Entanglement scaling at first order phase transitions

First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations. When a 1QPT is crossed in the vicinity of a second order one (2QPT), due to the correlation length divergence of the latter, the corresponding ground state is modified and it becomes increasingly difficult to determine the order of the transition when the size of the system is finite. Here we show that, in such situations, it is possible to apply finite size scaling to entanglement measures, as it has recently been done for the order parameters and the energy gap, in order to recover the correct thermodynamic limit. Such a finite size scaling can unambigously discriminate between first and second order phase transitions in the vicinity of multricritical points even when the singularities displayed by entanglement measures lead to controversial results

The Rhombi-Chain Bose-Hubbard Model: geometric frustration and interactions

We explore the effects of geometric frustration within a one-dimensional Bose-Hubbard model using a chain of rhombi subject to a magnetic flux. The competition of tunnelling, self-interaction and magnetic flux gives rise to the emergence of a pair-superfluid (pair-Luttinger liquid) phase besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases. We compute the complete phase diagram of the model by identifying characteristic properties of the pair-Luttinger liquid phase such as pair correlation functions and structure factors and find that the pair-Luttinger liquid phase is very sensitive to changes away from perfect frustration (half-flux). We provide some proposals to make the model more resilient to variants away from perfect frustration. We also study the bipartite entanglement properties of the chain. We discover that, while the scaling of the block entropy pair-superfluid and of the single-particle superfluid leads to the same central charge, the properties of the low-lying entanglement spectrum levels reveal their fundamental difference.Comment: 12 pages, 11 figure

Uptake of purines in <i>Plasmodium falciparum</i>-infected human erythrocytes is mostly mediated by the human Equilibrative Nucleoside Transporter and the human Facilitative Nucleobase Transporter

&lt;b&gt;Background&lt;/b&gt;: Plasmodium parasites are unable to synthesize purines de novo and have to salvage them from the host. Due to this limitation in the parasite, purine transporters have been an area of focus in the search for anti-malarial drugs. Although the uptake of purines through the human equilibrative nucleoside transporter (hENT1), the human facilitative nucleobase transporter (hFNT1) and the parasite-induced new permeation pathway (NPP) has been studied, no information appears to exist on the relative contribution of these three transporters to the uptake of adenosine and hypoxanthine. Using the appropriate transporter inhibitors, the role of each of these salvage pathways to the overall purine transport in intraerythrocytic Plasmodium falciparum was systematically investigated. &lt;b&gt;Methods&lt;/b&gt;: The transport of adenosine, hypoxanthine and adenine into uninfected and P. falciparum-infected human erythrocytes was investigated in the presence or absence of classical inhibitors of the hFNT1, hENT1 and NPP. The effective inhibition of the various transporters by the classical inhibitors was verified using appropriate known substrates. The ability of high concentration of unlabelled substrates to saturate these transporters was also studied. &lt;b&gt;Results&lt;/b&gt;: Transport of exogenous purine into infected or uninfected erythrocytes occurred primarily through saturable transporters rather than through the NPP. Hypoxanthine and adenine appeared to enter erythrocytes mainly through the hFNT1 nucleobase transporter whereas adenosine entered predominantly through the hENT1 nucleoside transporter. The rate of purine uptake was approximately doubled in infected cells compared to uninfected erythrocytes. In addition, it was found that the rate of adenosine uptake was considerably higher than the rate of hypoxanthine uptake in infected human red blood cells (RBC). It was also demonstrated that furosemide inhibited the transport of purine bases through hFNT1. &lt;b&gt;Conclusion&lt;/b&gt;: Collectively, the data obtained in this study clearly show that the endogenous host erythrocyte transporters hENT1 and hFNT1, rather than the NPP, are the major route of entry of purine into parasitized RBC. Inhibitors of hENT1 and hFNT1, as well as the NPP, should be considered in the development of anti-malarials targeted to purine transport

On best rank one approximation of tensors

In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating iterations will always converge to a semi-maximal point. (A critical point in several vector variables is semi-maximal if it is maximal with respect to each vector variable, while other vector variables are kept fixed.) We present several numerical examples that illustrate the computational performance of the new method in comparison to the alternating least square method.Comment: 17 pages and 6 figure

Eigenvectors of tensors and algorithms for Waring decomposition

A Waring decomposition of a (homogeneous) polynomial f is a minimal sum of powers of linear forms expressing f. Under certain conditions, such a decomposition is unique. We discuss some algorithms to compute the Waring decomposition, which are linked to the equation of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a general cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem).Comment: 32 pages; three Macaulay2 files as ancillary files. Revised with referee's suggestions. Accepted JS

Development of reverse-transcription PCR techniques to analyse the density and sex ratio of gametocytes in genetically diverse Plasmodium chabaudi infections

We have developed cross-genotype and genotype-specific quantitative reverse-transcription PCR (qRT-PCR) assays to detect and quantify the number of parasites, transmission stages (gametocytes) and male gametocytes in blood stage Plasmodium chabaudi infections. Our cross-genotype assays are reliable, repeatable and generate counts that correlate strongly (R(2)s > 90%) with counts expected from blood smears. Our genotype-specific assays can distinguish and quantify different stages of genetically distinct parasite clones (genotypes) in mixed infections and are as sensitive as our cross-genotype assays. Using these assays we show that gametocyte density and gametocyte sex ratios vary during infections for two genetically distinct parasite lines (genotypes) and present the first data to reveal how sex ratio is affected when each genotype experiences competition in mixed-genotype infections. Successful infection of mosquito vectors depends on both gametocyte density and their sex ratio and we discuss the implications of competition in genetically diverse infections for transmission success

Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility

Recent advances on IMF research

Here I discuss recent work on brown dwarfs, massive stars and the IMF in general. The stellar IMF can be well described by an invariant two-part power law in present-day star-formation events within the Local Group of galaxies. It is nearly identical in shape to the pre-stellar core mass function. The majority of brown dwarfs follow a separate IMF. Evidence from globular clusters and ultra-compact dwarf galaxies has emerged that IMFs may have been top heavy depending on the star-formation rate density. The IGIMF then ranges from bottom heavy at low galaxy-wide star formation rates to being top-heavy in galaxy-scale star bursts.Comment: 6 pages, LaTeX, to appear in The Labyrinth of Star Formation, 18-22 June 2012, Crete, (eds.) D. Stamatellos, S. Goodwin, and D. Ward-Thompson, Springer, in press; replaced version: very minor corrections plus the addition of reference Smith & Lucey (2013) on the bottom-heavy IMF in elliptical galaxie

Astro2020 Science White Paper: Triggered High-Priority Observations of Dynamic Solar System Phenomena

Unexpected dynamic phenomena have surprised solar system observers in the past and have led to important discoveries about solar system workings. Observations at the initial stages of these events provide crucial information on the physical processes at work. We advocate for long-term/permanent programs on ground-based and space-based telescopes of all sizes - including Extremely Large Telescopes (ELTs) - to conduct observations of high-priority dynamic phenomena, based on a predefined set of triggering conditions. These programs will ensure that the best initial dataset of the triggering event are taken; separate additional observing programs will be required to study the temporal evolution of these phenomena. While not a comprehensive list, the following are notional examples of phenomena that are rare, that cannot be anticipated, and that provide high-impact advances to our understandings of planetary processes. Examples include: new cryovolcanic eruptions or plumes on ocean worlds; impacts on Jupiter, Saturn, Uranus, or Neptune; extreme eruptions on Io; convective superstorms on Saturn, Uranus, or Neptune; collisions within the asteroid belt or other small-body populations; discovery of an interstellar object passing through our solar system (e.g. 'Oumuamua); and responses of planetary atmospheres to major solar flares or coronal mass ejections.Comment: Astro2020 white pape