1,071 research outputs found
Counting Realizations of Laman Graphs on the Sphere
We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space
Real rank boundaries and loci of forms
In this article we study forbidden loci and typical ranks of forms with
respect to the embeddings of given by the line
bundles . We introduce the Ranestad-Schreyer locus corresponding to
supports of non-reduced apolar schemes. We show that, in those cases, this is
contained in the forbidden locus. Furthermore, for these embeddings, we give a
component of the real rank boundary, the hypersurface dividing the minimal
typical rank from higher ones. These results generalize to a class of
embeddings of . Finally, in connection with real
rank boundaries, we give a new interpretation of the
hyperdeterminant.Comment: 17 p
Relating L-Resilience and Wait-Freedom via Hitting Sets
The condition of t-resilience stipulates that an n-process program is only
obliged to make progress when at least n-t processes are correct. Put another
way, the live sets, the collection of process sets such that progress is
required if all the processes in one of these sets are correct, are all sets
with at least n-t processes.
We show that the ability of arbitrary collection of live sets L to solve
distributed tasks is tightly related to the minimum hitting set of L, a minimum
cardinality subset of processes that has a non-empty intersection with every
live set. Thus, finding the computing power of L is NP-complete.
For the special case of colorless tasks that allow participating processes to
adopt input or output values of each other, we use a simple simulation to show
that a task can be solved L-resiliently if and only if it can be solved
(h-1)-resiliently, where h is the size of the minimum hitting set of L.
For general tasks, we characterize L-resilient solvability of tasks with
respect to a limited notion of weak solvability: in every execution where all
processes in some set in L are correct, outputs must be produced for every
process in some (possibly different) participating set in L. Given a task T, we
construct another task T_L such that T is solvable weakly L-resiliently if and
only if T_L is solvable weakly wait-free
Study of the Impact of Graphite Orientation and Ion Transport on EDLC Performance
The article of record as published may be found at http://dx.doi.org/10.3390/ ma15010155A model study of electric double layer capacitor (EDLC)-style capacitors in which the electrodes were composed of low surface area-oriented flakes of graphite that compressed to form a paper-like morphology has suggested that ion transport rates significantly impact EDLC energy and power density. Twelve capacitors were constructed, each using the same model electrode material and the same aqueous NaCl electrolyte, but differing in relative electrode orientation, degree of electrode compression, and presence/absence of an ionic transport salt bridge. All were tested with a galvanostat over a range of discharge currents. Significant differences in energy and power density and estimated series resistance were found as a function of all the factors listed, indicating that capacitor performance is not simply a function of the electrode surface area. This simple postulation was advanced and tested against data: net ion (Na+, Cl?) âvelocityâ during both charge and discharge significantly impacts capacitive performance
Combinatorics of Bricard's octahedra
We re-prove the classification of motions of an octahedron â obtained by Bricard at the beginning of the XX century â by means of combinatorial objects satisfying some elementary rules. The explanations of these rules rely on the use of a well-known creation of modern algebraic geometry, the moduli space of stable rational curves with marked points, for the description of configurations of graphs on the sphere. Once one accepts the objects and the rules, the classification becomes elementary (though not trivial) and can be enjoyed without the need of a very deep background on the topic
A Superstabilizing -Approximation Algorithm for Dynamic Steiner Trees
In this paper we design and prove correct a fully dynamic distributed
algorithm for maintaining an approximate Steiner tree that connects via a
minimum-weight spanning tree a subset of nodes of a network (referred as
Steiner members or Steiner group) . Steiner trees are good candidates to
efficiently implement communication primitives such as publish/subscribe or
multicast, essential building blocks for the new emergent networks (e.g. P2P,
sensor or adhoc networks). The cost of the solution returned by our algorithm
is at most times the cost of an optimal solution, where is the
group of members. Our algorithm improves over existing solutions in several
ways. First, it tolerates the dynamism of both the group members and the
network. Next, our algorithm is self-stabilizing, that is, it copes with nodes
memory corruption. Last but not least, our algorithm is
\emph{superstabilizing}. That is, while converging to a correct configuration
(i.e., a Steiner tree) after a modification of the network, it keeps offering
the Steiner tree service during the stabilization time to all members that have
not been affected by this modification
Strong Equivalence Relations for Iterated Models
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical
representation, has become standard for applying topological reasoning to
distributed computing. Its modular structure makes it easier to analyze than
the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS).
It is known that AS and IIS are equivalent with respect to \emph{wait-free
task} computability: a distributed task is solvable in AS if and only if it
solvable in IIS. We observe, however, that this equivalence is not sufficient
in order to explore solvability of tasks in \emph{sub-models} of AS (i.e.
proper subsets of its runs) or computability of \emph{long-lived} objects, and
a stronger equivalence relation is needed. In this paper, we consider
\emph{adversarial} sub-models of AS and IIS specified by the sets of processes
that can be \emph{correct} in a model run. We show that AS and IIS are
equivalent in a strong way: a (possibly long-lived) object is implementable in
AS under a given adversary if and only if it is implementable in IIS under the
same adversary. %This holds whether the object is one-shot or long-lived.
Therefore, the computability of any object in shared memory under an
adversarial AS scheduler can be equivalently investigated in IIS
Anonymous Asynchronous Systems: The Case of Failure Detectors
Due the multiplicity of loci of control, a main issue distributed systems have to cope with lies in the uncertainty on the system state created by the adversaries that are asynchrony, failures, dynamicity, mobility, etc. Considering message-passing systems, this paper considers the uncertainty created by the net effect of three of these adversaries, namely, asynchrony, failures, and anonymity. This means that, in addition to be asynchronous and crash-prone, the processes have no identity. Trivially, agreement problems (e.g., consensus) that cannot be solved in presence of asynchrony and failures cannot be solved either when adding anonymity. The paper consequently proposes anonymous failure detectors to circumvent these impossibilities. It has several contributions. First it presents three classes of failure detectors (denoted AP, Aâ© and Aâ) and show that they are the anonymous counterparts of the classes of perfect failure detectors, eventual leader failure detectors and quorum failure detectors, respectively. The class Aâ is new and showing it is the anonymous counterpart of the class â is not trivial. Then, the paper presents and proves correct a genuinely anonymous consensus algorithm based on the pair of anonymous failure detector classes (Aâ©, Aâ) (âgenuinelyâ means that, not only processes have no identity, but no process is aware of the total number of processes). This new algorithm is not a âstraightforward extensionâ of an algorithm designed for non-anonymous systems. To benefit from Aâ, it uses a novel message exchange pattern where each phase of every round is made up of sub-rounds in which appropriate control information is exchanged. Finally, the paper discusses the notions of failure detector class hierarchy and weakest failure detector class for a given problem in the context of anonymous systems
Charge distribution in two-dimensional electrostatics
We examine the stability of ringlike configurations of N charges on a plane
interacting through the potential . We interpret the equilibrium distributions in terms of a shell
model and compare predictions of the model with the results of numerical
simulations for systems with up to 100 particles.Comment: LaTe
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