Layout Decomposition for Quadruple Patterning Lithography and Beyond

For next-generation technology nodes, multiple patterning lithography (MPL) has emerged as a key solution, e.g., triple patterning lithography (TPL) for 14/11nm, and quadruple patterning lithography (QPL) for sub-10nm. In this paper, we propose a generic and robust layout decomposition framework for QPL, which can be further extended to handle any general K-patterning lithography (K$>$4). Our framework is based on the semidefinite programming (SDP) formulation with novel coloring encoding. Meanwhile, we propose fast yet effective coloring assignment and achieve significant speedup. To our best knowledge, this is the first work on the general multiple patterning lithography layout decomposition.Comment: DAC'201

RNA-Seq identifies SPGs as a ventral skeletal patterning cue in sea urchins

The sea urchin larval skeleton offers a simple model for formation of developmental patterns. The calcium carbonate skeleton is secreted by primary mesenchyme cells (PMCs) in response to largely unknown patterning cues expressed by the ectoderm. To discover novel ectodermal cues, we performed an unbiased RNA-Seq-based screen and functionally tested candidates; we thereby identified several novel skeletal patterning cues. Among these, we show that SLC26a2/7 is a ventrally expressed sulfate transporter that promotes a ventral accumulation of sulfated proteoglycans, which is required for ventral PMC positioning and skeletal patterning. We show that the effects of SLC perturbation are mimicked by manipulation of either external sulfate levels or proteoglycan sulfation. These results identify novel skeletal patterning genes and demonstrate that ventral proteoglycan sulfation serves as a positional cue for sea urchin skeletal patterning

Waves and patterning in developmental biology: vertebrate segmentation and feather bud formation as case studies

In this article we will discuss the integration of developmental patterning mechanisms with waves of competency that control the ability of a homogeneous field of cells to react to pattern forming cues and generate spatially heterogeneous patterns. We base our discussion around two well known patterning events that take place in the early embryo: somitogenesis and feather bud formation. We outline mathematical models to describe each patterning mechanism, present the results of numerical simulations and discuss the validity of each model in relation to our example patterning processes

Young Children's Mathematical Patterning

YOUNG CHILDREN'S MATHEMATICAL PATTERNING Jillian Fox Queensland University of Technology, Brisbane, Australia Mathematical patterning is fundamental to the development of mathematics. Steen (1990), in fact, argued that "Mathematics is the science and language of patterns" (p. 5). The years prior to formal schooling (pre-compulsory education and care services) are widely recognised as a period of critical development where the salient role of patterning features significantly. In a multi-case study children’s engagement in mathematical patterning experiences was investigated as was the teachers’ involvement in, and influence on these experiences. The study was conducted in one preschool and one preparatory year setting. These sites were typical learning environments for Queensland children in the year prior to compulsory schooling. Multiple sources of data were collected. These data comprised semi-structured interviews with each teacher, copies of their daily programs and video-taped observation of the classes. Ten episodes of mathematical patterning were identified and categorised as teacher-planned, teacher-initiated, or child-initiated. Two episodes were initiated by children and the other eight were guided by the teachers. The nature of the teacher intervention in the child-initiated activities was of particular interest. Frameworks were developed to guide the examination of these episodes, with these frameworks being informed by the conceptual framework of Stein, Grover and Henningsen (1996). The findings of this case study suggest that child-initiated episodes containing mathematical patterning are productive learning occurrences. During unstructured play times, children initiated activities that explored repeating patterns, pattern language, and the elements of linear patterns. These episodes were rich opportunities where children shared, refined, and developed their knowledge of patterns. Thus, child-initiated experiences can be powerful learning opportunities with the potential to develop children’s knowledge of mathematical patterning in meaningful contexts. The findings also suggest that teachers’ understanding of patterning as well as their engagement in, and influence on child-initiated episodes impacts significantly on the outcomes of the event. Teachers play a myriad of salient roles to assist the development of mathematical patterning. The role of the teacher in questioning, providing resources, being involved, and offering encouragement has the potential to enrich mathematical patterning experiences and extend the children’s existing knowledge. Likewise, teachers’ limited knowledge of patterning concepts and processes, and the confines of their teaching competencies can hinder the outcomes of patterning events. The poster will illustrate some of the above findings and will include a focus on how teachers’ intervention can either extend or inhibit children’s development of mathematical patterning. Many early childhood professionals now agree that children should be "guided if not taught" to do some mathematics (Ginsburg et. al., 1999). When teachers understand what to teach, when to teach, and how to teach, they can provide rich opportunities for children to engage in patterning experiences, and capitalise on child-initiated learning activities. Ginsburg, H. P., Inoue, N. & Seo, K. H. (1999). Young children doing mathematics: Observations of everyday activities. In J. Copely (Ed.). Mathematics in the early years (pp.88-99). Reston, VA. National Council of Teachers of Mathematics. Steen, L. A. (Ed.). (1990). On the shoulders of giants: New approaches to numeracy. Washington DC: National Academy Press in Stein, M. K., Grover, B. W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Education Research Journal, 33, 455-488

Cell patterning on photolithographically defined parylene-C:SiO2 substrates

Cell patterning platforms support broad research goals, such as construction of predefined in vitro neuronal networks and the exploration of certain central aspects of cellular physiology. To easily combine cell patterning with Multi-Electrode Arrays (MEAs) and silicon-based ‘lab on a chip’ technologies, a microfabrication-compatible protocol is required. We describe a method that utilizes deposition of the polymer parylene-C on SiO(2 )wafers. Photolithography enables accurate and reliable patterning of parylene-C at micron-level resolution. Subsequent activation by immersion in fetal bovine serum (or another specific activation solution) results in a substrate in which cultured cells adhere to, or are repulsed by, parylene or SiO(2) regions respectively. This technique has allowed patterning of a broad range of cell types (including primary murine hippocampal cells, HEK 293 cell line, human neuron-like teratocarcinoma cell line, primary murine cerebellar granule cells, and primary human glioma-derived stem-like cells). Interestingly, however, the platform is not universal; reflecting the importance of cell-specific adhesion molecules. This cell patterning process is cost effective, reliable, and importantly can be incorporated into standard microfabrication (chip manufacturing) protocols, paving the way for integration of microelectronic technology

Speed of reaction diffusion in embryogenesis

Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis

Pattern stabilization through parameter alternation in a nonlinear optical system

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation, and the measured spatial frequencies of the patterns.Comment: 12 pages, 5 figures. To appear in PR

Comparison of Power Dependence of Microwave Surface Resistance of Unpatterned and Patterned YBCO Thin Film

The effect of the patterning process on the nonlinearity of the microwave surface resistance $R_S$ of YBCO thin films is investigated. With the use of a sapphire dielectric resonator and a stripline resonator, the microwave $R_S$ of YBCO thin films was measured before and after the patterning process, as a function of temperature and the rf peak magnetic field in the film. The microwave loss was also modeled, assuming a $J_{rf}^2$ dependence of $Z_S(J_{rf})$ on current density $J_{rf}$. Experimental and modeled results show that the patterning has no observable effect on the microwave residual $R_S$ or on the power dependence of $R_S$.Comment: Submitted to IEEE Trans. MT

Reversible DNA micro-patterning using the fluorous effect

We describe a new method for the immobilisation of DNA into defined patterns with sub-micron resolution, using the fluorous effect. The method is fully reversible via a simple solvent wash, allowing the patterning, regeneration and re-patterning of surfaces with no degradation in binding efficiency following multiple removal/attachment cycles of different DNA sequences

Linear signaling in the Toll-Dorsal pathway of Drosophila: activated Pelle kinase specifies all threshold outputs of gene expression while the bHLH protein Twist specifies a subset

Differential activation of the Toll receptor leads to the formation of a broad Dorsal nuclear gradient that specifies at least three patterning thresholds of gene activity along the dorsoventral axis of precellular embryos. We investigate the activities of the Pelle kinase and Twist basic helix-loop-helix (bHLH) transcription factor in transducing Toll signaling. Pelle functions downstream of Toll to release Dorsal from the Cactus inhibitor. Twist is an immediate-early gene that is activated upon entry of Dorsal into nuclei. Transgenes misexpressing Pelle and Twist were introduced into different mutant backgrounds and the patterning activities were visualized using various target genes that respond to different thresholds of Toll-Dorsal signaling. These studies suggest that an anteroposterior gradient of Pelle kinase activity is sufficient to generate all known Toll-Dorsal patterning thresholds and that Twist can function as a gradient morphogen to establish at least two distinct dorsoventral patterning thresholds. We discuss how the Dorsal gradient system can be modified during metazoan evolution and conclude that Dorsal-Twist interactions are distinct from the interplay between Bicoid and Hunchback, which pattern the anteroposterior axis