Fuel Efficient Computation in Passive Self-Assembly

In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which particles are modeled by four-sided squares with glue types assigned to each tile edge. The assembly process is driven by positive and negative force interactions between glue types, allowing for tile assemblies floating in the plane to combine and break apart over time. We refer to this type of assembly model as passive in that the constituent parts remain unchanged throughout the assembly process regardless of their interactions. A computationally universal system is said to be fuel efficient if the number of tiles used up per computation step is bounded by a constant. Work within this model has shown how fuel guzzling tile systems can perform universal computation with only positive strength glue interactions. Recent work has introduced space-efficient, fuel-guzzling universal computation with the addition of negative glue interactions and the use of a powerful non-diagonal class of glue interactions. Other recent work has shown how to achieve fuel efficient computation within active tile self-assembly. In this paper we utilize negative interactions in the tile self-assembly model to achieve the first computationally universal passive tile self-assembly system that is both space and fuel-efficient. In addition, we achieve this result using a limited diagonal class of glue interactions

Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D

We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no temperature 1 assembly system has been shown to build a shape with a tile complexity smaller than the diameter of the shape. In contrast, we show that temperature 1 self-assembly in 3 dimensions, even when growth is restricted to at most 1 step into the third dimension, is capable of simulating a large class of temperature 2 systems, in turn permitting the simulation of arbitrary Turing machines and the assembly of $n\times n$ squares in near optimal $O(\log n)$ tile complexity. Further, we consider temperature 1 probabilistic assembly in 2D, and show that with a logarithmic scale up of tile complexity and shape scale, the same general class of temperature $\tau=2$ systems can be simulated with high probability, yielding Turing machine simulation and $O(\log^2 n)$ assembly of $n\times n$ squares with high probability. Our results show a sharp contrast in achievable tile complexity at temperature 1 if either growth into the third dimension or a small probability of error are permitted. Motivated by applications in nanotechnology and molecular computing, and the plausibility of implementing 3 dimensional self-assembly systems, our techniques may provide the needed power of temperature 2 systems, while at the same time avoiding the experimental challenges faced by those systems

Neorealism’s Power and Restraint: A Tribute to Waltz on his 100th Birthday

Kenneth Waltz constructed a pure theory of international politics by isolating structural from unit-level causes. Today’s return of great-power politics signals the persistent relevance of Waltz’s notion of patterns and regularities driven by structural-systemic forces. We have entered an unbalanced bipolar world, in which America still exceeds China in every important category of national power but the gap is narrowing. The relative-power trajectories of the two sides now frames the structural dynamics of their relationship, and how others perceive and calculate their strategic competition. No longer occupying a position of “primacy” either globally or in the Asian Pacific region, the United States now tends to exaggerate, not underestimate, the perceived threat from China in the economic and security realms. More broadly, the world is transitioning from hegemonic order to global disharmony and a restored balance of power—what I refer to as a “Dissent” phase of history. In this phase, disruption of global stability comes not only from the emergence of a counter-hegemonic alliance, which begins to voice its dissatisfaction with the status-quo order and underlying social purpose.   It also comes from the hegemon itself, which behaves in ways that undermine its own order—an order that it now sees as not only unprofitable but a drain on its wasting assets through sponging allies and the exorbitant costs of delivering global public goods

When Home Videos Leave the Home: Personal Video Practices of College Students

Personal videos, videos taken by common people to document their lives, are a ubiquitous and regular aspect of social life which remains strikingly understudied in Sociology. Bourdieu (1990) and Chalfen (1987) have both produced works examining the uses of personal photography and video in the context of families; and both suggest that video plays an important role in fostering group solidarity within families. However, as a body of scholarship (Van House (2011), Lange (2011), van Dijck (2008)) shows, recent shifts in technology (namely the emergence of camera phones and social media) may greatly alter contemporary video and photo practices. In this context, this study aims to understand the personal video practices of contemporary college students, particularly in regards to group solidarity and presentation of the self, through a series of eleven in-depth semi-structured interviews conducted with Hamilton College students. The findings of the study suggest that technological shifts have expanded the uses of personal video to include presentation of self and identity formation. At the same time, however, the social function of personal video as a tool for solidarity seems to remain a central use of contemporary video. This study illuminates the uses of personal video by college students while also demonstrating the ways in which foundational sociological theories can be modified to help understand the modern, digital, social world

Size-Dependent Tile Self-Assembly: Constant-Height Rectangles and Stability

We introduce a new model of algorithmic tile self-assembly called size-dependent assembly. In previous models, supertiles are stable when the total strength of the bonds between any two halves exceeds some constant temperature. In this model, this constant temperature requirement is replaced by an nondecreasing temperature function $\tau : \mathbb{N} \rightarrow \mathbb{N}$ that depends on the size of the smaller of the two halves. This generalization allows supertiles to become unstable and break apart, and captures the increased forces that large structures may place on the bonds holding them together. We demonstrate the power of this model in two ways. First, we give fixed tile sets that assemble constant-height rectangles and squares of arbitrary input size given an appropriate temperature function. Second, we prove that deciding whether a supertile is stable is coNP-complete. Both results contrast with known results for fixed temperature.Comment: In proceedings of ISAAC 201