Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

From Comparison to Indices: A disabling perspective on the history of happiness

oai:ojs.hcs.pitt.edu:article/134Who should be considered the most unhappy, the blind or the deaf? The intensive debate over this issue in the early 19th century is the outset of our study of how during the last two hundred years disability and happiness have become inextricably connected. On the basis of our historical analysis we have identified characteristics that also can be found in current happiness interpretations, namely the persistent role played by activation, professional intervention, and alignment with normative behaviors. In order to highlight this intimate connection between past and present we subsequently focus on the contemporary preoccupation with the happiness of people with disabilities, exemplified by research on the so-called “disability paradox” and the development of happiness indices within the behavioral sciences. Our thesis is that applying perspectives from disability studies to happiness research uncovers processes of exclusion and other modalities of power previously overlooked. In our examples, we recognize a desire to lay bare the inside of disabled people’s minds and impose on them un/happy subjectivities. We furthermore argue that the way we think of, and treat, both disability and happiness, i. e. by systematization and professionalization, belongs to a rationalization process which risks colonizing the emotional realm of disabled people. Thus we suggest a research program that ‘dis/ables’ happiness studies and, aided by historical analysis, reconsiders the emotional dimension of disability

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model and a non-integrable extended Hubbard model, and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.Comment: 13 pages, 4 pages appendix, 8 figure

Nonlocal resources in the presence of Superselection Rules

Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the \emph{superselection induced variance} of local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation and mixed state entanglement.Comment: 4 page

Minimally Entangled Typical Thermal State Algorithms

We discuss a method based on sampling minimally entangled typical thermal states (METTS) that can simulate finite temperature quantum systems with a computational cost comparable to ground state DMRG. Detailed implementations of each step of the method are presented, along with efficient algorithms for working with matrix product states and matrix product operators. We furthermore explore how properties of METTS can reveal characteristic order and excitations of systems and discuss why METTS form an efficient basis for sampling. Finally, we explore the extent to which the average entanglement of a METTS ensemble is minimal.Comment: 18 pages, 14 figure