1,820 research outputs found
Fourier algebras on homogeneous spaces
No full textAbstractSpectral synthesis and operator synthesis on a homogeneous space G/K, where K is a compact subgroup of a locally compact group G, are studied. Injection theorem for sets of spectral synthesis for A(G/K) is proved, extending the classical result of Reiter and more recent results of Kaniuth–Lau, Parthasarathy–Prakash and others. A simple direct image theorem for spectral synthesis is proved and an extension of the subgroup theorem and an alternate proof of the injection theorem are obtained as consequences. The relation between synthesis in the Fourier algebra A(G/K) and an appropriate Varopoulos algebra is obtained, subsuming earlier results of Varopoulos, Spronk–Turowska and Parthasarathy–Prakash. Study of relations between spectral synthesis and operator synthesis pioneered by Arveson and carried forward recently by Shulman–Turowska, Parthasarathy–Prakash and Ludwig–Turowska is undertaken on homogeneous spaces. Operator space methods are needed for this study, and more specifically, a characterisation of completely bounded multipliers on A(G/K) as the invariant part of a suitable weak⁎ Haagerup tensor product (or the space of Schur multipliers) is given and is used for this study
Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations
No full textWe present, for the first time, the result (from 2008) that (normal, strongly
continuous) Markov semigroups on ( a separable Hilbert
space) admit a Hudson-Parthasarathy dilation (that is, a dilation to a cocycle
perturbation of a noise) if and only if the Markov semigroup is spatial (that
is, if it dominates an elementary CP-semigroup). The proof is by general
abstract nonsense (taken from Arveson's classification of -semigroups on
by Arveson systems up to cocycle conjugacy) and not, as usual,
by constructing the cocycle as a solution of a quantum stochastic differential
equation in the sense of Hudson and Parthasarathy. All other results that make
similar statements (especially, [Mem. Amer. Math. Soc. 240 (2016), vi+126
pages, arXiv:0901.1798]) for more general -algebras) have been proved
later by suitable adaptations of the methods exposed here. (They use Hilbert
module techniques, which we carefully avoid here in order to make the result
available without any appeal to Hilbert modules.
sj-pdf-1-jcb-10.1177_0271678X231153728 - Supplemental material for Dynamic cerebral autoregulation measured by diffuse correlation spectroscopy
No full textSupplemental material, sj-pdf-1-jcb-10.1177_0271678X231153728 for Dynamic cerebral autoregulation measured by diffuse correlation spectroscopy by Christopher G Favilla, Michael T Mullen, Farhan Kahn, Izad-Yar Daniel Rasheed, Steven R Messe, Ashwin B Parthasarathy and Arjun G Yodh in Journal of Cerebral Blood Flow & Metabolism</p
Testing for fullerenes in geologic materials: oklo carbonaceous substances, karelian shungites, sudbury black tuff: comment and reply
No full textThe presence of low concentrations of fullerenes has been reported from numerous terrestrial and meteoritic sources (Buseck, 2002). In a recent paper, Mossman et al. (2003) present mass spectra of carbonaceous substances using laser desorption ionization (LDI) and high-resolution electron-impact mass spectrometry. The authors confirm the presence of fullerenes in the Onaping Formation, Black Tuff from Sudbury, Ontario, but do not find fullerenes in carbon-rich shungite rocks from the Lake Onega region of Karelia, Russia. They conclude that the earlier observation of fullerenes in Karelian shungite may have been due to the intrusion of basic igneous rocks and attribute the absence of fullerenes in the four shungite samples they studied to the possible heterogeneity of shungites. However, the authors also argue: "Alternative explanations include the possibility that fullerenes do not occur in shungite, or that the discovery of fullerenes in shungite may have been an artifact of the analyses" (Mossman et al., 2003, p. 257). Moreover, the authors conclude that natural fullerenes appear to form exclusively in extraterrestrial samples. We disagree with these conclusions. The first discovery of natural fullerenes in a geological sample was reported in shungite from Karelia (Buseck et al., 1992). Ebbesen et al. (1995) speculated that the fullerenes found in shungite were products of a localized event or were due to an experimental artifact; these arguments were challenged by Buseck and Tsipursky (1995). We subsequently reported the presence of fullerenes in shungite samples from Kondopoga (60 km southwest of Shunga), a different locality in Karelia (Parthasarathy et al., 1998). The sample was a bright shungite with ~10 wt% carbon. We used electron-impact ionization mass spectrometer (EIMS) in our experiments for the characterization of fullerenes. In contrast to LDI, which is known to create fullerenes under laser irradiance, EIMS is very safe for detecting fullerenes. The presence of fullerenes in Karelian shungite was confirmed independently by powder X-ray diffraction (XRD) and 13C-nuclear magnetic resonance (NMR) experiments (Parthasarathy et al., 1998). Hence, we do not agree with Mossman et al. (2003) that the fullerenes reported from shungite were due to experimental artifacts. As has been pointed out by many people, Mossman et al. (2003) among them, Karelian shungite is highly heterogeneous. Fullerenes have only been found in the glassy variety of bright shungite (Buseck et al., 1992; Parthasarathy et al., 1998). We have carried out a series of experiments exploring the presence of fullerenes in shungite from different areas of Karelia. We present here a typical mass spectra obtained from a dull shungite, in which the total carbon content was estimated to be 60 wt%. Figure 1 shows the mass spectrum of the carbonaceous matter extracted from a dull shungite and exhibits the absence of fullerene. Out of twelve Karelian shungite samples we found fullerenes in only three samples, all of which are bright shungite of glassy nature (Parthasarathy et al., 1998)
Malliavin's theorem for weak synthesis on nonabelian groups
No full textAbstractMalliavin's celebrated theorem on the failure of spectral synthesis for the Fourier algebra A(G) on nondiscrete abelian groups was strengthened to give failure of weak synthesis by Parthasarathy and Varma. We extend this to nonabelian groups by proving that weak synthesis holds for A(G) if and only if G is discrete. We give the injection theorem and the inverse projection theorem for weak X-spectral synthesis, as well as a condition for the union of two weak X-spectral sets to be weak X-spectral for an A(G)-submodule X of VN(G). Relations between weak X-synthesis in A(G) and A(G×G) and the Varopoulos algebra V(G) are explored. The concept of operator synthesis was introduced by Arveson. We extend several recent investigations on operator synthesis by defining and studying, for a V∞(G)-submodule M of B(L2(G)), sets of weak M-operator synthesis. Relations between X-Ditkin sets and M-operator Ditkin sets and between weak X-spectral synthesis and weak M-operator synthesis are explored
From quantum stochastic differential equations to Gisin-Percival state diffusion
No full textStarting from the quantum stochastic differential equations of Hudson and Parthasarathy Commun. Math. Phys. 93, 301 (1984) and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space �(L2(�+)�(�n��n)) and the Hilbert space L2(μ), where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion (B(t),t�0), we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation N. Gisin and J. Percival, J. Phys. A 167, 315 (1992). This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories. © 2017 Author(s)
Viscous streaming-enhanced inertial particle transport
No full textFluidic devices operating at the micro- and milli-meter scales employ several fundamental tasks involving pumping, mixing, separation, sorting, storing and transport of different fluids (or) species. An attractive fluid mechanism that can be leveraged to fulfill these wide range of tasks is viscous streaming, a non-linear effect characteristic of the scales above. In this thesis, we first show that numerical simulations based on the Remeshed Vortex Method (RVM) can accurately and efficiently capture viscous streaming dynamics. We test this algorithm on a wide variety of settings while simultaneously exhibiting the resultant streaming flow--structures, demonstrating both streaming's capability of effecting flow control and our solver's robustness in capturing these structures. We then consider the problem of an idealized two-dimensional inertial particle transport and prove that transport can be augmented by sensibly utilizing the streaming mechanism. We then successfully perform a forward--design study to devise shapes capable of enhanced transport using this mechanism, capitalizing on the insights gained from our demonstrations above. We envison such transport applications in the emergent technology of miniature robots, capable of traversing our blood stream to deliver payloads of therapeutical drugs.Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2020-12-01The student, Tejaswin Parthasarathy, accepted the attached license on 2018-12-12 at 17:19.The student, Tejaswin Parthasarathy, submitted this Thesis for approval on 2018-12-12 at 17:27.This Thesis was approved for publication on 2018-12-13 at 16:32.DSpace SAF Submission Ingestion Package generated from Vireo submission #13309 on 2019-02-08 at 11:42:06Made available in DSpace on 2019-02-08T18:44:46Z (GMT). No. of bitstreams: 2
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Coauthor prediction for junior researchers
No full textResearch collaboration can bring in different perspectives and generate more productive results. However, finding an appropriate collaborator can be difficult due to the lacking of sufficient information. Link prediction is a related technique for collaborator discovery; but its focus has been mostly on the core authors who have relatively more publications. We argue that junior researchers actually need more help in finding collaborators. Thus, in this paper, we focus on coauthor prediction for junior researchers. Most of the previous works on coauthor prediction considered global network feature and local network feature separately, or tried to combine local network feature and content feature. But we found a significant improvement by simply combing local network feature and global network feature. We further developed a regularization based approach to incorporate multiple features simultaneously. Experimental results demonstrated that this approach outperformed the simple linear combination of multiple features. We further showed that content features, which were proved to be useful in link prediction, can be easily integrated into our regularization approach. © 2013 Springer-Verlag
Lipschitzian Q-matrices are P-matrices
No full textIn this note, we show that Lipschitzian Q-matrices are P-matrices by obtaining a necessary condition on Lipschitzian Q 0-matrices. The sufficiency of this condition has also been established by the first two authors along with another coauthor (Murthy, Parthasarathy and Sriparna, 1995)
A Quest to Unravel the Metric Structure Behind Perturbed Networks
No full textGraphs and network data are ubiquitous across a wide spectrum of scientific and application domains. Often in practice, an input graph can be considered as an observed snapshot of a (potentially
continuous) hidden domain or process. Subsequent analysis, processing, and inferences are then performed on this observed graph. In this paper we advocate the perspective that an observed graph is often a noisy version of some discretized 1-skeleton of a hidden domain, and specifically we will consider the following natural network model: We assume that there is a true graph G^* which is a certain proximity graph for points sampled from a hidden domain X; while the observed graph G is an Erdos-Renyi type perturbed version of G^*.
Our network model is related to, and slightly generalizes, the much-celebrated small-world network model originally proposed by Watts and Strogatz. However, the main question we aim to answer is orthogonal to the usual studies of network models (which often focuses on characterizing / predicting behaviors and properties of real-world networks). Specifically, we aim to recover the metric structure of G^* (which reflects that of the hidden space X as we will show) from the observed graph G. Our main result is that a simple filtering process based on the Jaccard index can recover this metric within a multiplicative factor of 2 under our network model. Our work makes one step towards the general question of inferring structure of a hidden space from its observed noisy graph representation. In addition, our results also provide a theoretical understanding for Jaccard-Index-based denoising approaches
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