scholarly journals Symbolic and automatic differentiation of languages

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-18
Author(s):  
Conal Elliott
Keyword(s):  
Automatic Differentiation ◽  
Building Blocks ◽  
Regular Expressions ◽  
Operational Strategies ◽  
Language Differentiation ◽  
Algebraic Properties ◽  
Essential Idea ◽  
Language Membership ◽  
Kleene Closure

Formal languages are usually defined in terms of set theory. Choosing type theory instead gives us languages as type-level predicates over strings. Applying a language to a string yields a type whose elements are language membership proofs describing how a string parses in the language. The usual building blocks of languages (including union, concatenation, and Kleene closure) have precise and compelling specifications uncomplicated by operational strategies and are easily generalized to a few general domain-transforming and codomain-transforming operations on predicates. A simple characterization of languages (and indeed functions from lists to any type) captures the essential idea behind language “differentiation” as used for recognizing languages, leading to a collection of lemmas about type-level predicates. These lemmas are the heart of two dual parsing implementations—using (inductive) regular expressions and (coinductive) tries—each containing the same code but in dual arrangements (with representation and primitive operations trading places). The regular expression version corresponds to symbolic differentiation, while the trie version corresponds to automatic differentiation. The relatively easy-to-prove properties of type-level languages transfer almost effortlessly to the decidable implementations. In particular, despite the inductive and coinductive nature of regular expressions and tries respectively, we need neither inductive nor coinductive/bisimulation arguments to prove algebraic properties.

Conjugated oligomers incorporating azulene building blocks – seven- vs. five-membered ring connectivity

2014 ◽  
Vol 5 (11) ◽  
pp. 4483-4489 ◽  
Author(s):  
Elizabeth Amir ◽  
Masahito Murai ◽  
Roey J. Amir ◽  
John S. Cowart ◽  
Michael L. Chabinyc ◽  
...  
Keyword(s):  
Building Blocks ◽  
Membered Ring ◽  
Synthesis And Characterization ◽  
Conjugated Oligomers

The properties of isomeric azulene derivatives based on 7- versus 5-membered ring substitution were examined by the synthesis and characterization of well-defined electroactive oligomers.

scholarly journals Recent Progress in the Synthesis and Characterization of Diarylethene-based MOFs

2014 ◽  
Vol 70 (a1) ◽  
pp. C1223-C1223
Author(s):  
Jason Benedict ◽  
Ian Walton ◽  
Dan Patel ◽  
Jordan Cox
Keyword(s):  
Chemical Properties ◽  
Building Blocks ◽  
Synthesis And Characterization ◽  
Next Generation ◽  
Design Synthesis ◽  
Thermally Induced ◽  
Potential Applications ◽  
External Stimuli ◽  
Physical And Chemical

Metal-organic Frameworks (MOFs) remain an extremely active area of research given the wide variety of potential applications and the enormous diversity of structures that can be created from their constituent building blocks. While MOFs are typically employed as passive materials, next-generation materials will exhibit structural and/or electronic changes in response to applied external stimuli including light, charge, and pH. Herein we present recent results in which advanced photochromic diarylethenes are combined with MOFs through covalent and non-covalent methods to create photo-responsive permanently porous crystalline materials. This presentation will describe the design, synthesis, and characterization of next-generation photo-switchable diarylethene based ligands which are subsequently used to photo-responsive MOFs. These UBMOF crystals are, by design, isostructural with previously reported non-photoresponsive frameworks which enables a systematic comparison of their physical and chemical properties. While the photoswitching of the isolated ligand in solution is fully reversible, the cycloreversion reaction is suppressed in the UBMOF single crystalline phase. Spectroscopic evidence for thermally induced cycloreversion will be presented, as well as a detailed analysis addressing the limits of X-ray diffraction techniques applied to these systems.

scholarly journals Geometry of Multiprimary Display Colors II: Metameric Control Sets and Gamut Tiling Color Control Functions

2021 ◽  
Author(s):  
Carlos Rodriguez-Pardo ◽  
Gaurav Sharma
Keyword(s):  
Broad Class ◽  
Convex Polytope ◽  
Building Blocks ◽  
Complete Characterization ◽  
Mathematical Framework ◽  
Control Functions ◽  
Control Sets ◽  
Multiple Alternative ◽  
Color Control

<div>For multiprimary displays that have four or more primaries, a color may be reproduced using multiple alternative control vectors. We provide a complete characterization of the Metameric Control Set (MCS), i.e., the set of control vectors that reproduce a given color on the display. Specifically, we show that MCS is a convex polytope whose vertices are control vectors obtained from (parallelepiped) tilings of the gamut, i.e., the range of colors that the display can produce. The mathematical framework that we develop: (a) characterizes gamut tilings in terms of fundamental building blocks called facet spans, (b) establishes that the vertices of the MCS are fully characterized by the tilings of the gamut, and (c) introduces a methodology for the efficient enumeration of gamut tilings. The framework reveals the fundamental inter-relations between the geometry of the MCS and the geometry of the gamut developed in a companion Part I paper, and provides insight into alternative strategies for color control. Our characterization of tilings and the strategy for their enumeration also advance knowledge in geometry, providing new approaches and computational results for the enumeration of tilings for a broad class of zonotopes in R<sup>3</sup>.</div>

Synthesis and characterization of new tetra-substituted porphyrins with exo-donor carboxylic groups as building blocks for supramolecular architectures: Catalytic and structural studies of their metalated derivatives

2010 ◽  
Vol 14 (09) ◽  
pp. 804-814 ◽  
Author(s):  
Lucia Carlucci ◽  
Gianfranco Ciani ◽  
Simona Maggini ◽  
Davide M. Proserpio ◽  
Fabio Ragaini ◽  
...  
Keyword(s):  
Building Blocks ◽  
Supramolecular Organization ◽  
Silver Complexes ◽  
Structural Studies ◽  
Polymeric Compound ◽  
X Ray ◽  
X Ray Crystallography ◽  
Supramolecular Architectures ◽  
Carboxylic Groups

We report herein the synthesis of the porphyrins 5,10,15,20-tetrakis(4-carboxybiphenyl)-porphyrin (H2TCBP) and 5,10,15,20-tetrakis(4-carboxy-2,6-dimethylbiphenyl)porphyrin (H2TCDMBP) bearing diphenyl units on meso-positions, and of their cobalt and silver derivatives. The silver complexes of H2TCDMBP and of H2TCPP ( H2TCPP = 5 ,10,15,20-tetrakis(4-carboxyphenyl)porphyrin) were investigated by X-ray crystallography and their supramolecular organization elucidated. Co(TCBP) was reacted with copper formate, yielding a polymeric compound that showed a catalytic activity in the benzylic amination of hydrocarbons using arylazide as aminating agent.

Physicochemical Characterization of α-, β-, and γ-Cyclodextrins Bioesterified with Decanoate Chains Used As Building Blocks of Colloidal Nanoparticles

2011 ◽  
Vol 12 (8) ◽  
pp. 3031-3038 ◽  
Author(s):  
Luc Choisnard ◽  
Annabelle Gèze ◽  
Cécile Vanhaverbeke ◽  
Josias B. G. Yaméogo ◽  
Jean-Luc Putaux ◽  
...  
Keyword(s):  
Physicochemical Characterization ◽  
Building Blocks ◽  
Colloidal Nanoparticles

scholarly journals Building blocks for the chemistry of perfluorinated alkoxyaluminates [Al{OC(CF3)3}4]−: simplified preparation and characterization of Li+–Cs+, Ag+, NH4+, N2H5+ and N2H7+ salts

2020 ◽  
Vol 49 (23) ◽  
pp. 7766-7773 ◽  
Author(s):  
Przemysław J. Malinowski ◽  
Tomasz Jaroń ◽  
Małgorzata Domańska ◽  
John M. Slattery ◽  
Manuel Schmitt ◽  
...  
Keyword(s):  
Physicochemical Characterization ◽  
Building Blocks

Convenient synthetic protocols for a number of salts of [Al{OC(CF3)3}4]− together with their thorough physicochemical characterization are presented.

scholarly journals Design, synthesis, and characterization of novel nanowire structures for photovoltaics and intracellular probes

2011 ◽  
Vol 83 (12) ◽  
pp. 2153-2169 ◽  
Author(s):  
Bozhi Tian ◽  
Charles M. Lieber
Keyword(s):  
Critical Role ◽  
Physical Property ◽  
Building Blocks ◽  
Materials Synthesis ◽  
Design Synthesis ◽  
Unique System ◽  
Challenges And Opportunities ◽  
Iterative Control ◽  
Novel Applications

Semiconductor nanowires (NWs) represent a unique system for exploring phenomena at the nanoscale and are expected to play a critical role in future electronic, optoelectronic, and miniaturized biomedical devices. Modulation of the composition and geometry of nanostructures during growth could encode information or function, and realize novel applications beyond the conventional lithographical limits. This review focuses on the fundamental science aspects of the bottom-up paradigm, which are synthesis and physical property characterization of semiconductor NWs and NW heterostructures, as well as proof-of-concept device concept demonstrations, including solar energy conversion and intracellular probes. A new NW materials synthesis is discussed and, in particular, a new “nano-tectonic” approach is introduced that provides iterative control over the NW nucleation and growth for constructing 2D kinked NW superstructures. The use of radial and axial p-type/intrinsic/n-type (p-i-n) silicon NW (Si-NW) building blocks for solar cells and nanoscale power source applications is then discussed. The critical benefits of such structures and recent results are described and critically analyzed, together with some of the diverse challenges and opportunities in the near future. Finally, results are presented on several new directions, which have recently been exploited in interfacing biological systems with NW devices.

Synthesis of Graphene-ZnO Heterogeneous Nanostructures by Chemical Vapor Deposition

2011 ◽  
Vol 1348 ◽  
Author(s):  
Jian Lin ◽  
Miroslav Penchev ◽  
Guoping Wang ◽  
Rajat K Paul ◽  
Jiebin Zhong ◽  
...  
Keyword(s):  
Optical Properties ◽  
Chemical Vapor Deposition ◽  
Vapor Deposition ◽  
Three Dimensional ◽  
Chemical Vapor ◽  
Building Blocks ◽  
Zno Nanostructures ◽  
Large Area ◽  
Graphene Layers

ABSTRACTIn this work, we report the synthesis and characterization of three dimensional heterostructures graphene nanostructures (HGN) comprising continuous large area graphene layers and ZnO nanostructures, fabricated via chemical vapor deposition. Characterization of large area HGN demonstrates that it consists of 1-5 layers of graphene, and exhibits high optical transmittance and enhanced electrical conductivity. Electron microscopy investigation of the three dimensional heterostructures shows that the morphology of ZnO nanostructures is highly dependent on the growth temperature. It is observed that ordered crystalline ZnO nanostructures are preferably grown along the <0001> direction. Ultraviolet spectroscopy indicates that the CVD grown HGN layers has excellent optical properties. A combination of electrical and optical properties of graphene and ZnO building blocks in ZnO based HGN provides unique characteristics for opportunities in future optoelectronic devices.

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