Chern-Simons action for zero-mode supporting gauge fields in three dimensions

Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized values for gauge fields that lead to zero modes of the corresponding Dirac operator. Here we show that this conjecture is wrong by constructing an explicit counter-example.Comment: version as published in PRD, minor change

The asymptotic limits of zero modes of massless Dirac operators

Asymptotic behaviors of zero modes of the massless Dirac operator $H=\alpha\cdot D + Q(x)$ are discussed, where $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac matrices, $D=\frac{1}{i} \nabla_x$, and $Q(x)=\big(q_{jk} (x) \big)$ is a $4\times 4$ Hermitian matrix-valued function with $| q_{jk}(x) | \le C ^{-\rho}$, $\rho >1$. We shall show that for every zero mode $f$, the asymptotic limit of $|x|^2f(x)$ as $|x| \to +\infty$ exists. The limit is expressed in terms of an integral of $Q(x)f(x)$.Comment: 9 page

Investigation of the Nicole model

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behaviour to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur

Associative memory in gene regulation networks

The pattern of gene expression in the phenotype of an organism is determined in part by the dynamical attractors of the organism’s gene regulation network. Changes to the connections in this network over evolutionary time alter the adult gene expression pattern and hence the fitness of the organism. However, the evolution of structure in gene expression networks (potentially reflecting past selective environments) and its affordances and limitations with respect to enhancing evolvability is poorly understood in general. In this paper we model the evolution of a gene regulation network in a controlled scenario. We show that selected changes to connections in the regulation network make the currently selected gene expression pattern more robust to environmental variation. Moreover, such changes to connections are necessarily ‘Hebbian’ – ‘genes that fire together wire together’ – i.e. genes whose expression is selected for in the same selective environments become co-regulated. Accordingly, in a manner formally equivalent to well-understood learning behaviour in artificial neural networks, a gene expression network will therefore develop a generalised associative memory of past selected phenotypes. This theoretical framework helps us to better understand the relationship between homeostasis and evolvability (i.e. selection to reduce variability facilitates structured variability), and shows that, in principle, a gene regulation network has the potential to develop ‘recall’ capabilities normally reserved for cognitive systems

A Stellar Census of the Tucana-Horologium Moving Group

We report the selection and spectroscopic confirmation of 129 new late-type (K3-M6) members of the Tuc-Hor moving group, a nearby (~40 pc), young (~40 Myr) population of comoving stars. We also report observations for 13/17 known Tuc-Hor members in this spectral type range, and that 62 additional candidates are likely to be unassociated field stars; the confirmation frequency for new candidates is therefore 129/191 = 67%. We have used RVs, Halpha emission, and Li6708 absorption to distinguish contaminants and bona fide members. Our expanded census of Tuc-Hor increases the known population by a factor of ~3 in total and by a factor of ~8 for members with SpT>K3, but even so, the K-M dwarf population of Tuc-Hor is still markedly incomplete. The spatial distribution of members appears to trace a 2D sheet, with a broad distribution in X and Y, but a very narrow distribution (+/-5 pc) in Z. The corresponding velocity distribution is very small, with a scatter of +/-1.1 km/s about the mean UVW velocity. We also show that the isochronal age (20--30 Myr) and the lithium depletion age (40 Myr) disagree, following a trend seen in other PMS populations. The Halpha emission follows a trend of increasing EW with later SpT, as seen for young clusters. We find that members have been depleted of lithium for spectral types of K7.0-M4.5. Finally, our purely kinematic and color-magnitude selection procedure allows us to test the efficiency and completeness for activity-based selection of young stars. We find that 60% of K-M dwarfs in Tuc-Hor do not have ROSAT counterparts and would be omitted in Xray selected samples. GALEX UV-selected samples using a previously suggested criterion for youth achieve completeness of 77% and purity of 78%. We suggest new selection criteria that yield >95% completeness for ~40 Myr populations.(Abridged)Comment: Accepted to AJ; 28 pages, 12 figures, 5 tables in emulateapj forma

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.Comment: 64 pages, 8 figure