Finally, we present a generalized algorithm for diluting a sample S in minimum (1 : 1) mix-split steps when two or more arbitrary concentrations of S (diluted with the same buffer) are supplied as inputs. The feasibility analysis also leads to the characterization of the total space of input stock solutions from which a given target mixture can be derived, and conversely, the space of all target ratios, which are derivable from a given set of input reagents with arbitrary CFs. Next, an algorithm is proposed which produces the desired target ratio of N reagents in O(Nd) mix-split steps, where N (? 3) denotes the number of constituent fluids in the mixture. In this article, we first study the feasibility properties for the generalized mixing problem under the (1: 1) mix-split model with an allowable error in the target CFs not exceeding 1/2d, where the integer d is user specified and denotes the desired accuracy level of CF. An intriguing question is whether or not a given target ratio is feasible to produce from such a general input condition. No algorithm is yet known for preparing a target mixture of fluids with a given ratio when its constituents are supplied with random concentrations. In many real-life scenarios, the stock solutions consist of samples/reagents with multiple CFs. However, all methods for such automatic sample preparation suffer from a drawback that they assume the availability of input fluids in pure form, that is, each with an extreme concentration factor (CF) of 100%. Finally, we provide a discussion on the challenges and the future research directions toward practically realizing the Si-photonics and PICs.ĭigital microfluidic (DMF) biochips are recently being advocated for fast on-chip implementation of biochemical laboratory assays or protocols, and several algorithms for diluting and mixing of reagents have been reported. The aim of this survey is to start with the fundamental optical concepts and then move to the latest research domains of design and synthesis of PICs. This paper presents an extensive survey of recent work reported in the literature on the domains of logic circuit design, synthesis, and physical design automation for implementing PICs. In order to efficiently design larger, complex and reliable PICs, the photonic design automation techniques are being explored as electronic design automation techniques have been investigated in case of very large-scale integration circuits. Several optical switching devices using different technologies have been designed and experimentally demonstrated, which further helps in implementing PICs. The integration of electronic and optical circuits on a single chip has opened up new directions of research in the domain of digital logic design and synthesis of photonic integrated circuits (PICs). In recent years, silicon photonics (Si-photonics) have received significant attention among researchers due to complementary metal-oxide semiconductor compatibility, and the characteristics of high-speed and low-power dissipation.
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