1,163 research outputs found
A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays
Chemical reaction systems with a low to moderate number of molecules are
typically modeled as discrete jump Markov processes. These systems are
oftentimes simulated with methods that produce statistically exact sample paths
such as the Gillespie Algorithm or the Next Reaction Method. In this paper we
make explicit use of the fact that the initiation times of the reactions can be
represented as the firing times of independent, unit rate Poisson processes
with internal times given by integrated propensity functions. Using this
representation we derive a modified Next Reaction Method and, in a way that
achieves efficiency over existing approaches for exact simulation, extend it to
systems with time dependent propensities as well as to systems with delays.Comment: 25 pages, 1 figure. Some minor changes made to add clarit
Incorporating postleap checks in tau-leaping
By explicitly representing the reaction times of discrete chemical systems as
the firing times of independent, unit rate Poisson processes, we develop a new
adaptive tau-leaping procedure. The procedure developed is novel in that
accuracy is guaranteed by performing postleap checks. Because the
representation we use separates the randomness of the model from the state of
the system, we are able to perform the postleap checks in such a way that the
statistics of the sample paths generated will not be biased by the rejections
of leaps. Further, since any leap condition is ensured with a probability of
one, the simulation method naturally avoids negative population valuesComment: Final version. Minor change
Structure of the Energy Landscape of Short Peptides
We have simulated, as a showcase, the pentapeptide Met-enkephalin
(Tyr-Gly-Gly-Phe-Met) to visualize the energy landscape and investigate the
conformational coverage by the multicanonical method. We have obtained a
three-dimensional topographic picture of the whole energy landscape by plotting
the histogram with respect to energy(temperature) and the order parameter,
which gives the degree of resemblance of any created conformation with the
global energy minimum (GEM).Comment: 17 pages, 4 figure
Maximizing Maximal Angles for Plane Straight-Line Graphs
Let be a plane straight-line graph on a finite point set
in general position. The incident angles of a vertex
of are the angles between any two edges of that appear consecutively in
the circular order of the edges incident to .
A plane straight-line graph is called -open if each vertex has an
incident angle of size at least . In this paper we study the following
type of question: What is the maximum angle such that for any finite set
of points in general position we can find a graph from a certain
class of graphs on that is -open? In particular, we consider the
classes of triangulations, spanning trees, and paths on and give tight
bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that
were omitted in the previous version are now include
Approximating the minimum directed tree cover
Given a directed graph with non negative cost on the arcs, a directed
tree cover of is a rooted directed tree such that either head or tail (or
both of them) of every arc in is touched by . The minimum directed tree
cover problem (DTCP) is to find a directed tree cover of minimum cost. The
problem is known to be -hard. In this paper, we show that the weighted Set
Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to
approximate DTCP with the same ratio as for SCP. We show that this expectation
can be satisfied in some way by designing a purely combinatorial approximation
algorithm for the DTCP and proving that the approximation ratio of the
algorithm is with is the maximum outgoing degree of
the nodes in .Comment: 13 page
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
Furrow Diking Technology for Agricultural Water Conservation and its Impact on Crop Yields in Texas
Furrow diking is a practical, efficient and low-cost technique to conserve water and increase crop yields. Improvements in diker design and the increased use of herbicides have resulted in the rapid spread of furrow diking in the Texas High Plains and other regions.
To quantify the long-term effects of diking on crop yields, a computer simulation approach was used. Three crop models for sorghum, corn and cotton were combined with surface runoff hydrology algorithms, based on the USDA-SCS curve number methodology. The combination models called SORDIKE, CORDIKE and COTDIKE were run to determine the effects of conserving the runoff (by diking) on crop yields. Three scenarios of not diking, diking in the growing season, and diking all year were simulated. Daily weather data for 25 years from five Texas regions were used for the analyses. Depending on the location, furrow diking in the growing season increased average annual sorghum yields by 320 to 570 kg/ha, corn yields by 180 to 570 kg/ha, and cotton lint yields by 10 to 20 kg/ha. Diking the land throughout the year increased mean annual yields by 440 to 1080 kg/ha of sorghum, 210 to 800 kg/ha of corn and 10 to 30 kg/ha of cotton lint. The study indicated that furrow diking can be a valuable management practice for about 3.4 million ha of cropped area in the semi-arid and sub-humid regions of Texas. The practice may be useful in other areas also, to mitigate the effects of short duration moisture stress on crop yields
Colored extrinsic fluctuations and stochastic gene expression
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise', is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored'). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high-throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks
Optimizing information flow in small genetic networks. I
In order to survive, reproduce and (in multicellular organisms)
differentiate, cells must control the concentrations of the myriad different
proteins that are encoded in the genome. The precision of this control is
limited by the inevitable randomness of individual molecular events. Here we
explore how cells can maximize their control power in the presence of these
physical limits; formally, we solve the theoretical problem of maximizing the
information transferred from inputs to outputs when the number of available
molecules is held fixed. We start with the simplest version of the problem, in
which a single transcription factor protein controls the readout of one or more
genes by binding to DNA. We further simplify by assuming that this regulatory
network operates in steady state, that the noise is small relative to the
available dynamic range, and that the target genes do not interact. Even in
this simple limit, we find a surprisingly rich set of optimal solutions.
Importantly, for each locally optimal regulatory network, all parameters are
determined once the physical constraints on the number of available molecules
are specified. Although we are solving an over--simplified version of the
problem facing real cells, we see parallels between the structure of these
optimal solutions and the behavior of actual genetic regulatory networks.
Subsequent papers will discuss more complete versions of the problem
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