Modelling nonlinear stochastic dynamics in financial time series

For analysing financial time series two main opposing viewpoints exist, either capital markets are completely stochastic and therefore prices follow a random walk, or they are deterministic and consequently predictable. For each of these views a great variety of tools exist with which it can be tried to confirm the hypotheses. Unfortunately, these methods are not well suited for dealing with data characterised in part by both paradigms. This thesis investigates these two approaches in order to model the behaviour of financial time series. In the deterministic framework methods are used to characterise the dimensionality of embedded financial data. The stochastic approach includes here an estimation of the unconditioned and conditional return distributions using parametric, non- and semi-parametric density estimation techniques. Finally, it will be shown how elements from these two approaches could be combined to achieve a more realistic model for financial time series.

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations.

Dynamics of cholesteric liquid crystals in the presence of a random magnetic field:stochastic dynamics of cholesteric liquid crystal

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Glutaredoxin-1 Is up-regulated in preeclampsia and increases soluble Flt-1 expression

INTRODUCTION: Preeclampsia is a vascular disorder in pregnancyand is biochemical characterization by high soluble Flt-1 and lowplacenta growth factor as well as an imbalance in redox homeostasis.During conditions of high oxidative stress, cysteine residues on keyproteins are reversibly altered by S-glutathionylation, modifying theirfunction. Glutaredoxin-1 (Glrx) enzymatically catalyzes the removal of S-glutathione adducts, conferring reversible signaling dynamics toproteins with redox-sensitive cysteines. The role of Glrx in preeclampsiais unknown.METHODS: Immunohistochemistry and Western blot analysis for Glrx orglutathione were conducted on human placenta samples collected pre-termfrom early onset preeclamptic patients (n=10) or non-preeclamptic induceddeliveries (n=9). Human endothelial cells were infected with adenovirusencoding Glrx or LacZ prior to the cells being exposed to hypoxia (0.1%O2, 24h) to measure changes in soluble Flt-1 (sFlt-1). Quantitative PCRand ELISA were used to measure sFlt-1 at mRNA and protein level.RESULTS: Immunohistochemical staining for GSH revealed lowerS-glutathionylation adducts in preeclampsia placenta in comparison tocontrols. Glrx expression, which catalyses de-glutathionylation wasenhanced in early onset preeclampsia compared to pre-term controlsamples. In contrast, no change was observed in preeclamptic and IUGRplacentas at full term. In endothelial cells overexpressing Glrx, sFlt-1expression was dramatically enhanced at mRNA (3-fold P<0.05) andprotein level (5 fold P>0.01, n=4) after hypoxia andoverexpressing Glrxin mice enhanced levels of circulating sFlt-1 during in vivo ischemia.CONCLUSIONS: Enhanced Glrx expression in preeclamptic placentain line with an apparent decrease in S-glutathionylation may leavekey proteins susceptible to irreversible oxidation in conditions of highoxidative stress.

Protein oxidation:role in signalling and detection by mass spectrometry

Proteins can undergo a wide variety of oxidative post-translational modifications (oxPTM); while reversible modifications are thought to be relevant in physiological processes, non-reversible oxPTM may contribute to pathological situations and disease. The oxidant is also important in determining the type of oxPTM, such as oxidation, chlorination or nitration. The best characterized oxPTMs involved in signalling modulation are partial oxidations of cysteine to disulfide, glutathionylated or sulfenic acid forms that can be reversed by thiol reductants. Proline hydroxylation in HIF signalling is also quite well characterized, and there is increasing evidence that specific oxidations of methionine and tyrosine may have some biological roles. For some proteins regulated by cysteine oxidation, the residues and molecular mechanism involved have been extensively studied and are well understood, such as the protein tyrosine phosphatase PTP1B and MAP3 kinase ASK1, as well as transcription factor complex Keap1-Nrf2. The advances in understanding of the role oxPTMs in signalling have been facilitated by advances in analytical technology, in particular tandem mass spectrometry techniques. Combinations of peptide sequencing by collisionally induced dissociation and precursor ion scanning or neutral loss to select for specific oxPTMs have proved very useful for identifying oxidatively modified proteins and mapping the sites of oxidation. The development of specific labelling and enrichment procedures for S-nitrosylation or disulfide formation has proved invaluable, and there is ongoing work to establish analogous methods for detection of nitrotyrosine and other modifications.

Redox signalling and detection of protein oxidation by mass spectrometry

It is now recognised that redox control of proteins plays an important role in many signalling pathways both in health and disease. Proteins can undergo a wide variety of oxidative post-translational modifications (oxPTM); while the reversible modifications are thought to be most important in physiological processes, non-reversible oxPTM may contribute to pathological situations and disease. The oxidant is also important in determining the type of oxPTM (chlorination, nitration, etc.), and the susceptibilities of residues vary depending on their structural location. The best characterized oxPTMs involved in signalling modulation are partial oxidations of cysteine to the disulfide, glutathionylated or sulfenic acid forms, but there is increasing evidence that specific oxidations of methionine and tyrosine may have some biological roles. Well understood examples of oxidative regulation include protein tyrosine phosphatases, e.g. PTP1B/C, and members of the MAPK pathways such as MEKK1 and ASK1. Transcription factors such as NFkB and Nrf-2 are also regulated by redox-active cysteines. Improved methods for analysing specific oxPTMs in biological samples are critical for understanding the physiological and pathological roles of these changes, and tandem or MS3 mass spectrometry techniques interfaced with nano-LC separation are being now used. MS3 fragmentation markers for a variety of oxidized residues including tyrosine, tryptophan and proline have been identified, and a precursor ion scanning method that allows the selective identification of these oxPTMs in complex samples has been developed. Such advances in technology offer potential for biomarker development, disease diagnosis and understanding pathology.

Wave kinetics of random fibre lasers

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the auto-catalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

The spatial distribution and temporal dynamics of brain regions activated during the perception of object and non-object patterns

Both animal and human studies suggest that the efficiency with which we are able to grasp objects is attributable to a repertoire of motor signals derived directly from vision. This is in general agreement with the long-held belief that the automatic generation of motor signals by the perception of objects is based on the actions they afford. In this study, we used magnetoencephalography (MEG) to determine the spatial distribution and temporal dynamics of brain regions activated during passive viewing of object and non-object targets that varied in the extent to which they afforded a grasping action. Synthetic Aperture Magnetometry (SAM) was used to localize task-related oscillatory power changes within specific frequency bands, and the time course of activity within given regions-of-interest was determined by calculating time-frequency plots using a Morlet wavelet transform. Both single subject and group-averaged data on the spatial distribution of brain activity are presented. We show that: (i) significant reductions in 10-25 Hz activity within extrastriate cortex, occipito-temporal cortex, sensori-motor cortex and cerebellum were evident with passive viewing of both objects and non-objects; and (ii) reductions in oscillatory activity within the posterior part of the superior parietal cortex (area Ba7) were only evident with the perception of objects. Assuming that focal reductions in low-frequency oscillations (< 30 Hz) reflect areas of heightened neural activity, we conclude that: (i) activity within a network of brain areas, including the sensori-motor cortex, is not critically dependent on stimulus type and may reflect general changes in visual attention; and (ii) the posterior part of the superior parietal cortex, area Ba7, is activated preferentially by objects and may play a role in computations related to grasping. © 2006 Elsevier Inc. All rights reserved.

Identifying and correcting non-Markov states in peptide conformational dynamics

Conformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valine-proline-alanine-leucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of ˜ 50 ps and longer. However, at the time scale of 30–40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

Investigating the role of cholesterol in the formation of non-ionic surfactant based bilayer vesicles:thermal analysis and molecular dynamics

The aim of this research was to investigate the molecular interactions occurring in the formulation of non-ionic surfactant based vesicles composed monopalmitoyl glycerol (MPG), cholesterol (Chol) and dicetyl phosphate (DCP). In the formulation of these vesicles, the thermodynamic attributes and surfactant interactions based on molecular dynamics, Langmuir monolayer studies, differential scanning calorimetry (DSC), hot stage microscopy and thermogravimetric analysis (TGA) were investigated. Initially the melting points of the components individually, and combined at a 5:4:1 MPG:Chol:DCP weight ratio, were investigated; the results show that lower (90 C) than previously reported (120-140 C) temperatures could be adopted to produce molten surfactants for the production of niosomes. This was advantageous for surfactant stability; whilst TGA studies show that the individual components were stable to above 200 C, the 5:4:1 MPG:Chol:DCP mixture show ∼2% surfactant degradation at 140 C, compared to 0.01% was measured at 90 C. Niosomes formed at this lower temperature offered comparable characteristics to vesicles prepared using higher temperatures commonly reported in literature. In the formation of niosome vesicles, cholesterol also played a key role. Langmuir monolayer studies demonstrated that intercalation of cholesterol in the monolayer did not occur in the MPG:Chol:DCP (5:4:1 weight ratio) mixture. This suggests cholesterol may support bilayer assembly, with molecular simulation studies also demonstrating that vesicles cannot be built without the addition of cholesterol, with higher concentrations of cholesterol (5:4:1 vs 5:2:1, MPG:Chol:DCP) decreasing the time required for niosome assembly. © 2013 Elsevier B.V.

Non-Markov state model of peptide dynamics

A hidden Markov state model has been applied to classical molecular dynamics simulated small peptide in explicit water. The methodology allows increasing the time resolution of the model and describe the dynamics with the precision of 0.3 ps (comparing to 6 ps for the standard methodology). It also permits the investigation of the mechanisms of transitions between the conformational states of the peptide. The detailed description of one of such transitions for the studied molecule is presented. © 2012 Elsevier B.V. All rights reserved.