The power of quantum Fourier sampling

How powerful are Quantum Computers? Despite the prevailing belief that Quantum Computers are more powerful than their classical counterparts, this remains a conjecture backed by little formal evidence. Shor's famous factoring algorithm [Shor97] gives an example of a problem that can be solved efficiently on a quantum computer with no known efficient classical algorithm. Factoring, however, is unlikely to be NP-Hard, meaning that few unexpected formal consequences would arise, should such a classical algorithm be discovered. Could it then be the case that any quantum algorithm can be simulated efficiently classically? Likewise, could it be the case that Quantum Computers can quickly solve problems much harder than factoring? If so, where does this power come from, and what classical computational resources do we need to solve the hardest problems for which there exist efficient quantum algorithms?

We make progress toward understanding these questions through studying the relationship between classical nondeterminism and quantum computing. In particular, is there a problem that can be solved efficiently on a Quantum Computer that cannot be efficiently solved using nondeterminism? In this thesis we address this problem from the perspective of sampling problems. Namely, we give evidence that approximately sampling the Quantum Fourier Transform of an efficiently computable function, while easy quantumly, is hard for any classical machine in the Polynomial Time Hierarchy. In particular, we prove the existence of a class of distributions that can be sampled efficiently by a Quantum Computer, that likely cannot be approximately sampled in randomized polynomial time with an oracle for the Polynomial Time Hierarchy.

Our work complements and generalizes the evidence given in Aaronson and Arkhipov's work [AA2013] where a different distribution with the same computational properties was given. Our result is more general than theirs, but requires a more powerful quantum sampler.

Diseño de un aerogenerador de muy baja potencia para la alimentación de sistemas eléctricos aislados

[ES]En este Proyecto se desarrolla el diseño y la optimización de un aerogenerador de muy pequeña potencia enfocado a alimentar sistemas eléctricos aislados; concretamente, un sistema de iluminación. Se analizan todos los componentes del sistema aerogenerador, comparando las diversas alternativas posibles y eligiendo soluciones sencillas, baratas y eficientes para cada uno de ellos. Asimismo, se lleva a cabo un primer dimensionamiento de los mismos. El esfuerzo de diseño se ha centrado en las palas, por considerarse el componente más crítico y menos normalizado. Se han estudiado herramientas para su análisis detallado y su optimización desde el punto de vista aerodinámico, y éstas han sido implementadas en Matlab. Esto ha permitido generar un diseño óptimo ajustado a las necesidades del sistema. Asimismo, se han realizado las correspondientes tareas de planificación, analizado los múltiples beneficios de tipo técnico, económico, social y ambiental que la ejecución del presente Proyecto reportará, haciendo una programación completa del mismo y un análisis de los costes que supondrá.

Alienação e transcendência: da insuficiência do Estatuto da Cidade para a constituição de um Direito da Cidade com viés crítico

O instituto da gestão democrática da cidade ocupa lugar central nos debates e nas reflexões acerca do Direito da Cidade e do Estatuto da Cidade. Especificamente no que se refere ao conteúdo dessas reflexões, a gestão democrática alcança impressionante consenso, não sendo coisa fácil encontrar razões no sentido de negar a validade da construção de uma cidadania ativa para gestão dos negócios urbanos. Este trabalho quer entender, concretamente, a razão do citado consenso, ancorado em uma concepção crítica que tenta chamar atenção para aspectos do social que não costumam ser contemplados pela análise realizada entre os juristas que se dedicam ao tema. Neste sentido, questões como a da alienação do trabalho e sua relação com a alienação política e a situação real das cidades a partir da categoria de análise da FES (formação econômica e social) não devem ser ignoradas quando das discussões sobre as possibilidades de efetivação de atuação citadina ativa nas cidades brasileiras. Em tempo, é necessário, a partir das categorias destacadas, analisar criticamente os instrumentos do Estatuto da Cidade para que não se permitam maiores ilusões acerca do estado de coisas aqui discutido.

Violence in the Medieval Church before the First Crusade

The attitude of the medieval church towards violence before the First Crusade in 1095 underwent a significant institutional evolution, from the peaceful tradition of the New Testament and the Roman persecution, through the prelate-led military campaigns of the Carolingian period and the Peace of God era. It would be superficially easy to characterize this transformation as the pragmatic and entirely secular response of a growing power to the changing world. However, such a simplification does not fully do justice to the underlying theology. While church leaders from the 5th Century to the 11th had vastly different motivations and circumstances under which to develop their responses to a variety of violent activities, the teachings of Augustine of Hippo provided a unifying theme. Augustine’s just war theology, in establishing which conflicts are acceptable in the eyes of God, focused on determining whether a proper causa belli or basis for war exists, and then whether a legitimate authority declares and leads the war. Augustine masterfully integrated aspects of the Old and New Testaments to create a lasting and compelling case for his definition of justified violence. Although at different times and places his theology has been used to support a variety of different attitudes, the profound influence of his work on the medieval church’s evolving position on violence is clear.

Estudo do efeito magnetocalórico em sistemas magnéticos com terras raras

O efeito magnetocalórico, base da refrigeração magnética, é caracterizado por duas quantidades: a variação isotérmica da entropia (ΔST) e a variação adiabática da temperatura (ΔTS); que são obtidas sob variações na intensidade de um campo magnético aplicado. Em sistemas que apresentam anisotropia magnética, pode‐se definir o efeito magnetocalórico anisotrópico, o qual, por definição, é calculado sob variações na direção de aplicação de um campo magnético cuja intensidade mantém‐se fixa, e é caracterizado por duas quantidades: a variação anisotrópico‐isotérmica da entropia (ΔSan) e a variação anisotrópico‐adiabática da temperatura (ΔTan). O efeito magnetocalórico e o efeito magnetocalórico anisotrópico foram estudados nos compostos intermetálicos formados por terras e outros materiais não magnéticos: RNi2, RNi5, RZn e Gd1‐nPrnAl2. Os cálculos foram feitos partindo de hamiltonianos modelo que incluem as interações de troca, Zeeman, de campo cristalino e quadrupolar.

Análisis de la influencia de la orientación de las fibras metálicas en la resistencia de la matriz de hormigón de acuerdo al Ensayo Barcelona

[ES]El objetivo de este trabajo de fin de grado es analizar la influencia que tiene la cuantía y orientación de fibras metálicas presentes en el interior de probetas de hormigón autocompactante y cuyo objetivo es reforzar y aumentar la resistencia a tracción de este material. Se expondrán las propiedades que combina el HACRFA gracias a la autocompactación del hormigón y la inclusión de fibras en su interior y los beneficios que este nuevo material aporta. Por otro lado, se tratara de situar este estudio en un contexto, analizando a la vez cuál es el alcance y los objetivos más importantes que se han tenido en cuenta. A continuación, y a modo de complementación de su contexto, este trabajo tiene un estado del arte, en el que se mencionarán métodos y ensayos necesarios para llegar a un resultado que permita predecir cuál será la resistencia del material, y por tanto su tenacidad o capacidad de absorber energía, sin necesidad de emplear más que un método fácil y rápido, obviando el resto de ensayos destructivos utilizados en este trabajo. Para tal fin, se establece una metodología que, gracias a ensayos de laboratorio, permita establecer una relación entre el método sencillo que se ha mencionado, el método inductivo, y un resultado teórico de la tenacidad que presenta el HACRFA. Se observará cómo la desviación entre los ensayos experimentales y los resultados teóricos obtenidos es prácticamente nula, despreciando situaciones en las que se presenten comportamientos muy diferentes debido a fallos durante los ensayos.

I. Foehn winds of southern California. II. Foehn wind cyclo-genesis. III. Weather conditions associated with the Akron disaster. IV. The Los Angeles storm of December 30, 1933 to January 1, 1934

I. Foehn winds of southern California.
An investigation of the hot, dry and dust laden winds occurring in the late fall and early winter in the Los Angeles Basin and attributed in the past to the influences of the desert regions to the north revealed that these currents were of a foehn nature. Their properties were found to be entirely due to dynamical heating produced in the descent from the high level areas in the interior to the lower Los Angeles Basin. Any dust associated with the phenomenon was found to be acquired from the Los Angeles area rather than transported from the desert. It was found that the frequency of occurrence of a mild type foehn of this nature during this season was sufficient to warrant its classification as a winter monsoon. This results from the topography of the Los Angeles region which allows an easy entrance to the air from the interior by virtue of the low level mountain passes north of the area. This monsoon provides the mild winter climate of southern California since temperatures associated with the foehn currents are far higher than those experienced when maritime air from the adjacent Pacific Ocean occupies the region.

II. Foehn wind cyclo-genesis.
Intense anticyclones frequently build up over the high level regions of the Great Basin and Columbia Plateau which lie between the Sierra Nevada and Cascade Mountains to the west and the Rocky Mountains to the east. The outflow from these anticyclones produce extensive foehns east of the Rockies in the comparatively low level areas of the middle west and the Canadian provinces of Alberta and Saskatchewan. Normally at this season of the year very cold polar continental air masses are present over this territory and with the occurrence of these foehns marked discontinuity surfaces arise between the warm foehn current, which is obliged to slide over a colder mass, and the Pc air to the east. Cyclones are easily produced from this phenomenon and take the form of unstable waves which propagate along the discontinuity surface between the two dissimilar masses. A continual series of such cyclones was found to occur as long as the Great Basin anticyclone is maintained with undiminished intensity.

III. Weather conditions associated with the Akron disaster.
This situation illustrates the speedy development and propagation of young disturbances in the eastern United States during the spring of the year under the influence of the conditionally unstable tropical maritime air masses which characterise the region. It also furnishes an excellent example of the superiority of air mass and frontal methods of weather prediction for aircraft operation over the older methods based upon pressure distribution.

IV. The Los Angeles storm of December 30, 1933 to January 1, 1934.
This discussion points out some of the fundamental interactions occurring between air masses of the North Pacific Ocean in connection with Pacific Coast storms and the value of topographic and aerological considerations in predicting them. Estimates of rainfall intensity and duration from analyses of this type may be made and would prove very valuable in the Los Angeles area in connection with flood control problems.

Creation of temporary ponds for amphibians in northern and central Europe

More than 4000 ponds have been created or restored in Denmark since 1985 as part of a large-scale pond-digging programme to protect endangered amphibians in particular and pond flora and fauna in general. Most ponds are created on private land with public financing. The programme was triggered by, among other factors, a drastic decline in amphibian populations in Denmark between 1940 and 1980. However, in recent years there has been an increased awareness in Denmark that temporary ponds are important for the conservation of some of the most rare amphibian species, such as fire-bellied toad Bombina bombina, natterjack toad Bufo calamita and green toad Bufo viridis. Other rare species such as moor frog Rana arvalis and European tree frog Hyla arborea also benefit from temporary ponds. The last 15 years of work on the conservation of endangered species and their habitats has resulted in a last-minute rescue and a subsequent growth in the size of most Danish populations of fire-bellied toad and green toad; some populations of the relatively more common natterjack toad have also increased. The creation of temporary ponds plays an important role in the success of these three species. The creation of ponds to help restore viable populations of the most rare amphibians has not been easy. To study the conditions that may need to be created, Danish herpetologists searched for areas with temporary ponds that had good water quality, natural hydrological conditions and a management regime influenced by traditional agricultural methods. The paper gives an overview of pond creation and restoration projects in Denmark and Poland and their significance for amphibian diversity.

Use of Artificial Eelgrass Mats by Saltmarsh-Nesting Common Terns (Sterna hirundo)

Terns and skimmers nesting on saltmarsh islands often suffer large nest losses due to tidal and storm flooding. Nests located near the center of an island and on wrack (mats of dead vegetation, mostly eelgrass Zostera) are less susceptible to flooding than those near the edge of an island and those on bare soil or in saltmarsh cordgrass (Spartina alterniflora). In the 1980’s Burger and Gochfeld constructed artificial eelgrass mats on saltmarsh islands in Ocean County, New Jersey. These mats were used as nesting substrate by common terns (Sterna hirundo) and black skimmers (Rynchops niger). Every year since 2002 I have transported eelgrass to one of their original sites to make artificial mats. This site, Pettit Island, typically supports between 125 and 200 pairs of common terns. There has often been very little natural wrack present on the island at the start of the breeding season, and in most years natural wrack has been most common along the edges of the island. The terns readily used the artificial mats for nesting substrate. Because I placed artificial mats in the center of the island, the terns have often avoided the large nest losses incurred by terns nesting in peripheral locations. However, during particularly severe flooding events even centrally located nests on mats are vulnerable. Construction of eelgrass mats represents an easy habitat manipulation that can improve the nesting success of marsh-nesting seabirds.

矩阵理论在半导体激光器耦合中的应用

傍轴近似下的光学矩阵理论，可以简化光束传输计算过程，使光学系统设计更为方便。将ABCD变换矩阵方法引入到耦合光学系统的设计中，运用高斯光束的ABCD法则，详尽地给出了某一耦合方式下的半导体激光器耦合入单模光纤系统的设计；另一方面，对系统的耦合损耗与耦合距离的关系进行了理论计算，并把计算结果与最近的实验报道做了比较，它们基本相吻合，说明此方法是可行的、合理的。从整个设计及理论计算来看，ABCD矩阵方法减少了复杂的计算，从而简化了设计过程，与通常的衍射计算相比，它不失为一种方便、有效的方法，同时它对生产半导体

Optimal Data Distributions in Machine Learning

In the first part of the thesis we explore three fundamental questions that arise naturally when we conceive a machine learning scenario where the training and test distributions can differ. Contrary to conventional wisdom, we show that in fact mismatched training and test distribution can yield better out-of-sample performance. This optimal performance can be obtained by training with the dual distribution. This optimal training distribution depends on the test distribution set by the problem, but not on the target function that we want to learn. We show how to obtain this distribution in both discrete and continuous input spaces, as well as how to approximate it in a practical scenario. Benefits of using this distribution are exemplified in both synthetic and real data sets.

In order to apply the dual distribution in the supervised learning scenario where the training data set is fixed, it is necessary to use weights to make the sample appear as if it came from the dual distribution. We explore the negative effect that weighting a sample can have. The theoretical decomposition of the use of weights regarding its effect on the out-of-sample error is easy to understand but not actionable in practice, as the quantities involved cannot be computed. Hence, we propose the Targeted Weighting algorithm that determines if, for a given set of weights, the out-of-sample performance will improve or not in a practical setting. This is necessary as the setting assumes there are no labeled points distributed according to the test distribution, only unlabeled samples.

Finally, we propose a new class of matching algorithms that can be used to match the training set to a desired distribution, such as the dual distribution (or the test distribution). These algorithms can be applied to very large datasets, and we show how they lead to improved performance in a large real dataset such as the Netflix dataset. Their computational complexity is the main reason for their advantage over previous algorithms proposed in the covariate shift literature.

In the second part of the thesis we apply Machine Learning to the problem of behavior recognition. We develop a specific behavior classifier to study fly aggression, and we develop a system that allows analyzing behavior in videos of animals, with minimal supervision. The system, which we call CUBA (Caltech Unsupervised Behavior Analysis), allows detecting movemes, actions, and stories from time series describing the position of animals in videos. The method summarizes the data, as well as it provides biologists with a mathematical tool to test new hypotheses. Other benefits of CUBA include finding classifiers for specific behaviors without the need for annotation, as well as providing means to discriminate groups of animals, for example, according to their genetic line.

Mitigating Scarring and Inflammation during Corneal Wound Healing using Nanofiber-Hydrogel Scaffolds

Due to the universal lack of donor tissue, there has been emerging interest in engineering materials to stimulate living cells to restore the features and functions of injured organs. We are particularly interested in developing materials for corneal use, where the necessity to maintain the tissue’s transparency presents an additional challenge. Every year, there are 1.5 – 2 million new cases of monocular blindness due to irregular healing of corneal injuries, dwarfing the approximately 150,000 corneal transplants performed. The large gap between the need and availability of cornea transplantation motivates us to develop a wound-healing scaffold that can prevent corneal blindness.

To develop such a scaffold, it is necessary to regulate the cells responsible for repairing the damaged cornea, namely myofibroblasts, which are responsible for the disordered and non-refractive index matched scar that leads to corneal blindness. Using in vitro assays, we identified that protein nanofibers of certain orientation can promote cell migration and modulate the myofibroblast phenotype. The nanofibers are also transparent, easy to handle and non-cytotoxic. To adhere the nanofibers to a wound bed, we examined the use of two different in situ forming hydrogels: an artificial extracellular matrix protein (aECM)-based gel and a photo-crosslinkable heparin-based gel. Both hydrogels can be formed within minutes, are transparent upon gelation and are easily tunable.

Using an in vivo mouse model for epithelial defects, we show that our corneal scaffolds (nanofibers together with hydrogel) are well-tolerated (no inflammatory response or turbidity) and support epithelium regrowth. We developed an ex vivo corneal tissue culture model where corneas that are wounded and treated with our scaffold can be cultured while retaining their ability to repair wounds for up to 21 days. Using this technique, we found that the aECM-based treatment induced a more favorable wound response than the heparin-based treatment, prompting us to further examine the efficacy of the aECM-based treatment in vivo using a rabbit model for stromal wounds. Results show that treated corneas have fewer myofibroblasts and immune cells than untreated ones, indicating that our corneal scaffold shows promise in promoting a calmer wound response and preventing corneal haze formation.

Cultivation methods for Lemnaceae [Translation from: Wiadomosci Botaniczne 7(2) 153-164, 1963]

Representatives from the family of Lemnaceae (duckweed) make ideal experimental material for research into a succession of phytophysiological processes with regard to growth rate and vegetative reproduction. They are also easy to maintain in sterile cultures. Lemnaceae belong to the higher flowering plants (flowers are rarely produced), however they are distinguished by a much simplified morphological and anatomical structure. As water plants they possess the advantage, that they can be cultivated in synthetic media under laboratory conditions controlled by the application of both a known light intensity and temperature. This paper describes experimental research of growth of Lemnaceae in different conditions. Some of the variables were mineral media, illumination and aeration.

Enantioselective Total Synthesis of Diketopiperazinecontaining Natural Products: (–)-Lansai B, (+)-Nocardioazines A and B, and (–)-Acetylapoaranotin

Diketopiperazine (DKP) motif is found in a wide range of biologically active natural products. This work details our efforts toward two classes of DKP-containing natural products.

Class one features the pyrroloindoline structure, derived from tryptophans. Our group developed a highly enantioselective (3 + 2) formal cycloaddition between indoles and acrylates to provide pyrroloindoline products possessing three stereocenters. Utilizing this methodology, we accomplished asymmetric total synthesis of three natural products: (–)-lansai B, (+)-nocardioazines A and B. Total synthesis of (–)-lansai B was realized in six steps, and featured an amino acid dimerization strategy. The total synthesis of (+)-nocardioazine B was also successfully completed in ten steps. Challenges were met in approaching (+)-nocardioazine A, where a seemingly easy last-step epoxidization did not prove successful. After re-examining our synthetic strategy, an early-stage epoxidation strategy was pursued, which eventually yielded a nine-step total synthesis of (+)-nocardioazine A.

Class two is the epidithiodiketopiperazine (ETP) natural products, which possesses an additional episulfide bridge in the DKP core. With the goal of accessing ETPs with different peripheral structures for structure-activity relationship studies, a highly divergent route was successfully developed, which was showcased in the formal synthesis of (–)-emethallicin E and (–)-haematocin, and the first asymmetric synthesis of (–)-acetylapoaranotin.

Optical interconnection for neural networks by use of a self-imaging function

A grating-lens combination unit is developed to form a scaling self-transform function that can self-image on scale. Then an array of many such grating-lens units is used for the optical interconnection of a two-dimensional neural network, and experiments are carried out. We find that our idea is feasible, the optical interconnection system is simple, and optical adjustment is easy. (C) 1998 Optical Society of America.