Non-Cold Dark Matter from Primordial Black Hole Evaporation

Dark matter coupled solely gravitationally can be produced through the decay of primordial black holes in the early universe. If the dark matter is lighter than the initial black hole temperature, it could be warm enough to be subject to structure formation constraints. In this paper we perform a more precise determination of these constraints. We first evaluate the dark matter phase-space distribution, without relying on the instantaneous decay approximation. We then interface this phase-space distribution with the Boltzmann code CLASS to extract the corresponding matter power spectrum, which we find to match closely those of warm dark matter models, albeit with a different dark matter mass. This mapping allows us to extract constraints from Lyman-$\alpha$ data without the need to perform hydrodynamical simulations. We robustly rule out the possibility, consistent with previous analytic estimates, of primordial black holes having come to dominate the energy density of the universe and simultaneously given rise to all the DM through their decay. Consequences and implications for dark radiation and leptogenesis are also briefly discussed.Comment: 33 pages, 4 figure

Anomalous Drude Model

A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long tail and even a non-vanishing first moment. The collision averaged motion is either regular diffusive or L\'evy-flight like. The anomalous diffusion coefficients show complex scaling laws. The conductivity can be calculated in the diffusive regime. The model is of interest for the phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter

Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele

We establish a connection between two recently-proposed approaches to the understanding of the geometric origin of the Fu-Kane-Mele invariant $\mathrm{FKM} \in \mathbb{Z}_2$, arising in the context of 2-dimensional time-reversal symmetric topological insulators. On the one hand, the $\mathbb{Z}_2$ invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes it is possible to provide an expression for $\mathrm{FKM}$ containing the square root of the Wess-Zumino amplitude for a certain $U(N)$-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above mentioned Wess-Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov-Wiegmann formula for fields $\mathbb{T}^2 \to U(N)$, of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.Comment: 23 pages, 1 figure. To appear in Letters in Mathematical Physic

Interacting fermions in self-similar potentials

We consider interacting spinless fermions in one dimension embedded in self-similar quasiperiodic potentials. We examine generalizations of the Fibonacci potential known as precious mean potentials. Using a bosonization technique and a renormalization group analysis, we study the low-energy physics of the system. We show that it undergoes a metal-insulator transition for any filling factor, with a critical interaction that strongly depends on the position of the Fermi level in the Fourier spectrum of the potential. For some positions of the Fermi level the metal-insulator transition occurs at the non interacting point. The repulsive side is an insulator with a gapped spectrum whereas in the attractive side the spectrum is gapless and the properties of the system are described by a Luttinger liquid. We compute the transport properties and give the characteristic exponents associated to the frequency and temperature dependence of the conductivity.Comment: 18 pages, 10 EPS figure

Aloinjertos en artrodesis vertebrales extensas

La cirugía de las deformidades, fracturas y tumores vertebrales requiere frecuentemente artrodesis amplias, lo cual conlleva la dificultad de obtener suficiente injerto óseo autólogo (particularmente en niños y en casos de deformidades paralíticas) y la necesidad de una segunda incisión, con el consiguiente aumento del tiempo quirúrgico y eventual morbilidad. Estudiamos 52 pacientes afectos de deformidades, fracturas o tumores vertebrales que fueron intervenidos mediante artrodesis vertebral extensa, en los que se utilizó aloinjerto de cabeza femoral como hueso esponjoso para aumentar la cantidad obtenida del propio lecho de artrodesis (estructuras posteriores). Además, en tres ocasiones se utilizó como injerto óseo intersomático un fragmento de cabeza femoral tallado a medida, realizándose una costotransversectomía para su colocación. El seguimiento fue entre 1 y 4 años. La única complicación observada fue la aparición de seromas de resolución espontánea en los 15 primeros casos. Posteriormente este problema se evitó con el lavado repetido del injerto, una vez triturado, con suero fisiológico caliente. En nuestra experiencia, la utilización de aloinjertos óseos permitió disminuir el tiempo quirúrgico de las intervenciones y a su vez evitar nuevas incisiones, sin reducir se las posibilidades de obtener una correcta artrodesis vertebral

Z_2 Invariants of topological insulators as geometric obstructions

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones

Characterization of Rhodamine-123 as a Tracer Dye for Use In In vitro Drug Transport Assays

Fluorescent tracer dyes represent an important class of sub-cellular probes and allow the examination of cellular processes in real-time with minimal impact upon these processes. Such tracer dyes are becoming increasingly used for the examination of membrane transport processes, as they are easy-to-use, cost effective probe substrates for a number of membrane protein transporters. Rhodamine 123, a member of the rhodamine family of flurone dyes, has been used to examine membrane transport by the ABCB1 gene product, MDR1. MDR1 is viewed as the archetypal drug transport protein, and is able to efflux a large number of clinically relevant drugs. In addition, ectopic activity of MDR1 has been associated with the development of multiple drug resistance phenotype, which results in a poor patient response to therapeutic intervention. It is thus important to be able to examine the potential for novel compounds to be MDR1 substrates. Given the increasing use rhodamine 123 as a tracer dye for MDR1, a full characterisation of its spectral properties in a range of in vitro assay-relevant media is warranted. Herein, we determine λmax for excitation and emission or rhodamine 123 and its metabolite rhodamine 110 in commonly used solvents and extraction buffers, demonstrating that fluorescence is highly dependent on the chemical environment: Optimal parameters are 1% (v/v) methanol in HBSS, with λex = 505 nm, λem = 525 nm. We characterise the uptake of rhodamine 123 into cells, via both passive and active processes, and demonstrate that this occurs primarily through OATP1A2-mediated facilitated transport at concentrations below 2 µM, and via micelle-mediated passive diffusion above this. Finally, we quantify the intracellular sequestration and metabolism of rhodamine 123, demonstrating that these are both cell line-dependent factors that may influence the interpretation of transport assays

Classification of Inhibitors of Hepatic Organic Anion Transporting Polypeptides (OATPs): Influence of Protein Expression on Drug–Drug Interactions

ABSTRACT: The hepatic organic anion transporting poly-peptides (OATPs) influence the pharmacokinetics of several drug classes and are involved in many clinical drug−drug interactions. Predicting potential interactions with OATPs is, therefore, of value. Here, we developed in vitro and in silico models for identification and prediction of specific and general inhibitors of OATP1B1, OATP1B3, and OATP2B1. The maximal transport activity (MTA) of each OATP in human liver was predicted from transport kinetics and protein quantification. We then used MTA to predict the effects of a subset of inhibitors on atorvastatin uptake in vivo. Using a data set of 225 drug-like compounds, 91 OATP inhibitors were identified. In silico models indicated that lipophilicity and polar surface area are key molecular features of OATP inhibition. MTA predictions identified OATP1B1 and OATP1B3 as major determinants of atorvastatin uptake in vivo. The relative contributions to overall hepatic uptake varied with isoform specificities of the inhibitors

Virtual Patients and Sensitivity Analysis of the Guyton Model of Blood Pressure Regulation: Towards Individualized Models of Whole-Body Physiology

Mathematical models that integrate multi-scale physiological data can offer insight into physiological and pathophysiological function, and may eventually assist in individualized predictive medicine. We present a methodology for performing systematic analyses of multi-parameter interactions in such complex, multi-scale models. Human physiology models are often based on or inspired by Arthur Guyton's whole-body circulatory regulation model. Despite the significance of this model, it has not been the subject of a systematic and comprehensive sensitivity study. Therefore, we use this model as a case study for our methodology. Our analysis of the Guyton model reveals how the multitude of model parameters combine to affect the model dynamics, and how interesting combinations of parameters may be identified. It also includes a “virtual population” from which “virtual individuals” can be chosen, on the basis of exhibiting conditions similar to those of a real-world patient. This lays the groundwork for using the Guyton model for in silico exploration of pathophysiological states and treatment strategies. The results presented here illustrate several potential uses for the entire dataset of sensitivity results and the “virtual individuals” that we have generated, which are included in the supplementary material. More generally, the presented methodology is applicable to modern, more complex multi-scale physiological models