Gaussian and Non-Gaussian operations on non-Gaussian state: engineering non-Gaussianity

Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive) Glauber-Sudarshan $P$-representation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully characterized by direct detection of photon numbers. In particular, the non-Gaussianity of the state is a characteristics that must be assessed by phase-sensitive measurements. We also show that the non-Gaussianity of conditional states can be manipulated by choosing suitable conditioning values and composition of phase-averaged states

Multi-Entity Dependence Learning with Rich Context via Conditional Variational Auto-encoder

Multi-Entity Dependence Learning (MEDL) explores conditional correlations among multiple entities. The availability of rich contextual information requires a nimble learning scheme that tightly integrates with deep neural networks and has the ability to capture correlation structures among exponentially many outcomes. We propose MEDL_CVAE, which encodes a conditional multivariate distribution as a generating process. As a result, the variational lower bound of the joint likelihood can be optimized via a conditional variational auto-encoder and trained end-to-end on GPUs. Our MEDL_CVAE was motivated by two real-world applications in computational sustainability: one studies the spatial correlation among multiple bird species using the eBird data and the other models multi-dimensional landscape composition and human footprint in the Amazon rainforest with satellite images. We show that MEDL_CVAE captures rich dependency structures, scales better than previous methods, and further improves on the joint likelihood taking advantage of very large datasets that are beyond the capacity of previous methods.Comment: The first two authors contribute equall

On the Existence of Consistent Price Systems

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs for certain processes that fail to have the CFS property. In particular this condition gives sufficient conditions, under which a continuous function of a process with CFS admits a CPS, while the CFS property might be lost.Comment: To appear in "Stochastic Analysis and Applications". Keywords: Consistent pricing systems, No-arbitrage, Transaction costs, Full support, Conditional Full Support, Stability under Composition with Continuous Function

Theory and Use of Conditional Composition

[No abstract available

Managing Debt Stability

This paper presents a simple model in which debt management stabilizes the debt-to-GDP ratio in face of shocks to real returns and output growth and thus supports fiscal restraint in ensuring sustainability. The optimal composition of public debt is derived by looking at the relative impact of the risk and cost of alternative debt instruments on the cost of missing the stabilization target. The optimal debt structure is a function of the expected return differentials between debt instruments, of the conditional variance of their returns and of the conditional covariances of their returns with output growth and inflation. We then explore how the relevant covariances and thus the optimal choice of debt instruments depend on the monetary regime and on Central Bank preferences for output stabilization, inflation control and interest-rate smoothing. Finally, we estimate the composition of public debt that would have supported debt stabilization in OECD countries over the last two decades. The empirical evidence suggests that the public debt should have a long maturity and a large share of it should be indexed to the price level.debt management, debt structure, debt stabilization, inflation indexation, interest rates