Smallest disentangling state spaces for general entangled bipartite quantum states

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].

Vacant parking area estimation through background subtraction and transience map analysis

A method for estimating the dimensions of non-delimited free parking areas by using a static surveillance camera is proposed. The proposed method is specially designed to tackle the main challenges of urban scenarios (multiple moving objects, outdoor illumination conditions and occlusions between vehicles) with no training. The core of this work is the temporal analysis of the video frames to detect the occupancy variation of the parking areas. Two techniques are combined: background subtraction using a mixture of Gaussians to detect and track vehicles and the creation of a transience map to detect the parking and leaving of vehicles. The authors demonstrate that the proposed method yields satisfactory estimates on three real scenarios while being a low computational cost solution that can be applied in any kind of parking area covered by a single camera.

On Gruenhage spaces, separating σ-isolated families, and their relatives

We prove that, given a topological space X, the following conditions are equivalent. (α) X is a Gruenhage space. (β) X has a countable cover by sets of small local diameter (property SLD) by F∩G sets. (γ) X has a separating σ-isolated family M⊂F∩G. (δ) X has a one-to-one continuous map into a metric space which has a σ-isolated base of F∩G sets. Besides, we provide an example which shows Fragmentability ⇏ property SLD ⇏ the space to be Gruenhage.

WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

Resistance performances: (Re)constructing spaces of resistance and contention in the 2010-2011 University of Puerto Rico student movement

On the night of April 20, 2010, a group of students from the University of Puerto Rico (UPR), Río Piedras campus, met to organize an indefinite strike that quickly broadened into a defense of accessible public higher education of excellence as a fundamental right and not a privilege. Although the history of student activism in the UPR can be traced back to the early 1900s, the 2010-2011 strike will be remembered for the student activists’ use of new media technologies as resources that rapidly prompted and aided the numerous protests. ^ This activist research entailed a critical ethnography and a critical discourse analysis (CDA) of traditional and alternative media coverage and treatment during the 2010 -2011 UPR student strike. I examined the use of the 2010-2011 UPR student activists’ resistance performances in constructing local, corporeal, and virtual spaces of resistance and contention during their movement. In particular, I analyzed the different tactics and strategies of resistance or repertoire of collective actions that student activists used (e.g. new media technologies) to frame their collective identities via alternative news media’s (re)presentation of the strike, while juxtaposing the university administration’s counter-resistance performances in counter-framing the student activists’ collective identity via traditional news media representations of the strike. I illustrated how both traditional and alternative media (re)presentations of student activism developed, maintained, and/or modified students activists’ collective identities. ^ As such, the UPR student activism’s success should not be measured by the sum of demands granted, but by the sense of community achieved and the establishment of networks that continue to create resistance and change. These networks add to the debate surrounding Internet activism and its impact on student activism. Ultimately, the results of this study highlight the important role student movements have had in challenging different types of government policies and raising awareness of the importance of an accessible public higher education of excellence.^

Retail centers for community : addressing both pedestrian and car traffic

The purpose of this thesis was to redesign a commercial center in Miami, Florida in a manner that incorporates the needs of pedestrians as well as the automobile. In my research, I studied projects that had been successful at integrating cars in retail design. I applied the strategies learned from this research to the design of a center that creates a positive interaction of pedestrian and car traffic, addressing the needs of the surrounding community. I designed a master plan that includes a mix of residential, retail, commercial and parking space. The parking is designed so that the retail center is not dominated by surface parking. Rather, the automobile is introduced into the different layers of the proposed buildings. The design focused on connecting pedestrian plazas and parking areas beneath them through the introduction of light and greenery. The findings show how a shopping center might transform the area around it by including spaces for residential, civic, cultural and social functions, as well as for the automotive infrastructure that make those functions possible.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Equivalent norms in polynomial spaces and applications.

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy Littlewood constants for 2-homogeneous polynomials on l(p)(2) spaces, 2 < p <= infinity. We also provide lower estimates for the Hardy-Littlewood constants for polynomials of higher degrees.

Lighting ambiances and materialities of wood in architecture: a comparative evaluation of the quality of spaces in relation to interior finishes

Le bois est un matériau souvent utilisé par les architectes pour améliorer l’ambiance générale d’un espace, mais peu de recherches en présentent l’impact réel du matériau sur les impressions visuelles et les effets lumineux. Cette recherche étudie l’influence de la matérialité du bois par rapport à la création d’ambiances d’éclairage spécifiques dans l’architecture. Plus particulièrement, elle se concentre sur l’impact des panneaux décoratifs en bois à générer de la diversité lumineuse dans les espaces intérieurs et son potentiel à améliorer la satisfaction environnementale et l’efficacité énergétique. La recherche utilise des maquettes à l’échelle pour leur précision dans la représentation des ambiances lumineuses d’espaces éclairés naturellement ainsi que les technologies récentes d’imagerie digitale pour capturer et analyser les résultats. La méthodologie permet la comparaison entre les différents réglages des espaces intérieurs créés par une sélection des types de matérialités du bois: la réflectance (valeur), la couleur et la réflectivité. Les modalités spatiales sont comparées en présence d’ensoleillement direct et sous des conditions de ciel couvert puisque les modèles d’éclairage et les ambiances diffèrent considérablement. Les résultats permettent d’établir une discussion sur les ambiances en termes de brillance et de contraste, sur la couleur ainsi que la répartition des zones lumineuses dans l’espace. La recherche souligne le rôle des matérialités que peuvent prendre le bois pour optimiser la diversité lumineuse et la création d’ambiances visuellement confortables, ainsi que ses possibilités d’améliorer les ambiances architecturales par rapport à la lumière.