67,961 research outputs found
Self-Replicating Strands that Self-Assemble into User-Specified Meshes
It has been argued that a central objective of nanotechnology is to make
products inexpensively, and that self-replication is an effective approach to
very low-cost manufacturing. The research presented here is intended to be a
step towards this vision. In previous work (JohnnyVon 1.0), we simulated
machines that bonded together to form self-replicating strands. There were two
types of machines (called types 0 and 1), which enabled strands to encode
arbitrary bit strings. However, the information encoded in the strands had no
functional role in the simulation. The information was replicated without being
interpreted, which was a significant limitation for potential manufacturing
applications. In the current work (JohnnyVon 2.0), the information in a strand
is interpreted as instructions for assembling a polygonal mesh. There are now
four types of machines and the information encoded in a strand determines how
it folds. A strand may be in an unfolded state, in which the bonds are straight
(although they flex slightly due to virtual forces acting on the machines), or
in a folded state, in which the bond angles depend on the types of machines. By
choosing the sequence of machine types in a strand, the user can specify a
variety of polygonal shapes. A simulation typically begins with an initial
unfolded seed strand in a soup of unbonded machines. The seed strand replicates
by bonding with free machines in the soup. The child strands fold into the
encoded polygonal shape, and then the polygons drift together and bond to form
a mesh. We demonstrate that a variety of polygonal meshes can be manufactured
in the simulation, by simply changing the sequence of machine types in the
seed
Bouncing Cosmologies: Progress and Problems
We review the status of bouncing cosmologies as alternatives to cosmological
inflation for providing a description of the very early universe, and a source
for the cosmological perturbations which are observed today. We focus on the
motivation for considering bouncing cosmologies, the origin of fluctuations in
these models, and the challenges which various implementations face.Comment: 30 pages, 6 figures; references adde
A Falsification View of Success Typing
Dynamic languages are praised for their flexibility and expressiveness, but
static analysis often yields many false positives and verification is
cumbersome for lack of structure. Hence, unit testing is the prevalent
incomplete method for validating programs in such languages.
Falsification is an alternative approach that uncovers definite errors in
programs. A falsifier computes a set of inputs that definitely crash a program.
Success typing is a type-based approach to document programs in dynamic
languages. We demonstrate that success typing is, in fact, an instance of
falsification by mapping success (input) types into suitable logic formulae.
Output types are represented by recursive types. We prove the correctness of
our mapping (which establishes that success typing is falsification) and we
report some experiences with a prototype implementation.Comment: extended versio
Lower Bounds on Quantum Query Complexity
Shor's and Grover's famous quantum algorithms for factoring and searching
show that quantum computers can solve certain computational problems
significantly faster than any classical computer. We discuss here what quantum
computers_cannot_ do, and specifically how to prove limits on their
computational power. We cover the main known techniques for proving lower
bounds, and exemplify and compare the methods.Comment: survey, 23 page
On Projective Equivalence of Univariate Polynomial Subspaces
We pose and solve the equivalence problem for subspaces of ,
the dimensional vector space of univariate polynomials of degree . The group of interest is acting by projective transformations
on the Grassmannian variety of -dimensional
subspaces. We establish the equivariance of the Wronski map and use this map to
reduce the subspace equivalence problem to the equivalence problem for binary
forms
Literature Review: Diverting Mentally Ill Offenders from Jail
This literature review describes literature available on the topic of diverting mentally ill offenders from jail; outlines major themes found in the literature; analyzed programs described in the literature by type; and highlights recommendations from the literature.Criminal Justice Systems ProjectIntroduction / Description of Literature / Common Themes / Analysis / Recommendation / Abstracts / Bibliograph
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