Supersymmetry and Fredholm modules over quantized spaces

The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute the explicit formula for the Chern character on generators of the Toeplitz C^* -algebra.Comment: 24

Matrix Cartan superdomains, super Toeplitz operators, and quantization

We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C^* -algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck's constant tends to zero.Comment: 52

Whanaungatanga: Sybil-proof routing with social networks

Decentralized systems, such as distributed hash tables, are subject to the Sybil attack, in which an adversary creates many false identities to increase its influence. This paper proposes a routing protocol for a distributed hash table that is strongly resistant to the Sybil attack. This is the first solution to this problem with sublinear run time and space usage. The protocol uses the social connections between users to build routing tables that enable Sybil-resistant distributed hash table lookups. With a social network of N well-connected honest nodes, the protocol can tolerate up to O(N/log N) "attack edges" (social links from honest users to phony identities). This means that an adversary has to fool a large fraction of the honest users before any lookups will fail. The protocol builds routing tables that contain O(N log^(3/2) N) entries per node. Lookups take O(1) time. Simulation results, using social network graphs from LiveJournal, Flickr, and YouTube, confirm the analytical results

Synergistic effects of tethered growth factors and adhesion ligands on DNA synthesis and function of primary hepatocytes cultured on soft synthetic hydrogels

The composition, presentation, and spatial orientation of extracellular matrix molecules and growth factors are key regulators of cell behavior. Here, we used self-assembling peptide nanofiber gels as a modular scaffold to investigate how fibronectin-derived adhesion ligands and different modes of epidermal growth factor (EGF) presentation synergistically regulate multiple facets of primary rat hepatocyte behavior in the context of a soft gel. In the presence of soluble EGF, inclusion of dimeric RGD and the heparin binding domain from fibronectin (HB) increased hepatocyte aggregation, spreading, and metabolic function compared to unmodified gels or gels modified with a single motif, but unlike rigid substrates, gels failed to induce DNA synthesis. Tethered EGF dramatically stimulated cell aggregation and spreading under all adhesive ligand conditions and also preserved metabolic function. Surprisingly, tethered EGF elicited DNA synthesis on gels with RGD and HB. Phenotypic differences between soluble and tethered EGF stimulation of cells on peptide gels are correlated with differences in expression and phosphorylation the EGF receptor and its heterodimerization partner ErbB2, and activation of the downstream signaling node ERK1/2. These modular matrices reveal new facets of hepatocellular biology in culture and may be more broadly useful in culture of other soft tissues.United States. ArmyHertz Foundation (Graduate Fellowship)National Institute for Biomedical Imaging and Bioengineering (U.S.) (R01EB003805)National Institute of Dental and Craniofacial Research (U.S.) (R01DE019523)Massachusetts Institute of Technology. Center for Environmental Health Sciences (National Institute of Environmental Health Sciences P30ES002109)Massachusetts Institute of Technology. Center for Environmental Health Sciences (National Institute of Environmental Health Sciences R01ES015241)Armed Forces Institute of Regenerative Medicin

Statistical distinguishability between unitary operations

The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always exists a finite number $N$ such that $U_1^{\otimes N}$ and $U_2^{\otimes N}$ are perfectly distinguishable, although they were not in the single-copy case. This result can be extended to any finite set of unitary transformations. Finally, a fidelity for one-qubit gates, which satisfies many useful properties from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to any finite set of gate

A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant $\lambda$ for $|\lambda| |\log T| \le K$ where $K$ is some numerical constant and $T$ is the temperature. Furthermore in that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior which is that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our results prove also that in dimension two any transition temperature must be non-perturbative in the coupling constant, a result expected on physical grounds. The proof exploits the specific momentum conservation rules in two dimensions.Comment: 4 pages, no figure

On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisation theorem holds true under more general hypotheses.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to conform to accepted version, title changed as wel

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte

Multiplicative cascade models for fine spatial downscaling of rainfall: parameterization with rain gauge data

Capturing the spatial distribution of high-intensity rainfall over short-time intervals is critical for accurately assessing the efficacy of urban stormwater drainage systems. In a stochastic simulation framework, one method of generating realistic rainfall fields is by multiplicative random cascade (MRC) models. Estimation of MRC model parameters has typically relied on radar imagery or, less frequently, rainfall fields interpolated from dense rain gauge networks. However, such data are not always available. Furthermore, the literature is lacking estimation procedures for spatially incomplete datasets. Therefore, we proposed a simple method of calibrating an MRC model when only data from a moderately dense network of rain gauges is available, rather than from the full rainfall field. The number of gauges needs only be sufficient to adequately estimate the variance in the ratio of the rain rate at the rain gauges to the areal average rain rate across the entire spatial domain. In our example for Warsaw, Poland, we used 25 gauges over an area of approximately 1600 km(2). MRC models calibrated using the proposed method were used to downscale 15-min rainfall rates from a 20 by 20 km area to the scale of the rain gauge capture area. Frequency distributions of observed and simulated 15-min rainfall at the gauge scale were very similar. Moreover, the spatial covariance structure of rainfall rates, as characterized by the semivariogram, was reproduced after allowing the probability density function of the random cascade generator to vary with spatial scale.Keywords: Time, Multicomponent decomposition, Fields, Simulation, Disaggregation, Mesoscale rainfall, Scale universal multifractals, Stochastic model

Functional Integral Construction of the Thirring model: axioms verification and massless limit

We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader axioms. The corresponding Ward Identities have anomalies which are not linear in the coupling and which violate the anomaly non-renormalization property. Additional anomalies are present in the closed equation for the interacting propagator, obtained by combining a Schwinger-Dyson equation with Ward Identities.Comment: 55 pages, 9 figure