36,229 research outputs found
Asynchronous approach in the plane: A deterministic polynomial algorithm
In this paper we study the task of approach of two mobile agents having the
same limited range of vision and moving asynchronously in the plane. This task
consists in getting them in finite time within each other's range of vision.
The agents execute the same deterministic algorithm and are assumed to have a
compass showing the cardinal directions as well as a unit measure. On the other
hand, they do not share any global coordinates system (like GPS), cannot
communicate and have distinct labels. Each agent knows its label but does not
know the label of the other agent or the initial position of the other agent
relative to its own. The route of an agent is a sequence of segments that are
subsequently traversed in order to achieve approach. For each agent, the
computation of its route depends only on its algorithm and its label. An
adversary chooses the initial positions of both agents in the plane and
controls the way each of them moves along every segment of the routes, in
particular by arbitrarily varying the speeds of the agents. A deterministic
approach algorithm is a deterministic algorithm that always allows two agents
with any distinct labels to solve the task of approach regardless of the
choices and the behavior of the adversary. The cost of a complete execution of
an approach algorithm is the length of both parts of route travelled by the
agents until approach is completed. Let and be the initial
distance separating the agents and the length of the shortest label,
respectively. Assuming that and are unknown to both agents, does
there exist a deterministic approach algorithm always working at a cost that is
polynomial in and ? In this paper, we provide a positive answer to
the above question by designing such an algorithm
Asynchronous Approach in the Plane: A Deterministic Polynomial Algorithm
In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other\u27s range of vision. The agents execute the same deterministic algorithm and are assumed to have a compass showing the cardinal directions as well as a unit measure. On the other hand, they do not share any global coordinates system (like GPS), cannot communicate and have distinct labels. Each agent knows its label but does not know the label of the other agent or the initial position of the other agent relative to its own. The route of an agent is a sequence of segments that are subsequently traversed in order to achieve approach. For each agent, the computation of its route depends only on its algorithm and its label. An adversary chooses the initial positions of both agents in the plane and controls the way each of them moves along every segment of the routes, in particular by arbitrarily varying the speeds of the agents. Roughly speaking, the goal of the adversary is to prevent the agents from solving the task, or at least to ensure that the agents have covered as much distance as possible before seeing each other. A deterministic approach algorithm is a deterministic algorithm that always allows two agents with any distinct labels to solve the task of approach regardless of the choices and the behavior of the adversary. The cost of a complete execution of an approach algorithm is the length of both parts of route travelled by the agents until approach is completed.
Let Delta and l be the initial distance separating the agents and the length of (the binary representation of) the shortest label, respectively. Assuming that Delta and l are unknown to both agents, does there exist a deterministic approach algorithm whose cost is polynomial in Delta and l?
Actually the problem of approach in the plane reduces to the network problem of rendezvous in an infinite oriented grid, which consists in ensuring that both agents end up meeting at the same time at a node or on an edge of the grid. By designing such a rendezvous algorithm with appropriate properties, as we do in this paper, we provide a positive answer to the above question.
Our result turns out to be an important step forward from a computational point of view, as the other algorithms allowing to solve the same problem either have an exponential cost in the initial separating distance and in the labels of the agents, or require each agent to know its starting position in a global system of coordinates, or only work under a much less powerful adversary
Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials
In this paper we show a new way of constructing deterministic polynomial-time
approximation algorithms for computing complex-valued evaluations of a large
class of graph polynomials on bounded degree graphs. In particular, our
approach works for the Tutte polynomial and independence polynomial, as well as
partition functions of complex-valued spin and edge-coloring models.
More specifically, we define a large class of graph polynomials
and show that if and there is a disk centered at zero in the
complex plane such that does not vanish on for all bounded degree
graphs , then for each in the interior of there exists a
deterministic polynomial-time approximation algorithm for evaluating at
. This gives an explicit connection between absence of zeros of graph
polynomials and the existence of efficient approximation algorithms, allowing
us to show new relationships between well-known conjectures.
Our work builds on a recent line of work initiated by. Barvinok, which
provides a new algorithmic approach besides the existing Markov chain Monte
Carlo method and the correlation decay method for these types of problems.Comment: 27 pages; some changes have been made based on referee comments. In
particular a tiny error in Proposition 4.4 has been fixed. The introduction
and concluding remarks have also been rewritten to incorporate the most
recent developments. Accepted for publication in SIAM Journal on Computatio
Parameter Estimation for Mechanical Systems Using an Extended Kalman Filter
This paper proposes a new computational approach based on the Extended Kalman Filter (EKF) in order to apply the polynomial chaos theory to the problem of parameter estimation, using direct stochastic collocation. The Kalman filter formula is used at each time step in order to update the polynomial chaos of the uncertain states and the uncertain parameters. The main advantage of this method is that the estimation comes in the form of a probability density function rather than a deterministic value, combined with the fact that simulations using polynomial chaos methods are much faster than Monte Carlo simulations. The proposed method is applied to a nonlinear four degree of freedom roll plane model of a vehicle, in which an uncertain mass with an uncertain position is added on the roll bar. A major drawback was identified: the EKF can diverge when using a high sampling frequency, which might prevent the use of enough data to obtain accurate results when a low sampling frequency is necessary. When applying the polynomial chaos theory to the EKF, numerical errors can accumulate even faster than in the general case due to the truncation in the polynomial chaos expansions, which is illustrated on a simple example. An alternative EKF approach which consists of applying the filter formula on all the observations at once usually yields better results, but can still sometimes fail to produce very accurate results. Therefore, using different sampling rates in order to verify the coherence of the results and comparing the results to a different approach is strongly recommended
Deterministic Rendezvous at a Node of Agents with Arbitrary Velocities
We consider the task of rendezvous in networks modeled as undirected graphs.
Two mobile agents with different labels, starting at different nodes of an
anonymous graph, have to meet. This task has been considered in the literature
under two alternative scenarios: weak and strong. Under the weak scenario,
agents may meet either at a node or inside an edge. Under the strong scenario,
they have to meet at a node, and they do not even notice meetings inside an
edge. Rendezvous algorithms under the strong scenario are known for synchronous
agents. For asynchronous agents, rendezvous under the strong scenario is
impossible even in the two-node graph, and hence only algorithms under the weak
scenario were constructed. In this paper we show that rendezvous under the
strong scenario is possible for agents with restricted asynchrony: agents have
the same measure of time but the adversary can arbitrarily impose the speed of
traversing each edge by each of the agents. We construct a deterministic
rendezvous algorithm for such agents, working in time polynomial in the size of
the graph, in the length of the smaller label, and in the largest edge
traversal time.Comment: arXiv admin note: text overlap with arXiv:1704.0888
Deterministic meeting of sniffing agents in the plane
Two mobile agents, starting at arbitrary, possibly different times from
arbitrary locations in the plane, have to meet. Agents are modeled as discs of
diameter 1, and meeting occurs when these discs touch. Agents have different
labels which are integers from the set of 0 to L-1. Each agent knows L and
knows its own label, but not the label of the other agent. Agents are equipped
with compasses and have synchronized clocks. They make a series of moves. Each
move specifies the direction and the duration of moving. This includes a null
move which consists in staying inert for some time, or forever. In a non-null
move agents travel at the same constant speed, normalized to 1. We assume that
agents have sensors enabling them to estimate the distance from the other agent
(defined as the distance between centers of discs), but not the direction
towards it. We consider two models of estimation. In both models an agent reads
its sensor at the moment of its appearance in the plane and then at the end of
each move. This reading (together with the previous ones) determines the
decision concerning the next move. In both models the reading of the sensor
tells the agent if the other agent is already present. Moreover, in the
monotone model, each agent can find out, for any two readings in moments t1 and
t2, whether the distance from the other agent at time t1 was smaller, equal or
larger than at time t2. In the weaker binary model, each agent can find out, at
any reading, whether it is at distance less than \r{ho} or at distance at least
\r{ho} from the other agent, for some real \r{ho} > 1 unknown to them. Such
distance estimation mechanism can be implemented, e.g., using chemical sensors.
Each agent emits some chemical substance (scent), and the sensor of the other
agent detects it, i.e., sniffs. The intensity of the scent decreases with the
distance.Comment: A preliminary version of this paper appeared in the Proc. 23rd
International Colloquium on Structural Information and Communication
Complexity (SIROCCO 2016), LNCS 998
Polynomial Chaos Expansion method as a tool to evaluate and quantify field homogeneities of a novel waveguide RF Wien Filter
For the measurement of the electric dipole moment of protons and deuterons, a
novel waveguide RF Wien filter has been designed and will soon be integrated at
the COoler SYnchrotron at J\"ulich. The device operates at the harmonic
frequencies of the spin motion. It is based on a waveguide structure that is
capable of fulfilling the Wien filter condition ()
\textit{by design}. The full-wave calculations demonstrated that the waveguide
RF Wien filter is able to generate high-quality RF electric and magnetic
fields. In reality, mechanical tolerances and misalignments decrease the
simulated field quality, and it is therefore important to consider them in the
simulations. In particular, for the electric dipole moment measurement, it is
important to quantify the field errors systematically. Since Monte-Carlo
simulations are computationally very expensive, we discuss here an efficient
surrogate modeling scheme based on the Polynomial Chaos Expansion method to
compute the field quality in the presence of tolerances and misalignments and
subsequently to perform the sensitivity analysis at zero additional
computational cost.Comment: 12 pages, 19 figure
Approximating the Permanent of a Random Matrix with Vanishing Mean
We show an algorithm for computing the permanent of a random matrix with
vanishing mean in quasi-polynomial time. Among special cases are the Gaussian,
and biased-Bernoulli random matrices with mean 1/lnln(n)^{1/8}. In addition, we
can compute the permanent of a random matrix with mean 1/poly(ln(n)) in time
2^{O(n^{\eps})} for any small constant \eps>0. Our algorithm counters the
intuition that the permanent is hard because of the "sign problem" - namely the
interference between entries of a matrix with different signs. A major open
question then remains whether one can provide an efficient algorithm for random
matrices of mean 1/poly(n), whose conjectured #P-hardness is one of the
baseline assumptions of the BosonSampling paradigm
Attractor reconstruction of an impact oscillator for parameter identification
Peer reviewedPreprin
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