Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets

2019 ◽  
Vol 277 (1) ◽  
pp. 255-278 ◽  
Author(s):  
Li-Xiang An ◽  
Liu He ◽  
Xing-Gang He
Keyword(s):  
Riesz Product ◽  
Product Measures

scholarly journals On Riesz product measures; mutual absolute continuity and singularity

1988 ◽  
Vol 38 (2) ◽  
pp. 63-93 ◽  
Author(s):  
Shelby J. Kilmer ◽  
Sadahiro Saeki
Keyword(s):  
Absolute Continuity ◽  
Riesz Product ◽  
Product Measures

scholarly journals Lp-convergence of a certain class of product martingales

1994 ◽  
Vol 37 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Stamatis Koumandos
Keyword(s):  
Sufficient Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
Riesz Product ◽  
Product Measures ◽  
Nikodym Derivative

We establish the Kakutani dichotomy property for two generalized Rademacher–Riesz product measures μ, ν that either μ, ν are equivalent measures or they are mutually singular according as a certain series converges or diverges. We further give sufficient conditions so that in the equivalence case the Radon–Nikodym derivative dμ/dν belongs to Lp(v) for all positive real numbers p, by proving that a certain product martingale converges in Lp(v) for p ≧ 1.

scholarly journals To what extent and why adolescents do or do not support future tobacco control measures: a multimethod study in the Netherlands

2017 ◽  
Vol 27 (5) ◽  
pp. 596-599 ◽  
Author(s):  
Michael Schreuders ◽  
Naomi A Lagerweij ◽  
Bas van den Putte ◽  
Anton E Kunst
Keyword(s):  
The Netherlands ◽  
Tobacco Control ◽  
Control Measures ◽  
Price Increases ◽  
Mixed Support ◽  
Mixed Method Design ◽  
Product Measures ◽  
Group Interviews ◽  
Political Leverage ◽  
High Support

BackgroundIn the Netherlands, the adoption of new tobacco control measures is needed to further reduce rates of adolescent smoking. Adolescents’ support for future measures could increase the likelihood of adoption as this provides political leverage for tobacco control advocates. There is, however, scant evidence about to what extent and why adolescents support future measures. We therefore assessed adolescents’ support for a range of future measures and explored the criteria that adolescents use to underpin their support.MethodsA mixed-method design involved surveys and group interviews with fourth-year students (predominantly 15–16 years). The survey, completed by 345 adolescents, included statements about future tobacco control measures and a smoke-free future where nobody starts or continues smoking. Thereafter, 15 adolescents participated in five group interviews to discuss their support for future measures.ResultsThe survey showed that adolescents generally support a smoke-free future. They expressed most support for product measures, mixed support for smoke-free areas, ambivalent support for price increases and least support for sales restrictions. The group interviews revealed that differences in support were explained by adolescents’ criteria that future measures should: have the potential to be effective, not violate individuals’ right to smoke, protect children from pro-smoking social influences and protect non-smokers from secondhand smoke.ConclusionAdolescents’ high support for a smoke-free future does not lead to categorical support for any measure. Addressing the underlying criteria may increase adolescents’ support and therewith provide political leverage for the adoption of future measures.

scholarly journals Implementation of a Hamming distance–like genomic quantum classifier using inner products on ibmqx2 and ibmq_16_melbourne

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Kunal Kathuria ◽  
Aakrosh Ratan ◽  
Michael McConnell ◽  
Stefan Bekiranov
Keyword(s):  
Hamming Distance ◽  
Training Sample ◽  
General Purpose ◽  
Inner Product ◽  
Matching Problems ◽  
Binary Operations ◽  
Inner Products ◽  
Training Class ◽  
Dot Product ◽  
Product Measures

Abstract Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product–based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute’s existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product–based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance–based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product–based classifier. The classifiers implement an inner product between N = 2n dimension test and train vectors using n Fredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary number m of samples that can be classically summed into one input string to effectively execute all test–train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are $O(\log {N})$ O ( log N ) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.

Sign in / Sign up

Export Citation Format

Share Document