244 research outputs found
Optimal strategies for a game on amenable semigroups
The semigroup game is a two-person zero-sum game defined on a semigroup S as
follows: Players 1 and 2 choose elements x and y in S, respectively, and player
1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the
semigroup is amenable in the sense of Day and von Neumann, one can extend the
set of classical strategies, namely countably additive probability measures on
S, to include some finitely additive measures in a natural way. This extended
game has a value and the players have optimal strategies. This theorem extends
previous results for the multiplication game on a compact group or on the
positive integers with a specific payoff. We also prove that the procedure of
extending the set of allowed strategies preserves classical solutions: if a
semigroup game has a classical solution, this solution solves also the extended
game.Comment: 17 pages. To appear in International Journal of Game Theor
Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field
We consider a theoretical model for a nonlinear nanomechanical resonator
coupled to a superconducting microwave resonator. The nanomechanical resonator
is driven parametrically at twice its resonance frequency, while the
superconducting microwave resonator is driven with two tones that differ in
frequency by an amount equal to the parametric driving frequency. We show that
the semi-classical approximation of this system has an interesting fixed point
bifurcation structure. In the semi-classical dynamics a transition from stable
fixed points to limit cycles is observed as one moves from positive to negative
detuning. We show that signatures of this bifurcation structure are also
present in the full dissipative quantum system and further show that it leads
to mixed state entanglement between the nanomechanical resonator and the
microwave cavity in the dissipative quantum system that is a maximum close to
the semi-classical bifurcation. Quantum signatures of the semi-classical
limit-cycles are presented.Comment: 36 pages, 18 figure
Graph states in phase space
The phase space for a system of qubits is a discrete grid of points, whose axes are labeled in terms of the elements of the
finite field \Gal{2^n} to endow it with proper geometrical properties. We
analyze the representation of graph states in that phase space, showing that
these states can be identified with a class of non-singular curves. We provide
an algebraic representation of the most relevant quantum operations acting on
these states and discuss the advantages of this approach.Comment: 14 pages. 2 figures. Published in Journal of Physics
INDEPENDENT DISCOVERIES IN GRAPH THEORY *
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72829/1/j.1749-6632.1979.tb17761.x.pd
The Complexity of the Empire Colouring Problem
We investigate the computational complexity of the empire colouring problem
(as defined by Percy Heawood in 1890) for maps containing empires formed by
exactly countries each. We prove that the problem can be solved in
polynomial time using colours on maps whose underlying adjacency graph has
no induced subgraph of average degree larger than . However, if , the problem is NP-hard even if the graph is a forest of paths of arbitrary
lengths (for any , provided .
Furthermore we obtain a complete characterization of the problem's complexity
for the case when the input graph is a tree, whereas our result for arbitrary
planar graphs fall just short of a similar dichotomy. Specifically, we prove
that the empire colouring problem is NP-hard for trees, for any , if
(and polynomial time solvable otherwise). For arbitrary
planar graphs we prove NP-hardness if for , and , for . The result for planar graphs also proves the NP-hardness of colouring
with less than 7 colours graphs of thickness two and less than colours
graphs of thickness .Comment: 23 pages, 12 figure
Застосування інтервальних нормобаричних гіпоксичних тренувань для амеліорації впливу бальнеотерапевтичного комплексу курорту Трускавець на резистентність до гіпоксії та вегетативну нервову систему
В клинико-физиологическом наблюдении за детьми с вегетативной дистонией показано, что дополнение стандартного бальнеотерапевтического комплекса курорта Трускавец интервальной нормобарической гипоксической тренировкой предотвращает снижение теста Штанге и сопутствующее ему усугубление симпатотонического сдвига вегетативного гомеостаза, а также усиливает положительное влияние бальнеотерапии на тест Штанге, сопровождаемое ваготоническим сдвигом вегетативного гомеостаза.In the clinical-physiological monitoring of children with vegetative dystonia is shown that the addition of standard balneotherapeutic complex spa Truskavets interval normobaric hypoxic training prevents the reduction of the hypoxic test Stange and the concomitant worsening sympathotonic shift of vegetative homeostasis, but also enhances the positive effect of balneotherapy on the test Stange, accompanied by a shift of autonomic vagotonic homeostasis
Crystal constructions in Number Theory
Weyl group multiple Dirichlet series and metaplectic Whittaker functions can
be described in terms of crystal graphs. We present crystals as parameterized
by Littelmann patterns and we give a survey of purely combinatorial
constructions of prime power coefficients of Weyl group multiple Dirichlet
series and metaplectic Whittaker functions using the language of crystal
graphs. We explore how the branching structure of crystals manifests in these
constructions, and how it allows access to some intricate objects in number
theory and related open questions using tools of algebraic combinatorics
Vertex labeling and routing in expanded Apollonian networks
We present a family of networks, expanded deterministic Apollonian networks,
which are a generalization of the Apollonian networks and are simultaneously
scale-free, small-world, and highly clustered. We introduce a labeling of their
vertices that allows to determine a shortest path routing between any two
vertices of the network based only on the labels.Comment: 16 pages, 2 figure
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