Lost and found: the radial quantum number of Laguerre-Gauss modes

We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.Comment: Some minor typos fixed

On the Detection of CMB B-modes from Ground at Low Frequency

The primordial CMB $B$-mode search is on the spotlight of the scientific community due to the large amount of cosmological information that is encoded in the primeval signal. However, the detection of this signal is challenging from the data analysis point of view, due to the relative low amplitude compared to the foregrounds, the lensing contamination coming from the leakage of $E$-modes, and the instrumental noise. Here, we studied the viability of the detection of the primordial polarization $B$-mode with a ground-based telescope operating in the microwave low-frequency regime (i.e., from 10GHz-120GHz) in a handful of different scenarios: i. the instrument's channels distribution and noise, ii. the tensor-to-scalar ratio ($r$) detectability considering different possible $r$ values and degrees of delensing, iii. the effect of including a possible source of polarized anomalous microwave emission (AME), iv. the strengths and weaknesses of different observational strategies and, v. the atmospheric and systematic noise impact on the recovery. We focused mainly on the removal of galactic foregrounds as well as noise contamination by applying a full-parametric pixel-based maximum likelihood component separation technique. Moreover, we developed a numerical methodology to estimate the residuals power spectrum left after component separation, which allow us to mitigate possible biases introduced in the primordial $B$-mode power spectrum reconstruction. Among many other results, we found that this sort of experiment is capable of detecting Starobinsky's $r$ even when no delensing is performed or, a possible polarized AME contribution is taken into account. Besides, we showed that this experiment is a powerful complement to other on-ground or satellite missions, such as LiteBIRD, since it can help significantly with the low-frequency foregrounds characterization.Comment: 28 pages, 18 figures, submitted to JCA

Linear programming model to minimize the production costs of an adhesive tape company

Production in large quantities of different varieties of products creates issues in finding an optimal planning solution. Adhesive tapes companies face that challenge. A multi-phased methodology is proposed to minimize production costs. In this it is considered different production variables. First phase divided a problem into subproblems to minimize computational complexity through an incidence matrix. Second phase formulated a linear programming model to determine production optimal batch sizes. Consequently, model is applied in a real company. Results showed a decrease in production costs in a range of 14%-43% for the different manufactured groups of components. In this way it is expected that more companies can apply similar models to improve their production indicators

Stability of the selfsimilar dynamics of a vortex filament

In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (LIE). Our main result is the stability of the selfsimilar dynamics of small pertubations of a given selfsimilar solution. The proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations. A main ingredient in the proof is the control of the evolution of weighted norms for a cubic 1-D Schr\"odinger equation, connected to the binormal flow by Hasimoto's transform.Comment: revised version, 36 page

Leveraging on Digital Signage Networks to Bring Connectivity IOT Devices

The number of Internet-connected devices exceeds the world’s population by more than three times and this figure is expected to be doubled within the next five years. The Internet of Things is a concept that describes this trend and outlines certain aspects of design and functionality that new devices should incorporate for a successful integration into the Internet. In this respect, Digital Signage networks traditionally used for audiovisual media, accomplish many of the characteristics of the Internet of Things devices: interoperability, mobility, scalability and ubiquity, both in terms of access and control of devices and regarding the information they generate. This paper raises the power to employ a proposed Digital Signage network as a substrate to connect other types of devices that can benefit from the advantages of this kind of networks. For that aim, the main problems for this integration are discussed, mainly those related to the bidirectional tunneling scheme used in the proposed Digital Signage solution. The effects of this tunneling approach are analyzed in scenarios with bandwidth constraints, and different solutions are proposed. Tunneling performance in mobility is improved, to increase the amount of Internet of Things devices and applications that can benefit from this type of network. El número de dispositivos conectados a Internet supera actualmente a la población mundial por más de tres veces y se espera que esta cifra se duplique en los próximos cinco años. El Internet de las Cosas es un concepto que describe esta tendencia y perfila ciertos aspectos de diseño y funcionalidad que los nuevos dispositivos deben incorporar para lograr una integración exitosa en Internet. En este sentido, las redes digital signage utilizadas tradicionalmente para los medios de comunicación audiovisual cumplen muchas de las características requeridas en el contexto del Internet de las Cosas: interoperabilidad, movilidad, escalabilidad y ubicuidad; relativas tanto al acceso y control de dispositivos como a la información que estos generan. En este trabajo se plantea el poder de emplear la red digital signage propuesta como sustrato para poder conectar otros tipos de dispositivos para que así puedan aprovechar las ventajas de estas redes. Para ese fin, se discuten los principales problemas existentes en esta integración, prestando especial atención al esquema de túnel bidireccional utilizado en la solución digital signage propuesta. Los efectos de este enfoque de tunelación se analizan en escenarios con limitaciones de ancho de banda y se proponen diferentes soluciones. Con ello se consigue mejorar el rendimiento del túnel en movilidad, facilitando la integración de más dispositivos al Internet de las Cosas al permitir que puedan integrarse en este tipo de redes

Redes Digital Signage como sustrato para brindar conectividad a dispositivos IoT

El número de dispositivos conectados a Internet supera actualmente a la población mundial por más de tres veces y previsiblemente, esta cifra se duplicará en cinco años. El Internet de las Cosas es un concepto que describe esta tendencia y perfila ciertos aspectos de diseño y funcionalidad que los nuevos dispositivos deben incorporar para lograr una integración exitosa en Internet. En este sentido, las redes Digital Signage empleadas tradicionalmente para difundir comunicación audiovisual, cumplen muchas de las características recogidas en el paradigma del Internet de las Cosas. En este trabajo se plantea el poder emplear la red Digital Signage propuesta como sustrato para conectar otros tipos de dispositivos que puedan beneficiarse de las ventajas de estas redes, especialmente en escenarios de movilidad. Tras analizar los problemas de latencia inherentes a este esquema de comunicación y presentar soluciones factibles, se concluye que esta propuesta sería funcional en dispositivos móviles.The number of Internet-connected devices exceeds the world's population by more than three times and this figure is expected to be doubled within the next five years. The Internet of Things is a concept that describes this trend and outlines certain aspects of design and functionality that new devices should incorporate for a successful integration into the Internet. In this respect, Digital Signage networks traditionally used for audiovisual media, accomplish many of the characteristics of the Internet of Things devices. This paper raises the power to employ a proposed Digital Signage network as a substrate to connect other types of devices that can benefit from the advantages of this kind of networks, particularly in mobility scenarios. After analyzing the latency issues arising from this communication scheme and presenting feasible solutions, it is concluded that this proposal would be functional on mobile devices