Linear operators and their spectra with applications to quantum mechanics.

From lectures given at the New York university Institute for mathematica and mechanics, by R. Cournat and others.

Philosophy and psychology pamphlets

A collection of miscellaneous pamphlets.

Analysis of edge detection algorithms on DIAL /

Mode of access: Internet.

El impacto del enfoque léxico sobre la adquisición de la competencia léxica en aprendices de español como lengua extranjera

Este estudio presenta los resultados de una investigación que examina la efectividad del enfoque léxico como forma de instrucción explícita sobre la adquisición de la competencia léxica en aprendices de español como lengua extranjera. El estudio esta guiado por dos preguntas de investigación. La primera pregunta de investigación (PI 1) examina el impacto del enfoque léxico sobre la adquisición de la competencia léxica. La segunda pregunta de investigación (PI 2) examina si la efectividad del enfoque léxico en el grupo de alumnos examinados viene condicionada por las creencias de los participantes acerca de las estrategias empleadas en dicho método. La aplicación del enfoque léxico se basó en una propuesta pedagógica consistente en una unidad didáctica de creación propia. Se analizaron los datos obtenidos tanto de forma cuantitativa como cualitativa. Los resultados confirmaron empíricamente la validez del enfoque léxico como principio metodológico para adquirir la competencia léxica. Del mismo modo, se encontró una relación entre las creencias de los participantes y las estrategias de aprendizaje empleadas.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Fungible dynamics: There are only two types of entangling multiple-qubit interactions

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

Beating the urge: Implications of research into substance-related desires

Despite the advent of improved pharmacological treatments to alleviate substance-related desires, psychological approaches will continue to be required. However, the current psychological treatment that most specifically focuses on desires and their management-cue exposure (CE)-has not lived up to its original promise. This paper argues that current psychological approaches to desire do not adequately incorporate our knowledge about the factors that trigger, maintain, and terminate episodes of desire. It asserts that the instigation and maintenance of desires involve both associative and elaborative processes. Understanding the processes triggering the initiation of intrusive thoughts may assist in preventing some episodes, but occasional intrusions will be inevitable. A demonstration of the ineffectiveness of thought suppression may discourage its use as a coping strategy for desire-related intrusions, and mindfulness meditation plus cognitive therapy may help in accepting their occurrence and letting them go. Competing tasks may be used to reduce elaboration of desires, and competing sensory images may have particular utility. The application of these procedures during episodes that are elicited in the clinic may allow the acquisition of more effective strategies to address desires in the natural environment. (C) 2004 Elsevier Ltd. All rights reserved.

Do dogs (canis familiaris) understand invisible displacement?

Domestic dogs (Canis familiaris) perform above chance on invisible displacement tasks despite showing few other signs of possessing the necessary representational abilities. Four experiments investigated how dogs find an object that has been hidden in 1 of 3 opaque boxes. Dogs passed the task under a variety of control conditions, but only if the device used to displace the object ended up adjacent to the target box after the displacement. These results suggest that the search behavior of dogs was guided by simple associative rules rather than mental representation of the object's past trajectory. In contrast, Experiment 5 found that on the same task, 18- and 24-month-old children showed no disparity between trials in which the displacement device was adjacent or nonadjacent to the target box.

Cognitive fit between conceptual schemas and internal problem representations: The case of geospatio-temporal conceptual schema comprehension

Geospatio-temporal conceptual models provide a mechanism to explicitly represent geospatial and temporal aspects of applications. Such models, which focus on both what and when/where, need to be more expressive than conventional conceptual models (e.g., the ER model), which primarily focus on what is important for a given application. In this study, we view conceptual schema comprehension of geospatio-temporal data semantics in terms of matching the external problem representation (that is, the conceptual schema) to the problem-solving task (that is, syntactic and semantic comprehension tasks), an argument based on the theory of cognitive fit. Our theory suggests that an external problem representation that matches the problem solver's internal task representation will enhance performance, for example, in comprehending such schemas. To assess performance on geospatio-temporal schema comprehension tasks, we conducted a laboratory experiment using two semantically identical conceptual schemas, one of which mapped closely to the internal task representation while the other did not. As expected, we found that the geospatio-temporal conceptual schema that corresponded to the internal representation of the task enhanced the accuracy of schema comprehension; comprehension time was equivalent for both. Cognitive fit between the internal representation of the task and conceptual schemas with geospatio-temporal annotations was, therefore, manifested in accuracy of schema comprehension and not in time for problem solution. Our findings suggest that the annotated schemas facilitate understanding of data semantics represented on the schema.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Eigenvalues of Casimir invariants for Uq[osp(m|n)]

For each quantum superalgebra U-q[osp(m parallel to n)] with m > 2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated. (c) 2005 American Institute of Physics.

Some twisted results

The Drinfeld twist for the opposite quasi-Hopf algebra, H-COP, is determined and is shown to be related to the (second) Drinfeld twist on a quasi-Hopf algebra. The twisted form of the Drinfeld twist is investigated. In the quasi-triangular case, it is shown that the Drinfeld u-operator arises from the equivalence of H-COP to the quasi-Hopf algebra induced by twisting H with the R-matrix. The Altschuler-Coste u-operator arises in a similar way and is shown to be closely related to the Drinfeld u-operator. The quasi-cocycle condition is introduced and is shown to play a central role in the uniqueness of twisted structures on quasi-Hopf algebras. A generalization of the dynamical quantum Yang-Baxter equation, called the quasi-dynamical quantum Yang-Baxter equation, is introduced.