679 research outputs found
Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model
We study the phase synchronized clusters in the diffusively coupled maps on
the Cayley tree networks for heterogeneous delay values. Cayley tree networks
comprise of two parts: the inner nodes and the boundary nodes. We find that
heterogeneous delays lead to various cluster states, such as; (a) cluster state
consisting of inner nodes and boundary nodes, and (b) cluster state consisting
of only boundary nodes. The former state may comprise of nodes from all the
generations forming self-organized cluster or nodes from few generations
yielding driven clusters depending upon on the parity of heterogeneous delay
values. Furthermore, heterogeneity in delays leads to the lag synchronization
between the siblings lying on the boundary by destroying the exact
synchronization among them. The time lag being equal to the difference in the
delay values. The Lyapunov function analysis sheds light on the destruction of
the exact synchrony among the last generation nodes. To the end we discuss the
relevance of our results with respect to their applications in the family
business as well as in understanding the occurrence of genetic diseases.Comment: 9 pages, 11 figure
IDEAS project - Data Informed Platform for Health feasibility study in Uttar Pradesh
The IDEAS project sought to improve the health and survival of mothers and babies through generating evidence to inform policy and practice. This data collection contains topic guides and other research tools used to assess the feasibility of introducing a Data Informed Platform for Health (DIPH), in order to bring together key data from the public and private health sector on inputs and processes that may influence maternal and newborn health. The DIPH was intended to promote the use of local data for decision-making and priority setting at local health administration level, and for programme appraisal and comparison at regional and zonal level
Synchronization in Delayed Multiplex Networks
We study impact of multiplexing on the global phase synchronizability of
different layers in the delayed coupled multiplex networks. We find that at
strong couplings, the multiplexing induces the global synchronization in sparse
networks. The introduction of global synchrony depends on the connection
density of the layers being multiplexed, which further depends on the
underlying network architecture. Moreover, multiplexing may lead to a
transition from a quasi-periodic or chaotic evolution to a periodic evolution.
For the periodic case, the multiplexing may lead to a change in the period of
the dynamical evolution. Additionally, delay in the couplings may bring upon
synchrony to those multiplex networks which do not exhibit synchronization for
the undelayed evolution. Using a simple example of two globally connected
layers forming a multiplex network, we show how delay brings upon a possibility
for the inter layer global synchrony, that is not possible for the undelayed
evolution.Comment: 6 pages, 9 figure
Role of delay in the mechanism of cluster formation
We study the role of delay in phase synchronization and phenomena responsible
for cluster formation in delayed coupled maps on various networks. Using
numerical simulations, we demonstrate that the presence of delay may change the
mechanism of unit to unit interaction. At weak coupling values, same parity
delays are associated with the same phenomenon of cluster formation and exhibit
similar dynamical evolution. Intermediate coupling values yield rich
delay-induced driven cluster patterns. A Lyapunov function analysis sheds light
on the robustness of the driven clusters observed for delayed bipartite
networks. Our results reveal that delay may lead to a completely different
relation, between dynamical and structural clusters, than observed for the
undelayed case.Comment: 4+ pages, 4 figues, PRE Rapid Communication (in press
An Analysis of the First Passage to the Origin (FPO) Distribution
What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this first passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a fixed n and also the posterior distribution of m when we are given that m follows some known prior distribution
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