On an efficient multiple time step Monte Carlo simulation of the SABR model

textabstractIn this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options

Rapamycin impact on VWAT.

<p>(<b>A</b>) Representative sections of H&E-stained VWAT of Ve- or Rapa-treated mice. Scale bars represent 100 µm. Black arrows target to infiltrating cells. (<b>B</b>) Adipocyte diameter distribution of the VWAT of 5 Ve-treated and 5 Rapa-treated HFD-fed mice (Rapa: ▪, Ve: □). (<b>C</b>) RT-qPCR analysis of VWAT, after 22 injections (Rapa: ▪, Ve: □): Expression levels of T-cell (<i>Cd4</i>, <i>Cd8</i>, <i>FoxP3</i>), B-cell (<i>Cd20</i>) and macrophage (<i>Cd68</i>, <i>F4/80</i>) specific markers and of leukocyte migratory factors (<i>Icam-1</i>, <i>Mcp-1</i>) specific markers (normalized to <i>Eef2</i> expression). Data are expressed as mean ± S.E.M. of 8 to 10 mice per group. <b>^#</b><i>p</i><0.05, ^##<i>p</i><0.01. (<b>D</b>) Representative sections of the VWAT from Ve- or Rapa-treated mice immunostained with F4/80 Ab (brown color). Scale bars represent 100 µm (left). Quantification of F4/80 positive signal on VWAT sections by Image J (Rapa: ▪, Ve: □) (right). Data are expressed as mean ± S.E.M. of 5 mice per group. ^##<i>p</i><0.01.</p

Tissue-specific effects of rapamycin on inflammation.

<p>(<b>A</b>) Venn diagrams of microarray data representing the number of genes deregulated in the VWAT from Ve- or Rapa-treated mice (respectively; red and blue circle). Genes deregulated at least by 1.5-fold at <i>p</i><0.01 were considered for pathway analysis. (<b>B</b>) IPA analysis: Functional enrichment analysis showing the top 10 biological functions significantly deregulated in the VWAT of Rapa-treated mice compared to controls. (<b>C</b>) Expression profiling of genes implicated in the top deregulated pathways: downregulated genes (green) <i>versus</i> upregulated genes (red). (<b>D</b>) RT-qPCR analysis of VWAT, after 22 injections (Rapa: ▪, Ve: □): Expression levels of inflammatory cytokines (<i>Il-1α</i>, <i>Il-1β</i>, <i>Il-6</i> and <i>Tnfα</i>) and anti-inflammatory cytokines (<i>Il-4</i> and <i>Il-10</i>) (normalized to <i>Eef2</i> expression) (n = 8 to 10 mice per group). (<b>E</b>) IL-6, MCP-1, TNF-α and IL-10 levels in supernatants of VWAT explants (Rapa: ▪, Ve: □). ELISA values were normalized to the weight of VWAT explants and are expressed in ng/ml/g VWAT (n = 5 mice per group). (<b>F</b>) IL-6, TNF-α and IL-10 levels in blood (Rapa: ▪, Ve: □). ELISA values are in pg/ml (n = 8 to 10 mice per group). (<b>G</b>) RT-qPCR analysis of liver, after 22 injections (Rapa: ▪, Ve: □): Expression levels of inflammatory cytokines (<i>Il-1α</i>, <i>Il-1β</i>, <i>Il-6</i> and <i>Tnfα</i>) and anti-inflammatory cytokines (<i>Il-4</i> and <i>Il-10</i>) (normalized to <i>Eef2</i> expression) (n = 8 to 10 mice per group). (<b>D–G</b>) Data are expressed as mean ± S.E.M. <b>^#</b><i>p</i><0.05, ^##<i>p</i><0.01, <b>^###</b><i>p</i><0.001.</p

Effect of rapamycin on mTORC1 and mTORC2 activities.

<p>(<b>A</b>) Rapamycin blood levels (Rapa: ▪, Ve: □). Mice were bled before, and at days 1 and 7 post-injection. Results are expressed as mean ± S.E.M. of 2 mice per group. (<b>B</b>) Western blot analysis of S6K1 (total and T389-phosphorylated) and AKT (total and S437-phosphorylated) in VWAT, muscle and liver. Each lane represents an individual mouse (5 mice per group were analyzed, 3 representative mice per group are figured). Quantification of the signals was done using Image J (Rapa: ▪, Ve: □). Data are expressed as mean ± S.E.M. of 3 mice per group. ^#<i>p</i><0.05.</p

Effect of rapamycin on the expression of MDSCs specific genes by MDSCs purified from adipose tissue and liver (22 weeks post-injection).

<p>(<b>A</b>) RT-qPCR analysis of MDSCs purified from VWAT, after 22 injections (Rapa: ▪, Ve: □): Expression levels of <i>Arg1</i>, <i>Nos2</i> and <i>C/EBP-β</i> (normalized to <i>Eef2</i> expression) (n = 5 mice per group). (<b>B</b>) RT-qPCR analysis of MDSCs purified from the liver, after 22 injections (Rapa: ▪, Ve: □): Expression levels of <i>Arg1</i>, <i>Nos2</i> and <i>C/EBP-β</i> (normalized to <i>Eef2</i> expression) (n = 5 mice per group). (<b>A</b>–<b>B</b>) Data are expressed as mean ± S.E.M. of 5 mice per group. ^##<i>p<</i>0.01, ^###<i>p<</i>0.001.</p

Body weight gain, feeding behavior and thermogenesis in rapamycin-treated mice.

<p>(<b>A</b>) Time course of body weight gain (%) measured over rapamycin treatment. Mice were fed on HFD for 6 weeks before receiving rapamycin (Rapa: •) or vehicle (Ve: ○) once a week for 22 weeks. (<b>B</b>) Masses (g) of visceral (perigonadal) white adipose tissue (VWAT), subcutaneous white adipose tissue (SCWAT), interscapular brown adipose tissue (BAT), liver and pancreas at 22 weeks (Rapa: ▪, Ve: □). (<b>C</b>) Cumulative food intake (g/day/mouse) (Rapa: ▪, Ve: □). (<b>D</b>) Oxygen consumption (Vo₂) (ml/min/kg∧0.75) measured by indirect calorimetry over a 36-hour monitoring period (Rapa: •, Ve: ○). (<b>E</b>) Energy expenditure (kcal/day/Kg∧0.75) measured using indirect calorimetry over a 36-hour monitoring period (Rapa: ▪, Ve: □). (<b>F</b>) Core body temperature (°C) (Rapa: ▪, Ve: □). (<b>G</b>) Serum total ketone bodies (mmol/l) in 12-hours fasted mice (Rapa: ▪, Ve: □). (<b>H</b>) Representative sections of H&E-stained BAT of Ve- or Rapa-treated mice. Scale bars represent 50 µm. (<b>I</b>) Real-time quantitative PCR (RT-qPCR) analysis of BAT, after 22 injections (Rapa: ▪, Ve: □): Expression levels of <i>Ucp-1</i>, <i>Ucp-2</i>, <i>Ucp-3</i>, <i>Cpt1b</i>, <i>Pgc-1α</i> and <i>Prdm16</i> (normalized to <i>Eef2</i> expression). (<b>A–I</b>) Data are expressed as mean ± S.E.M. of 8 to 10 mice per group. ^#<i>p<</i>0.05, ^##<i>p<</i>0.01, ^###<i>p</i><0.001.</p

Beneficial Metabolic Effects of Rapamycin Are Associated with Enhanced Regulatory Cells in Diet-Induced Obese Mice

<div><p>The “mechanistic target of rapamycin” (mTOR) is a central controller of growth, proliferation and/or motility of various cell-types ranging from adipocytes to immune cells, thereby linking metabolism and immunity. mTOR signaling is overactivated in obesity, promoting inflammation and insulin resistance. Therefore, great interest exists in the development of mTOR inhibitors as therapeutic drugs for obesity or diabetes. However, despite a plethora of studies characterizing the metabolic consequences of mTOR inhibition in rodent models, its impact on immune changes associated with the obese condition has never been questioned so far. To address this, we used a mouse model of high-fat diet (HFD)-fed mice with and without pharmacologic mTOR inhibition by rapamycin. Rapamycin was weekly administrated to HFD-fed C57BL/6 mice for 22 weeks. Metabolic effects were determined by glucose and insulin tolerance tests and by indirect calorimetry measures of energy expenditure. Inflammatory response and immune cell populations were characterized in blood, adipose tissue and liver. In parallel, the activities of both mTOR complexes (<i>e. g.</i> mTORC1 and mTORC2) were determined in adipose tissue, muscle and liver. We show that rapamycin-treated mice are leaner, have enhanced energy expenditure and are protected against insulin resistance. These beneficial metabolic effects of rapamycin were associated to significant changes of the inflammatory profiles of both adipose tissue and liver. Importantly, immune cells with regulatory functions such as regulatory T-cells (Tregs) and myeloid-derived suppressor cells (MDSCs) were increased in adipose tissue. These rapamycin-triggered metabolic and immune effects resulted from mTORC1 inhibition whilst mTORC2 activity was intact. Taken together, our results reinforce the notion that controlling immune regulatory cells in metabolic tissues is crucial to maintain a proper metabolic status and, more generally, comfort the need to search for novel pharmacological inhibitors of the mTOR signaling pathway to prevent and/or treat metabolic diseases.</p></div

Age-dependent BMI loci.

<p>Effect estimates (beta ±95CI) per standard deviation in BMI and risk allele for loci showing age-differences in men & women ≤50y compared to men & women >50y. Loci are ordered by greater magnitude of effect in men & women ≤50y compared to men & women >50y. (95%CI: 95% confidence interval; BMI: body mass index; SD: standard deviation, *Newly identified loci).</p

Fifteen BMI loci showing significant age-differences in adults ≤50y compared to adults >50y.

<p>Chr: Chromosome; Pos: position; EAF: Effect Allele Frequency; EA: Effect allele; OA: Other allele</p><p>^a ‘Yes’ if the locus is mentioned as BMI locus for the first time</p><p>^b Effect allele is according to the BMI increasing allele according to the associated sex.</p><p>The table shows the age-group specific (sex-combined) results, ordered by largest to smallest effect in adults ≤50y. All loci were detected by the screen on age-difference that included the a-priori filter on <i>P</i>_{<i>Overall</i>} < 10⁻⁵. The age- and sex-specific results (four strata) and more detailed information on the loci are given in <b><a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005378#pgen.1005378.s020" target="_blank">S4 Table</a></b>.</p

Forty-four WHR_adjBMI loci showing significant sex-differences.

<p>Chr: Chromosome; Pos: position; EAF: Effect Allele Frequency; EA: Effect allele; OA: Other allele</p><p>^a ‘Yes’ if the locus is mentioned as WHR_adjBMI locus for the first time</p><p>^b ‘Yes’ if the sex-difference in the effect on WHR_adjBMI is reported for the first time</p><p>^c Effect allele is according to the WHR_adjBMI increasing allele according to the associated sex.</p><p>The table shows the sex-specific (age-group combined) results, ordered by largest, positive effect in women to largest, negative effect in women. The age- and sex-specific results (four strata), more detailed information on the loci and on the screens for which they were detected are given in <b><a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005378#pgen.1005378.s021" target="_blank">S5 Table</a></b>.</p