Segmentation algorithm for non-stationary compound Poisson processes

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated to a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galvan, et al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm outperforms the original one for regime switching compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.Comment: 11 pages, 11 figure

Effects of strain on the electronic structure of VO_2

We present cluster-DMFT (CTQMC) calculations based on a downfolded tight-binding model in order to study the electronic structure of vanadium dioxide (VO_2) both in the low-temperature (M_1) and high-temperature (rutile) phases. Motivated by the recent efforts directed towards tuning the physical properties of VO_2 by depositing films on different supporting surfaces of different orientations we performed calculations for different geometries for both phases. In order to investigate the effects of the different growing geometries we applied both contraction and expansion for the lattice parameter along the rutile c-axis in the 3-dimensional translationally invariant systems miming the real situation. Our main focus is to identify the mechanisms governing the formation of the gap characterizing the M_1 phase and its dependence on strain. We found that the increase of the band-width with compression along the axis corresponding to the rutile c-axis is more important than the Peierls bonding-antibonding splitting

How does the market react to your order flow?

We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contributions coming from different market participants and study how their behaviour is interconnected. We find evidence that (1) brokers are very heterogeneous in liquidity provision -- some are consistently liquidity providers while others are consistently liquidity takers. (2) The behaviour of brokers is strongly conditioned on the actions of {\it other} brokers. In contrast brokers are only weakly influenced by the impact of their own previous orders. (3) The total impact of market orders is the result of a subtle compensation between the same broker pushing the price in one direction and the liquidity provision of other brokers pushing it in the opposite direction. These results enforce the picture of market dynamics being the result of the competition between heterogeneous participants interacting to form a complicated market ecology.Comment: 22 pages, 5+9 figure

Optimised Baranyai partitioning of the second quantised Hamiltonian

Simultaneous measurement of multiple Pauli strings (tensor products of Pauli matrices) is the basis for efficient measurement of observables on quantum computers by partitioning the observable into commuting sets of Pauli strings. We present the implementation and optimisation of the Baranyai grouping method for second quantised Hamiltonian partitioning in molecules up to CH$_4$ (cc-pVDZ, 68 qubits) and efficient construction of the diagonalisation circuit in $O(N)$ quantum gates, compared to $O(N^2)$, where $N$ is the number of qubits. We show that this method naturally handles sparsity in the Hamiltonian and produces a $O(1)$ number of groups for linearly scaling Hamiltonians, such as those formed by molecules in a line; rising to $O(N^3)$ for fully connected two-body Hamiltonians. While this is more measurements than some other schemes it allows for the flexibility to move Pauli strings and optimise the variance. We also present an explicit optimisation for spin-symmetry which reduces the number of groups by a factor of $8$, without extra computational effort

Submillimeter CO emission from shock-heated gas in the L1157 outflow

We present the CO J=6-5, 4-3, and 3-2 spectra from the blueshifted gas of the outflow driven by the low-mass class 0 protostar in the L1157 dark cloud. Strong submillimeter CO emission lines with T_mb > 30 K have been detected at 63" (~0.13 pc) south from the protostar. It is remarkable that the blue wings in the submillimeter lines are stronger by a factor of 3-4 than that of the CO J=1-0 emission line. The CO line ratios suggest that the blueshifted lobe of this outflow consists of moderately dense gas of n(H_2) = (1-3)x10^4 cm^-3 heated to T_kin = 50-170 K.It is also suggested that the kinetic temperature of the outflowing gas increases from ~80 K near the protostar to ~170 K at the shocked region in the lobe center, toward which the largest velocity dispersion of the CO emission is observed. A remarkable correlation between the kinetic temperature and velocity dispersion of the CO emission along the lobe provides us with direct evidence that the molecular gas at the head of the jet-driven bow shock is indeed heated kinematically. The lower temperature of ~80 K measured at the other shocked region near the end of the lobe is explained if this shock is in a later evolutionary stage, in which the gas has been cooled mainly through radiation of the CO rotational lines.Comment: 10 pages, 4 PDF figures, APJL in pres