The Electrostatic Ion Beam Trap : a mass spectrometer of infinite mass range

We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and show that the stability of the trapping is ruled by a Hill's equation. This unexpectedly demonstrates that an EIBT, in the reference frame of the ions works very similar to a quadrupole trap. The parallelism between these two kinds of traps is illustrated by comparing experimental and theoretical stability diagrams of the EIBT. The main difference with quadrupole traps is that the stability depends only on the ratio of the acceleration and trapping electrostatic potentials, not on the mass nor the charge of the ions. All kinds of ions can be trapped simultaneously and since parametric resonances are proportional to the square root of the charge/mass ratio the EIBT can be used as a mass spectrometer of infinite mass range

Derived bracket construction and Manin products

We will extend the classical derived bracket construction to any algebra over a binary quadratic operad. We will show that the derived product construction is a functor given by the Manin white product with the operad of permutation algebras. As an application, we will show that the operad of prePoisson algebras is isomorphic to Manin black product of the Poisson operad with the preLie operad. We will show that differential operators and Rota-Baxter operators are, in a sense, Koszul dual to each other.Comment: This is the final versio

Critical exponents of directed percolation measured in spatiotemporal intermittency

A new experimental system showing a transition to spatiotemporal intermittency is presented. It consists of a ring of hundred oscillating ferrofluidic spikes. Four of five of the measured critical exponents of the system agree with those obtained from a theoretical model of directed percolation.Comment: 7 pages, 12 figures, submitted to PR

Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled in detail, is the existence of a second Hopf algebra structure. By comparing group-like elements in suitable completions of these two Hopf algebras, we derive a particular map which we dub post-Lie Magnus expansion. These results are then considered in the case of Semenov-Tian-Shansky's double Lie algebra, where a post-Lie algebra is defined in terms of solutions of modified classical Yang-Baxter equation. In this context, we prove a factorization theorem for group-like elements. An explicit exponential solution of the corresponding Lie bracket flow is presented, which is based on the aforementioned post-Lie Magnus expansion.Comment: 49 pages, no-figures, review articl

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

Technical report: liquid overlay technique allows the generation of homogeneous osteosarcoma, glioblastoma, lung and prostate adenocarcinoma spheroids that can be used for drug cytotoxicity measurements

Introduction: The mechanisms involved in cancer initiation, progression, drug resistance, and disease recurrence are traditionally investigated through in vitro adherent monolayer (2D) cell models. However, solid malignant tumor growth is characterized by progression in three dimensions (3D), and an increasing amount of evidence suggests that 3D culture models, such as spheroids, are suitable for mimicking cancer development. The aim of this report was to reaffirm the relevance of simpler 3D culture methods to produce highly reproducible spheroids, especially in the context of drug cytotoxicity measurements. Methods: Human A549 lung adenocarcinoma, LnCaP prostate adenocarcinoma, MNNG/HOS osteosarcoma and U251 glioblastoma cell lines were grown into spheroids for 20 days using either Liquid Overlay Technique (LOT) or Hanging Drop (HD) in various culture plates. Their morphology was examined by microscopy. Sensitivity to doxorubicin was compared between MNNG/HOS cells grown in 2D and 3D. Results: For all cell lines studied, the morphology of spheroids generated in round-bottom multiwell plates was more repeatable than that of those generated in flat-bottom multiwell plates. HD had no significant advantage over LOT when the spheroids were cultured in round-bottom plates. Finally, the IC50 of doxorubicin on MNNG/HOS cultured in 3D was 18.8 times higher than in 2D cultures (3D IC50 = 15.07 ± 0.3 µM; 2D IC50 = 0.8 ± 0.4 µM; *p < 0.05). Discussion: In conclusion, we propose that the LOT method, despite and because of its simplicity, is a relevant 3D model for drug response measurements that could be scaled up for high throughput screening

Avalanches in the Weakly Driven Frenkel-Kontorova Model

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values a erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power-laws which is a key feature of self-organized criticality (SOC). It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For strong damping a regular behavior occurs where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are build up by sound waves and shock waves. Shock waves can turn their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in Phys. Rev.

On post-Lie algebras, Lie--Butcher series and moving frames

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie algebras, used in numerical analysis to study geometric properties of flows on euclidean spaces. Motivated by the analysis of flows on manifolds and homogeneous spaces, we investigate algebras arising from flat connections with constant torsion, leading to the definition of post-Lie algebras, a generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately associated with euclidean geometry, post-Lie algebras occur naturally in the differential geometry of homogeneous spaces, and are also closely related to Cartan's method of moving frames. Lie--Butcher series combine Butcher series with Lie series and are used to analyze flows on manifolds. In this paper we show that Lie--Butcher series are founded on post-Lie algebras. The functorial relations between post-Lie algebras and their enveloping algebras, called D-algebras, are explored. Furthermore, we develop new formulas for computations in free post-Lie algebras and D-algebras, based on recursions in a magma, and we show that Lie--Butcher series are related to invariants of curves described by moving frames.Comment: added discussion of post-Lie algebroid

Three-dimensional in vitro culture models in oncology research

Cancer is a multifactorial disease that is responsible for 10 million deaths per year. The intra- and inter-heterogeneity of malignant tumors make it difficult to develop single targeted approaches. Similarly, their diversity requires various models to investigate the mechanisms involved in cancer initiation, progression, drug resistance and recurrence. Of the in vitro cell-based models, monolayer adherent (also known as 2D culture) cell cultures have been used for the longest time. However, it appears that they are often less appropriate than the three-dimensional (3D) cell culture approach for mimicking the biological behavior of tumor cells, in particular the mechanisms leading to therapeutic escape and drug resistance. Multicellular tumor spheroids are widely used to study cancers in 3D, and can be generated by a multiplicity of techniques, such as liquid-based and scaffold-based 3D cultures, microfluidics and bioprinting. Organoids are more complex 3D models than multicellular tumor spheroids because they are generated from stem cells isolated from patients and are considered as powerful tools to reproduce the disease development in vitro. The present review provides an overview of the various 3D culture models that have been set up to study cancer development and drug response. The advantages of 3D models compared to 2D cell cultures, the limitations, and the fields of application of these models and their techniques of production are also discussed