Non-Paraxial Accelerating Beams

We present the spatially accelerating solutions of the Maxwell equations. Such non-paraxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams. For both TE and TM polarizations, the beams exhibit shape-preserving bending with sub-wavelength features, and the Poynting vector of the main lobe displays a turn of more than 90 degrees. We show that these accelerating beams are self-healing, analyze their properties, and compare to the paraxial Airy beams. Finally, we present the new family of periodic accelerating beams which can be constructed from our solutions

Lower bounds on the size of semidefinite programming relaxations

We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the linear image of the feasible region of any SDP (i.e., any spectrahedron) of dimension less than $2^{n^c}$, for some constant $c > 0$. This result yields the first super-polynomial lower bounds on the semidefinite extension complexity of any explicit family of polytopes. Our results follow from a general technique for proving lower bounds on the positive semidefinite rank of a matrix. To this end, we establish a close connection between arbitrary SDPs and those arising from the sum-of-squares SDP hierarchy. For approximating maximum constraint satisfaction problems, we prove that SDPs of polynomial-size are equivalent in power to those arising from degree-$O(1)$ sum-of-squares relaxations. This result implies, for instance, that no family of polynomial-size SDP relaxations can achieve better than a 7/8-approximation for MAX-3-SAT

Field theoretic approach to the counting problem of Hamiltonian cycles of graphs

A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around the saddle point, one obtains an estimate for the number which reflects characteristics of graphs well. The accuracy of the estimate is verified by applying it to 2d square lattices with various boundary conditions. This is the first example of extracting meaningful information from the quadratic approximation to the field theory representation.Comment: 5 pages, 3 figures, uses epsf.sty. Estimates for the site entropy and the gamma exponent indicated explicitl

The effects of the pre-pulse on capillary discharge extreme ultraviolet laser

In the past few years collisionally pumped extreme ultraviolet (XUV) lasers utilizing a capillary discharge were demonstrated. An intense current pulse is applied to a gas filled capillary, inducing magnetic collapse (Z-pinch) and formation of a highly ionized plasma column. Usually, a small current pulse (pre-pulse) is applied to the gas in order to pre-ionize it prior to the onset of the main current pulse. In this paper we investigate the effects of the pre-pulse on a capillary discharge Ne-like Ar XUV laser (46.9nm). The importance of the pre-pulse in achieving suitable initial conditions of the gas column and preventing instabilities during the collapse is demonstrated. Furthermore, measurements of the amplified spontaneous emission (ASE) properties (intensity, duration) in different pre-pulse currents revealed unexpected sensitivity. Increasing the pre-pulse current by a factor of two caused the ASE intensity to decrease by an order of magnitude - and to nearly disappear. This effect is accompanied by a slight increase in the lasing duration. We attribute this effect to axial flow in the gas during the pre-pulse.Comment: 4 pages, 4 figure

Some Controversial Opinions on Software-Defined Data Plane Services

Several recent proposals, namely Software Defined Networks (SDN), Network Functions Virtualization (NFV) and Network Service Chaining (NSC), aim to transform the network into a programmable platform, focusing respectively on the control plane (SDN) and on the data plane (NFV/NSC). This paper sits on the same line of the NFV/NSC proposals but with a more long-term horizon, and it presents its considerations on some controversial aspects that arise when considering the programmability of the data plane. Particularly, this paper discusses the relevance of data plane vs control plane services, the importance of the hardware platform, and the necessity to standardize northbound and southbound interfaces in future software-defined data plane service

Improving heterogeneous system efficiency : architecture, scheduling, and machine learning

Computer architects are beginning to embrace heterogeneous systems as an effective method to utilize increases in transistor densities for executing a diverse range of workloads under varying performance and energy constraints. As heterogeneous systems become more ubiquitous, architects will need to develop novel CPU scheduling techniques capable of exploiting the diversity of computational resources. In recognizing hardware diversity, state-of-the-art heterogeneous schedulers are able to produce significant performance improvements over their predecessors and enable more flexible system designs. Nearly all of these, however, are unable to efficiently identify the mapping schemes which will result in the highest system performance. Accurately estimating the performance of applications on different heterogeneous resources can provide a significant advantage to heterogeneous schedulers for identifying a performance maximizing mapping scheme to improve system performance. Recent advances in machine learning techniques including artificial neural networks have led to the development of powerful and practical prediction models for a variety of fields. As of yet, however, no significant leaps have been taken towards employing machine learning for heterogeneous scheduling in order to maximize system throughput. The core issue we approach is how to understand and utilize the rise of heterogeneous architectures, benefits of heterogeneous scheduling, and the promise of machine learning techniques with respect to maximizing system performance. We present studies that promote a future computing model capable of supporting massive hardware diversity, discuss the constraints faced by heterogeneous designers, explore the advantages and shortcomings of conventional heterogeneous schedulers, and pioneer applying machine learning to optimize mapping and system throughput. The goal of this thesis is to highlight the importance of efficiently exploiting heterogeneity and to validate the opportunities that machine learning can offer for various areas in computer architecture.Arquitectos de computadores estan empesando a diseñar systemas heterogeneos como una manera efficiente de usar los incrementos en densidades de transistors para ejecutar una gran diversidad de programas corriendo debajo de differentes condiciones y requisitos de energia y rendimiento (performance). En cuanto los sistemas heterogeneos van ganando popularidad de uso, arquitectos van a necesitar a diseñar nuevas formas de hacer el scheduling de las applicaciones en los cores distintos de los CPUs. Schedulers nuevos que tienen en cuenta la heterogeniedad de los recursos en el hardware logran importantes beneficios en terminos de rendimiento en comparacion con schedulers hecho para sistemas homogenios. Pero, casi todos de estos schedulers heterogeneos no son capaz de poder identificar la esquema de mapping que produce el rendimiento maximo dado el estado de los cores y las applicaciones. Estimando con precision el rendimiento de los programas ejecutando sobre diferentes cores de un CPU es un a gran ventaja para poder identificar el mapping para lograr el mejor rendimiento posible para el proximo scheduling quantum. Desarollos nuevos en la area de machine learning, como redes neurales, han producido predictores muy potentes y con gran precision in disciplinas numerosas. Pero en estos momentos, la aplicacion de metodos de machine learning no se han casi explorados para poder mejorar la eficiencia de los CPUs y menos para mejorar los schedulers para sistemas heterogeneos. El tema de enfoque en esta tesis es como poder entender y utilizar los sistemas heterogeneos, los beneficios de scheduling para estos sistemas, y como aprovechar las promesas de los metodos de machine learning con respeto a maximizer el redimiento de el Sistema. Presentamos estudios que dan una esquema para un modelo de computacion para el futuro capaz de dar suporte a recursos heterogeneos en gran escala, discutimos las restricciones enfrentados por diseñadores de sistemas heterogeneos, exploramos las ventajas y desventajas de las ultimas schedulers heterogeneos, y abrimos el camino de usar metodos de machine learning para optimizer el mapping y rendimiento de un sistema heterogeneo. El objetivo de esta tesis es destacar la imporancia de explotando eficientemente la heterogenidad de los recursos y tambien validar las oportunidades para mejorar la eficiencia en diferente areas de arquitectura de computadoras que pueden ser realizadas gracias a machine learning.Postprint (published version

The Effect of Neutral Atoms on Capillary Discharge Z-pinch

We study the effect of neutral atoms on the dynamics of a capillary discharge Z-pinch, in a regime for which a large soft-x-ray amplification has been demonstrated. We extended the commonly used one-fluid magneto-hydrodynamics (MHD) model by separating out the neutral atoms as a second fluid. Numerical calculations using this extended model yield new predictions for the dynamics of the pinch collapse, and better agreement with known measured data.Comment: 4 pages, 4 postscript figures, to be published in Phys. Rev. Let