6,455 research outputs found
Dependent randomized rounding for clustering and partition systems with knapsack constraints
Clustering problems are fundamental to unsupervised learning. There is an
increased emphasis on fairness in machine learning and AI; one representative
notion of fairness is that no single demographic group should be
over-represented among the cluster-centers. This, and much more general
clustering problems, can be formulated with "knapsack" and "partition"
constraints. We develop new randomized algorithms targeting such problems, and
study two in particular: multi-knapsack median and multi-knapsack center. Our
rounding algorithms give new approximation and pseudo-approximation algorithms
for these problems. One key technical tool, which may be of independent
interest, is a new tail bound analogous to Feige (2006) for sums of random
variables with unbounded variances. Such bounds are very useful in inferring
properties of large networks using few samples
Fast, large volume, GPU enabled simulations for the Ly-alpha forest: power spectrum forecasts for baryon acoustic oscillation experiments
High redshift measurements of the baryonic acoustic oscillation scale (BAO)
from large Ly-alpha forest surveys represent the next frontier of dark energy
studies. As part of this effort, efficient simulations of the BAO signature
from the Ly-alpha forest will be required. We construct a model for producing
fast, large volume simulations of the Ly-alpha forest for this purpose.
Utilising a calibrated semi-analytic approach, we are able to run very large
simulations in 1 Gpc^3 volumes which fully resolve the Jeans scale in less than
a day on a desktop PC using a GPU enabled version of our code. The Ly-alpha
forest spectra extracted from our semi-analytical simulations are in excellent
agreement with those obtained from a fully hydrodynamical reference simulation.
Furthermore, we find our simulated data are in broad agreement with
observational measurements of the flux probability distribution and 1D flux
power spectrum. We are able to correctly recover the input BAO scale from the
3D Ly-alpha flux power spectrum measured from our simulated data, and estimate
that a BOSS-like 10^4 deg^2 survey with ~15 background sources per square
degree and a signal-to-noise of ~5 per pixel should achieve a measurement of
the BAO scale to within ~1.4 per cent. We also use our simulations to provide
simple power-law expressions for estimating the fractional error on the BAO
scale on varying the signal-to-noise and the number density of background
sources. The speed and flexibility of our approach is well suited for exploring
parameter space and the impact of observational and astrophysical systematics
on the recovery of the BAO signature from forthcoming large scale spectroscopic
surveys.Comment: 16 pages, 11 figures, accepted to MNRA
A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems
This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all the linear fractional programming models on the given set of constraints were solved separately. Next, all the linear fractional objective functions were linearized, membership functions of objective functions and decision variables controlled by decision-makers at the highest level calculated, and a fuzzy multi-objective linear programming model formed and solved as linear goal programming problem by using simplex algorithm. The efficiency of the proposed algorithm was investigated using an economic example, and the obtained results compared with those obtained using an existing method
A REVIEW OF APPLICATIONS OF MULTIPLE - CRITERIA DECISION-MAKING TECHNIQUES TO FISHERIES
Management of public resources, such as fisheries, is a complex task. Society, in general, has a number of goals that it hopes to achieve from the use of public resources. These include conservation, economic, and social objectives. However, these objectives often conflict, due to the varying opinions of the many stakeholders. It would appear that the techniques available in the field of multiple-criteria decision-making (MCDM) are well suited to the analysis and determination of fisheries management regimes. However, to date, relatively few publications exist using such MCDM methods compared to other applicational fields, such as forestry, agriculture, and finance. This paper reviews MCDM applied to fishery management by providing an overview of the research published to date. Conclusions are drawn regarding the success and applicability of these techniques to analyzing fisheries management problems.Resource /Energy Economics and Policy,
Spectral Efficiency and Energy Efficiency Tradeoff in Massive MIMO Downlink Transmission with Statistical CSIT
As a key technology for future wireless networks, massive multiple-input
multiple-output (MIMO) can significantly improve the energy efficiency (EE) and
spectral efficiency (SE), and the performance is highly dependant on the degree
of the available channel state information (CSI). While most existing works on
massive MIMO focused on the case where the instantaneous CSI at the transmitter
(CSIT) is available, it is usually not an easy task to obtain precise
instantaneous CSIT. In this paper, we investigate EE-SE tradeoff in single-cell
massive MIMO downlink transmission with statistical CSIT. To this end, we aim
to optimize the system resource efficiency (RE), which is capable of striking
an EE-SE balance. We first figure out a closed-form solution for the
eigenvectors of the optimal transmit covariance matrices of different user
terminals, which indicates that beam domain is in favor of performing RE
optimal transmission in massive MIMO downlink. Based on this insight, the RE
optimization precoding design is reduced to a real-valued power allocation
problem. Exploiting the techniques of sequential optimization and random matrix
theory, we further propose a low-complexity suboptimal two-layer
water-filling-structured power allocation algorithm. Numerical results
illustrate the effectiveness and near-optimal performance of the proposed
statistical CSI aided RE optimization approach.Comment: Typos corrected. 14 pages, 7 figures. Accepted for publication on
IEEE Transactions on Signal Processing. arXiv admin note: text overlap with
arXiv:2002.0488
Approximating the Permanent with Fractional Belief Propagation
We discuss schemes for exact and approximate computations of permanents, and
compare them with each other. Specifically, we analyze the Belief Propagation
(BP) approach and its Fractional Belief Propagation (FBP) generalization for
computing the permanent of a non-negative matrix. Known bounds and conjectures
are verified in experiments, and some new theoretical relations, bounds and
conjectures are proposed. The Fractional Free Energy (FFE) functional is
parameterized by a scalar parameter , where
corresponds to the BP limit and corresponds to the exclusion
principle (but ignoring perfect matching constraints) Mean-Field (MF) limit.
FFE shows monotonicity and continuity with respect to . For every
non-negative matrix, we define its special value to be the
for which the minimum of the -parameterized FFE functional is
equal to the permanent of the matrix, where the lower and upper bounds of the
-interval corresponds to respective bounds for the permanent. Our
experimental analysis suggests that the distribution of varies for
different ensembles but always lies within the interval.
Moreover, for all ensembles considered the behavior of is highly
distinctive, offering an emprirical practical guidance for estimating
permanents of non-negative matrices via the FFE approach.Comment: 42 pages, 14 figure
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