A new and simple concept of tunable two-chip microcavities for filter applications in WDM systems

Abstract In this paper, we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose parameters can be computed explicitly (rather than estimated by optimization), and illustrate its applicability to a wide range of data types. The preprocessing step then consists of representing data sets as simple measures. The theoretical foundation consists of a dyadic product formula representation lemma, and a visualization theorem. We also define an additive multiscale noise model that can be used to sample from dyadic measures and a more general multiplicative multiscale noise model that can be used to perturb continuous functions, Borel measures, and dyadic measures. The first two results are based on theorems in [15, 3, 1]. The representation uses the very simple concept of a dyadic tree and hence is widely applicable, easily understood, and easily computed. Since the data sample is represented as a measure, subsequent analysis can exploit statistical and measure theoretic concepts and theories. Because the representation uses the very simple concept of a dyadic tree defined on the universe of a data set, and the parameters are simply and explicitly computable and easily interpretable and visualizable, we hope that this approach will be broadly useful to mathematicians, statisticians, and computer scientists who are intrigued by or involved in data science, including its mathematical foundations.

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Forest Restoration: Simple Concept, Complex Process

Forest Research Open Access ◽

10.4172/2168-9776.1000e104 ◽

2013 ◽

Vol 02 (01) ◽

Author(s):

John D Waldron

Keyword(s):

Forest Restoration ◽

Simple Concept ◽

Complex Process

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Graph Theory of Chemical Series and Broad Categorization of Clusters

International Journal of Chemistry ◽

10.5539/ijc.v10n1p17 ◽

2018 ◽

Vol 10 (1) ◽

pp. 17

Author(s):

Enos Masheija Rwantale Kiremire

Keyword(s):

Graph Theory ◽

Transition Metal ◽

Metal Clusters ◽

Transition Metal Clusters ◽

Recent Introduction ◽

Simple Concept ◽

Wide Range ◽

Nuclear Clusters

The recent introduction of skeletal numbers has made it much easier to analyze and categorize a wide range of many chemical clusters. In the process, it has been found that a large number of transition metal clusters with and without ligands are capped and do possess closo nuclear clusters. On the basis of the nuclear index, the clusters have been categorized into groups. The categorization of the clusters will greatly assist in promoting deeper understanding and the synthesis of novel clusters and their applications. A simple concept of graph theory of capping clusters has been introduced.

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Off-Label Medication: From a Simple Concept to Complex Practical Aspects

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph181910447 ◽

2021 ◽

Vol 18 (19) ◽

pp. 10447

Author(s):

Carmen-Maria Rusz ◽

Bianca-Eugenia Ősz ◽

George Jîtcă ◽

Amalia Miklos ◽

Mădălina-Georgiana Bătrînu ◽

...

Keyword(s):

Rare Diseases ◽

Drug Repurposing ◽

Regulatory Agencies ◽

Systematic Research ◽

Clinical Practices ◽

Safe Practice ◽

Safety Issues ◽

Off Label ◽

Simple Concept ◽

Approved Drugs

Off-label use of drugs is widely known as unapproved use of approved drugs, and it can be perceived as a relatively simple concept. Even though it has been in existence for many years, prescribing and dispensing of drugs in an off-label regimen is still a current issue, triggered especially by unmet clinical needs. Several therapeutic areas require off-label approaches; therefore, this practice is challenging for prescribing physicians. Meanwhile, the regulatory agencies are making efforts in order to ensure a safe practice. The present paper defines the off-label concept, and it describes its regulation, together with several complex aspects associated with clinical practices regarding rare diseases, oncology, pediatrics, psychiatry therapeutic areas, and the safety issues that arise. A systematic research of the literature was performed, using terms, such as “off-label”, ”prevalence”, ”rare diseases”, ”oncology”, ”psychiatry”, ”pediatrics”, and ”drug repurposing”. There are several reasons for which off-label practice remains indispensable in the present; therefore, efforts are made worldwide, by the regulatory agencies and governmental bodies, to raise awareness and to ensure safe practice, while also encouraging further research.

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