Kauffman picture of normal and tumor states as attractors in an abstract state space is used in order to interpret gene expression data for 15 cancer localizations obtained from The Cancer Genome Atlas. A principal component analysis of this data unveils the following qualitative aspects about tumors: 1) The state of a tissue in gene expression space can be described by a few variables. In particular, there is a single variable describing the progression from a normal tissue to a tumor. 2) Each cancer localization is characterized by a gene expression profile, in which genes have specific weights in the definition of the cancer state. There are no less than 2500 differentially-expressed genes, which lead to power-like tails in the expression distribution functions. 3) Tumors in different localizations share hundreds or even thousands of differentially expressed genes. There are 6 genes common to the 15 studied tumor localizations. 4) The tumor region is a kind of attractor. Tumors in advanced stages converge to this region independently of patient age or genetic characteristics. 5) There is a landscape of cancer in gene expression space with an approximate border separating normal tissues from tumors.

In many situations, the gene expression signature is a unique marker of the biological state. We study the modification of the gene expression distribution function when the biological state of a system experiences a change. This change may be the result of a selective pressure, as in the Long Term Evolution Experiment with E. Coli populations, or the progression to Alzheimer disease in aged brains, or the progression from a normal tissue to the cancer state. The first two cases seem to belong to a class of transitions, where the initial and final states are relatively close to each other, and the distribution function for the differential expressions is short ranged, with a tail of only a few dozens of strongly varying genes. In the latter case, cancer, the initial and final states are far apart and separated by a low-fitness barrier. The distribution function shows a very heavy tail, with thousands of silenced and over-expressed genes. We characterize the biological states by means of their principal component representations, and the expression distribution functions by their maximal and minimal differential expression values and the exponents of the Pareto laws describing the tails.

A consistent semiquantitative theoretical analysis of electronic Raman scattering from many-electron quantum dots under resonance excitation conditions has been performed. The theory is based on random-phase-approximation-like wave functions, with the Coulomb interactions treated exactly, and hole valence-band mixing accounted for within the Kohn-Luttinger Hamiltonian framework. The widths of intermediate and final states in the scattering process, although treated phenomenologically, play a significant role in the calculations, particularly for well-above-band-gap excitation. The calculated polarized and unpolarized Raman spectra reveal a great complexity of features and details when the incident light energy is swept from below, through, and above the quantum dot band gap. Incoming and outgoing resonances dramatically modify the Raman intensities of the single-particle, charge-density, and spin-density excitations. The theoretical results are presented in detail and discussed with regard to experimental observations.

We show that the combined effect of photon emission and Coulomb interactions may drive an exciton-polariton system towards a dynamical coherent state, even without phonon thermalization or any other relaxation mechanism. Exact diagonalization results for a finite system (a multilevel quantum dot interacting with the lowest-energy photon mode of a microcavity) are presented in support of this statement.