1,328 research outputs found
When Can You Fold a Map?
We explore the following problem: given a collection of creases on a piece of
paper, each assigned a folding direction of mountain or valley, is there a flat
folding by a sequence of simple folds? There are several models of simple
folds; the simplest one-layer simple fold rotates a portion of paper about a
crease in the paper by +-180 degrees. We first consider the analogous questions
in one dimension lower -- bending a segment into a flat object -- which lead to
interesting problems on strings. We develop efficient algorithms for the
recognition of simply foldable 1D crease patterns, and reconstruction of a
sequence of simple folds. Indeed, we prove that a 1D crease pattern is
flat-foldable by any means precisely if it is by a sequence of one-layer simple
folds.
Next we explore simple foldability in two dimensions, and find a surprising
contrast: ``map'' folding and variants are polynomial, but slight
generalizations are NP-complete. Specifically, we develop a linear-time
algorithm for deciding foldability of an orthogonal crease pattern on a
rectangular piece of paper, and prove that it is (weakly) NP-complete to decide
foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper,
(2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a
square piece of paper, and (3) crease patterns without a mountain/valley
assignment.Comment: 24 pages, 19 figures. Version 3 includes several improvements thanks
to referees, including formal definitions of simple folds, more figures,
table summarizing results, new open problems, and additional reference
Simple Wriggling is Hard unless You Are a Fat Hippo
We prove that it is NP-hard to decide whether two points in a polygonal
domain with holes can be connected by a wire. This implies that finding any
approximation to the shortest path for a long snake amidst polygonal obstacles
is NP-hard. On the positive side, we show that snake's problem is
"length-tractable": if the snake is "fat", i.e., its length/width ratio is
small, the shortest path can be computed in polynomial time.Comment: A shorter version is to be presented at FUN 201
Design and Construction of a Double Inversion Recombination Switch for Heritable Sequential Genetic Memory
Background: Inversion recombination elements present unique opportunities for computing and information encoding in biological systems. They provide distinct binary states that are encoded into the DNA sequence itself, allowing us to overcome limitations posed by other biological memory or logic gate systems. Further, it is in theory possible to create complex sequential logics by careful positioning of recombinase recognition sites in the sequence. Methodology/Principal Findings: In this work, we describe the design and synthesis of an inversion switch using the fim and hin inversion recombination systems to create a heritable sequential memory switch. We have integrated the two inversion systems in an overlapping manner, creating a switch that can have multiple states. The switch is capable of transitioning from state to state in a manner analogous to a finite state machine, while encoding the state information into DNA. This switch does not require protein expression to maintain its state, and ‘‘remembers’ ’ its state even upon cell death. We were able to demonstrate transition into three out of the five possible states showing the feasibility of such a switch. Conclusions/Significance: We demonstrate that a heritable memory system that encodes its state into DNA is possible, and that inversion recombination system could be a starting point for more complex memory circuits. Although the circuit di
Epigenetic Chromatin Silencing: Bistability and Front Propagation
The role of post-translational modification of histones in eukaryotic gene
regulation is well recognized. Epigenetic silencing of genes via heritable
chromatin modifications plays a major role in cell fate specification in higher
organisms. We formulate a coarse-grained model of chromatin silencing in yeast
and study the conditions under which the system becomes bistable, allowing for
different epigenetic states. We also study the dynamics of the boundary between
the two locally stable states of chromatin: silenced and unsilenced. The model
could be of use in guiding the discussion on chromatin silencing in general. In
the context of silencing in budding yeast, it helps us understand the phenotype
of various mutants, some of which may be non-trivial to see without the help of
a mathematical model. One such example is a mutation that reduces the rate of
background acetylation of particular histone side-chains that competes with the
deacetylation by Sir2p. The resulting negative feedback due to a Sir protein
depletion effect gives rise to interesting counter-intuitive consequences. Our
mathematical analysis brings forth the different dynamical behaviors possible
within the same molecular model and guides the formulation of more refined
hypotheses that could be addressed experimentally.Comment: 19 pages, 5 figure
Vibrational Enhancement of the Effective Donor - Acceptor Coupling
The paper deals with a simple three sites model for charge transfer phenomena
in an one-dimensional donor (D) - bridge (B) - acceptor (A) system coupled with
vibrational dynamics of the B site. It is found that in a certain range of
parameters the vibrational coupling leads to an enhancement of the effective
donor - acceptor electronic coupling as a result of the formation of the
polaron on the B site. This enhancement of the charge transfer efficiency is
maximum at the resonance, where the effective energy of the fluctuating B site
coincides with the donor (acceptor) energy.Comment: 5 pages, 3 figure
AI Researchers, Video Games Are Your Friends!
If you are an artificial intelligence researcher, you should look to video
games as ideal testbeds for the work you do. If you are a video game developer,
you should look to AI for the technology that makes completely new types of
games possible. This chapter lays out the case for both of these propositions.
It asks the question "what can video games do for AI", and discusses how in
particular general video game playing is the ideal testbed for artificial
general intelligence research. It then asks the question "what can AI do for
video games", and lays out a vision for what video games might look like if we
had significantly more advanced AI at our disposal. The chapter is based on my
keynote at IJCCI 2015, and is written in an attempt to be accessible to a broad
audience.Comment: in Studies in Computational Intelligence Studies in Computational
Intelligence, Volume 669 2017. Springe
The statistical mechanics of complex signaling networks : nerve growth factor signaling
It is becoming increasingly appreciated that the signal transduction systems
used by eukaryotic cells to achieve a variety of essential responses represent
highly complex networks rather than simple linear pathways. While significant
effort is being made to experimentally measure the rate constants for
individual steps in these signaling networks, many of the parameters required
to describe the behavior of these systems remain unknown, or at best,
estimates. With these goals and caveats in mind, we use methods of statistical
mechanics to extract useful predictions for complex cellular signaling
networks. To establish the usefulness of our approach, we have applied our
methods towards modeling the nerve growth factor (NGF)-induced differentiation
of neuronal cells. Using our approach, we are able to extract predictions that
are highly specific and accurate, thereby enabling us to predict the influence
of specific signaling modules in determining the integrated cellular response
to the two growth factors. We show that extracting biologically relevant
predictions from complex signaling models appears to be possible even in the
absence of measurements of all the individual rate constants. Our methods also
raise some interesting insights into the design and possible evolution of
cellular systems, highlighting an inherent property of these systems wherein
particular ''soft'' combinations of parameters can be varied over wide ranges
without impacting the final output and demonstrating that a few ''stiff''
parameter combinations center around the paramount regulatory steps of the
network. We refer to this property -- which is distinct from robustness -- as
''sloppiness.''Comment: 24 pages, 10 EPS figures, 1 GIF (makes 5 multi-panel figs + caption
for GIF), IOP style; supp. info/figs. included as brown_supp.pd
Cutting Polygons into Small Pieces with Chords: Laser-Based Localization
Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the "size" of a piece. In particular, we consider the area, the diameter, and the radius of the largest inscribed circle as a measure of the size of a piece. We also consider different objectives, either minimizing the maximum size of a piece for a given number of chords, or minimizing the number of chords that achieve a given size threshold for the pieces. We give hardness results for polygons with holes and approximation algorithms for multiple variants of the problem
Algorithms for Stable Matching and Clustering in a Grid
We study a discrete version of a geometric stable marriage problem originally
proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which
points in the plane are stably matched to cluster centers, as prioritized by
their distances, so that each cluster center is apportioned a set of points of
equal area. We show that, for a discretization of the problem to an
grid of pixels with centers, the problem can be solved in time , and we experiment with two slower but more practical algorithms and
a hybrid method that switches from one of these algorithms to the other to gain
greater efficiency than either algorithm alone. We also show how to combine
geometric stable matchings with a -means clustering algorithm, so as to
provide a geometric political-districting algorithm that views distance in
economic terms, and we experiment with weighted versions of stable -means in
order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th
International Workshop on Combinatorial Image Analysis, June 19-21, 2017,
Plovdiv, Bulgari
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