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In questioning the completeness of quantum mechanics, Einstein–Podolsky–Rosen (EPR) claimed that from the outcomes of local experiments performed on an entangled system, it was possible to ascribe simultaneous reality to the values of certain incompatible observables. As EPR acknowledged, the inevitable disturbance of quantum measurements prevents the precise verification of these assertions on a single system. However, the EPR elements of reality can still be tested at the ensemble level through weak measurements—which minimally disturb the measured system—by interpreting the EPR assertions as assertions about weak values that follow from the outcomes of projective measurements. Here, we report an implementation of such a test through joint weak measurements followed by post-selection on polarization-entangled photon pairs. Our results show that there is a correspondence between the obtained joint weak values and the inferred elements of reality in the polarization version of the EPR assertions. In their seminal but controversial paper, Einstein–Podolsky–Rosen (EPR) claimed that one could infer simultaneous values of certain non-commuting observables. Using weak and strong measurements in entangled photons, the authors show a correspondence between joint weak values and the inferred elements of reality in the polarization version of the EPR assertions.

Este artículo cuantifica los efectos sobre la actividad productiva en Colombia que tiene la pandemia por COVID-19 y las medidas de contención, mitigación y recu­peración adoptadas para enfrentarla. Además, se estudian los efectos distributivos, considerando distintos tipos de hogares, para analizar su impacto en los secto­res más vulnerables de la economía. Para ello, se construyó un modelo CGE que resume el comportamiento de la economía colombiana y permite simular los cho­ques por COVID-19. Se encontró un crecimiento económico de 4,6 % en 2021 que sería insuficiente para que el PIB alcance niveles prepandemia. Los efectos socia­les serían devastadores en términos de pobreza, que luego de elevarse en cerca de ocho puntos porcentuales durante 2020, podría seguir aumentando hacia 2021 por efecto de la parcial recuperación de los mercados laborales.

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability distributions converge to the value of the moment map. For invertible states we prove that the measures satisfy the large deviation principle with an explicitly given rate function., 24 pages. See related work today by Franks and Walter

As shown in Aharonov (Phys Rev A 72(5):052111, 2005), in an arbitrary-strength quantum measurement performed on a pre- and post-selected system, the quantum state that describes the conditional response of the apparatus can be decomposed as a superposition of states, each of which encodes a weak measurement of the measured observable. In this paper, we introduced a new scheme of weak value tomography, which allows one to image the weak measurement components underlying the spectral distributions of a strong measurement. We also show how coarse-grained features of the strong spectral distributions can be connected to features that can be extracted from the weak value tomography of a strong measurement.

Spanish Abstract: Este paper describe la transicion energetica que ha tenido el Reino Unido para alcanzar una generacion mediante energias renovables del 25% en 2016 y reducir las emisiones per capita de CO2, las cuales pasaron de 10.744.1 kg CO2/pc en 1990 a 6.560.2 en 2016. Pero al mismo tiempo estudios empiezan a evidenciar que a pesar de que la reforma de este mercado electrico ha dado un gran paso hacia adelante, aun enfrenta serios desafios debido a la reduccion de los mecanismos de apoyo de la energia renovable y a la inestabilidad politica que ha tenido esta economia y, por tanto, los inversionistas han optado por concentrarse en la gestion de sus activos existentes en lugar de planear un mayor crecimiento. English Abstract: This paper describes the UK's energy transition to achieve 25% renewable energy generation by 2016 and reduce per capita CO2 emissions from 10,744.1 kg CO2/pc in 1990 to 6,560.2 in 2016. But at the same time, studies are beginning to show that although the reform of the electricity market in the United Kingdom has taken a big step forward, it still faces serious challenges due to the reduction of support mechanisms for renewable energy and the political instability that this economy has had, and, therefore, investors have chosen to concentrate on managing their existing assets rather than planning for further growth.

Spanish Abstract: La politica energetica alemana ha sido, sin duda, un referente a nivel mundial enlo relativo a energias renovables. Con la implementacion de la Ley de energias renovables (Erneuerbare Energien Gesetz) en 2000, el 36% del consumo bruto de electricidad en 2018 provino de fuentes renovables. Ademas, las emisiones de gases de efecto invernadero cayeron en 328 millones de toneladas entre 1990 y 2016, al pasar de 1264 a 936 mill ton de CO2. No obstante, esto tambien ha incrementado el costo de las restricciones, en 2017, alcanzo un nuevo record de 1400 millones de euros y el precio al consumidor final se incremento sustancialmente, siendo uno de los mas altos de la Union Europea, pero ya han venido reduciendose, conforme ha reducido el costo de las nuevas tecnologias. Aun asi, el consenso de la sociedad, es que vale la pena pagar esos sobrecostos. Por tanto, es importante conocer el programa de transicion energetica que ha vivido Alemania y sus efectos, el cual es el objetivo de este paper. English Abstract: Despite the fact that the installed capacity in nuclear energy in the French electricity market still represents the highest percentage, 47% in 2017, non-conventional renewable energies resources, wind and solar, already represent 17% of the total installed capacity; however, in terms of generation, 70% remains nuclear. Furthermore, this market is one of the few in the European Union that has implemented a reliability mechanism and where the tariff for the provision of electricity service promotes a demand response program based on critical peak prices, in order to guarantee the reliability of supply. It is therefore important to know the energy transformation program launched in 2015 in France in order to promote green growth, reduce greenhouse emissions and strengthen energy independence; moreover, what has been done to implement smart grids in this market, which is the aim of this paper.

Spanish Abstract: La politica energetica alemana ha sido, sin duda, un referente a nivel mundial enlo relativo a energias renovables. Con la implementacion de la Ley de energias renovables (Erneuerbare Energien Gesetz) en 2000, el 36% del consumo bruto de electricidad en 2018 provino de fuentes renovables. Ademas, las emisiones de gases de efecto invernadero cayeron en 328 millones de toneladas entre 1990 y 2016, al pasar de 1264 a 936 mill ton de CO2. No obstante, esto tambien ha incrementado el costo de las restricciones, en 2017, alcanzo un nuevo record de 1400 millones de euros y el precio al consumidor final se incremento sustancialmente, siendo uno de los mas altos de la Union Europea, pero ya han venido reduciendose, conforme ha reducido el costo de las nuevas tecnologias. Aun asi, el consenso de la sociedad, es que vale la pena pagar esos sobrecostos. Por tanto, es importante conocer el programa de transicion energetica que ha vivido Alemania y sus efectos, el cual es el objetivo de este paper English Abstract: German energy policy has undoubtedly been a worldwide benchmark for renewable energy. With the implementation of the Renewable Energy Sources Act in 2000, 36% of gross electricity consumption in 2018 came from renewable sources. In addition, greenhouse gas emissions fell by 328 million tonnes between 1990 and 2016. However, this has also increased the cost of stabilizing the grid, reaching a new record of 1.4 billion euros in 2017 and the price to the final consumer increased substantially, being one of the highest in the European Union. However, it has already been reducing, as it has reduced the cost of new technologies. Even so, the consensus of society is that these extra costs are worth paying. Therefore, it is important to know the energy transition program that Germany has experienced and its effects, which is the objective of this paper.

The problem of N particles interacting through pairwise central forces is notoriously intractable for N ≥ 3 . Some remarkable specific cases have been solved in one dimension. Here we show that the guiding center approximation—valid for charges moving in two dimensions in the limit of large constant magnetic fields—simplifies the three-body problem for an arbitrary interparticle interaction invariant under rotations and translations, making it solvable by quadratures. A spinorial representation for the system is introduced, which allows a visualization of its phase space as the corresponding Bloch sphere. Finally, a discussion of the quantization of the problem is presented.

We propose a multipartite extension of Matsumoto and Hayashi's distortion-free entanglement concentration protocol, which takes $n$ copies of a general multipartite state and, via local measurements, produces a maximally-entangled multipartite state between local spaces of dimensions $\sim 2^{n E_i}$, where $E_i$ are the local entropies of the input state. However, the extended protocol is generally not universal in the sense that for the same measurement outcomes, the output state will still depend on the input state. Our main result is that when specialized to any state in the multiqubit W class, the protocol is also universal, so that as in the biparatite version, the output is a unique, maximally-entangled state for each given set of measurement outcomes. Our analysis brings to the forefront a new and interesting family of maximally-entangled multipartite states, which we term Kronecker states. A recurrence relation to obtain the coefficients of the W-class Kronecker states is also given., Comment: 13 pages, 3 figures. Paper has been sectioned and an additional section has been included where we show how to calculate the coefficients of the W-class Kronecker states

En este trabajo se aborda un modelo de equilibrio general dinamico estocastico neoclasico para comprobar el efecto de la politica monetaria convencional y no convencional sobre la actividad economica y los precios. Los resultados muestran que en una economia abierta y pequena con tipo de cambio flexible, un choque negativo de politica monetaria no convencional, generado a traves de una disminucion en las reservas internacionales, disminuye el producto, el empleo, empeora la balanza comercial y tiene efectos sobre los precios via disminucion del circulante. Por su parte, un choque negativo de politica monetaria convencional (aumento de la tasa de interes) afecta negativamente el producto, disminuye la inflacion y genera una reevaluacion de la tasa de cambio. Lo anterior es evidencia de que los bancos centrales disponen no solo de la tasa de interes como instrumento principal de politica, sino tambien de intervenciones no convencionales, via la hoja balance, que pueden afectar tambien a otras variables, como la tasa de cambio.

La restricción cuantitativa a las importaciones produce una distorsión en el mecanismo e mercado, pues impide que los agentes económicos realicen sus planes de consumo. En el presente artículo se presenta un modelo sencillo, basado en la función de Armington, para analizar los efectos que sobre el bienestar del consumidor producen tales restricciones, se presenta una cuantificación de la pérdida de bienestar de los consumidores colombianos con motivo de la restricción existente en 1985, y se discute el concepto de precio equivalente y su uso en la evaluación del racionamiento mediante modelos de equilibrio general computables.

Membrane mechanical elastic properties regulate a variety of cellular processes involving local membrane deformation, such as ion channel function and vesicle fusion. In this work, we used molecular dynamics simulations to estimate the local elastic properties of a membrane. For this, we calculated the energy needed to extract a DOPE lipid molecule, modified with a linker chain, from a POPC bilayer membrane using the umbrella sampling technique. Although the extraction energy entails several contributions related not only to elastic deformation but also to solvation, careful analysis of the potential of mean force (PMF) allowed us to dissect the elastic contribution. With this information, we calculated an effective linear spring constant of 44 ± 4 kJ·nm(-2)·mol(-1) for the DOPC membrane, in agreement with experimental estimates. The membrane deformation profile was determined independently during the stretching process in molecular detail, allowing us to fit this profile to a previously proposed continuum elastic model. Through this approach, we calculated an effective membrane spring constant of 42 kJ·nm(-2)·mol(-1), which is in good agreement with the PMF calculation. Furthermore, the solvation energy we derived from the data is shown to match the solvation energy estimated from critical micelle formation constants. This methodology can be used to determine how changes in lipid composition or the presence of membrane modifiers can affect the elastic properties of a membrane at a local level.

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form $\amp{\psi_f}{\psi}$, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established., Comment: 11 pages, 1 figure, revtex4

Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure inherent to quantum mechanics, which is naturally described in the language of weak values, and which is accessible experimentally via weak measurements. Using as an illustration, a gedanken-experiment due to Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence between a) a pair of classically contradictory assertions about the locations of an electron and a positron, and b) the results of weak measurements of their location. The internal consistency of these results is due to the novel way by which quantum mechanics "resolves" the paradox: first, by allowing for two distinguishable manifestations of how the electron and positron can be at the same location: either as single particles or as a pair; and secondly, by allowing these properties to take either sign. In particular, we discuss the experimental meaning of a {\em negative} number of electron-positron pairs., Comment: 7 pages, 1 figure

A number of important results in quantum information theory can be connected quite elegantly to the representation theory of the symmetric group through a quantum analogue of the classical information-theoretic "method of types" that arises naturally from the Schur-Weyl duality. We will give a brief introduction to this connection and brie y discuss some of the results that follow from it, such as quantum source compression rates, entanglement concentration rates, quantum entropy inequalities, and the admissisble spectra of partial density matrices from pure, multipartite entangled states.

Desarrollamos un modelo DSGE de la economia colombiana para evaluar el efecto de la politica fiscal sobre el empleo informal y distribucion del ingreso. El modelo recrea una economia pequena y abierta, con la persistente desigualdad de ingresos, un alto grado de informalidad, y las diferentes posibilidades de intervencion del gobierno. Este documento evalua las consecuencias de los pagos de transferencia del gobierno a los hogares con ingresos mas bajos. Encontramos que si bien los pagos de transferencias tienen un efecto positivo sobre la distribucion del ingreso, su financiacion requiere un ajuste en las finanzas publicas (reducir el gasto o aumentar los ingresos a traves del uso de diversos impuestos), tienen efectos negativos sobre la economia en su conjunto.

The concept of the weak value has proved to be a powerful and operationally grounded framework for the assignment of physical properties to a quantum system at any given time. More importantly, this framework has allowed us to identify a whole range of surprising quantum effects, or “miracles”, which are readily testable but which lie buried “under the noise” when the results of measurements are not post-selected. In all cases, these miracles have to do with the fact that weak values can take values lying outside the conventional ranges of quantum expectation values. We explore the extent to which such miracles are possible within the weak value framework. As we show, given appropriate initial and final states, it is generally possible to produce any set of weak values that is consistent with the linearity of weak values, provided that the states are entangled states of the system with some external ancillary system. Through a simple constructive proof, we obtain a recipe for arbitrary quantum miracles, and give examples of some interesting applications. In particular, we show how the classical description of an infinitely-localized point in phase-space is contained in the weak-value framework augmented by quantum entanglement. [Editor’s note: for a video of the talk given by Prof. Botero at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-27.]

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson's theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance., Comment: 34 pages, 7 figures. Paper has been restructured with first section presenting all the results, with proofs in subsequent sections

The folklore notion of the "Non-Locality of Quantum Mechanics" is examined from the point of view of hidden-variables theories according to Belinfante's classification in his Survey of Hidden Variables Theories. It is here shown that in the case of EPR, there exist hidden variables theories that successfully reproduce quantum-mechanical predictions, but which are explicitly local. Since such theories do not fall into Belinfante's classification, we propose an expanded classification which includes similar theories, which we term as theories of the "third" kind. Causal implications of such theories are explored. -Pacs: 03.65.Bz

What is light and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: Geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has been considered to be a very simple business as well. It's not so. As we show here the classical limit of quantum optics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects., 4 pages, 2 figures

Spanish Abstract: En este articulo se utiliza un modelo dinamico estocastico de equilibrio general (DSGE) neoclasico para evaluar el impacto de choques de oferta (productividad) y demanda (comercio externo) sobre el desempeno economico. Ademas, se analizan decisiones de politica economica, en especial, el efecto del gasto publico sobre la economia segun las condiciones en que este se realice. Los ejercicios realizados muestran que con un modelo de economia abierta, una politica expansiva de gasto publico incrementa en el corto plazo el empleo y el producto, pero se incurre en un costo futuro adicional, que parece sugerir un impacto superior al beneficio alcanzado en el corto plazo.English Abstract: We use a Dynamic Stochastic General Equilibrium (DSGE) model to evaluate the effect of supply (productivity) and demand (foreign trade) shocks on the economy. In addition, this paper analyzes the impact of policies, specifically the effect of public spending under given economic environments. Our results show that, in an open economy model, an expansionary policy of public spending increases employment and production in the short run, but carries an additional future cost, which appears to be greater than the short term benefit.

Entre las funciones del Fondo Nacional del Café –FNC- está la de garantizar a los productores la compra de la totalidad de su producción a un precio previamente establecido, y que es el mismo en todas las localidades donde existen pueblos de compra de las Cooperativas de Caficultores, independientemente de su distancia a los centros de acopio, de procesamiento o de exportación de café. Esta política de compra implica un subsidio a los productores de las regiones de más difícil acceso, por cuanto los gastos de transporte son asumidos por el Fondo. En éste artículo se exploran los efectos que tendría sobre el bienestar de los productores el cambio del actual sistema de precios por uno en el que se pagará el café a un precio único en el sitio de procesamiento. Se concluye que las variaciones en el excedente de los productores con respecto a su beneficio son, a lo sumo, del 5% hacia arriba o hacia abajo, según que resulten beneficiados o perjudicados con el cambio en el sistema de precios, y ello tanto si se supone una oferta de elasticidad constante como sise construye a partir de una función de producción tipo Cobb- Douglas.

Spanish Abstract: Los modelos de Equilibrio General Dinamico Estocastico (DSGE), parten de la teoria de equilibrio general aplicado que tiene influencia en la macroeconomia contemporanea. Su metodologia explica los fenomenos economicos agregados, derivados de los principios microeconomicos y, como elemento especial se tiene que no son vulnerables a la critica de Lucas. Ademas, toman en cuenta que la economia se ve afectada por perturbaciones aleatorias. En esta direccion, su analisis de tipo empirico apunta hacia la busqueda de los elementos generadores de las fluctuaciones economicas. En este trabajo se presenta una revision de literatura sobre la discusion teorica de las fluctuaciones economicas, con el fin de reflexionar acerca del desarrollo de la macroeconomia moderna, culminando dicha reflexion con un una resena de los DSGE.English Abstract: Models of Dynamic Stochastic General Equilibrium (DSGE) are based on the theory of general equilibrium that influences contemporary macroeconomics. This instrument explains the aggregate economic phenomena derived from microeconomic principles, and, as a special characteristic, the DSGE models are not vulnerable to the Lucas critique. Also, those consider that the economy is affected by random shocks. In this sense, empirical analysis seeks for the sources of economic fluctuations. This paper presents an overview of the theoretical literature on economic fluctuations in order to reflect on the development of modern macroeconomics, the reflection culminating with an overview of the DSGE

Spanish Abstract: El presente articulo presenta un modelo sencillo de acelerador financiero, en el que a partir de la solucion del problema de optimizacion intertemporal del flujo de renta del empresario en condiciones de competencia monopolistica, es posible evaluar el impacto de dichos descuentos, asi como tambien el impacto de la politica monetaria, sobre el stock deseado de capital y la inversion deseada. El modelo es un modelo de equilibrio parcial, pero ilustra adecuadamente la forma como la politica monetaria y la politica tributaria inciden sobre las decisiones de los empresarios, y puede ser integrado posteriormente a un modelos dinamicos de equilibrio general, que permitan formular de manera expresa las funciones de impulso-respuesta de las variables macroeconomicas a posibles shocks en las politicas monetaria y fiscal.English Abstract: There has been a lot of discussion in Colombia lately regarding the impact of the tax reduction on productive assets buying on investment. This paper presents a simple financial accelerator model, that departs from the intertemporal optimization problem of firms income flow under monopoly competition, it is possible to evaluate the impact of these discounts, and it is also possible to evaluate the roll of monetary policy the desired capital stock and investment. The model is a partial equilibrium model, but it appropriately shows the way in which monetary and fiscal policies have impact on firms' decisions, and it can be later incorporated into dynamic general model that clearly allowed formulating the macroeconomic variables impulse-response functions to possible monetary and fiscal policies shocks.

Este trabajo busca investigar las propiedades de la demanda residencial de energía eléctrica en dos ciudades colombianas (Bogotá y Medellín) en el periodo 19790- 1983. La modelación económica de este tipo de mercado tiene características peculiares: la discriminación de precios de los monopolios de distribución implica que las diferentes clases de consumidores enfrentan una curva de oferta ascendente que impide la agregación “horizontal” de la demanda. Se requiere, entonces, una agregación de las formas reducidas finales de las diferentes clases de consumidores. No se utilizan los procedimientos usuales de Mínimos Cuadrados en Dos Etapas, pues se busca aprovechar la información deterministica disponible sobre la curva de oferta en cada periodo de las observaciones. A pesar de que la forma estructural tiene formas funcionales bastante simples, la forma reducida final no es linealizable, y en consecuencia se utiliza un algoritmo no lineal de estimación. Los resultados econométricos son estadísticamente aceptables y concuerdan con las proposiciones microeconómicas convencionales.

Este articulo se ocupa de la conveniencia de una regla fiscal de balance estructural para Colombia. En primer lugar (seccion A) se examina el papel y la racionalidad de las reglas fiscales y se estudia el tema de su diseno. La seccion (B) esta dedicada al examen de la regla fiscal Chilena y sus impactos macroeconomicos. En la seccion (C) se hace una revision sucinta de las tendencias de largo plazo del gasto publico en Colombia, de su desempeno reciente y sus principales inflexibilidades y se examinan las recomendaciones que, en materia institucional, hizo recientemente la Comision Independiente del Gasto publico. Usando un modelo de equilibrio general, la seccion (D) realiza una simulacion de los impactos que -en el evento de una crisis futura- una regla fiscal tendria sobre el crecimiento, el empleo y la pobreza. En fin la seccion (E) se ocupa de los problemas de diseno y, de manera muy preliminar, de los pasos institucionales necesarios para la puesta en marcha de una regla fiscal de balance estructural en el pais.

Spanish Abstract: El presente articulo aborda el analisis de esos esquemas, de sus consecuencias, y de su adecuacion a las necesidades del sector: en la seccion segunda se describe brevemente como han operado esos esquemas en la practica en Colombia; en la tercera se revisa la literatura economica sobre el tema; en la cuarta se aborda el analisis desde un punto de vista conceptual y teorico; y en la seccion quinta se plantean algunas conclusiones.English Abstract: This paper analyses two sanitary service market structures, free market and concurrency of service providers, taking into account their consequences and their adjustment to the sector needs. The paper briefly describes how such structures have operated in Colombia and presents an analysis under a conceptual and theoretic point of view. Finally some conclusions are exposed.

We discuss conditions under which joint outcomes of simultaneous measurements of non-commuting canonical observables can be inferred with arbitrary precision. The feat is possible for certain pre- and postselections involving entanglement with ancillary systems.

Spanish Abstract: En general, se admite que la decision de inversion es una decision de optimizacion dinamica,en la que el inversionista elije el nivel de inversion considerando su retorno futuro. Los problemas de optimizacion dinamica se resuelven por tres caminos alternativos: calculo de variaciones; teoria de control optimo, y programacion dinamica. En los tres casos, el problema parte de considerar dos tipos de variables: las variables de estado y las variables de control.English Abstract: It is generally admitted that investment decisions are dynamic optimization decisions, in which the investor chooses investment level considering its future returns. This kind of dynamic optimization problems can be solved by three different ways: calculation of variations, optimal control theory and dynamic programming. This paper examines these three different strategies.

Spanish Abstract: El presente articulo busca analizar un mecanismo por el cual los precios de las importaciones incidan en los precios domesticos, cuando estos son fijados por las empresas, en un modelo de competencia imperfecta. En la seccion siguiente se plantea el modelo general, de acuerdo al cual empresas que producen bienes diferenciados determinan un margen optimo sobre costos en la fijacion de precios. La seccion tercera introduce la competencia de importaciones, y el impacto que sobre dicho margen tiene su precio. La seccion cuarta analiza la posible calibracion del modelo, para ocuparse la quinta seccion de algunas conclusiones.English Abstract: This paper analyses a mechanism by which import prices affect domestic prices, when these are established by the firms in an imperfect competition model. The paper presents a general model in which firms that produced differentiated goods determine an optimal margin over the costs in price fixing process. In addition, imports competition is introduced and its impact of its price on the mentioned margin.

Spanish Abstract: Mediante un modelo de equilibrio general computable, en el que se discrimina un sector informal en la economia, se modela el sector formal como un mercado de competencia monopolistica. Ademas de incluir mercados de trabajo discriminados, este modelo tambien evalua el impacto del creciente flujo de inversion extranjera, del aumento de precio de los bienes basicos, y del aumento del volumen de las exportaciones sobre la economia colombiana. Se concluye que algo mas de la mitad del crecimiento observado puede explicarse por el efecto de los factores mencionados. No obstante, se senala la importancia de las politicas internas para aprovechar las coyunturas favorables, y para minimizar el efecto de circunstancias negativas sobre el desempeno economico.English Abstract: Based on a computable general equilibrium model, in which an informal sector in the economy is discriminated, the formal sector is modeled as a monopolistic competition market. In addition to include discriminated labour markets, this model also includes the assessment impacts such as the increment of:foreign investment flows, price of commodities, and the volume of exports in the Colombian economy. This paper concludes that just over half of the observed growth can be explained by the effect of the above factors, and highlights the importance of domestic policies to take advantage of the good times, and to minimize the effect of negative circumstances on economic performance.

Este documento presenta un cálculo del Costo de uso del capital para Colombia en el periodo 1990-2007. Seguidamente, contrasta este cálculo con la dinámica de la inversión en el mismo periodo. Se encuentra que la relación entre inversión y costo de uso es muy estrecha, y se comprueba que el enorme crecimiento de la inversión en los últimos periodos está asociado a niveles bajos y estables del costo de uso del capital.

Spanish Abstract: El presente trabajo se ocupa de analizar la relacion entre crecimiento, pobreza y distribucion del ingreso, desde la optica del equilibrio general computable, y mediante ejercicios de estatica comparativa realizados para la economia colombiana. La investigacion se ha llevado a cabo por solicitud de la Mision para el Diseno de una Estrategia para la Reduccion de la Pobreza y la Desigualdad (MERPD), y ha sido financiada por el Banco Mundial. English Abstract: This paper examines the relationship between growth, poverty and income distribution, from a general equilibrium perspective using comparative static exercises conducted for the Colombian economy. The article was carried out at the request of the Mission to Design a Strategy for Reducing Poverty and Inequality (MERPD), and has been financed by the World Bank.

Spanish Abstract: Este documento presenta un calculo del Costo de uso del capital para Colombia en el periodo 1990-2007. Seguidamente, contrasta este calculo con la dinamica de la inversion en el mismo periodo. Se encuentra que la relacion entre inversion y costo de uso es muy estrecha, y se comprueba que el enorme crecimiento de la inversion en los ultimos periodos esta asociado a niveles bajos y estables del costo de uso del capital.English Abstract: This paper presents the construction of the use cost of capital for the Colombian economy in 1990-2007. Then, this calculation is contrasted with the dynamic of investment in the same period. It is found that the relation between investment and use cost of capital is very narrow, and it is proved that the large growth of investment in the last periods is associated with low and stable levels of the use cost of capital.

The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and post-selected ensembles, and if the selections involve entangled states with some other system. We show that the problem is related to the problem of assigning weak values to a continuous family of operators, and give explicit examples where this problem is solvable. Some foundational implications are briefly discussed., Comment: 5 pages, no figures. Revised version: corrected typos, particularly in Eq. 8, and expanded references

We discuss the consequences of the Aharonov-Bohm (AB) effect in setups involving several charged particles, wherein none of the charged particles encloses a closed loop around the magnetic flux. We show that in such setups, the AB phase is encoded either in the relative phase of a bipartite or multipartite entangled photons states, or alternatively, gives rise to an overall AB phase that can be measured relative to another reference system. These setups involve processes of annihilation or creation of electron-hole pairs. We discuss the relevance of such effects in ``vacuum birefringence" in QED, and comment on their connection to other known effects.

We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a \emph{definite} mechanical effect on a measuring probe specifically designed to minimize the back-reaction on the measured system. We then present a new framework for general measurement conditions (where the back-reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as \emph{quantum averages of weak values}. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework., 13 pages, 6 figures, Revtex 4. Paper has been shortened. Section on large- sample measurements has been removed. The discussion on this topic has been deferred to a future publication