RNS derivation of N-point disk amplitudes from the revisited S-matrix approach

In the past year, in arXiv:1208.6066 we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the ${\alpha'}^N$ terms of the OSLEEL using open superstring $n$-point amplitudes in which $n$ is very much lower than $(N+2)$ (which is the order of the required amplitude to obtain those ${\alpha'}^N$ terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger in arXiv:1106.2645, using the Pure Spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4, 5, 6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the $\alpha'$ expansions for these amplitudes up to ${\alpha'}^6$ order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.Comment: 77 pages, 3 figure

Structural Identifiability Analysis via Extended Observability and Decomposition

7 páginasStructural identifiability analysis of nonlinear dynamic models requires symbolic manipulations, whose computational cost rises very fast with problem size. This hampers the application of these techniques to the large models which are increasingly common in systems biology. Here we present a method to assess parametric identifiability based on the framework of nonlinear observability. Essentially, our method considers model parameters as particular cases of state variables with zero dynamics, and evaluates structural identifiability by calculating the rank of a generalized observability-identifiability matrix. If a model is unidentifiable as a whole, the method determines the identifiability of its individual parameters. For models whose size or complexity prevents the direct application of this procedure, an optimization approach is used to decompose them into tractable subsystems. We demonstrate the feasibility of this approach by applying it to three well-known case studiesPeer reviewe

The use of platelets microparticles and associated factors for improve the endometrium pontentiallity

Motivation: Despite, the high advances in assisted reproductive technology (ART), with technics like: i) intrauterine insemination (IUI); ii) in vitro fertilization (IVF) and; iii) intracytoplasmic sperm injection (ISCI); the rate of success still remains very low, about 30-33%. Implantation is a highly controlled process, involving a dialogue between the endometrium and the implanting embryo, which is crucial for the establishment and maintenance of pregnancy (Pafilis et al., 2007). When the endometrium is receptive and available to establish this dialogue is called the “window of implantation” (WOI). Nowadays, large amounts of resources are being invested are to find a way to improve or boost the potentiality of the endometrium. Objective: Characterize the effect of the microparticules and factors, derived from the activation of Platelets, to the endometrium with the goal of raise the ratio of embryo implantation.Methods: An in vitro model of embryo implantation, is used two different cell lines: Hec-1A in monolayer culture simulating the endometrium and JAR as trophoblast models (pseudoembryos). These lines are co-incubated using five different concentrations of MPPs and factors to quantify the ratio of adhesion. Finally, 192 genes that have been shown to be related to endometrial receptivity are studied using qPCR by BioMark HD Fluidigm.Conclusion: Through the use of MPPs and different factors (before and after embryo transfer) in this two cell lines and the 192 genes, it is intended to observe different changes in the transcriptomic endometrial profile, producing morphological and molecular changes that improves the endometrial receptivity during the WOI for a successful implantation raising the number of pregnancies

Controllability and accessibility analysis of nonlinear biosystems

Background: We address the problem of determining the controllability and accessibility of nonlinear biosystems. We consider models described by affine-in-inputs ordinary differential equations, which are adequate for a wide array of biological processes. Roughly speaking, the controllability of a dynamical system determines the possibility of steering it from an initial state to any point in its neighbourhood; accessibility is a weaker form of controllability. Methods: While the methodology for analysing the controllability of linear systems is well established, its generalization to the nonlinear case has proven elusive. Thus, a number of related but different properties – including different versions of accessibility, reachability or weak local controllability – have been defined to approach its study, and several partial results exist in lieu of a general test. Here, leveraging the applicable results from differential geometric control theory, we source sufficient conditions to assess nonlinear controllability, as well as a necessary and sufficient condition for accessibility. Results: We develop an algorithmic procedure to evaluate these conditions efficiently, and we provide its open source implementation. Using this software tool, we analyse the accessibility and controllability of a number of models of biomedical interest. While some of them are fully controllable, we find others that are not, as is the case of some models of EGF and NF����B signalling networks. Conclusions: The contributions in this paper facilitate the accessibility and controllability analysis of nonlinear models, not only in biomedicine but also in other areas in which they have been rarely performed to date.Agencia Estatal de Investigación | Ref. PID2020-113992RA-I00Agencia Estatal de Investigación | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00