8,030 research outputs found
Complexity Analysis of Balloon Drawing for Rooted Trees
In a balloon drawing of a tree, all the children under the same parent are
placed on the circumference of the circle centered at their parent, and the
radius of the circle centered at each node along any path from the root
reflects the number of descendants associated with the node. Among various
styles of tree drawings reported in the literature, the balloon drawing enjoys
a desirable feature of displaying tree structures in a rather balanced fashion.
For each internal node in a balloon drawing, the ray from the node to each of
its children divides the wedge accommodating the subtree rooted at the child
into two sub-wedges. Depending on whether the two sub-wedge angles are required
to be identical or not, a balloon drawing can further be divided into two
types: even sub-wedge and uneven sub-wedge types. In the most general case, for
any internal node in the tree there are two dimensions of freedom that affect
the quality of a balloon drawing: (1) altering the order in which the children
of the node appear in the drawing, and (2) for the subtree rooted at each child
of the node, flipping the two sub-wedges of the subtree. In this paper, we give
a comprehensive complexity analysis for optimizing balloon drawings of rooted
trees with respect to angular resolution, aspect ratio and standard deviation
of angles under various drawing cases depending on whether the tree is of even
or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns
out that some are NP-complete while others can be solved in polynomial time. We
also derive approximation algorithms for those that are intractable in general
Generating Hermite polynomial excited squeezed states by means of conditional measurements on a beam splitter
A scheme for conditional generating a Hermite polynomial excited squeezed
vacuum states (HESVS) is proposed. Injecting a two-mode squeezed vacuum state
(TMSVS) into a beam splitter (BS) and counting the photons in one of the output
channels, the conditional state in the other output channel is just a HESVS. To
exhibit a number of nonclassical effects and non-Guassianity, we mainly
investigate the photon number distribution, sub-Poissonian distribution,
quadrature component distribution, and quasi-probability distribution of the
HPESVS. We find that its nonclassicality closely relates to the control
parameter of the BS, the squeezed parameter of the TMSVS, and the photon number
of conditional measurement. These further demonstrate that performing the
conditional measurement on a BS is an effective approach to generate
non-Guassian state.Comment: 8 pages, 8 figures. arXiv admin note: text overlap with
arXiv:quant-ph/9703039 by other author
New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case
As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by
employing the formula of operators' Weyl ordering expansion and the bipartite
entangled state representation we find new two-fold complex integration
transformation about the Wigner operator (in its entangled form) in phase space
quantum mechanics and its inverse transformation. In this way, some operator
ordering problems can be solved and the contents of phase space quantum
mechanics can be enriched.Comment: 8 pages, 0 figure
Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian
Based on the technique of integration within an ordered product (IWOP) of
operators we introduce the Fresnel operator for converting Caldirola-Kanai
Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel
operator with the parameters A,B,C,D corresponds to classical optical Fresnel
transformation, these parameters are the solution to a set of partial
differential equations set up in the above mentioned converting process. In
this way the exact wavefunction solution of the Schr\"odinger equation governed
by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed
number state. The corresponding Wigner function is derived by virtue of the
Weyl ordered form of the Wigner operator and the order-invariance of Weyl
ordered operators under similar transformations. The method used here can be
suitable for solving Schr\"odinger equation of other time-dependent
oscillators.Comment: 6 pages, 2 figure
Developing a teaching chatbot for learning tools and equipment in technology classrooms
Using and applying tools and equipment for designing and building projects has always been indispensable in living technology classrooms. However, students must be aware of their proper use to avoid mistakes and safety concerns. In recent years, chatbots have been widely used in various fields, offering instant, interactive responses, and their application in educational contexts has also increased rapidly. Therefore, this study developed a chatbot for LINE, a popular messaging app in Asia, for teaching standard hand tools and equipment in living technology classrooms at secondary schools. This chatbot covered (1) measuring tools, (2) hand tools, (3) power tools and equipment, and others. A total of 49 tools and pieces of equipment were included. The instructional content for each consisted of (1) instructions, (2) operating procedures and skills, and (3) troubleshooting and maintenance. The user interface adopted point-and-click forms and graphical menus to quickly guide users searching for specific information. In addition, users can enter relevant keywords and the chatbot will answer the corresponding content. The chatbot is expected to solve student questions more efficiently and assist teachers, improving the effectiveness and convenience of these hands-on lessons
Using prosody in Cantonese-speaking children with severe dysarthria: caregiver and speaker variables
Thesis (B.Sc)--University of Hong Kong, 2007.Also available in print.A dissertation submitted in partial fulfilment of the requirements for the Bachelor of Science (Speech and Hearing Sciences), The University of Hong Kong, June 30, 2007.published_or_final_versionSpeech and Hearing SciencesBachelorBachelor of Science in Speech and Hearing Science
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