Gabor Szabo

Gabor Szabo
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Mathematics - Operator Algebras (13)
 
Physics - Optics (5)
 
Physics - Physics and Society (4)
 
Physics - Disordered Systems and Neural Networks (3)
 
Physics - Statistical Mechanics (3)
 
Computer Science - Computers and Society (3)
 
Mathematics - Dynamical Systems (3)
 
Quantitative Biology - Quantitative Methods (1)
 
Computer Science - Human-Computer Interaction (1)
 
Computer Science - Information Retrieval (1)

Publications Authored By Gabor Szabo

Configuration of three different concave silver core-shell nanoresonators was numerically optimized to enhance the excitation and emission of embedded silicon vacancy (SiV) diamond color centers simultaneously. According to the tradeoff between the radiative rate enhancement and quantum efficiency (QE) conditional optimization was performed to ensure ~2-3-4 and 5-fold apparent cQE enhancement of SiV color centers with ~10% intrinsic QE. The enhancement spectra, as well as the near-field and charge distribution were inspected to uncover the physics underlying behind the optical responses. Read More

In this paper, we accomplish two objectives. Firstly, we extend and improve some results in the theory of (semi-)strongly self-absorbing C*-dynamical systems, which was introduced and studied in previous work. In particular, this concerns the theory when restricted to the case where all the semi-strongly self-absorbing actions are assumed to be unitarily regular, which is a mild technical condition. Read More

We show an equivariant Kirchberg-Phillips-type absorption theorem for pointwise outer actions of discrete amenable groups on Kirchberg algebras with respect to natural model actions on the Cuntz algebras $\mathcal{O}_\infty$ and $\mathcal{O}_2$. This generalizes results known for finite groups and poly-$\mathbb{Z}$ groups. The model actions are induced by faithful unitary representations of a given amenable group, and are strongly self-absorbing. Read More

We introduce a notion of Rokhlin dimension for one parameter automorphism groups of C*-algebras. This generalizes Kishimoto's Rokhlin property for flows, and is analogous to the notion of Rokhlin dimension for actions of the integers and other discrete groups introduced by the authors and Zacharias in previous papers. We show that finite nuclear dimension and absorption of a strongly self-absorbing C*-algebra are preserved under forming crossed products by flows with finite Rokhlin dimension, and that these crossed products are stable. Read More

A novel numerical methodology has been developed, which makes possible to optimize arbitrary emitting dipole and plasmonic nano-resonator configuration with an arbitrary objective function. By selecting quantum efficiency as the objective function that has to be maximized at preselected Purcell factor criteria, optimization of plasmonic nanorod based configurations has been realized to enhance fluorescence of NV and SiV color centers in diamond. Gold and silver nanorod based configurations have been optimized to enhance excitation and emission separately, as well as both processes simultaneously, and the underlying nanophotonical phenomena have been inspected comparatively. Read More

We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on $\mathrm{C}^*$-algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key ingredients in our approach are the concept of sequentially split $*$-homomorphisms, and the use of braided tensor products instead of ordinary tensor products. We show that various structure results carry over from the classical theory to this more general setting. Read More

This is a continuation of the study of strongly self-absorbing actions of locally compact groups on C*-algebras. Given a strongly self-absorbing action $\gamma: G\curvearrowright\mathcal{D}$, we establish permanence properties for the class of separable C*-dynamical systems absorbing $\gamma$ tensorially up to cocycle conjugacy. Generalizing results of both Toms-Winter and Dadarlat-Winter, it is proved that the desirable equivariant analogues of the classical permanence properties hold in this context. Read More

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of being a split-injective inclusion of $\mathrm{C}^*$-algebras. We show for a sequentially split $*$-homomorphism that a multitude of $\mathrm{C}^*$-algebraic approximation properties pass from the target algebra to the domain algebra, including virtually all important approximation properties currently used in the classification theory of $\mathrm{C}^*$-algebras. Read More

We show that separable, nuclear and strongly purely infinite C*-algebras have finite nuclear dimension. In fact, the value is at most three. This exploits a deep structural result of Kirchberg and R{\o}rdam on strongly purely infinite C*-algebras that are homotopic to zero in an ideal-system preserving way. Read More

We introduce and study strongly self-absorbing actions of locally compact groups on C*-algebras. This is an equivariant generalization of a strongly self-absorbing C*-algebra to the setting of C*-dynamical systems. The main result is the following equivariant McDuff-type absorption theorem: A cocycle action $(\alpha,u): G\curvearrowright A$ on a separable C*-algebra is cocycle conjugate to its tensorial stabilization with a strongly self-absorbing action $\gamma: G\curvearrowright\mathcal{D}$, if and only if there exists an equivariant and unital $*$-homomorphism from $\mathcal{D}$ into the central sequence algebra of $A$. Read More

Dispersion characteristics of four types of superconducting nanowire single photon detectors, nano-cavity-array- (NCA-), nano-cavity-deflector-array- (NCDA-), nano-cavity-double-deflector-array- (NCDDA-) and nano-cavity-trench-array- (NCTA-) integrated (I-A-SNSPDs) devices was optimized in three periodicity intervals commensurate with half-, three-quarter- and one SPP wavelength. The optimal configurations capable of maximizing NbN absorptance correspond to periodicity dependent tilting in S-orientation (90{\deg} azimuthal orientation). In NCAI-A-SNSPDs absorptance maxima are reached at the plasmonic Brewster angle (PBA) due to light tunneling. Read More

We develop a simple three compartment model based on mass balance equations which quantitatively describes the dynamics of breath methane concentration profiles during exercise on an ergometer. With the help of this model it is possible to estimate the endogenous production rate of methane in the large intestine by measuring breath gas concentrations of methane. Read More

Configurations capable of maximizing both absorptance and polarization contrast were determined for 1550 nm polarized light illumination of different plasmonic structure integrated superconducting nanowire single-photon detectors (SNSPDs) consisting of p=264 nm and P=792 nm periodic niobium-nitride (NbN) patterns on silica substrate. Global NbN absorptance maxima appear in case of p/s-polarized light illumination in S/P-orientation (gamma=90 azimuthal angle) and the highest polarization contrast is attained in S-orientation of all devices. Common nanophotonical origin of absorptance enhancement is collective resonance on nano-cavity-gratings with different profiles, which is promoted by coupling between localized modes in quarter wavelength MIM nano-cavities and laterally synchronized Brewster-Zenneck-type surface waves in integrated SNSPDs possessing a three-quarter-wavelength-scaled periodicity. Read More

We introduce the concept of Rokhlin dimension for actions of residually finite groups on C*-algebras, extending previous notions of Rokhlin dimension for actions of finite groups and the integers, as introduced by Hirshberg, Winter and the third author. If the group has a box space of finite asymptotic dimension, then actions with finite Rokhlin dimension preserve the property of having finite nuclear dimension, when passing to the crossed product C*-algebra. A detailed study of the asymptotic dimension of box spaces shows that finitely generated, virtually nilpotent groups have box spaces with finite asymptotic dimension, providing a reasonably large class of examples. Read More

Let $G$ be a metrizable compact group, $A$ a separable C*-algebra and $\alpha$ a strongly continuous action of $G$ on $A$. Provided that $\alpha$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in E-theory passes from $A$ to the crossed product C*-algebra $A\rtimes_\alpha G$ and the fixed point algebra $A^\alpha$. This extends a result by Gardella in the case that $G$ is the circle and $A$ is nuclear. Read More

This paper serves as a source of examples of Rokhlin actions or locally representable actions of finite groups on C*-algebras satisfying a certain UHF-absorption condition. We show that given any finite group $G$ and a separable, unital C*-algebra $A$ that absorbs $M_{|G|^\infty}$ tensorially, one can lift any group homomorphism $G\to\operatorname{Aut}(A)/{\approx_u}$ to an honest Rokhlin action $\gamma$ of $G$ on $A$. Unitality may be dropped in favour of stable rank one or being stable. Read More

We investigate symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such outer action has Rokhlin dimension at most 1. A consequence of these observations is a relationship between the nuclear dimension of an $\mathcal{O}_\infty$-absorbing C*-algebra and its $\mathcal{O}_2$-stabilization. Read More

We study the topological variant of Rokhlin dimension for topological dynamical systems (X,{\alpha},Z^m) in the case where X is assumed to have finite covering dimension. Finite Rokhlin dimension in this sense is a property that implies finite Rokhlin dimension of the induced action on C*-algebraic level, as was discussed in a recent paper by Ilan Hirshberg, Wilhelm Winter and Joachim Zacharias. In particular, it implies under these conditions that the transformation group C*-algebra has finite nuclear dimension. Read More

An integrated interference and colloid sphere lithography (IICL) is presented to produce complex plasmonic structures consisting of wavelength-scaled periodic arrays of nano-objects with arbitrary array symmetry and controllable nano-scaled sub-structure. The IICL method is based on illumination of colloid sphere monolayers by interference patterns synchronized with sphere arrays along arbitrary crystallographic directions. This nano-kaleidoscope method enables to tune four structure parameters independently: the symmetry and characteristic periodicity of the interference pattern might be varied by the wavelength, number and angle of incidence of the interfering beams; the colloid-spheres' diameter-scaled distance between the nano-objects is controllable by the relative orientation of the interference pattern with respect to the hexagonal lattice of colloid spheres; the size of individual nano-objects is determined by the colloid-spheres diameter and by the light wavelength and is influenced by power density; the sub-structure size-parameter sensitively depends on the polarization state and can be tuned with the nano-object size simultaneously. Read More

Social media generates a prodigious wealth of real-time content at an incessant rate. From all the content that people create and share, only a few topics manage to attract enough attention to rise to the top and become temporal trends which are displayed to users. The question of what factors cause the formation and persistence of trends is an important one that has not been answered yet. Read More

We present a method for accurately predicting the long time popularity of online content from early measurements of user access. Using two content sharing portals, Youtube and Digg, we show that by modeling the accrual of views and votes on content offered by these services we can predict the long-term dynamics of individual submissions from initial data. In the case of Digg, measuring access to given stories during the first two hours allows us to forecast their popularity 30 days ahead with remarkable accuracy, while downloads of Youtube videos need to be followed for 10 days to attain the same performance. Read More

Web sites where users create and rate content as well as form networks with other users display long-tailed distributions in many aspects of behavior. Using behavior on one such community site, Essembly, we propose and evaluate plausible mechanisms to explain these behaviors. Unlike purely descriptive models, these mechanisms rely on user behaviors based on information available locally to each user. Read More

We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. Read More

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabasi-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for the problem. Read More

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabasi-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows a demonstration of why the distribution approaches a Gaussian in the limit of N large. Read More

We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar-Parisi-Zhang equation for a negative non-linearity \lambda. This is possible since the phase transition is of first-order, with no diverging correlation length as the transition is approached from below. The morphology of the still-active and pinned configurations and the interface velocity are compared to the PNG picture. Read More