wave packets carrying intrinsic angular momentum is generally influenced by spin-orbit interactions. This is the main mechanism behind spin Hall effects, which result in wave packets following spin-dependent trajectories. Spin Hall effects have been observed in several experiments for electrons in condensed matter systems and for light propagating in inhomogeneous optical media. Similar effects have also been predicted for wave packets propagating in inhomogeneous gravitational fields. We give a brief introduction to gravitational spin Hall effects, emphasizing the analogies with the spin Hall effect of light in optics. Furthermore, we review the most promising astrophysical avenues that could lead to experimental observations of the gravitational spin Hall effect