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

Lanthanide alkyl and silyl compounds: synthesis, reactivity and catalysts for green chemistry

The last few decades have witnessed enormous research in the field of organometallic lanthanide chemistry. Our research group has developed a few rare earth alkyl compounds containing tris(dimethylsilyl)methyl ligand and explored their reactivity. This thesis focusses on extending the study of lanthanide alkyl and silyl compounds to develop strategies for their synthesis and explore their reactivity and role as catalysts in processes such as hydrosilylation and cross-dehydrocoupling. Two novel ligands, alkyl, –C(SiHMe2)3 and silyl, –Si(SiHMe2)3 have been used to synthesize homoleptic organometallic lanthanide complexes. The silyl anion, KSi(SiHMe2)3, is prepared from the reaction of KOtBu and Si(SiHMe2)4. A single crystal X-ray diffraction study shows that KSi(SiHMe2)3 crystallizes as a chain of alternating K cations and Si(SiHMe2)3 anions with K coordinated to the central Si atoms and the three Si-H moieties oriented toward the next K atom. A series of lanthanum, cerium, praseodymium, neodymium, and samarium alkyl compounds and ytterbium and yttrium silyl compounds are synthesized and their characterization, reactivity and role as catalysts are described. These compounds are synthesized by salt metathesis reaction between the metal halide and an equiv. amount of KC(SiHMe2)3 and KSi(SiHMe2)3 ligands. The lanthanide tris(alkyl) compounds are solvent free compounds while lanthanide bis(silyl) compounds are THF coordinated and unstable at room temperature. All these compounds are highly air- and moisture-sensitive. Interestingly, spectroscopic characterization and X-ray analysis reveal that all the lanthanide alkyl compounds contain classical and non-classical β-SiH interactions with the metal center and undergo β-SiH abstraction by Lewis acids, such as B(C6F5)3 while the lanthanide silyl compounds lack such non-classical interactions with the metal center. The reactions of Ln{C(SiHMe2)3}3 (Ln = La, Ce, Pr, Nd) with one and two equiv. of B(C6F5)3 gives Ln{C(SiHMe2)3}2HB(C6F5)3, and LnC(SiHMe2)3{HB(C6F5)3}2, respectively and an equiv. amount of 1,3-disilacyclobutane dimer, {Me2Si-C(SiHMe2)2}2 as the by-product. The monocations, Ln{C(SiHMe2)3}2HB(C6F5)3 are used as catalysts for hydrosilylation of α,β- unsaturated esters to selectively yield α-silyl esters. α-Silyl esters are isolated in high yields from a range of α,β-unsaturated esters and hydrosilanes. The divalent bis(alkyl) lanthanide compounds, Ln{C(SiHMe2)3}2THF2 (Ln = Yb, Sm) are synthesized by salt metathesis of lanthanide halide and two equiv. of KC(SiHMe2)3 in THF. Reactions with one or two equiv. of B(C6F5)3 generate LnC(SiHMe2)3HB(C6F5)3 and an equiv. amount of 1,3-disilacyclobutane dimer, {Me2Si-C(SiHMe2)2}2. Ln{C(SiHMe2)3}2THF2 undergoes reaction with 1,3-di-tert-butylimidazol-2-ylidene (ImtBu) to yield Ln{C(SiHMe2)3}2ImtBu in non-polar solvent. A single crystal X-ray diffraction and spectroscopic study of Ln{C(SiHMe2)3}2THF2 and Ln{C(SiHMe2)3}2ImtBu reveal the presence of classical and non-classical interactions with the metal center. Ln{C(SiHMe2)3}2ImtBu (Ln = Yb, Sm) is an efficient catalyst for cross-dehydrocoupling of organosilanes and amines to yield silazanes at room temperature in high yields. Kinetic studies of the catalytic system indicate a first-order dependence on silane and amine concentrations. Lanthanide silyl compounds, Yb{Si(SiHMe2)3}2THF3 and Cl3Y{Si(SiHMe2)3}2(Et2O)].2K(Et2O)2 are synthesized by salt metathesis of lanthanide halide and two or three equiv. of KSi(SiHMe2)3 ligand. Yb{Si(SiHMe2)3}2THF3 is the first example of homoleptic Ln(II) silyl compound characterized by X-ray diffraction having trigonal bipyramidal geometry around the ytterbium center. Yb{Si(SiHMe2)3}2THF3 reacts with ancillary ligand, TlToM to yield ToM2Yb revealing lability of the silyl ligand

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

Impact of leader on cluster synchronization

5 pages, 5 figuresNon peer reviewedPostprin

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

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