Linear response theory in stock markets

Linear response theory relates the response of a system to a weak external force with its dynamics in equilibrium, subjected to fluctuations. Here, this framework is applied to financial markets; in particular we study the dynamics of a set of stocks from the NASDAQ during the last 20 years. Because unambiguous identification of external forces is not possible, critical events are identified in the series of stock prices as sudden changes, and the stock dynamics following an event is taken as the response to the external force. Linear response theory is applied with the log-return as the conjugate variable of the force, providing predictions for the average response of the price and return, which agree with observations, but fails to describe the volatility because this is expected to be beyond linear response. The identification of the conjugate variable allows us to define the perturbation energy for a system of stocks, and observe its relaxation after an event.

An empirical study of derivative-free-optimization algorithms for targeted black-box attacks in deep neural networks

We perform a comprehensive study on the performance of derivative free optimization (DFO) algorithms for the generation of targeted black-box adversarial attacks on Deep Neural Network (DNN) classifiers assuming the perturbation energy is bounded by an $$\ell _\infty$$ ℓ ∞ constraint and the number of queries to the network is limited. This paper considers four pre-existing state-of-the-art DFO-based algorithms along with a further developed algorithm built on BOBYQA, a model-based DFO method. We compare these algorithms in a variety of settings according to the fraction of images that they successfully misclassify given a maximum number of queries to the DNN. The experiments disclose how the likelihood of finding an adversarial example depends on both the algorithm used and the setting of the attack; algorithms limiting the search of adversarial example to the vertices of the $$\ell ^\infty$$ ℓ ∞ constraint work particularly well without structural defenses, while the presented BOBYQA based algorithm works better for especially small perturbation energies. This variance in performance highlights the importance of new algorithms being compared to the state-of-the-art in a variety of settings, and the effectiveness of adversarial defenses being tested using as wide a range of algorithms as possible.

Case Dependence of Multiscale Interactions between Multisource Perturbations for Convection-Permitting Ensemble Forecasting during SCMREX

This study examines the case dependence of the multiscale characteristics of initial condition (IC) and model physics (MO) perturbations and their interactions in a convection-permitting ensemble prediction system (CPEPS), focusing on the 12-h forecasts of precipitation perturbation energy. The case dependence of forecast performances of various ensemble configurations is also examined to gain guidance for CPEPS design. Heavy-rainfall cases over Southern China during the Southern China Monsoon Rainfall Experiment (SCMREX) in May 2014 were discriminated between the strongly and weakly forced events in terms of synoptic-scale forcing, each of which included 10 cases. In the cases with weaker forcing, MO perturbations showed larger influences while the enhancements of convective activities relative to the control member due to IC perturbations were less evident, leading to smaller dispersion reduction due to adding MO perturbations to IC perturbations. Such dispersion reduction was more sensitive to IC and MO perturbation methods in the weakly and strongly forced cases, respectively. The dispersion reduction improved the probabilistic forecasts of precipitation, with more evident improvements in the cases with weaker forcing. To improve the benefits of dispersion reduction in forecasts, it is instructive to elaborately consider the case dependence of dispersion reduction, especially the various sensitivities of dispersion reduction to different-source perturbation methods in various cases, in CPEPS design.

Observed Shear-Relative Rainfall Asymmetries Associated with Landfalling Tropical Cyclones

This study examines the shear-relative rainfall spatial distribution of tropical cyclones (TCs) during landfall based on the 19-year (1998–2016) TRMM satellite 3B42 rainfall estimate dataset and investigates the role of upper-tropospheric troughs on the rainfall intensity and distribution after TCs make a landfall over the six basins of Atlantic (ATL), eastern and central Pacific (EPA), northwestern Pacific (NWP), northern Indian Ocean (NIO), southern Indian Ocean (SIO), and South Pacific (SPA). The results show that the wavenumber 1 perturbation can contribute ∼ 50% of the total perturbation energy of total TC rainfall. Wavenumber 1 rainfall asymmetry presents the downshear-left maxima in the deep-layer vertical wind shear between 200 and 850 hPa for all the six basins prior to making a landfall. In general, wavenumber 1 rainfall tends to decrease less if there is an interaction between TCs and upper-level troughs located at the upstream of TCs over land. The maximum TC rain rate distributions tend to be located at the downshear-left (downshear) quadrant under the high (low)-potential vorticity conditions.

Static Perturbation Theory and Derivative Properties

Perturbation theory (PT) is a method by which the energies and wavefunctions of a system of interest are expressed in terms of the known solutions of a presumably simpler reference system. The Rayleigh-Schrodinger expressions for the wavefunctions and energies of exact states are derived up to 3rd and 4th order, respectively. A simple application deals with substitution effects on the absorption color of organic chromophores. The Moller-Plesset correlation energy is derived in 2nd order (MP2). It is then shown how bi-linear perturbations associated with the electric and magnetic field operators of chapter 21 define properties such as polarizability, magnetizability or susceptibility, nuclear magnetic resonance shielding and spin-spin coupling, harmonic nuclear vibrational frequencies, and many other properties. The bi-linear magnetic perturbation energy is derived for paramagnetic systems with low-energy thermally populated degenerate states. The chapter concludes with a description of derivative techniques for approximate quantum chemical methods.