University of Waterloo

About: University of Waterloo is a education organization based out in Waterloo, Ontario, Canada. It is known for research contribution in the topics: Population & Context (language use). The organization has 36093 authors who have published 93906 publications receiving 2948139 citations. The organization is also known as: UW & uwaterloo.

Solving sparse linear equations over finite fields

Abstract: A "coordinate recurrence" method for solving sparse systems of linear equations over finite fields is described. The algorithms discussed all require O(n_{1}(\omega + n_{1})\log^{k}n_{1}) field operations, where n_{1} is the maximum dimension of the coefficient matrix, \omega is approximately the number of field operations required to apply the matrix to a test vector, and the value of k depends on the algorithm. A probabilistic algorithm is shown to exist for finding the determinant of a square matrix. Also, probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error.

Mapping features to models: a template approach based on superimposed variants

Abstract: Although a feature model can represent commonalities and variabilities in a very concise taxonomic form, features in a feature model are merely symbols. Mapping features to other models, such as behavioral or data specifications, gives them semantics. In this paper, we propose a general template-based approach for mapping feature models to concise representations of variability in different kinds of other models. We show how the approach can be applied to UML 2.0 activity and class models and describe a prototype implementation.

Black hole chemistry: thermodynamics with Lambda

Abstract: We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach, the mass of the black hole is no longer regarded as internal energy, rather it is identified with the chemical enthalpy. This leads to an extended dictionary for black hole thermodynamic quantities, in particular a notion of thermodynamic volume emerges for a given black hole spacetime. This volume is conjectured to satisfy the reverse isoperimetric inequality—an inequality imposing a bound on the amount of entropy black hole can carry for a fixed thermodynamic volume. New thermodynamic phase transitions naturally emerge from these identifications. Namely, we show that black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. We also review the recent attempts at extending the AdS/CFT dictionary in this setting, discuss the connections with horizon thermodynamics, applications to Lifshitz spacetimes, and outline possible future directions in this field.

Exact and approximate unitary 2-designs and their application to fidelity estimation

Abstract: We develop the concept of a unitary $t$-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group $U({2}^{n})$ on $n$ qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an $O(n)$-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on $n$ qubits with quantum circuits of size $O(n)$ without requiring any ancilla qubits, thereby improving upon previous approaches.

Bilevel and multilevel programming: A bibliography review

Abstract: This paper contains a bibliography of all references central to bilevel and multilevel programming that the authors know of. It should be regarded as a dynamic and permanent contribution since all the new and appropriate references that are brought to our attention will be periodically added to this bibliography. Readers are invited to suggest such additions, as well as corrections or modifications, and to obtain a copy of the LaTeX and BibTeX files that constitute this manuscript, using the guidelines contained in this paper. To classify some of the references in this bibliography a short overview of past and current research in bilevel and multilevel programming is included. For those who are interested in but unfamiliar with the references in this area, we hope that this bibliography facilitates and encourages their research.