Manipulation of single-photon states encoded in transverse spatial modes: possible and impossible tasks

Controlled generation and manipulation of photon states encoded in their spatial degrees of freedom is a crucial ingredient in many quantum information tasks exploiting higher-than-two dimensional encoding. Here, we prove the impossibility to arbitrarily modify $d$-level state superpositions (qu$d$its) for $d>2$, encoded in the transverse modes of light, with optical components associated to the group of symplectic transforms (Gaussian operations). Surprisingly, we also provide an explicit construction of how non-Gaussian operations acting on mode subspaces do enable to overcome the limit $d=2$. In addition, this set of operations realizes the full SU(3) algebra.Comment: Published in PR

Spin and Orbital angular momentum propagation in anisotropic media: theory

This paper is devoted to study the propagation of light beams carrying orbital angular momentum in optically anisotropic media. We first review some properties of homogeneous anisotropic media, and describe how the paraxial formalism is modified in order to proceed with a new approach dealing with a general setting of paraxial propagation along uniaxial inhomogeneous media. This approach is suitable for describing the space-variant-optical-axis phase plates

Spin-induced angular momentum switching

When light is transmitted through optically inhomogeneous and anisotropic media the spatial distribution of light can be modified according to its input polarization state. A complete analysis of this process, based on the paraxial approximation, is presented, and we show how it can be exploited to produce a spin-controlled-change in the orbital angular momentum of light beams propagating in patterned space-variant-optical-axis phase plates. We also unveil a new effect. The development of a strong modulation in the angular momentum change upon variation of the optical path through the phase plates.Comment: The original paper of the published version in Opt. Let

Hypoxic Cell Waves around Necrotic Cores in Glioblastoma: A Biomathematical Model and its Therapeutic Implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hiperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.Comment: 29 pages, 9 figure

Combined therapies of antithrombotics and antioxidants delay in silico brain tumor progression

Glioblastoma multiforme, the most frequent type of primary brain tumor, is a rapidly evolving and spatially heterogeneous high-grade astrocytoma that presents areas of necrosis, hypercellularity and microvascular hyperplasia. The aberrant vasculature leads to hypoxic areas and results in an increase of the oxidative stress selecting for more invasive tumor cell phenotypes. In our study we assay in silico different therapeutic approaches which combine antithrombotics, antioxidants and standard radiotherapy. To do so, we have developed a biocomputational model of glioblastoma multiforme that incorporates the spatio-temporal interplay among two glioma cell phenotypes corresponding to oxygenated and hypoxic cells, a necrotic core and the local vasculature whose response evolves with tumor progression. Our numerical simulations predict that suitable combinations of antithrombotics and antioxidants may diminish, in a synergetic way, oxidative stress and the subsequent hypoxic response. This novel therapeutical strategy, with potentially low or no toxicity, might reduce tumor invasion and further sensitize glioblastoma multiforme to conventional radiotherapy or other cytotoxic agents, hopefully increasing median patient overall survival time.Comment: 8 figure

Chemical Reactions Using a Non-Equilibrium Wigner Function Approach

A three-dimensional model of binary chemical reactions is studied. We consider an ab initio quantum two-particle system subjected to an attractive interaction potential and to a heat bath at thermal equilibrium at absolute temperature T>0 . Under the sole action of the attraction potential, the two particles can either be bound or unbound to each other. While at T=0 , there is no transition between both states, such a transition is possible when T>0 (due to the heat bath) and plays a key role as kBT approaches the magnitude of the attractive potential. We focus on a quantum regime, typical of chemical reactions, such that: (a) the thermal wavelength is shorter than the range of the attractive potential (lower limit on T) and (b) (3/2)kBT does not exceed the magnitude of the attractive potential (upper limit on T). In this regime, we extend several methods previously applied to analyze the time duration of DNA thermal denaturation. The two-particle system is then described by a non-equilibrium Wigner function. Under Assumptions (a) and (b), and for sufficiently long times, defined by a characteristic time scale D that is subsequently estimated, the general dissipationless non-equilibrium equation for the Wigner function is approximated by a Smoluchowski-like equation displaying dissipation and quantum effects. A comparison with the standard chemical kinetic equations is made. The time τ required for the two particles to transition from the bound state to unbound configurations is studied by means of the mean first passage time formalism. An approximate formula for τ, in terms of D and exhibiting the Arrhenius exponential factor, is obtained. Recombination processes are also briefly studied within our framework and compared with previous well-known methods

A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting.This research has been supported by grants awarded to VMPG by James S. Mc. Donnell Foundation, United States of America, 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer (collaborative award 220020560) and Junta de Comunidades de Castilla-La Mancha, Spain (grant number SBPLY/17/180501/000154). VMPG and GFC thank the funding from Ministerio de Ciencia e Innovacion, Spain (grant number PID2019-110895RB-I00). This research has also been supported by a grant awarded to GFC and JBB by the Junta de Comunidades de Castilla-La Mancha, Spain (grant number SBPLY/19/180501/000211). AMR received support from Asociacion Pablo Ugarte (http://www.asociacionpablougarte.es). JJS received support from Universidad de Castilla-La Mancha (grant number 2020-PREDUCLM-15634). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field

We put forward a method that allows the experimental determination of the entire spatial mode spectrum of any arbitrary monochromatic wave field in a plane normal to its propagation direction. For coherent optical fields, our spatial spectrum analyzer can be implemented with a small number of benchmark refractive elements embedded in a single Mach-Zehnder interferometer. We detail an efficient setup for measuring in the Hermite-Gaussian mode basis. Our scheme should also be feasible in the context of atom optics for analyzing the spatial profiles of macroscopic matter waves

CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathematical models

Immunotherapies use components of the patient immune system to selectively target cancer cells. The use of CAR T cells to treat B-cell malignancies --leukaemias and lymphomas-- is one of the most successful examples, with many patients experiencing long-lasting complete responses to this therapy. This treatment works by extracting the patient's T cells and adding them the CAR group, which enables them to recognize and target cells carrying the antigen CD19+, that is expressed in these haematological tumors. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T-cells. The model accounts for mature and progenitor B-cells, tumor cells, CAR T cells and side effects by incorporating the main biological processes involved. The model explains the early post-injection dynamics of the different compartments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that provides the maximum CAR T cell expansion in-vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19+ tumor relapses could be the result of the competition between tumor and CAR T cells analogous to predator-prey dynamics. We discuss this fact on the light of available evidences and the possibility of controlling relapses by early re-challenging of the tumor with stored CAR T cells

Las palmas entre los grupos cazadores-recolectores de la amazonia colombiana

We compare past and present systems of management of palms in the Colombian Amazon, based on archaeological studies of preceramic groups in the middle Caquetá region and ethnographic research on the nomadic Nukak people, who inhabit northeastern Guaviare department. Astrocaryum aculeatum, Attalea maripe, Mauritia flexuosa, Oenocarpus bataua, Oenocarpus bacaba y Oenocarpus mapora, have been used from the early Holocene through the present time. Among these, Oenocarpus bataua has remained the most important food species. We conclude that one of the mananging strategies of the tropical rain forest is the simultaneous improvement of ecological units, especially in the tertiary sedimentary plains, and that such management probably has a long history in the region.Se presenta una comparación sobre el manejo de las palmas en la Amazonia Colombiana, basado en los resultados de un estudio arqueológico de grupos precerámicos en la región del Medio Caquetá y uno etnográfico del pueblo nómada Nukak que habita la zona nororiental del departamento del Guaviare. Se encontró que Astrocaryum aculeatum, A ttalea maripa, Mauritia flexuosa, Oenocarpus bataua, Oenocarpus bacaba y Oenocarpus mapora son algunas de las palmas usadas desde el Holoceno temprano hasta el presente. Entre estas Oenocarpus bataua es la especie más importante como fuente de alimento. Así mismo, se concluye que una de las estrategias de manejo en el bosque húmedo tropical es el aprovechamiento simultáneo de diferentes unidades ecológicas, con predominio del plano sedimentario terciario. Es probable que este tipo de manejo tenga en la región una larga historia