594 research outputs found
Quantum matchgate computations and linear threshold gates
The theory of matchgates is of interest in various areas in physics and
computer science. Matchgates occur in e.g. the study of fermions and spin
chains, in the theory of holographic algorithms and in several recent works in
quantum computation. In this paper we completely characterize the class of
boolean functions computable by unitary two-qubit matchgate circuits with some
probability of success. We show that this class precisely coincides with that
of the linear threshold gates. The latter is a fundamental family which appears
in several fields, such as the study of neural networks. Using the above
characterization, we further show that the power of matchgate circuits is
surprisingly trivial in those cases where the computation is to succeed with
high probability. In particular, the only functions that are
matchgate-computable with success probability greater than 3/4 are functions
depending on only a single bit of the input
A Hypergraph Dictatorship Test with Perfect Completeness
A hypergraph dictatorship test is first introduced by Samorodnitsky and
Trevisan and serves as a key component in their unique games based \PCP
construction. Such a test has oracle access to a collection of functions and
determines whether all the functions are the same dictatorship, or all their
low degree influences are Their test makes queries and has
amortized query complexity but has an inherent loss of
perfect completeness. In this paper we give an adaptive hypergraph dictatorship
test that achieves both perfect completeness and amortized query complexity
.Comment: Some minor correction
DEVELOPMENT OF A DEVICE TO MEASURE THE BLADE TIP CLEARANCE OF AN AXIAL COMPRESSOR
Axial compressors, used in gas turbines, jet engines and also small scale power plants, are rotating, airfoil based compressors in which the working fluid flows parallel to the axis of rotation. There has been continuous struggle to maximize the efficiency of these compressors. One of the many ways to achieve the same is to minimize the tip clearance i.e. to reduce the distance between the blade tip and the housing. Experiments need to be conducted to measure the changes in the tip clearance while the compressor is operating. Conventional devices to measure this tip clearance have proven to be costly if a small scale application is under consideration. Our aim in this project is to develop a device which will measure the blade tip clearance of an axial flow compressor economically. The literature review, development of the device, its working and results will be discussed in this paper
Approximation Algorithms for Connected Maximum Cut and Related Problems
An instance of the Connected Maximum Cut problem consists of an undirected
graph G = (V, E) and the goal is to find a subset of vertices S V
that maximizes the number of edges in the cut \delta(S) such that the induced
graph G[S] is connected. We present the first non-trivial \Omega(1/log n)
approximation algorithm for the connected maximum cut problem in general graphs
using novel techniques. We then extend our algorithm to an edge weighted case
and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark
contrast to the classical max-cut problem, we show that the connected maximum
cut problem remains NP-hard even on unweighted, planar graphs. On the positive
side, we obtain a polynomial time approximation scheme for the connected
maximum cut problem on planar graphs and more generally on graphs with bounded
genus.Comment: 17 pages, Conference version to appear in ESA 201
On the Maximum Crossing Number
Research about crossings is typically about minimization. In this paper, we
consider \emph{maximizing} the number of crossings over all possible ways to
draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009]
conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a
drawing with vertices in convex position, that maximizes the number of edge
crossings. We disprove this conjecture by constructing a planar graph on twelve
vertices that allows a non-convex drawing with more crossings than any convex
one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the
maximum number of crossings of a geometric graph and that the weighted
geometric case is NP-hard to approximate. We strengthen these results by
showing hardness of approximation even for the unweighted geometric case and
prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Given an undirected graph , a collection of
pairs of vertices, and an integer , the Edge Multicut problem ask if there
is a set of at most edges such that the removal of disconnects
every from the corresponding . Vertex Multicut is the analogous
problem where is a set of at most vertices. Our main result is that
both problems can be solved in time , i.e.,
fixed-parameter tractable parameterized by the size of the cutset in the
solution. By contrast, it is unlikely that an algorithm with running time of
the form exists for the directed version of the problem, as
we show it to be W[1]-hard parameterized by the size of the cutset
A note on anti-coordination and social interactions
This note confirms a conjecture of [Bramoull\'{e}, Anti-coordination and
social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The
problem, which we name the maximum independent cut problem, is a restricted
version of the MAX-CUT problem, requiring one side of the cut to be an
independent set. We show that the maximum independent cut problem does not
admit any polynomial time algorithm with approximation ratio better than
, where is the number of nodes, and arbitrarily
small, unless P=NP. For the rather special case where each node has a degree of
at most four, the problem is still MAXSNP-hard.Comment: 7 page
Fast Distributed Approximation for Max-Cut
Finding a maximum cut is a fundamental task in many computational settings.
Surprisingly, it has been insufficiently studied in the classic distributed
settings, where vertices communicate by synchronously sending messages to their
neighbors according to the underlying graph, known as the or
models. We amend this by obtaining almost optimal
algorithms for Max-Cut on a wide class of graphs in these models. In
particular, for any , we develop randomized approximation
algorithms achieving a ratio of to the optimum for Max-Cut on
bipartite graphs in the model, and on general graphs in the
model.
We further present efficient deterministic algorithms, including a
-approximation for Max-Dicut in our models, thus improving the best known
(randomized) ratio of . Our algorithms make non-trivial use of the greedy
approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing
an unconstrained (non-monotone) submodular function, which may be of
independent interest
Reexamination of a multisetting Bell inequality for qudits
The class of d-setting, d-outcome Bell inequalities proposed by Ji and
collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive
integer d > 2, we show that the corresponding non-trivial Bell inequality for
probabilities provides the maximum classical winning probability of the
Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also
demonstrate that the general classical upper bounds given by Ji et al. are
underestimated, which invalidates many of the corresponding correlation
inequalities presented thereof. We remedy this problem, partially, by providing
the actual classical upper bound for d less than or equal to 13 (including
non-prime values of d). We further determine that for prime value d in this
range, most of these probability and correlation inequalities are tight, i.e.,
facet-inducing for the respective classical correlation polytope. Stronger
lower and upper bounds on the quantum violation of these inequalities are
obtained. In particular, we prove that once the probability inequalities are
given, their correlation counterparts given by Ji and co-workers are no longer
relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper
bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables
(substantially revised with new results on the tightness of the correlation
inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are
welcome
A provisional database for the silicon content of foods in the United Kingdom
Si may play an important role in bone formation and connective tissue metabolism. Although biological interest in this element has recently increased, limited literature exists on the Si content of foods. To further our knowledge and understanding of the relationship between dietary Si and human health, a reliable food composition database, relevant for the UK population, is required. A total of 207 foods and beverages, commonly consumed in the UK, were analysed for Si content. Composite samples were analysed using inductively coupled plasma–optical emission spectrometry following microwave-assisted digestion with nitric acid and H2O2. The highest concentrations of Si were found in cereals and cereal products, especially less refined cereals and oat-based products. Fruit and vegetables were highly variable sources of Si with substantial amounts present in Kenyan beans, French beans, runner beans, spinach, dried fruit, bananas and red lentils, but undetectable amounts in tomatoes, oranges and onions. Of the beverages, beer, a macerated whole-grain cereal product, contained the greatest level of Si, whilst drinking water was a variable source with some mineral waters relatively high in Si. The present study provides a provisional database for the Si content of UK foods, which will allow the estimation of dietary intakes of Si in the UK population and investigation into the role of dietary Si in human health.<br /
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