A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a fully coupled SDE-SPDE system when the order arrival rates tend to infinity and the impact of an individual order arrival on the book as well as the tick size tends to zero. The SDE describes the bid/ask price dynamics while the SPDE describes the volume dynamics.Comment: 43 page

A functional limit theorem for limit order books

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity, the impact of an individual order arrival on the book as well as the tick size tend to zero. The limits of the standing buy and sell volume densities are described by two linear stochastic partial differential equations, which are coupled with a two-dimensional reflected Brownian motion that is the limit of the best bid and ask price processes

Four-wave mixing in coupled semiconductor quantum dots

We present a theoretical analysis of four-wave mixing in coupled quantum dots subject to inhomogeneous broadening. For the biexciton transitions a clear signature of interdot-coupling appears in the spectra. The possibility of experimental observation is discussed

Correlated Photon-Pair Emission from a Charged Single Quantum Dot

The optical creation and recombination of charged biexciton and trion complexes in an (In,Ga)As/GaAs quantum dot is investigated by micro-photoluminescence spectroscopy. Photon cross-correlation measurements demonstrate the temporally correlated decay of charged biexciton and trion states. Our calculations provide strong evidence for radiative decay from the excited trion state which allows for a deeper insight into the spin configurations and their dynamics in these systems.Comment: 5 pages, 3 figures, submitted for publicatio

Practical Attacks Against Graph-based Clustering

Graph modeling allows numerous security problems to be tackled in a general way, however, little work has been done to understand their ability to withstand adversarial attacks. We design and evaluate two novel graph attacks against a state-of-the-art network-level, graph-based detection system. Our work highlights areas in adversarial machine learning that have not yet been addressed, specifically: graph-based clustering techniques, and a global feature space where realistic attackers without perfect knowledge must be accounted for (by the defenders) in order to be practical. Even though less informed attackers can evade graph clustering with low cost, we show that some practical defenses are possible.Comment: ACM CCS 201

Massive creation of entangled exciton states in semiconductor quantum dots

An intense laser pulse propagating in a medium of inhomogeneously broadened quantum dots massively creates entangled exciton states. After passage of the pulse all single-exciton states remain unpopulated (self-induced transparency) whereas biexciton coherence (exciton entanglement) is generated through two-photon transitions. We propose several experimental techniques for the observation of such unexpected behavior

Non-resonant dot-cavity coupling and its applications in resonant quantum dot spectroscopy

We present experimental investigations on the non-resonant dot-cavity coupling of a single quantum dot inside a micro-pillar where the dot has been resonantly excited in the s-shell, thereby avoiding the generation of additional charges in the QD and its surrounding. As a direct proof of the pure single dot-cavity system, strong photon anti-bunching is consistently observed in the autocorrelation functions of the QD and the mode emission, as well as in the cross-correlation function between the dot and mode signals. Strong Stokes and anti-Stokes-like emission is observed for energetic QD-mode detunings of up to ~100 times the QD linewidth. Furthermore, we demonstrate that non-resonant dot-cavity coupling can be utilized to directly monitor and study relevant QD s-shell properties like fine-structure splittings, emission saturation and power broadening, as well as photon statistics with negligible background contributions. Our results open a new perspective on the understanding and implementation of dot-cavity systems for single-photon sources, single and multiple quantum dot lasers, semiconductor cavity quantum electrodynamics, and their implementation, e.g. in quantum information technology.Comment: 17 pages, 4 figure

Multiple CaMKII Binding Modes to the Actin Cytoskeleton Revealed by Single-Molecule Imaging.

Localization of the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) to dendritic spine synapses is determined in part by the actin cytoskeleton. We determined binding of GFP-tagged CaMKII to tag-RFP-labeled actin cytoskeleton within live cells using total internal reflection fluorescence microscopy and single-molecule tracking. Stepwise photobleaching showed that CaMKII formed oligomeric complexes. Photoactivation experiments demonstrated that diffusion out of the evanescent field determined the track lifetimes. Latrunculin treatment triggered a coupled loss of actin stress fibers and the colocalized, long-lived CaMKII tracks. The CaMKIIα (α) isoform, which was previously thought to lack F-actin interactions, also showed binding, but this was threefold weaker than that observed for CaMKIIβ (β). The βE' splice variant bound more weakly than α, showing that binding by β depends critically on the interdomain linker. The mutations βT287D and αT286D, which mimic autophosphorylation states, also abolished F-actin binding. Autophosphorylation triggers autonomous CaMKII activity, but does not impair GluN2B binding, another important synaptic protein interaction of CaMKII. The CaMKII inhibitor tatCN21 or CaMKII mutations that inhibit GluN2B association by blocking binding of ATP (βK43R and αK42M) or Ca(2+)/calmodulin (βA303R) had no effect on the interaction with F-actin. These results provide the first rationale for the reduced synaptic spine localization of the αT286D mutant, indicating that transient F-actin binding contributes to the synaptic localization of the CaMKIIα isoform. The track lifetime distributions had a stretched exponential form consistent with a heterogeneously diffusing population. This heterogeneity suggests that CaMKII adopts different F-actin binding modes, which is most easily rationalized by multiple subunit contacts between the CaMKII dodecamer and the F-actin cytoskeleton that stabilize the initial weak (micromolar) monovalent interaction