12,143 research outputs found
Static Data Structure for Discrete Advance Bandwidth Reservations on the Internet
In this paper we present a discrete data structure for reservations of
limited resources. A reservation is defined as a tuple consisting of the time
interval of when the resource should be reserved, , and the amount of the
resource that is reserved, , formally .
The data structure is similar to a segment tree. The maximum spanning
interval of the data structure is fixed and defined in advance. The granularity
and thereby the size of the intervals of the leaves is also defined in advance.
The data structure is built only once. Neither nodes nor leaves are ever
inserted, deleted or moved. Hence, the running time of the operations does not
depend on the number of reservations previously made. The running time does not
depend on the size of the interval of the reservation either. Let be the
number of leaves in the data structure. In the worst case, the number of
touched (i.e. traversed) nodes is in any operation , hence the
running time of any operation is also
Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution
Analyses of serially-sampled data often begin with the assumption that the
observations represent discrete samples from a latent continuous-time
stochastic process. The continuous-time Markov chain (CTMC) is one such
generative model whose popularity extends to a variety of disciplines ranging
from computational finance to human genetics and genomics. A common theme among
these diverse applications is the need to simulate sample paths of a CTMC
conditional on realized data that is discretely observed. Here we present a
general solution to this sampling problem when the CTMC is defined on a
discrete and finite state space. Specifically, we consider the generation of
sample paths, including intermediate states and times of transition, from a
CTMC whose beginning and ending states are known across a time interval of
length . We first unify the literature through a discussion of the three
predominant approaches: (1) modified rejection sampling, (2) direct sampling,
and (3) uniformization. We then give analytical results for the complexity and
efficiency of each method in terms of the instantaneous transition rate matrix
of the CTMC, its beginning and ending states, and the length of sampling
time . In doing so, we show that no method dominates the others across all
model specifications, and we give explicit proof of which method prevails for
any given and endpoints. Finally, we introduce and compare three
applications of CTMCs to demonstrate the pitfalls of choosing an inefficient
sampler.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS247 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Topological Reduction of Tight-Binding Models on Complex Networks
Complex molecules and mesoscopic structures are naturally described by
general networks of elementary building blocks and tight-binding is one of the
simplest quantum model suitable for studying the physical properties arising
from the network topology. Despite the simplicity of the model, topological
complexity can make the evaluation of the spectrum of the tight-binding
Hamiltonian a rather hard task, since the lack of translation invariance rules
out such a powerful tool as Fourier transform. In this paper we introduce a
rigorous analytical technique, based on topological methods, for the exact
solution of this problem on branched structures. Besides its analytic power,
this technique is also a promising engineering tool, helpful in the design of
netwoks displaying the desired spectral features.Comment: 19 pages, 14 figure
Area Law Violations and Quantum Phase Transitions in Modified Motzkin Walk Spin Chains
Area law violations for entanglement entropy in the form of a square root has
recently been studied for one-dimensional frustration-free quantum systems
based on the Motzkin walks and their variations. Here we consider a Motzkin
walk with a different Hilbert space on each step of the walk spanned by
elements of a {\it Symmetric Inverse Semigroup} with the direction of each step
governed by its algebraic structure. This change alters the number of paths
allowed in the Motzkin walk and introduces a ground state degeneracy sensitive
to boundary perturbations. We study the frustration-free spin chains based on
three symmetric inverse semigroups, \cS^3_1, \cS^3_2 and \cS^2_1. The
system based on \cS^3_1 and \cS^3_2 provide examples of quantum phase
transitions in one dimensions with the former exhibiting a transition between
the area law and a logarithmic violation of the area law and the latter
providing an example of transition from logarithmic scaling to a square root
scaling in the system size, mimicking a colored \cS^3_1 system. The system
with \cS^2_1 is much simpler and produces states that continue to obey the
area law.Comment: 40 pages, 14 figures, A condensed version of this paper has been
submitted to the Proceedings of the 2017 Granada Seminar on Computational
Physics, Contains minor revisions and is closer to the Journal version. v3
includes an addendum that modifies the final Hamiltonian but does not change
the main results of the pape
Solution of an associating lattice gas model with density anomaly on a Husimi lattice
We study a model of a lattice gas with orientational degrees of freedom which
resemble the formation of hydrogen bonds between the molecules. In this model,
which is the simplified version of the Henriques-Barbosa model, no distinction
is made between donors and acceptors in the bonding arms. We solve the model in
the grand-canonical ensemble on a Husimi lattice built with hexagonal
plaquettes with a central site. The ground-state of the model, which was
originally defined on the triangular lattice, is exactly reproduced by the
solution on this Husimi lattice. In the phase diagram, one gas and two liquid
(high density-HDL and low density-LDL) phases are present. All phase
transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three
phases coexist at a triple point. A line of temperatures of maximum density
(TMD) in the isobars is found in the metastable GAS phase, as well as another
line of temperatures of minimum density (TmD) appears in the LDL phase, part of
it in the stable region and another in the metastable region of this phase.
These findings are at variance with simulational results for the same model on
the triangular lattice, which suggested a phase diagram with two critical
points. However, our results show very good quantitative agreement with the
simulations, both for the coexistence loci and the densities of particles and
of hydrogen bonds. We discuss the comparison of the simulations with our
results.Comment: 12 pages, 5 figure
Motzkin numbers of higher rank: Generating function and explicit expression
The generating function and an explicit expression is derived for the
(colored) Motzkin numbers of higher rank introduced recently. Considering the
special case of rank one yields the corresponding results for the conventional
colored Motzkin numbers for which in addition a recursion relation is given
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