Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC

AbstractMatsumoto, Saito and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing algorithms, the number of points is fixed in advance, but extensible point sets are preferred in some applications. In this paper, we propose a random search algorithm for extensible low-WAFOM point sets. For this, we introduce a method that uses lookup tables to compute WAFOM faster. Numerical results show that our extensible low-WAFOM point sets are comparable with Niederreiter–Xing sequences for some low-dimensional and smooth test functions.

Download Full-text

Existence of Higher Order Convergent Quasi-Monte Carlo Rules via Walsh Figure of Merit

Monte Carlo and Quasi-Monte Carlo Methods 2012 - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-642-41095-6_29 ◽

2013 ◽

pp. 569-579 ◽

Cited By ~ 3

Author(s):

Makoto Matsumoto ◽

Takehito Yoshiki

Keyword(s):

Monte Carlo ◽

Figure Of Merit ◽

Higher Order ◽

Quasi Monte Carlo

Download Full-text

Richardson extrapolation allows truncation of higher-order digital nets and sequences

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drz017 ◽

2019 ◽

Vol 40 (3) ◽

pp. 2052-2075

Author(s):

Takashi Goda

Keyword(s):

Rate Of Convergence ◽

Numerical Integration ◽

Search Algorithm ◽

Richardson Extrapolation ◽

Higher Order ◽

Unit Cube ◽

Optimal Rate ◽

Lattice Rules ◽

Optimal Rate Of Convergence ◽

Digital Nets

Abstract We study numerical integration of smooth functions defined over the $s$-dimensional unit cube. A recent work by Dick et al. (2019, Richardson extrapolation of polynomial lattice rules. SIAM J. Numer. Anal., 57, 44–69) has introduced so-called extrapolated polynomial lattice rules, which achieve the almost optimal rate of convergence for numerical integration, and can be constructed by the fast component-by-component search algorithm with smaller computational costs as compared to interlaced polynomial lattice rules. In this paper we prove that, instead of polynomial lattice point sets, truncated higher-order digital nets and sequences can be used within the same algorithmic framework to explicitly construct good quadrature rules achieving the almost optimal rate of convergence. The major advantage of our new approach compared to original higher-order digital nets is that we can significantly reduce the precision of points, i.e., the number of digits necessary to describe each quadrature node. This finding has a practically useful implication when either the number of points or the smoothness parameter is so large that original higher-order digital nets require more than the available finite-precision floating-point representations.

Download Full-text

Compact, Slotted, Printed Antennas for Dual-Band Communication in Future Wireless Sensor Networks

International Journal of Antennas and Propagation ◽

10.1155/2013/873234 ◽

2013 ◽

Vol 2013 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Constantine G. Kakoyiannis ◽

Philip Constantinou

Keyword(s):

Figure Of Merit ◽

Higher Order ◽

Dual Band ◽

Portable Devices ◽

Fractional Bandwidth ◽

Printed Antennas ◽

Higher Order Modes ◽

Half Wavelength ◽

Simple Figure ◽

Dual Band Antennas

Inverted-F antennas (IFAs) are a primary choice to implement the radiating system of portable devices. A tried and tested idea can remain topical if proven useful in modern applications. This paper shows that printed IFAs (PIFAs) are capable of forming robust, compact, dual-band radiating systems for wireless microsensors with an adjustable spacing between bands. Reactive tuning was applied by inductively loading the structures with prefractal slots; inductive slot loading degenerates higher-order resonances and increases the fractional bandwidth (FBW). The current distributions revealed that most of the element area is used for radiation at both resonances. In radiation terms, the antennas provide satisfactory gains and high efficiencies (≥82%). A simple figure of merit is used to compare the performance of the three PIFAs head to head. Operation at 2.5 GHz and 5.5 GHz indicated that changes in slot geometry almost double the FBW. The proposed antennas serve both the 5.15–5.35 GHz U-NII and the 5.8 GHz ISM bands; at the lower band, their size is less or equal to the half-wavelength dipole. This study of dual-band antennas also showed that the aggregate FBW of a PIFA is bounded; by degenerating higher-order modes, the designer redistributes whatever bandwidth is available by the antenna itself to the desired bands.

Download Full-text

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

Behavioral and Brain Sciences ◽

10.1017/s0140525x19000451 ◽

2019 ◽

Vol 42 ◽

Author(s):

Daniel J. Povinelli ◽

Gabrielle C. Glorioso ◽

Shannon L. Kuznar ◽

Mateja Pavlic

Keyword(s):

Temporal Reasoning ◽

Higher Order ◽

Important Case ◽

Human Cognition ◽

Relational Reasoning ◽

Dual Systems ◽

First Order ◽

Reasoning System ◽

Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Download Full-text

Seti Figure of Merit

International Astronomical Union Colloquium ◽

10.1017/s0252921100015293 ◽

1997 ◽

Vol 161 ◽

pp. 711-717 ◽

Cited By ~ 1

Author(s):

John W. Dreher ◽

D. Kent Cullers

Keyword(s):

Figure Of Merit ◽

Qualitative Difference ◽

Current Generation ◽

Detection Range ◽

Sky Surveys ◽

Independent Observations ◽

Good For

AbstractWe develop a figure of merit for SETI observations which is anexplicitfunction of the EIRP of the transmitters, which allows us to treat sky surveys and targeted searches on the same footing. For each EIRP, we calculate the product of terms measuring the number of stars within detection range, the range of frequencies searched, and the number of independent observations for each star. For a given set of SETI observations, the result is a graph of merit versus transmitter EIRP. We apply this technique to several completed and ongoing SETI programs. The results provide a quantitative confirmation of the expected qualitative difference between sky surveys and targeted searches: the Project Phoenix targeted search is good for finding transmitters in the 109to 1014W range, while the sky surveys do their best at higher powers. Current generation optical SETI is not yet competitive with microwave SETI.

Download Full-text