Classical theta constants vs. lattice theta series, and super string partition functions

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main technical tools adopted to realize the proposals: the classical theta constants and the lattice theta series. We compute the relevant Fourier coefficients in order to relate the two spaces. We will prove the equivalence up to genus 4. In genus five we will show that the solutions are equivalent modulo the Schottky form and coincide if we impose the vanishing of the cosmological constant.Comment: 21 page

Bone metabolic activity in hyperostosis cranialis interna measured with 18F-fluoride PET

F-18-Fluoride PET/CT is a relatively undervalued diagnostic test to measure bone metabolism in bone diseases. Hyperostosis cranialis interna (HCI) is a (hereditary) bone disease characterised by endosteal hyperostosis and osteosclerosis of the skull and the skull base. Bone overgrowth causes entrapment and dysfunction of several cranial nerves. The aim of this study is to compare standardised uptake values (SUVs) at different sites in order to quantify bone metabolism in the affected anatomical regions in HCI patients. Nine affected family members, seven non-affected family members and nine non-HCI non-family members underwent F-18-fluoride PET/CT scans. SUVs were systematically measured in the different regions of interest: frontal bone, sphenoid bone, petrous bone and clivus. Moreover, the average F-18-fluoride uptake in the entire skull was measured by assessing the uptake in axial slides. Visual assessment of the PET scans of affected individuals was performed to discover the process of disturbed bone metabolism in HCI. F-18-Fluoride uptake is statistically significantly higher in the sphenoid bone and clivus regions of affected family members. Visual assessment of the scans of HCI patients is relevant in detecting disease severity and the pattern of disturbed bone metabolism throughout life. F-18-Fluoride PET/CT is useful in quantifying the metabolic activity in HCI and provides information about the process of disturbed bone metabolism in this specific disorder. Limitations are a narrow window between normal and pathological activity and the influence of age. This study emphasises that F-18-fluoride PET/CT may also be a promising diagnostic tool for other metabolic bone disorders, even those with an indolent course

Vortices in polariton OPO superfluids

This chapter reviews the occurrence of quantised vortices in polariton fluids, primarily when polaritons are driven in the optical parametric oscillator (OPO) regime. We first review the OPO physics, together with both its analytical and numerical modelling, the latter being necessary for the description of finite size systems. Pattern formation is typical in systems driven away from equilibrium. Similarly, we find that uniform OPO solutions can be unstable to the spontaneous formation of quantised vortices. However, metastable vortices can only be injected externally into an otherwise stable symmetric state, and their persistence is due to the OPO superfluid properties. We discuss how the currents charactering an OPO play a crucial role in the occurrence and dynamics of both metastable and spontaneous vortices.Comment: 40 pages, 16 figure

Disorder Effects on Exciton-Polariton Condensates

The impact of a random disorder potential on the dynamical properties of Bose Einstein condensates is a very wide research field. In microcavities, these studies are even more crucial than in the condensates of cold atoms, since random disorder is naturally present in the semiconductor structures. In this chapter, we consider a stable condensate, defined by a chemical potential, propagating in a random disorder potential, like a liquid flowing through a capillary. We analyze the interplay between the kinetic energy, the localization energy, and the interaction between particles in 1D and 2D polariton condensates. The finite life time of polaritons is taken into account as well. In the first part, we remind the results of [G. Malpuech et al. Phys. Rev. Lett. 98, 206402 (2007).] where we considered the case of a static condensate. In that case, the condensate forms either a glassy insulating phase at low polariton density (strong localization), or a superfluid phase above the percolation threshold. We also show the calculation of the first order spatial coherence of the condensate versus the condensate density. In the second part, we consider the case of a propagating non-interacting condensate which is always localized because of Anderson localization. The localization length is calculated in the Born approximation. The impact of the finite polariton life time is taken into account as well. In the last section we consider the case of a propagating interacting condensate where the three regimes of strong localization, Anderson localization, and superfluid behavior are accessible. The localization length is calculated versus the system parameters. The localization length is strongly modified with respect to the non-interacting case. It is infinite in the superfluid regime whereas it is strongly reduced if the fluid flows with a supersonic velocity.Comment: chapter for a book "Exciton Polaritons in Microcavities: New Frontiers" by Springer (2012), the original publication is available at http://www.springerlink.co

mTORC1 Inhibition via Rapamycin Promotes Triacylglycerol Lipolysis and Release of Free Fatty Acids in 3T3â L1 Adipocytes

Signaling by mTOR complex 1 (mTORC1) promotes anabolic cellular processes in response to growth factors, nutrients, and hormonal cues. Numerous clinical trials employing the mTORC1 inhibitor rapamycin (aka sirolimus) to immunoâ suppress patients following organ transplantation have documented the development of hypertriglyceridemia and elevated serum free fatty acids (FFA). We therefore investigated the cellular role of mTORC1 in control of triacylglycerol (TAG) metabolism using cultured murine 3T3â L1 adipocytes. We found that treatment of adipocytes with rapamycin reduced insulinâ stimulated TAG storage ~50%. To determine whether rapamycin reduces TAG storage by upregulating lipolytic rate, we treated adipocytes in the absence and presence of rapamycin and isoproterenol, a β2â adrenergic agonist that activates the cAMP/protein kinase A (PKA) pathway to promote lipolysis. We found that rapamycin augmented isoproterenolâ induced lipolysis without altering cAMP levels. Rapamycin enhanced the isoproterenolâ stimulated phosphorylation of hormone sensitive lipase (HSL) on Serâ 563 (a PKA site), but had no effect on the phosphorylation of HSL S565 (an AMPK site). Additionally, rapamycin did not affect the isoproterenolâ mediated phosphorylation of perilipin, a protein that coats the lipid droplet to initiate lipolysis upon phosphorylation by PKA. These data demonstrate that inhibition of mTORC1 signaling synergizes with the βâ adrenergicâ cAMP/PKA pathway to augment phosphorylation of HSL to promote hormoneâ induced lipolysis. Moreover, they reveal a novel metabolic function for mTORC1; mTORC1 signaling suppresses lipolysis, thus augmenting TAG storage.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141428/1/lipd1089.pd

The mechanisms by which polyamines accelerate tumor spread

Increased polyamine concentrations in the blood and urine of cancer patients reflect the enhanced levels of polyamine synthesis in cancer tissues arising from increased activity of enzymes responsible for polyamine synthesis. In addition to their de novo polyamine synthesis, cells can take up polyamines from extracellular sources, such as cancer tissues, food, and intestinal microbiota. Because polyamines are indispensable for cell growth, increased polyamine availability enhances cell growth. However, the malignant potential of cancer is determined by its capability to invade to surrounding tissues and metastasize to distant organs. The mechanisms by which increased polyamine levels enhance the malignant potential of cancer cells and decrease anti-tumor immunity are reviewed. Cancer cells with a greater capability to synthesize polyamines are associated with increased production of proteinases, such as serine proteinase, matrix metalloproteinases, cathepsins, and plasminogen activator, which can degrade surrounding tissues. Although cancer tissues produce vascular growth factors, their deregulated growth induces hypoxia, which in turn enhances polyamine uptake by cancer cells to further augment cell migration and suppress CD44 expression. Increased polyamine uptake by immune cells also results in reduced cytokine production needed for anti-tumor activities and decreases expression of adhesion molecules involved in anti-tumor immunity, such as CD11a and CD56. Immune cells in an environment with increased polyamine levels lose anti-tumor immune functions, such as lymphokine activated killer activities. Recent investigations revealed that increased polyamine availability enhances the capability of cancer cells to invade and metastasize to new tissues while diminishing immune cells' anti-tumor immune functions

A New Mechanistic Scenario for the Origin and Evolution of Vertebrate Cartilage

The appearance of cellular cartilage was a defining event in vertebrate evolution because it made possible the physical expansion of the vertebrate “new head”. Despite its central role in vertebrate evolution, the origin of cellular cartilage has been difficult to understand. This is largely due to a lack of informative evolutionary intermediates linking vertebrate cellular cartilage to the acellular cartilage of invertebrate chordates. The basal jawless vertebrate, lamprey, has long been considered key to understanding the evolution of vertebrate cartilage. However, histological analyses of the lamprey head skeleton suggest it is composed of modern cellular cartilage and a putatively unrelated connective tissue called mucocartilage, with no obvious transitional tissue. Here we take a molecular approach to better understand the evolutionary relationships between lamprey cellular cartilage, gnathostome cellular cartilage, and lamprey mucocartilage. We find that despite overt histological similarity, lamprey and gnathostome cellular cartilage utilize divergent gene regulatory networks (GRNs). While the gnathostome cellular cartilage GRN broadly incorporates Runx, Barx, and Alx transcription factors, lamprey cellular cartilage does not express Runx or Barx, and only deploys Alx genes in certain regions. Furthermore, we find that lamprey mucocartilage, despite its distinctive mesenchymal morphology, deploys every component of the gnathostome cartilage GRN, albeit in different domains. Based on these findings, and previous work, we propose a stepwise model for the evolution of vertebrate cellular cartilage in which the appearance of a generic neural crest-derived skeletal tissue was followed by a phase of skeletal tissue diversification in early agnathans. In the gnathostome lineage, a single type of rigid cellular cartilage became dominant, replacing other skeletal tissues and evolving via gene cooption to become the definitive cellular cartilage of modern jawed vertebrates

Real-space collapse of a polariton condensate

Microcavity polaritons are two-dimensional bosonic fluids with strong nonlinearities, composed of coupled photonic and electronic excitations. In their condensed form, they display quantum hydrodynamic features similar to atomic Bose–Einstein condensates, such as long-range coherence, superfluidity and quantized vorticity. Here we report the unique phenomenology that is observed when a pulse of light impacts the polariton vacuum: the fluid which is suddenly created does not splash but instead coheres into a very bright spot. The real-space collapse into a sharp peak is at odd with the repulsive interactions of polaritons and their positive mass, suggesting that an unconventional mechanism is at play. Our modelling devises a possible explanation in the self-trapping due to a local heating of the crystal lattice, that can be described as a collective polaron formed by a polariton condensate. These observations hint at the polariton fluid dynamics in conditions of extreme intensities and ultrafast times