Showing papers by "Gilles Pagès published in 2013"

TRF2 inhibits a cell-extrinsic pathway through which natural killer cells eliminate cancer cells

Abstract: Dysfunctional telomeres suppress tumour progression by activating cell-intrinsic programs that lead to growth arrest. Increased levels of TRF2, a key factor in telomere protection, are observed in various human malignancies and contribute to oncogenesis. We demonstrate here that a high level of TRF2 in tumour cells decreased their ability to recruit and activate natural killer (NK) cells. Conversely, a reduced dose of TRF2 enabled tumour cells to be more easily eliminated by NK cells. Consistent with these results, a progressive upregulation of TRF2 correlated with decreased NK cell density during the early development of human colon cancer. By screening for TRF2-bound genes, we found that HS3ST4--a gene encoding for the heparan sulphate (glucosamine) 3-O-sulphotransferase 4--was regulated by TRF2 and inhibited the recruitment of NK cells in an epistatic relationship with TRF2. Overall, these results reveal a TRF2-dependent pathway that is tumour-cell extrinsic and regulates NK cell immunity.

Randomized urn models revisited using Stochastic Approximation

Abstract: This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in Bai and Hu (1999,2005) and Bai, Hu and Shen (2002). We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence and the asymptotic normality (CLT) of the normalized procedure under less stringent assumptions by calling upon the ODE and SDE methods. As a second step, we investigate a more involved family of models, known as multi-arm clinical trials, where the urn updating depends on the past performances of the treatments. By increasing the dimension of the state vector, our SA approach provides this time a new asymptotic normality result.

Linking JNK Activity to the DNA Damage Response.

Abstract: The activity of c-Jun N-terminal kinase (JNK) was initially described as ultraviolet- and oncogene-induced kinase activity on c-Jun. Shortly after this initial discovery, JNK activation was reported for a wider variety of DNA-damaging agents, including γ-irradiation and chemotherapeutic compounds. As the DNA damage response mechanisms were progressively uncovered, the mechanisms governing the activation of JNK upon genotoxic stresses became better understood. In particular, a recent set of papers links the physical breakage in DNA, the activation of the transcription factor NF-κB, the secretion of TNF-α, and an autocrine activation of the JNK pathway. In this review, we will focus on the pathway that is initiated by a physical break in the DNA helix, leading to JNK activation and the resultant cellular consequences. The implications of these findings will be discussed in the context of cancer therapy with DNA-damaging agents.

Optimal posting price of limit orders: learning by trading

Abstract: We model a trader interacting with a continuous market as an iterative algorithm that adjusts limit prices at a given rhythm and propose a procedure to minimize trading costs. We prove the $$a.s.$$ convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are met (notably, using the co-monotony principle). We illustrate our results with numerical experiments on both simulated and market data.

Pointwise convergence of the Lloyd algorithm in higher dimension

Abstract: We establish the pointwise convergence of the iterative Lloyd algorithm, also known as $k$-means algorithm, when the quadratic quantization error of the starting grid (with size $N\ge 2$) is lower than the minimal quantization error with respect to the input distribution is lower at level $N-1$. Such a protocol is known as the splitting method and allows for convergence even when the input distribution has an unbounded support. We also show under very light assumption that the resulting limiting grid still has full size $N$. These results are obtained without continuity assumption on the input distribution. A variant of the procedure taking advantage of the asymptotic of the optimal quantizer radius is proposed which always guarantees the boundedness of the iterated grids.

Functional Co-monotony of Processes with Applications to Peacocks and Barrier Options

Abstract: We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian bridge, Brownian diffusions, Liouville processes, fractional Brownian motion. As a first application, we recover and extend some recent results about peacock processes obtained by Hirsch et al. in (Peacocks and Associated Martingales, with Explicit Constructions, Bocconi & Springer, 2011, 430p) [see also (Peacocks sous l’hypothese de monotonie conditionnelle et caracterisation des 2-martingales en termes de peacoks, these de l’Universite de Lorraine, 2012, 169p)] which were themselves motivated by a former work of Carr et al. in (Finance Res. Lett. 5:162–171, 2008) about the sensitivities of Asian options with respect to their volatility and residual maturity (seniority). We also derive semi-universal bounds for various barrier options.

Multi-asset American options and parallel quantization

Abstract: We present a parallel implementation of the optimal quantization method on a grid computing. Its purpose is to price instantaneously multidimensional American options. Numerical tests are proceeded with variable number of processors, from 4 to 128. Finally a spatial extrapolation of Richardson-Romberg is introduced to speed up the convergence rate and stabilize the results.

Nonlinear Randomized Urn Models: a Stochastic Approximation Viewpoint

Abstract: This paper extends the link between stochastic approximation (SA) theory and randomized urn models developed in Laruelle, Pag{e}s (2013), and their applications to clinical trials introduced in Bai, HU (1999,2005) and Bai, Hu, Shen (2002). We no longer assume that the drawing rule is uniform among the balls of the urn (which contains d colors), but can be reinforced by a function f. This is a way to model risk aversion. Firstly, by considering that f is concave or convex and by reformulating the dynamics of the urn composition as an SA algorithm with remainder, we derive the a.s. convergence and the asymptotic normality (Central Limit Theorem, CLT) of the normalized procedure by calling upon the so-called ODE and SDE methods. An in-depth analysis of the case d=2 exhibits two different behaviors: A single equilibrium point when f is concave, and when f is convex, a transition phase from a single attracting equilibrium to a system with two attracting and one repulsive equilibrium points. The last setting is solved using results on non-convergence toward noisy and noiseless "traps" in order to deduce the a.s. convergence toward one of the attracting points. Secondly, the special case of a Polya urn (when the addition rule is the identity matrix) is analyzed, still using result from SA theory about "traps". Finally, these results are applied to a function with regular variation and to an optimal asset allocation in Finance.

Recursive marginal quantization of the Euler scheme of a diffusion process

Abstract: We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the Euler process and the proposed quantizations. We show in particular that at every discretization step $t\_k$ of the Euler scheme, this error is bounded by the cumulative quantization errors induced by the Euler operator, from times $t\_0=0$ to time $t\_k$. For numerics, we restrict our analysis to the one dimensional setting and show how to compute the optimal grids using a Newton-Raphson algorithm. We then propose a closed formula for the companion weights and the transition probabilities associated to the proposed quantizations. This allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework. Numerical tests are carried out for the Brownian motion and for the pricing of European options in a local volatility model. A comparison with the Monte Carlo simulations shows that the proposed method may sometimes be more efficient (w.r.t. both computational precision and time complexity) than the Monte Carlo method.

Contrasted effects of the multitarget TKi vandetanib on docetaxel-sensitive and docetaxel-resistant prostate cancer cell lines.

Abstract: Objectives Overexpression of epidermal growth factor receptor (EGFR) and angiogenic factors is associated with the progression of androgen-independent prostate cancer (AIPC). We examined the effects of vandetanib, an inhibitor of vascular endothelial growth factor (VEGFR), EGFR, and rearranged during transfection (RET) tyrosine-kinase activities, alone or combined with docetaxel, on PC3 docetaxel-sensitive (PC3wt) or docetaxel-resistant (PC3R) AIPC cell growth in vivo and in vitro. Methods Mice bearing PC3wt or PC3R tumors were treated for 3 weeks with vandetanib (25 or 50 mg/kg/d p.o., 5 d/wk), docetaxel (10 or 30 mg/kg i.p., 1 d/wk), or their combination (low or high doses). Xenograft tumors were analyzed for expression of Ki-67, EGFR, VEGFR2, and production of VEGFA. Results On PC3wt, vandetanib at both doses stimulated tumor growth, whereas docetaxel at both doses exerted strong growth-inhibiting effects. The low-dose vandetanib-docetaxel combination resulted in tumor growth similar to that of control, whereas the high-dose combination induced a significant antiproliferative effect. In contrast, on PC3R, the low-dose of vandetanib had no effect on tumor growth, whereas the high-dose of vandetanib significantly inhibited tumor growth. Docetaxel at both doses exerted moderate and transient antitumor effects. The combination of high-dose vandetanib with high-dose docetaxel resulted in antiproliferative effects, which were lower than expected from the sum of individual drug effects. Importantly, tumor analyses revealed overexpression of the EGFR/VEGFR pathways in PC3R relative to PC3wt. Conclusion Present results suggest that vandetanib should not be associated with docetaxel in treatment-naive or docetaxel-resistant prostate cancer (CaP). The use of high-dose vandetanib alone may warrant further investigation in patients with docetaxel-resistant AIPC overexpressing VEGFR/EGFR pathways.

Invariant measure of duplicated diffusions and application to Richardson-Romberg extrapolation

Abstract: With a view to numerical applications we address the following question: given an ergodic Brownian diffusion with a unique invariant distribution, what are the invariant distributions of the duplicated system consisting of two trajectories? We mainly focus on the interesting case where the two trajectories are driven by the same Brownian path. Under this assumption, we first show that uniqueness of the invariant distribution (weak confluence) of the duplicated system is essentially always true in the one-dimensional case. In the multidimensional case, we begin by exhibiting explicit counter-examples. Then, we provide a series of weak confluence criterions (of integral type) and also of a.s. pathwise confluence, depending on the drift and diffusion coefficients through a non-infinitesimal Lyapunov exponent. As examples, we apply our criterions to some non-trivially confluent settings such as classes of gradient systems with non-convex potentials or diffusions where the confluence is generated by the diffusive component. We finally establish that the weak confluence property is connected with an optimal transport problem. As a main application, we apply our results to the optimization of the Richardson-Romberg extrapolation for the numerical approximation of the invariant measure of the initial ergodic Brownian diffusion.

Invariant distribution of duplicated diffusions and application to Richardson-Romberg extrapolation

Abstract: With a view to numerical applications we address the following question: given an ergodic Brownian diffusion with a unique invariant distribution, what are the invariant distributions of the duplicated system consisting of two trajectories? We mainly focus on the interesting case where the two trajectories are driven by the same Brownian path. Under this assumption, we first show that uniqueness of the invariant distribution (weak confluence) of the duplicated system is essentially always true in the one-dimensional case. In the multidimensional case, we begin by exhibiting explicit counter-examples. Then, we provide a series of weak confluence criterions (of integral type) and also of a.s. pathwise confluence, depending on the drift and diffusion coefficients through a non-infinitesimal Lyapunov exponent. As examples, we apply our criterions to some non-trivially confluent settings such as classes of gradient systems with non-convex potentials or diffusions where the confluence is generated by the diffusive component. We finally establish that the weak confluence property is connected with an optimal transport problem. As a main application, we apply our results to the optimization of the Richardson-Romberg extrapolation for the numerical approximation of the invariant measure of the initial ergodic Brownian diffusion.