Dealing with the Inventory Risk. A solution to the market making problem

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho and Stoll and formalized mathematically by Avellaneda and Stoikov. The market is modeled using a reference price $S_t$ following a Brownian motion with standard deviation $\sigma$, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price $S_t$ and a market maker maximizes the expected utility of its P&L over a finite time horizon. We show that the Hamilton-Jacobi-Bellman equations associated to the stochastic optimal control problem can be transformed into a system of linear ordinary differential equations and we solve the market making problem under inventory constraints. We also shed light on the asymptotic behavior of the optimal quotes and propose closed-form approximations based on a spectral characterization of the optimal quotes

Observation of correlated-photon statistics using a single detector

We report experimental observations of correlated-photon statistics in the single-photon detection rate. The usual quantum interference in a two-photon polarization interferometer always accompanies a dip in the single detector counting rate, regardless of whether a dip or peak is seen in the coincidence rate. This effect is explained by taking into account all possible photon number states that reach the detector, rather than considering just the state post-selected by the coincidence measurement. We also report an interferometeric scheme in which the interference peak or dip in coincidence corresponds directly to a peak or dip in the single-photon detection rate.Comment: 4 pages, two-column (minor errors corrected.

Interference scheme to measure light-induced nonlinearities in Bose-Einstein condensates

Light-induced nonlinear terms in the Gross-Pitaevskii equation arise from the stimulated coherent exchange of photons between two atoms. For atoms in an optical dipole trap this effect depends on the spatial profile of the trapping laser beam. Two different laser beams can induce the same trapping potential but very different nonlinearities. We propose a scheme to measure light-induced nonlinearities which is based on this observation.Comment: 2 figure

Generalized Phase Synchronization in unidirectionally coupled chaotic oscillators

We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are driven by correlated (but not identical) inputs from the drive oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and clarify its characteristics using Lyapunov exponents and phase difference plots.Comment: 4 pages, 5 figure

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010

Matriptase activation of gq drives epithelial disruption and inflammation via RSK and DUOX

Epithelial tissues are primed to respond to insults by activating epithelial cell motility and rapid inflammation. Such responses are also elicited upon overexpression of the membrane-bound protease, Matriptase, or mutation of its inhibitor, Hai1. Unrestricted Matriptase activity also predisposes to carcinoma. How Matriptase leads to these cellular outcomes is unknown. We demonstrate that zebrafish hai1a mutants show increased H2O2, NfκB signalling, and IP3R -mediated calcium flashes, and that these promote inflammation, but do not generate epithelial cell motility. In contrast, inhibition of the Gq subunit in hai1a mutants rescues both the inflammation and epithelial phenotypes, with the latter recapitulated by the DAG analogue, PMA. We demonstrate that hai1a has elevated MAPK pathway activity, inhibition of which rescues the epidermal defects. Finally, we identify RSK kinases as MAPK targets disrupting adherens junctions in hai1a mutants. Our work maps novel signalling cascades mediating the potent effects of Matriptase on epithelia, with implications for tissue damage response and carcinoma progression

The <i>Castalia</i> mission to Main Belt Comet 133P/Elst-Pizarro

We describe Castalia, a proposed mission to rendezvous with a Main Belt Comet (MBC), 133P/Elst-Pizarro. MBCs are a recently discovered population of apparently icy bodies within the main asteroid belt between Mars and Jupiter, which may represent the remnants of the population which supplied the early Earth with water. Castalia will perform the first exploration of this population by characterising 133P in detail, solving the puzzle of the MBC’s activity, and making the first in situ measurements of water in the asteroid belt. In many ways a successor to ESA’s highly successful Rosetta mission, Castalia will allow direct comparison between very different classes of comet, including measuring critical isotope ratios, plasma and dust properties. It will also feature the first radar system to visit a minor body, mapping the ice in the interior. Castalia was proposed, in slightly different versions, to the ESA M4 and M5 calls within the Cosmic Vision programme. We describe the science motivation for the mission, the measurements required to achieve the scientific goals, and the proposed instrument payload and spacecraft to achieve these

Evaluating synergy between marbofloxacin and gentamicin in Pseudomonas aeruginosa strains isolated from dogs with otitis externa

The aim of this study was to determine antimicrobial susceptibility of Pseudomonas aeruginosa strains to marbofloxacin and gentamicin, and investigate the possible synergistic, additive, indifferent or antagonistic effects between the two agents. P. aeruginosa strains can develop resistance quickly against certain antibiotics if used alone, thus the need emerges to find synergistic combinations. A total of 68 P. aeruginosa strains isolated from dogs were examined. In order to describe interactions between marbofloxacin and gentamicin the checkerboard microdilution method was utilized. The MICs (minimum inhibitory concentrations) for marbofloxacin and gentamicin were in the range 0.25–64 mg/L and 0.25–32 mg/L, respectively. The combination of marbofloxacin and gentamicin was more effective with a MIC range of 0.031–8 mg/L and a MIC90 of 1 mg/L, compared to 16 mg/L for marbofloxacin alone and 8 mg/L for gentamicin alone. The FIC (fractional inhibitory concentration) indices ranged from 0.0945 (pronounced synergy) to 1.0625 (indifference). Synergy between marbofloxacin and gentamicin was found in 33 isolates. The mean FIC index is 0.546, which represents a partial synergistic/additive effect close to the full synergy threshold. In vitro results indicate that marbofloxacin and gentamicin as partially synergistic agents may prove clinically useful in combination therapy against P. aeruginosa infections. Although marbofloxacin is not used in the human practice, the interactions between fluoroquinolones and aminoglycosides may have importance outside the veterinary field

Methylation of all BRCA1 copies predicts response to the PARP inhibitor rucaparib in ovarian carcinoma

Accurately identifying patients with high-grade serous ovarian carcinoma (HGSOC) who respond to poly(ADP-ribose) polymerase inhibitor (PARPi) therapy is of great clinical importance. Here we show that quantitative BRCA1 methylation analysis provides new insight into PARPi response in preclinical models and ovarian cancer patients. The response of 12 HGSOC patient-derived xenografts (PDX) to the PARPi rucaparib was assessed, with variable dose-dependent responses observed in chemo-naive BRCA1/2-mutated PDX, and no responses in PDX lacking DNA repair pathway defects. Among BRCA1-methylated PDX, silencing of all BRCA1 copies predicts rucaparib response, whilst heterozygous methylation is associated with resistance. Analysis of 21 BRCA1-methylated platinum-sensitive recurrent HGSOC (ARIEL2 Part 1 trial) confirmed that homozygous or hemizygous BRCA1 methylation predicts rucaparib clinical response, and that methylation loss can occur after exposure to chemotherapy. Accordingly, quantitative BRCA1 methylation analysis in a pre-treatment biopsy could allow identification of patients most likely to benefit, and facilitate tailoring of PARPi therapy.Olga Kondrashova … M.K. Oehler … [et al.] (Australian Ovarian Cancer Study (AOCS)