488,333 research outputs found
The Algebra of Binary Search Trees
We introduce a monoid structure on the set of binary search trees, by a
process very similar to the construction of the plactic monoid, the
Robinson-Schensted insertion being replaced by the binary search tree
insertion. This leads to a new construction of the algebra of Planar Binary
Trees of Loday-Ronco, defining it in the same way as Non-Commutative Symmetric
Functions and Free Symmetric Functions. We briefly explain how the main known
properties of the Loday-Ronco algebra can be described and proved with this
combinatorial point of view, and then discuss it from a representation
theoretical point of view, which in turns leads to new combinatorial properties
of binary trees.Comment: 49 page
Weak Pseudo-Rationalizability
This paper generalizes rationalizability of a choice function by a single acyclic binary relation to
rationalizability by a set of such relations. Rather than selecting those options in a menu that are
maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function
selects those options that are maximal with respect to at least one binary relation in a given
set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple
functional properties. This result also generalizes Aizerman and Malishevski's characterization
of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total
orders
Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture
We elucidate the universal properties of the nonequilibrium steady states
(NESS) in a driven symmetric binary fluid mixture, an example of active
advection, in its miscible phase. We use the symmetries of the equations of
motion to establish the appropriate form of the structure functions which
characterise the statistical properties of the NESS of a driven symmetric
binary fluid mixture. We elucidate the universal properties described by the
scaling exponents and the amplitude ratios. Our results suggest that these
exponents and amplitude ratios vary continuously with the degree of
crosscorrelations between the velocity and the gradient of the concentration
fields. Furthermore, we demonstrate, in agreement with Celani et al, Phys. Rev.
Lett., 89, 234502 (2002, that the conventional structure functions as used in
passive scalar turbulence studies exhibit only simple scaling in the problem of
symmetric binary fluid mixture even in the weak concentration limit. We also
discuss possible experimental verifications of our results.Comment: To appear in JSTAT (letters) (2005
Pseudorandom binary functions on rooted plane trees
International audienceIn an earlier paper the authors considered r-almost s-uniform trees, i.e. rooted planar trees T such that the root has r successors, and every other vertex has s suc- cessors. They considered binary functions f : V (T ) → {−1, +1} defined on the set V (T ) of the vertices of such a tree T and studied the pseudorandomness of binary functions of this type. Here the authors extend the problem to general rooted plane trees: the measures of pseudorandomness of binary functions defined on trees of this type are introduced; the connection between these measures is analyzed; the size of these measures for truly random binary functions is studied; binary functions with strong pseudorandom properties are constructed; pseudorandom properties of impor- tant special binary functions are studied
Magneto-transport in a binary alloy ring
Magneto-transport properties are investigated in a binary alloy ring
subjected to an Aharonov-Bohm (AB) flux \phi within a single-band
non-interacting tight-binding framework. In the first part, we expose
analytically the behavior of persistent current in an isolated ordered binary
alloy ring as functions of electron concentration N_e and AB flux \phi. While,
in the second part of the article, we discuss electron transport properties
through a binary alloy ring attached to two semi-infinite one-dimensional
metallic electrodes. The effect of impurities is also analyzed. From our study
we propose that under suitable choices of the parameter values the system can
act as a p-type or an n-type semiconductor.Comment: 7 pages, 8 figure
Quantum Communications Based on Quantum Hashing
In this paper we consider an application of the recently proposed quantum
hashing technique for computing Boolean functions in the quantum communication
model. The combination of binary functions on non-binary quantum hash function
is done via polynomial presentation, which we have called a characteristic of a
Boolean function. Based on the characteristic polynomial presentation of
Boolean functions and quantum hashing technique we present a method for
computing Boolean functions in the quantum one-way communication model, where
one of the parties performs his computations and sends a message to the other
party, who must output the result after his part of computations. Some of the
results are also true in a more restricted Simultaneous Message Passing model
with no shared resources, in which communicating parties can interact only via
the referee. We give several examples of Boolean functions whose polynomial
presentations have specific properties allowing for construction of quantum
communication protocols that are provably exponentially better than classical
ones in the simultaneous message passing setting
Orbital L-functions for the space of binary cubic forms
We introduce the notion of orbital L-functions for the space of binary cubic
forms and investigate their analytic properties. We study their functional
equations and residue formulas in some detail. Aside from the intrinsic
interest, results from this paper are used to prove the existence of secondary
terms in counting functions for cubic fields. This is worked out in a companion
paper (arXiv:1102.2914).Comment: 49 pages; submitte
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