1,718 research outputs found
Modeling neutral evolution using an in nite-allele Markov branching process
We consider an in nite-allele Markov branching process (IAMBP). Our main focus
is the frequency spectrum of this process, i.e., the proportion of alleles having a given
number of copies at a speci ed time point. We derive the variance of the frequency
spectrum, which is useful for interval estimation and hypothesis testing for process
parameters. In addition, for a class of special IAMBP with birth and death o spring
distribution, we show that the mean of its limiting frequency spectrum has an explicit
form in terms of the hypergeometric function. We also derive an asymptotic expression
for convergence rate to the limit. Simulations are used to illustrate the results for the
birth and death process
Approximately EFX Allocations for Indivisible Chores
In this paper, we study how to fairly allocate a set of m indivisible chores
to a group of n agents, each of which has a general additive cost function on
the items. Since envy-free (EF) allocations are not guaranteed to exist, we
consider the notion of envy-freeness up to any item (EFX). In contrast to the
fruitful results regarding the (approximation of) EFX allocations for goods,
very little is known for the allocation of chores. Prior to our work, for the
allocation of chores, it is known that EFX allocations always exist for two
agents or general number of agents with identical ordering cost functions. For
general instances, no non-trivial approximation result regarding EFX allocation
is known. In this paper, we make progress in this direction by providing
several polynomial time algorithms for the computation of EFX and approximately
EFX allocations. We show that for three agents we can always compute a
4.45-approximation of EFX allocation. For n>=4 agents, our algorithm always
computes a (3n^2-n)-approximation. We also study the bi-valued instances, in
which agents have at most two cost values on the chores. For three agents, we
provide an algorithm for the computation of EFX allocations. For n>=4 agents,
we present algorithms for the computation of partial EFX allocations with at
most n-1 unallocated items; and (n-1)-approximation of EFX allocations.Comment: Include new results about partial EFX allocations and improved
results regarding approximate EFX allocation
Information-Coupled Turbo Codes for LTE Systems
We propose a new class of information-coupled (IC) Turbo codes to improve the
transport block (TB) error rate performance for long-term evolution (LTE)
systems, while keeping the hybrid automatic repeat request protocol and the
Turbo decoder for each code block (CB) unchanged. In the proposed codes, every
two consecutive CBs in a TB are coupled together by sharing a few common
information bits. We propose a feed-forward and feed-back decoding scheme and a
windowed (WD) decoding scheme for decoding the whole TB by exploiting the
coupled information between CBs. Both decoding schemes achieve a considerable
signal-to-noise-ratio (SNR) gain compared to the LTE Turbo codes. We construct
the extrinsic information transfer (EXIT) functions for the LTE Turbo codes and
our proposed IC Turbo codes from the EXIT functions of underlying convolutional
codes. An SNR gain upper bound of our proposed codes over the LTE Turbo codes
is derived and calculated by the constructed EXIT charts. Numerical results
show that the proposed codes achieve an SNR gain of 0.25 dB to 0.72 dB for
various code parameters at a TB error rate level of , which complies
with the derived SNR gain upper bound.Comment: 13 pages, 12 figure
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