7,371 research outputs found
Supersymmetry Across Nanoscale Heterojunction
We argue that supersymmetric transformation could be applied across the
heterojunction formed by joining of two mixed semiconductors. A general
framework is described by specifying the structure of ladder operators at the
junction for making quantitative estimation of physical quantities. For a
particular heterojunction device, we show that an exponential grading inside a
nanoscale doped layer is amenable to exact analytical treatment for a class of
potentials distorted by the junctions through the solutions of transformed
Morse-Type potentials.Comment: 7 pages, 2 figure
Minimum-Weight Edge Discriminator in Hypergraphs
In this paper we introduce the concept of minimum-weight edge-discriminators
in hypergraphs, and study its various properties. For a hypergraph , a function is said to be an {\it edge-discriminator} on if
, for all hyperedges , and
, for every two
distinct hyperedges . An {\it optimal
edge-discriminator} on , to be denoted by , is
an edge-discriminator on satisfying , where
the minimum is taken over all edge-discriminators on . We prove
that any hypergraph , with , satisfies ,
and equality holds if and only if the elements of are mutually
disjoint. For -uniform hypergraphs , it
follows from results on Sidon sequences that , and
the bound is attained up to a constant factor by the complete -uniform
hypergraph. Next, we construct optimal edge-discriminators for some special
hypergraphs, which include paths, cycles, and complete -partite hypergraphs.
Finally, we show that no optimal edge-discriminator on any hypergraph , with , satisfies
, which, in turn,
raises many other interesting combinatorial questions.Comment: 22 pages, 5 figure
New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials
We have generated, using an sl(2,R) formalism, several new classes of
quasi-solvable elliptic potentials, which in the appropriate limit go over to
the exactly solvable forms. We have obtained exact solutions of the
corresponding spectral problems for some real values of the potential
parameters. We have also given explicit expressions of the families of
associated orthogonal polynomials in the energy variable.Comment: 14 pages, 5 tables, LaTeX2
Enhanced information retrieval using domain-specific recommender models
The objective of an information retrieval (IR) system is to retrieve relevant items which meet a user information need. There is currently significant interest in personalized IR which seeks to improve IR effectiveness by incorporating a model of the user’s interests. However, in some situations
there may be no opportunity to learn about the interests of a specific user on a certain topic. In our work, we propose an IR approach which combines a recommender algorithm with IR methods to improve retrieval for domains where the system has no opportunity to learn prior information about the user’s knowledge of a domain for which they have not previously entered a query. We use search data from other previous users interested in the same topic to build a
recommender model for this topic. When a user enters a query on a topic, new to this user, an appropriate recommender model is selected and used to predict a ranking which the user may find interesting based on the behaviour of previous
users with similar queries. The recommender output is integrated with a standard IR method in a weighted linear combination to provide a final result for the user. Experiments using the INEX 2009 data collection with a simulated recommender training set show that our approach can improve on a baseline IR system
Upper tails and independence polynomials in random graphs
The upper tail problem in the Erd\H{o}s--R\'enyi random graph
asks to estimate the probability that the number of
copies of a graph in exceeds its expectation by a factor .
Chatterjee and Dembo showed that in the sparse regime of as
with for an explicit ,
this problem reduces to a natural variational problem on weighted graphs, which
was thereafter asymptotically solved by two of the authors in the case where
is a clique. Here we extend the latter work to any fixed graph and
determine a function such that, for as above and any fixed
, the upper tail probability is , where is the maximum degree of . As it turns out, the
leading order constant in the large deviation rate function, , is
governed by the independence polynomial of , defined as where is the number of independent sets of size in . For
instance, if is a regular graph on vertices, then is the
minimum between and the unique positive solution of
Quantum Cloning, Bell's Inequality and Teleportation
We analyze a possibility of using the two qubit output state from
Buzek-Hillery quantum copying machine (not necessarily universal quantum
cloning machine) as a teleportation channel. We show that there is a range of
values of the machine parameter for which the two qubit output state is
entangled and violates Bell-CHSH inequality and for a different range it
remains entangled but does not violate Bell-CHSH inequality. Further we observe
that for certain values of the machine parameter the two-qubit mixed state can
be used as a teleportation channel. The use of the output state from the
Buzek-Hillery cloning machine as a teleportation channel provides an additional
appeal to the cloning machine and motivation of our present work.Comment: 7 pages and no figures, Accepted in Journal of Physics
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