On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size $3n+1$ are in a bijection with binary trees of size $n$.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Autonomous object harvesting using synchronized optoelectronic microrobots

Optoelectronic tweezer-driven microrobots (OETdMs) are a versatile micromanipulation technology based on the application of light induced dielectrophoresis to move small dielectric structures (microrobots) across a photoconductive substrate. The microrobots in turn can be used to exert forces on secondary objects and carry out a wide range of micromanipulation operations, including collecting, transporting and depositing microscopic cargos. In contrast to alternative (direct) micromanipulation techniques, OETdMs are relatively gentle, making them particularly well suited to interacting with sensitive objects such as biological cells. However, at present such systems are used exclusively under manual control by a human operator. This limits the capacity for simultaneous control of multiple microrobots, reducing both experimental throughput and the possibility of cooperative multi-robot operations. In this article, we describe an approach to automated targeting and path planning to enable open-loop control of multiple microrobots. We demonstrate the performance of the method in practice, using microrobots to simultaneously collect, transport and deposit silica microspheres. Using computational simulations based on real microscopic image data, we investigate the capacity of microrobots to collect target cells from within a dissociated tissue culture. Our results indicate the feasibility of using OETdMs to autonomously carry out micromanipulation tasks within complex, unstructured environments

Combinatorics of Explicit Substitutions

International audienceλυ is an extension of the λ-calculus which internalises the calculusof substitutions. In the current paper, we investigate thecombinatorial properties of λυ focusing on the quantitativeaspects of substitution resolution. We exhibit an unexpectedcorrespondence between the counting sequence for λυ terms~andfamous Catalan numbers. As a by-product, we establish effectivesampling schemes for random λυ terms. We show that typical λυterms~represent, in a strong sense, non-strict computations in theclassic λ-calculu. Moreover, typically almost all substitutionsare in fact suspended, i.e.~unevaluated, under closures.Consequently, we argue that λυ is an intrinsically non-strictcalculus of explicit substitutions. Finally, we investigate thedistribution of various redexes governing the substitutionresolution in λυ and investigate the quantitative contribution ofvarious substitution primitives

The Map of Vilnius Graffiti as an Indicator of Social Urban Change: the Case Study of Naujininkai Neighborhood

This article, theoretically based on socio-spatial concepts of Lefebvre, de Certeau and their further interpreta - tions at the New Urban Sociology school (by Gottdiener, Zukin and others), examines the spread of graffiti in the urban space of Vilnius, the change of the local graffiti map during the years 2010–2013 and the possible social implications of the spotted modification of urban landscape. The qualitative research of Vilnius graffiti – which is understood both as an urban practice and an illicit urban inscription – and the case of Naujininkai neighborhood in particular, is based on data obtained from 1) in-depth interviews with experienced graffiti artists, 2) observation of graffiti in public space and 3) visual urban ethnography. Naujininkai neighborhood was attributed by local graffiti writers to the urban periphery in Vilnius graffiti map in 2010. However in 2010–2013 the visual development of urban landscape in Naujininkai indicates the trend, bringing the neigh- borhood a little closer to the urban core