Large Jumps Research Articles

2020 Hindsight: Should evolutionary virologists have expected the unexpected during a pandemic?

2020 Hindsight: Should evolutionary virologists have expected the unexpected during a pandemic?

Analysing emerging market returns with high-frequency data during the global financial crisis of 2007–2009

Nowadays, the majority of stock market trading is performed electronically, based on pre-programmed computer algorithms. We obtain five-minute high-frequency data from the Turkish Stock Exchange to investigate the data-generating process of emerging market returns during the global financial crisis of 2007–2009. We test tail behaviour and how data-generating processes changed during the intraday trading period in both crisis and non-crisis periods. We also examine whether price asymmetry has a significant effect on the diffusion and jump characteristics of emerging market returns. The results identify a clear increase in jumps with infinite activity in crisis periods and a decreased identification of jumps with finite activity in non-crisis periods. In crisis periods, the proportion of large and small jumps increased and the proportion of Brownian motion decreased. We show that data-generating processes are not stable during the intraday trading period, which fluctuates slightly, particularly right after the market opening times in the morning and in the afternoon. Finally, we conclude that there are many more stressful days in crisis periods than in non-crisis periods in emerging markets returns.

Moment bounds for dissipative semimartingales with heavy jumps

In this paper we show that if large jumps of an Itô-semimartingale X have a finite p-moment, p>0, the radial part of its drift is dominated by −|X|κ for some κ≥−1, and the balance condition p+κ>1 holds true, then under some further natural technical assumptions one has supt≥0E|Xt|pX<∞ for each pX∈(0,p+κ−1). The upper bound p+κ−1 is generically optimal. The proof is based on the extension of the method of Lyapunov functions to the semimartingale framework. The uniform moment estimates obtained in this paper are indispensable for the analysis of ergodic properties of Lévy driven stochastic differential equations and Lévy driven multi-scale systems.

Electro-Chemo-Mechanical Failure in a High-Performance Solid Oxide Cell

Fuel electrode-supported solid oxide cells (FE-SOC) offer the possibility of low operation temperatures and / or high power density through the incorporation of a thin, supported electrolyte between two highly active electrodes. However, integrating fuel electrodes with an ionic conductor that is different from that of the electrolyte into FE-SOC remains a challenge due to the interdiffusion phenomena during co-sintering of the half-cell. As a result, most FE-SOC use cermet fuel electrodes made from Ni and stabilized zirconia.Here, we present a FE-SOC based on a Ni-Gd0.1Ce0.9O2- d (GDC) fuel electrode, a three-layer GDC / zirconia / GDC electrolyte and an La0.58Sr0.4CoO3- d (LSC) air electrode. The electrolyte is fabricated by co-sintering a thin, screen-printed layer of GDC with the fuel electrode and support. Subsequent electrolyte layers are deposited via physical vapor deposition (PVD), and the air electrode is fabricated via screen printing. The total electrolyte thickness is less than 5 µm, enabling an area-specific ohmic resistance < 10 mΩ cm² at 700 °C. A current density of 1.6 Acm-² is achieved at a cell voltage of 800 mV and a temperature of 700 °C, using 10% H2O/H2 as fuel and air as oxidant. This performance is about twice as high as that of a conventional Jülich cell using Ni-YSZ and LSCF electrodes and a 10 µm YSZ electrolyte under similar conditions. An electrolysis current of 2 A cm-² was achieved at a cell voltage of 1.11 V, at a temperature of 800 °C and using 50% H2O/H2 and air. The conventional Jülich cell requires a cell voltage above 1.25 V under similar conditions. Under these conditions, the new cell achieves a cell efficiency of 84 %, compared to 73 % for the conventional cell.However, running high electrolysis currents at temperatures below 750 °C resulted in catastrophic cell failure, visible as large voltage jumps in the I-V curve. In addition, a decreasing OCV value with decreasing temperature indicated damage to the cell before the catastrophic failure. Post-test analysis found a large number of cracks in the electrolyte, nucleating at the fuel electrode / electrolyte interface and running toward the air electrode. We show that the likely cause for this failure is the electrochemical reduction and subsequent chemical expansion of the doped ceria electrolyte layer, necessitating a detailed study of the local mechanical stresses in the cell during operation.

Finite-time control of delay switched systems via input anti-bump switching

This article devotes to the finite-time (FT) input anti-bump switching control (SC) issue for a kind of delay switched systems (DSSs). Our objective is to carry the FT control while bringing down possible large jumps in the control input. First, a formulation of the alleviation for the control signal jumps is given. Second, by the multiple Lyapunov–Krasovskii functions method, a sufficient criterion is developed to derive the DSSs to hold both the FT H∞ performance combined with the input anti-bump switching performance, capturing the dual objectives control of the switched system, both transient performance aims. Also, via this criterion, these two performances are admitted not to be held by subsystems. Then, a switching index in conjunction with a switching controller are simultaneously constructed to solve the problem of the FT input anti-bump SC of DSSs. Finally, through the simulation verification of an F-18 aircraft model, the validity of the method driven is illustrated.

Judge Effects, Case Characteristics, and Plea Bargaining

A growing literature uses random assignment of cases to judges to examine criminal sentencing. To extend this line of work, we directly examine how judicial “harshness” varies with the seriousness of criminal conviction. Using a model that respects the mix of cases and the noise produced by small caseloads, we find that case severity is best viewed as an endogenous outcome of bargaining. We also find that harsher judges have a higher share of cases failing to reach a plea bargain, but perhaps surprisingly, there is little evidence that large jumps in expected incarceration lead to differential plea bargain outcomes.

What Triggers Stock Market Jumps?

We examine next-day newspaper accounts of large daily jumps in 16 national stock markets to assess their proximate cause, clarity as to cause, and the geographic source of the market-moving news. Our sample of 6,200 market jumps yields several findings. First, policy news – mainly associated with monetary policy and government spending – triggers a greater share of upward than downward jumps in all countries. Second, the policy share of upward jumps is inversely related to stock market performance in the preceding three months. This pattern strengthens in the postwar period. Third, market volatility is much lower after jumps triggered by monetary policy news than after other jumps, unconditionally and conditional on past volatility and other controls. Fourth, greater clarity as to jump reason also foreshadows lower volatility. Clarity in this sense has trended upwards over the past century. Finally, and excluding U.S. jumps, leading newspapers attribute one-third of jumps in their own national stock markets to developments that originate in or relate to the United States. The U.S. role in this regard dwarfs that of Europe and China.

Poisson Stable Solutions for Stochastic Differential Equations with Lévy Noise

In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-periodic, pseudo-recurrent and Poisson stable) solutions for semilinear stochastic differential equations driven by infinite dimensional Lévy noise with large jumps. Under suitable conditions on drift, diffusion and jump coefficients, we prove that there exist solutions which inherit the Poisson stability of coefficients. Further we show that these solutions are globally asymptotically stable in square-mean sense. Finally, we illustrate our theoretical results by several examples.

A general approach to sample path generation of infinitely divisible processes via shot noise representation

We establish a sample path generation scheme in a unified manner for general multivariate infinitely divisible processes based on shot noise representation of their integrators. The approximation is derived from the decomposition of the infinitely divisible process to three independent components based on jump sizes and timings: the large jumps over a compact time interval, small jumps over the entire time interval and large jumps over an unbounded time interval. The first component is taken as the approximation and is much simpler than simulation of general Gaussian processes, while the latter two components are analyzed as the error. We derive technical conditions for the two error terms to vanish in the limit and for the scaled component on small jumps to converge to a Gaussian process so as to enhance the accuracy of the weak approximation. We provide an extensive collection of examples to highlight the wide practicality of the proposed approach.

Sequential Learning of Cryptocurrency Volatility Dynamics: Evidence Based on a Stochastic Volatility Model with Jumps in Returns and Volatility

This paper studies the dynamics of cryptocurrency volatility using a stochastic volatility model with simultaneous and correlated jumps in returns and volatility. We estimate the model using an efficient sequential learning algorithm that allows for learning about multiple unknown model parameters simultaneously, with daily data on four popular cryptocurrencies. We find that these cryptocurrencies have quite different volatility dynamics. In particular, they exhibit different return-volatility relationships: While Ethereum and Litecoin show a negative relationship, Chainlink displays a positive one and interestingly, Bitcoin’s one changes from negative to positive in June 2016. We also provide evidence that the sequential learning algorithm helps better detect large jumps in the cryptocurrency market in real time. Overall, incorporating volatility jumps helps better capture the dynamic behavior of highly volatile cryptocurrencies.

Colored Lévy Noise-Induced Stochastic Dynamics in a Tri-Stable Hybrid Energy Harvester

Abstract The piezoelectric and electromagnetic hybrid vibration energy harvester (HVEH) has proven to be a favorable option to deal with the low power generation issue and overcome the drawbacks of each individual transduction mechanism. Besides, colored Lévy noise consisting of small perturbations, large jumps, and correlation time turns out to be a relatively suitable tool for describing the complex environments. For the purpose of enhancing the harvesting performance of HVEH, the stochastic dynamics induced by colored Lévy noise in a tri-stable HVEH is mainly investigated in this paper. The stationary probability density, the largest Lyapunov exponent, the signal-to-noise ratio, and the mean harvested power are calculated to explore the stochastic dynamics of system, such as the stochastic response, the stochastic stability, the stochastic resonance (SR), and the energy harvesting performance. The results show that the colored Lévy noise can induce stochastic P-bifurcation, D-bifurcation, and SR phenomenon. In particular, the comparisons between colored Lévy noise and colored Brownian noise in dynamics and harvesting performance are also discussed in detail. It is found that the colored Lévy noise can make a greater contribution than colored Brownian noise in the effective voltage and help to improve the mean harvested power through the SR effect.

Periodic Solutions of Stochastic Differential Equations Driven by Lévy Noises

In this paper, we first show the well-posedness of SDEs driven by Lévy noises under mild conditions. Then, we consider the existence and uniqueness of periodic solutions of the SDEs. To establish the ergodicity and uniqueness of periodic solutions, we investigate the strong Feller property and the irreducibility of the corresponding time-inhomogeneous semigroups when both small and large jumps are allowed in the equations. Doob’s celebrated theorem on the uniqueness of invariant measures for time-homogeneous Markov processes has been generalized to obtain the uniqueness of periodic measures for time-inhomogeneous Markov processes. Some examples are presented to illustrate our results.

Ball bouncing down rounded edge stairs: chaotic but tricky

The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a staircase consisting of rounded edge steps, as an example of a dissipative gravitational billiard, and to determine if its dynamics is chaotic. We derive a nonlinear recursion for the coordinates of the collisions, completed with numerical simulations, which indicate that the bouncing dynamics is chaotic, as also follows from elementary considerations regarding the Lyapunov exponent. It is, however, surprising that instead of permanent chaos, only the transient form is present. The main reason behind this is that a collision with the rounded edge of the step enhances the horizontal velocity leading to larger and larger jumps. Not even the introduction of a tangential coefficient of restitution (COR) on the curvature can hinder the flying away of some trajectories. There is also a chance for remaining trapped on a single step in the form of sliding, representing another possibility for escape. Therefore, chaoticity holds for long trajectories before any kind of escape takes place. We also show that an impact-velocity-dependent COR converts the dynamics to permanently chaotic with an underlying fractal attractor. Only elementary mathematics is required for the analytic calculations used, and we offer a set of problems to solve, as well as a user-friendly demo software on our website: https://theorphys.elte.hu/fiztan/stairs to facilitate experimentation and further understanding of this complex phenomenon.

Bank credit risk events and peers' equity value

This paper documents a negative cross-transmission of bank-idiosyncratic credit risk events to the equity value of peers comprising other banks, insurance and real estate firms inter alia. Large jumps in the idiosyncratic component of bank CDS spreads significantly reduce the equity value of peers, particularly on the event day. The negative externality does not hinge on the “information connectedness” between the two entities as proxied by characteristics such as common core line of business, common country or region, and inter-country common legal tradition. The negative externality is stronger in turmoil market conditions when risk-aversion levels are higher and/or investors are subject to pessimism. The more fragile the risk profile of the event bank and peer firm prior to the event the stronger the cross-transmission. The findings lend support to the wake-up call paradigm at micro level, and are insightful towards a better assessment of the vulnerability of the financial system.

Neural mode jump Monte Carlo.

Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method that increases convergence in systems composed of many metastable states. This method aims to connect metastable regions directly using generative neural networks in order to propose new configurations in the Markov chain and optimizes the acceptance probability of large jumps between modes in the configuration space. We provide a comprehensive theory as well as a training scheme for the network and demonstrate the method on example systems.

A posteriori error bounds for classical and mixed FEM’s for 4th-order elliptic equations with piece wise constant reaction coefficient having large jumps

We present guaranteed, robust and computable a posteriori error bounds for approximate solutions of the equation ΔΔu + κ 2 u = f by classical and mixed Ciarlet-Raviart finite element methods. We concentrate on the case when the reaction coefficient κ is subdomain (finite element) wise constant and chaotically varies between subdomains in the sufficiently wide range. It is proved that the bounds for the classical FEM’s are robust with respect to κ ∊ [0,ch −2], where c = const and h is the maximal size of finite elements, and possess additional useful features. The coefficients in fronts of two typical norms in their right parts only insignificantly worse than those for κ ≡ const, and the bounds can be calculated without resorting to the equilibration procedures. Besides, they are sharp at least for low order methods, if the testing moments and deflection in their right parts are found by accurate recovery procedures. The technique of derivation of the bounds is based on the approach similar to one used in our preceding papers for simpler problems.

What Triggers Stock Market Jumps?

We examine next-day newspaper accounts of large daily jumps in 16 national stock markets to assess their proximate cause, clarity as to cause, and the geographic source of the market-moving news. Our sample of 6,200 market jumps yields several findings. First, policy news – mainly associated with monetary policy and government spending – triggers a greater share of upward than downward jumps in all countries. Second, the policy share of upward jumps is inversely related to stock market performance in the preceding three months. This pattern strengthens in the postwar period. Third, market volatility is much lower after jumps triggered by monetary policy news than after other jumps, unconditionally and conditional on past volatility and other controls. Fourth, greater clarity as to jump reason also foreshadows lower volatility. Clarity in this sense has trended upwards over the past century. Finally, and excluding U.S. jumps, leading newspapers attribute one-third of jumps in their own national stock markets to developments that originate in or relate to the United States. The U.S. role in this regard dwarfs that of Europe and China.

Snap-shot topography measurement via dual-VCSEL and dual wavelength digital holographic interferometry

In this paper, we propose a dual-wavelength digital holographic interferometry method based on a compact dual vertical-cavity surface-emitting laser (VCSEL) source. The source simultaneously emits light from two highly stabilized coherent light sources with slightly different wavelengths. A highly stabilized and adjustable current source enables the application of digital holographic dual-wavelength techniques to measure the shape of an object with height steps of a few millimeters. The wavelength drift over 12 h over the entire measurement range, which was evaluated using a wavemeter, was smaller than 1 pm. In addition to the low measurement uncertainty at large height jumps, the dual-wavelength digital holographic system distinguishes itself by its robustness to environmental disturbances such as air turbulence, heat load, and/or mechanical vibrations. This is enabled via a fiber-based almost common-path single-shot digital holographic acquisition of the information of the two different wavelengths using angular multiplexing. The experimental setup and data evaluation are discussed, and we present measurements of non-cooperative objects with specular reflective and/or diffuse reflective surfaces having different colors.

Adaptability and the Pivot Penalty in Science

The ability to confront new questions, opportunities, and challenges is of fundamental importance to human progress and the resilience of human societies, yet the capacity of science to meet new demands remains poorly understood. Here we deploy a new measurement framework to investigate the scientific response to the COVID-19 pandemic and the adaptability of science as a whole. We find that science rapidly shifted to engage COVID-19 following the advent of the virus, with scientists across all fields making large jumps from their prior research streams. However, this adaptive response reveals a pervasive “pivot penalty,” where the impact of the new research steeply declines the further the scientists move from their prior work. The pivot penalty is severe amidst COVID-19 research, but it is not unique to COVID-19. Rather it applies nearly universally across the sciences, and has been growing in magnitude over the past five decades. While further features condition pivoting, including a scientist’s career stage, prior expertise and impact, collaborative scale, the use of new coauthors, and funding, we find that the pivot penalty persists and remains substantial regardless of these features, suggesting the pivot penalty acts as a fundamental friction that governs science’s ability to adapt. The pivot penalty not only holds key implications for the design of the scientific system and human capacity to confront emergent challenges through scientific advance, but may also be relevant to other social and economic systems, where shifting to meet new demands is central to survival and success.

Reorientational dynamics of molecules in liquid methane: A molecular dynamics simulation study

Rotational motion of molecules in liquids plays an important role in determining the liquids' Nuclear Magnetic Resonance (NMR) spin-relaxation properties. The traditional theory of NMR spin relaxation assumes that the reorientational dynamics of molecules in liquids can be described by a continuous-time rotational-diffusion random walk with a single rotational-diffusion coefficient. However, recent experimental and theoretical studies have demonstrated that the simple rotational-diffusion model does not fully capture the rotational dynamics of molecules in liquids: for example, the reorientation of molecules in liquid water occurs through a combination of continuous-time rotational diffusion and discrete, large angular jumps resulting from collective rearrangements of the hydrogen-bond network of water.In order to obtain further insights into the origin of large angular jumps in the rotational motion of liquid water, we studied the rotational dynamics of methane - an apolar, non‑hydrogen-bonding liquid with a spherically symmetric molecule. The reorientational propagator and the ensemble-averaged Legendre polynomial reorientational functions of liquid methane were analysed using molecular dynamics simulations. On the femtosecond timescale, the reorientational motion of methane molecules was found to be characterised by free-rotation gas-like Gaussian decay of the reorientational Legendre polynomials, a result consistent with the available experimental data for liquid methane. On the long timescale (picoseconds) the decay of the reorientational Legendre polynomials was exponential, suggestive of a Debye-like continuous-time rotational diffusion behaviour. However, the ratios of the exponential time constants for different orders of the Legendre polynomials failed to match the rotational-diffusion model. We discuss the implications of these findings for the understanding of rotational motion of molecules in hydrogen-bonding and non‑hydrogen-bonding liquids.