7,066 research outputs found
Asymptotically Locally Optimal Weight Vector Design for a Tighter Correlation Lower Bound of Quasi-Complementary Sequence Sets
A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low nontrivial aperiodic auto- and cross-correlation sums. For multicarrier code-division multiple-access applications, the availability of large QCSSs with low correlation sums is desirable. The generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of QCSSs. The bounding expression of GLB is a fractional quadratic function of a weight vector w and is expressed in terms of three additional parameters associated with QCSS: the set size K, the number of channels M, and the sequence length N. It is known that a tighter GLB (compared to the Welch bound) is possible only if the condition M ≥ 2 and K ≥ K̅ + 1, where K̅ is a certain function of M and N, is satisfied. A challenging research problem is to determine if there exists a weight vector that gives rise to a tighter GLB for all (not just some) K ≥ K̅ + 1 and M ≥ 2, especially for large N, i.e., the condition is asymptotically both necessary and sufficient. To achieve this, we analytically optimize the GLB which is (in general) nonconvex as the numerator term is an indefinite quadratic function of the weight vector. Our key idea is to apply the frequency domain decomposition of the circulant matrix (in the numerator term) to convert the nonconvex problem into a convex one. Following this optimization approach, we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the GLB under certain conditions
Sequence Design for Cognitive CDMA Communications under Arbitrary Spectrum Hole Constraint
To support interference-free quasi-synchronous code-division multiple-access
(QS-CDMA) communication with low spectral density profile in a cognitive radio
(CR) network, it is desirable to design a set of CDMA spreading sequences with
zero-correlation zone (ZCZ) property. However, traditional ZCZ sequences (which
assume the availability of the entire spectral band) cannot be used because
their orthogonality will be destroyed by the spectrum hole constraint in a CR
channel. To date, analytical construction of ZCZ CR sequences remains open.
Taking advantage of the Kronecker sequence property, a novel family of
sequences (called "quasi-ZCZ" CR sequences) which displays zero
cross-correlation and near-zero auto-correlation zone property under arbitrary
spectrum hole constraint is presented in this paper. Furthermore, a novel
algorithm is proposed to jointly optimize the peak-to-average power ratio
(PAPR) and the periodic auto-correlations of the proposed quasi-ZCZ CR
sequences. Simulations show that they give rise to single-user bit-error-rate
performance in CR-CDMA systems which outperform traditional non-contiguous
multicarrier CDMA and transform domain communication systems; they also lead to
CR-CDMA systems which are more resilient than non-contiguous OFDM systems to
spectrum sensing mismatch, due to the wideband spreading.Comment: 13 pages,10 figures,Accepted by IEEE Journal on Selected Areas in
Communications (JSAC)--Special Issue:Cognitive Radio Nov, 201
Robust Neutrino Constraints by Combining Low Redshift Observations with the CMB
We illustrate how recently improved low-redshift cosmological measurements
can tighten constraints on neutrino properties. In particular we examine the
impact of the assumed cosmological model on the constraints. We first consider
the new HST H0 = 74.2 +/- 3.6 measurement by Riess et al. (2009) and the
sigma8*(Omegam/0.25)^0.41 = 0.832 +/- 0.033 constraint from Rozo et al. (2009)
derived from the SDSS maxBCG Cluster Catalog. In a Lambda CDM model and when
combined with WMAP5 constraints, these low-redshift measurements constrain sum
mnu<0.4 eV at the 95% confidence level. This bound does not relax when allowing
for the running of the spectral index or for primordial tensor perturbations.
When adding also Supernovae and BAO constraints, we obtain a 95% upper limit of
sum mnu<0.3 eV. We test the sensitivity of the neutrino mass constraint to the
assumed expansion history by both allowing a dark energy equation of state
parameter w to vary, and by studying a model with coupling between dark energy
and dark matter, which allows for variation in w, Omegak, and dark coupling
strength xi. When combining CMB, H0, and the SDSS LRG halo power spectrum from
Reid et al. 2009, we find that in this very general model, sum mnu < 0.51 eV
with 95% confidence. If we allow the number of relativistic species Nrel to
vary in a Lambda CDM model with sum mnu = 0, we find Nrel =
3.76^{+0.63}_{-0.68} (^{+1.38}_{-1.21}) for the 68% and 95% confidence
intervals. We also report prior-independent constraints, which are in excellent
agreement with the Bayesian constraints.Comment: 19 pages, 6 figures, submitted to JCAP; v2: accepted version. Added
section on profile likelihood for Nrel, improved plot
Rent Rigidity, Asymmetric Information, and Volatility Bounds in Labor Markets
Recent findings have revived interest in the link between real wage rigidity and employment fluctuations, in the context of frictional labor markets. The standard search and matching model fails to generate substantial labor market fluctuations if wages are set by Nash bargaining, while it can generate fluctuations in excess of what is observed if wages are completely rigid. This suggests that less severe rigidity may suffice. We study a weaker notion of real rigidity, which arises only in frictional labor markets, where the wage is the sum of the worker's opportunity cost (the value of unemployment) and a rent. With wage rigidity this sum is acyclical; we consider rent rigidity, where only the rent is acyclical. We offer two contributions. First, we derive upper bounds on labor market volatility that apply if the model of wage determination generates weakly procyclical worker rents, and that are attained by rent rigidity. Quantitatively, the bounds are tight: rent rigidity generates no more than a third of observed volatility, an outcome that is closer to Nash bargaining than to wage rigidity. Second, we show that the bounds apply to a sequence of famous solutions to the bargaining problem under asymmetric information: at best they generate rigid rents but not rigid wages.
A framework for joint design of pilot sequence and linear precoder
Most performance measures of pilot-assisted multiple-input multiple-output systems are functions of the linear precoder and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in the famous work by Hassibi and Hochwald. Our framework aims to extend the work of Hassibi and Hochwald by allowing for transmit-side fading correlations, and by considering a class of utility functions of said effective SNR matrix, most notably including the well-known capacity lower bound used by Hassibi and Hochwald. We tackle the joint optimization problem by recasting the optimization of the precoder (resp. pilot sequence) subject to a fixed pilot sequence (resp. precoder) into a convex problem. Furthermore, we prove that joint optimality requires that the eigenbases of the precoder and pilot sequence be both aligned along the eigenbasis of the channel correlation matrix. We finally describe how to wrap all studied subproblems into an iteration that converges to a local optimum of the joint optimization.Peer ReviewedPostprint (author's final draft
Optimising portfolio diversification and dimensionality
A new framework for portfolio diversification is introduced which goes beyond
the classical mean-variance approach and portfolio allocation strategies such
as risk parity. It is based on a novel concept called portfolio dimensionality
that connects diversification to the non-Gaussianity of portfolio returns and
can typically be defined in terms of the ratio of risk measures which are
homogenous functions of equal degree. The latter arises naturally due to our
requirement that diversification measures should be leverage invariant. We
introduce this new framework and argue the benefits relative to existing
measures of diversification in the literature, before addressing the question
of optimizing diversification or, equivalently, dimensionality. Maximising
portfolio dimensionality leads to highly non-trivial optimization problems with
objective functions which are typically non-convex and potentially have
multiple local optima. Two complementary global optimization algorithms are
thus presented. For problems of moderate size and more akin to asset allocation
problems, a deterministic Branch and Bound algorithm is developed, whereas for
problems of larger size a stochastic global optimization algorithm based on
Gradient Langevin Dynamics is given. We demonstrate analytically and through
numerical experiments that the framework reflects the desired properties often
discussed in the literature
Self Assembled Clusters of Spheres Related to Spherical Codes
We consider the thermodynamically driven self-assembly of spheres onto the
surface of a central sphere. This assembly process forms self-limiting, or
terminal, anisotropic clusters (N-clusters) with well defined structures. We
use Brownian dynamics to model the assembly of N-clusters varying in size from
two to twelve outer spheres, and free energy calculations to predict the
expected cluster sizes and shapes as a function of temperature and inner
particle diameter. We show that the arrangements of outer spheres at finite
temperatures are related to spherical codes, an ideal mathematical sequence of
points corresponding to densest possible sphere packings. We demonstrate that
temperature and the ratio of the diameters of the inner and outer spheres
dictate cluster morphology and dynamics. We find that some N-clusters exhibit
collective particle rearrangements, and these collective modes are unique to a
given cluster size N. We present a surprising result for the equilibrium
structure of a 5-cluster, which prefers an asymmetric square pyramid
arrangement over a more symmetric arrangement. Our results suggest a promising
way to assemble anisotropic building blocks from constituent colloidal spheres.Comment: 15 pages, 10 figure
Tight Upper Bounds for Streett and Parity Complementation
Complementation of finite automata on infinite words is not only a
fundamental problem in automata theory, but also serves as a cornerstone for
solving numerous decision problems in mathematical logic, model-checking,
program analysis and verification. For Streett complementation, a significant
gap exists between the current lower bound and upper
bound , where is the state size, is the number of
Streett pairs, and can be as large as . Determining the complexity
of Streett complementation has been an open question since the late '80s. In
this paper show a complementation construction with upper bound for and for ,
which matches well the lower bound obtained in \cite{CZ11a}. We also obtain a
tight upper bound for parity complementation.Comment: Corrected typos. 23 pages, 3 figures. To appear in the 20th
Conference on Computer Science Logic (CSL 2011
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