Multichain Model Research Articles

Extracting portfolio management strategies from volatility transmission models in regime-changing environments: Evidence from GCC and global markets

Unlike previous studies, this paper uses the Multi-Chain Markov Switching model (MCMS) to examine portfolio management strategies based on volatility transmission between six domestic stock markets of Gulf Arab states (GCC) and global markets (i.e., the U.S. S&P 500 index and oil prices) and compares the results with those of the VAR model. Our volatility approach is range-based and not return-based which is traditionally used in estimating the optimal hedge ratios and portfolio weights. The results demonstrate the relative hedging effectiveness of the MCMS model compared to the VAR. We also highlight the time and regime dependency of the optimal hedge ratios and the portfolio weights for each selected pair of the considered markets conditional on the regime of the same market and the regimes of the other market. Policy implications on portfolio strategies under different states are also discussed.

Markov Switching GARCH Models for Bayesian Hedging on Energy Futures Markets

A new Bayesian multi-chain Markov Switching GARCH model for dynamic hedging in energy futures markets is developed by constructing a system of simultaneous equations for the return dynamics on the hedged portfolio and futures. More specifically, both the mean and variance of the hedged portfolio are assumed to be governed by two unobserved discrete state processes, while the futures dynamics is driven by a univariate hidden state process. The noise in both processes are characterized by a MS-GARCH model. This formulation has two main practical and conceptual advantages. First, the different states of the discrete processes can be identified as different volatility regimes. Secondly, the parameters can be easily interpreted as different hedging components. Our formulation also provides an avenue to analyze the contribution of the volatility dynamics and state probabilities to the optimal hedge ratio at each point in time. Moreover, the combination of the expected utility framework with regime-switching models allows the definition of a robust minimum variance hedging strategy to also account for parameter uncertainty. Evidence of changes in the optimal hedging strategies before and after the financial crisis is found when the proposed robust hedging strategy is applied to crude oil spot and futures markets.

Conditional mean first passage time in a Markov chain

Kemeny and Snell (Markov Chains, Van Nostrand, 1960) developed a computational procedure for calculating the conditional mean time to absorption in a designated absorbing state in an absorbing Markov chain which has multiple absorbing states plus a set of transient states, given that the chain will ultimately end up in the designated absorbing state. This paper extends the computational procedure developed by Kemeny and Snell so that it can be applied to a multichain which has at least one closed communicating class of non-absorbing recurrent states. The paper derives a formula for calculating the conditional mean first passage time from a transient state to a designated recurrent state in a multichain, when it is hypothesized that the multichain will eventually reach the recurrent closed class to which the designated recurrent state belongs. The procedure devised by Kemeny and Snell, augmented by the formula contributed by this paper, is applied to a simplified multichain chain model of a production process.

Cross-Correlation Contributions to Orientational Relaxations in Primitive Chain Network Simulations

Models for entangled polymer dynamics can be conveniently thought of as belonging to two major categories - multichain models, such as the Kremer-Grest model simulated using molecular dynamics and single chain models, such as the tube and sliplink models. The single chain models typically assume that each polymer chain moves essentially independently of the other chains in the system. Hence they also assume that the cross-correlations between the different chains make negligible contribution to the various physical quantities (for e.g., the time-dependent relaxation modulus). However, Cao and Likhtman [Phys Rev Lett 104, 207801 (2010)] using molecular dynamics simulations have shown that there exist significant cross-correlation contributions to the time-dependent orientational relaxation function. In this study, the effect of cross-correlation was investigated using the primitive chain network model, a multi-chain sliplink model. Orientational relaxation functions for both the subchain vectors between entanglements and also for the end-to-end vector of whole chain were evaluated. In the case of the subchain relaxation function (and which corresponds to the time-dependent relaxation modulus by the stress-optical rule), the cross-correlation contribution to the total relaxation function appears to progressively increase with time. Further, the ratio of the cross-correlation function to the total relaxation function reaches a maximum value of approximately 40 % in the terminal region. Besides indicating that the cross-correlation contributions to the total relaxation function are non-negligible, this also demonstrates that the relaxation spectrum itself is modified if the cross-correlation contribution is neglected from the total relaxation. Specifically, the cross-correlation contribution affects the relaxation spectrum in the time range where the effect of the constraint release process is expected to be important. On the other hand, the results indicate that effect of cross-correlations on the shape of the relaxation curve is not significant at long times around the terminal region and that the autocorrelation and the total correlation functions can be superimposed by rescaling the unit of modulus. In contrast, the contribution from cross-correlation to the end-to-end relaxation (that corresponds to the dielectric relaxation of type-A polymers) is less significant than that for the subchain relaxation. In fact, no significant difference was found in the prediction of dielectric relaxation between the end-to-end relaxation functions with and without the contribution of the cross-correlations.

MULTI-CHAIN MODEL WITH SUCCESSIVE COLLISION AND HIGH-ENERGY NUCLEUS–NUCLEUS COLLISIONS

High-energy nucleus–nucleus collisions are studied in the multi-chain model with successive collision. Analytic forms for the longitudinal momentum distribution of the inclusive reaction are discussed. It is shown that the longitudinal momentum distribution in nucleus–nucleus collisions is expressed in the Glauber probability with the hypergeometric distribution.

Multi-chain slip-spring model for entangled polymer dynamics

It has been established that entangled polymer dynamics can be reasonably described by single chain models such as tube and slip-link models. Although the entanglement effect is a result of hard-core interaction between chains, linkage between the single chain models and the real multi-chain system has not been established yet. In this study, we propose a multi-chain slip-spring model where bead-spring chains are dispersed in space and connected by slip-springs inspired by the single chain slip-spring model [A. E. Likhtman, Macromolecules 38, 6128 (2005)]. In this model the entanglement effect is replaced by the slip-springs, not by the hard-core interaction between beads so that this model is located in the niche between conventional multi-chain simulations and single chain models. The set of state variables are the position of beads and the connectivity (indices) of the slip-springs between beads. The dynamics of the system is described by the time evolution equation and stochastic transition dynamics for these variables. We propose a simple model which is based on the well-defined total free-energy and detailed balance condition. The free energy in our model contains a repulsive interaction between beads, which compensate the attractive interaction artificially generated by the slip-springs. The explicit expression of linear relaxation modulus is also derived by the linear response theory. We also propose a possible numerical scheme to perform simulations. Simulations reproduced expected bead number dependence in transitional regime between Rouse and entangled dynamics for the chain structure, the central bead diffusion, and the linear relaxation modulus.

Hemiphasmidic Side-Chain Liquid Crystalline Polymer: From Smectic C Phase to Columnar Phase with a Bundle of Chains as Its Building Block.

We synthesized a new hemiphasmidic side-chain liquid crystalline polymer (P-n, n is the number of carbons in alky tail of the side chain, n = 4-12) using free radical polymerization. The side chain of P-n has a biphenyl in the middle, linked to the polystyrene backbone and to the terminal phenyl group with three alkyl tails via only methyleneoxy units. Upon increasing n, the mesophase of P-n changes from bilayer smectic C to hexagonal columnar (Φh) phase with the a-dimension of ∼6 nm. Both of the mesophases are long-range ordered, which can be well aligned by simple shearing. The oriented Φh shows a quite low rotational disorder around the shear direction. Most likely, the Φh phase takes a bundle of chains (e.g., ∼five chains) rather than a single chain as its building block. This "multi-chain model" of the Φh phase may represent a new type of self-assembly in side-chain polymers.

Chain contraction and nonlinear stress damping in primitive chain network simulations

Doi and Edwards (DE) proposed that the relaxation of entangled linear polymers under large deformation occurs in two steps: the fast chain contraction (via the longitudinal Rouse mode of the chain backbone) and the slow orientational relaxation (due to reptation). The DE model assumes these relaxation processes to be independent and decoupled. However, this decoupling is invalid for a generalized convective constraint release (CCR) mechanism that releases the entanglement on every occasion of the contraction of surrounding chains. Indeed, the decoupling does not occur in the sliplink models where the entanglement is represented by the binary interaction (hooking) of chains. Thus, we conducted primitive chain network simulations based on a multichain sliplink model to investigate the chain contraction under step shear. The simulation quantitatively reproduced experimental features of the nonlinear relaxation modulus G(t,γ). Namely, G(t,γ) was cast in the time-strain separable form, G(t,γ)=h(γ)G(t) with h(γ)=damping function and G(t)=linear modulus, but this rigorous separability was valid only at times t comparable to the terminal relaxation time, although a deviation from this form was rather small (within ±10%) at t>τ(R) (longest Rouse relaxation time). A molecular origin of this delicate failure of time-strain separability at t∼τ(R) was examined for the chain contour length, subchain length, and subchain stretch. These quantities were found to relax in three steps, the fast, intermediate, and terminal steps, governed by the local force balance between the subchains, the longitudinal Rouse relaxation, and the reptation, respectively. The contributions of the terminal reptative mode to the chain length relaxation as well as the subchain length/stretch relaxation, not considered in the original DE model, emerged because the sliplinks (entanglement) were removed via the generalized CCR mechanism explained above and the reformation of the sliplinks was slow at around the chain center compared to the more rapidly fluctuating chain end. The number of monomers in the subchain were kept larger at the chain center than at the chain end because of the slow entanglement reformation at the center, thereby reducing the tension of the stretched subchain at the chain center compared to the DE prediction. This reduction of the tension at the chain center prevented completion of the length equilibration of subchains at t∼τ(R) (which contradicts to the DE prediction), and it forces the equilibration to complete through the reptative mode at t≫τ(R). The delicate failure of time-strain separability seen for G(t,γ) at t∼τ(R) reflects this retarded length equilibration.

A novel method for determining ground-referenced contacts during stair ascent: Comparing relative hip position to quiet standing hip height

Stair climbing can be measured using body-fixed sensors, whereby the origin and axes of the coordinate system are fixed with respect to the geometry of a body segment. These sensors can be part of a portable system, which provides the possibility to collect data in complex real-life environments. However due to the fact that the sensors are body-fixed, difficulties in determining the ground-based parameters of stair ascent can occur. The purpose of this study is to present a new approach for determining initial contacts based on a multi-chain biomechanical model combined with a new analysis method, in which relative hip height is compared to hip height during normal standing. Initial contacts obtained from the proposed method were compared to those obtained using an optical tracking device. An average absolute timing difference ranging from 0.04 (SD ± 0.03) to 0.06 (±0.03) s and a root mean square error ranging from 0.05 to 0.07 s were found between the two techniques. This shows that the new approach presented in this study can be used to accurately determine initial contacts during stair ascent using portable equipment.

Localization length in two-dimensional disordered systems: effects of evanescentmodes

We study the influence of evanescent modes on the scaling behavior of therenormalized localization length (RLL) in 2D disordered systems, using theδ-function potential strip model and the multichain tight-binding Anderson model. In theweak disorder regime we have evaluated the RLL for large numbers of modesM. It is shown that RLL shrinks with increasingM which indicates that the electron states will remain localized in an infinitely wide systemfor an arbitrarily small disorder, in agreement with existing theories. In the thermodynamiclimit () for the two models, we obtain the localization length in an infinitely large system. Weshow that the presence of evanescent modes enhances the RLL with respect to the valueobtained when evanescent modes are absent. We also derive an exact relationshipbetween the localization length and its corresponding average mean free path for anM-channel system for the case where propagating as well as evanescent channels arepresent.

Orientational Order in Nanolayers of Cast Polymer Films

The spontaneous ordering of fragments of chain molecules near the surface in polymer films is described in terms of the multichain model, which allows for local intra- and interchain segment orientational interactions, as well as for transversal fluctuation of their orientation as an approximation of strong planar orientation order in the layers. Chain packing in the plane-ordered state is impossible unless the interchain interaction parameter has a critical value. This value decreases with chain bending rigidity. The calculated dependences of the limiting values of the quadrupole orientation order parameter on the length of the Kuhn statistical segment describe reasonably well the experimental data obtained in a study of polymer homologue polysaccharides and sulfonated phenyl-containing polymers. The monolayer thickness in films of some polysaccharides and sulfonated phenyl-containing polymers has been calculated from the fit of the theoretical to the experimental data of the surface birefringence on the number of nanolayers.

Modeling Entangled Dynamics: Comparison between Stochastic Single-Chain and Multichain Models

To test the effectiveness of stochastic single-chain models in describing the dynamics of entangled polymers, we systematically compare one such model—the slip−spring model—to a multichain model solved using stochastic molecular dynamics (MD) simulations (the Kremer−Grest model). The comparison involves investigating if the single-chain model can adequately describe both a microscopic dynamical and a macroscopic rheological quantity for a range of chain lengths. Choosing a particular chain length in the slip−spring model, the parameter values that best reproduce the mean-square displacement of a group of monomers is determined by fitting to MD data. Using the same set of parameters we then test if the predictions of the mean-square displacements for other chain lengths agree with the MD calculations. We followed this by a comparison of the time dependent stress relaxation moduli obtained from the two models for a range of chain lengths. After identifying a limitation of the original slip−spring model in describing the static structure of the polymer chain as seen in MD, we remedy this by introducing a pairwise repulsive potential between the monomers in the chains. Poor agreement of the mean-square monomer displacements at short times can be rectified by the use of generalized Langevin equations for the dynamics and resulted in significantly improved agreement.

MALDI-TOF/TOF CID study of poly(α-methylstyrene) fragmentation reactions

MALDI-TOF/TOF CID experiments are reported for hydroxylated poly(alpha-methylstyrene) precursor ions (PAMS: m/z 1,445.9 (n = 10), 2,036.3 (n = 15), 2,626.7 (n = 20), 3,217.1 (n = 25), and 3,807.5 (n = 30), where the number of repeat units n corresponds to the oligomer mass numbers). The influences of structure, molecular weight, and kinetic energy on degradation mechanisms were examined to test the generality of our multi-chain fragmentation model developed for polystyrene. Our results indicate that poly(alpha-methylstyrene) free radicals are formed initially through multiple chain breaks and subsequently undergo a variety of depolymerization reactions to yield predominantly monomer and dimer species; the intensity of each species depends on the effective kinetic energy selected for the CID process. Each depolymerization mechanism is presented in detail with experimental and computational data to justify/rationalize the process and its kinetic energy dependence. These processes show the complex interrelationships between the various pathways along with preferred production of tertiary radicals, which suppresses the appearance of primary radicals. Additionally, Py-GC/MS experimental data are presented to allow a comparison of the multimolecular free radical reactions in pyrolysis with the unimolecular fragmentation reactions of MS/MS.

Prediction of fingers posture using artificial neural networks

Predicting the hand and fingers posture during grasping tasks is an important issue in the frame of biomechanics. In this paper, a technique based on neural networks is proposed to learn the inverse kinematics mapping between the fingertip 3D position and the corresponding joint angles. Finger movements are obtained by an instrumented glove and are mapped to a multichain model of the hand. From the fingertip desired position, the neural networks allow predicting the corresponding finger joint angles keeping the specific subject coordination patterns. Two sets of movements are considered in this study. The first one, the training set, consisting of free fingers movements is used to construct the mapping between fingertip position and joint angles. The second one, constructed for testing purposes, is composed of a sequence of grasping tasks of everyday-life objects. The maximal mean error between fingertip measured position and fingertip position obtained from simulated joint angles and forward kinematics is 0.99±0.76 mm for the training set and 1.49±1.62 mm for the test set. Also, the maximal RMS error of joint angles prediction is 2.85° and 5.10° for the training and test sets respectively, while the maximal mean joint angles prediction error is −0.11±4.34° and −2.52±6.71° for the training and test sets, respectively. Results relative to the learning and generalization capabilities of this architecture are also presented and discussed.

MALDI-TOF/TOF CID study of 4-alkyl-substituted polystyrene fragmentation reactions

MALDI-TOF/TOF CID experiments were conducted on a variety of hydrogen-terminated poly(4-methylstyrene), hydroxylated poly(t-butylstyrene), and polystyrene precursor ions: n = 10, 15, 20, 25, and 30, where the number of repeat units n corresponds to the oligomer mass number. The influences of structure, molecular weight, and effective collision kinetic energy on degradation mechanisms were examined to test the generality of our multi-chain fragmentation model developed for polystyrene. Each depolymerization mechanism is presented in detail with experimental and computational data to justify/rationalize its occurrence and effective kinetic energy dependence. These processes show the complex interrelationship between the various pathways along with preferred production of secondary radicals, which suppresses the appearance of primary radicals. Additionally, Py-GC/MS experimental data are presented, for comparison of the multimolecular free radical reactions in pyrolysis with the unimolecular fragmentation reactions of MS/MS.

Optimization of a special case of continuous-time Markov decision processes with compact action set

Performance optimization is considered for average-cost multichain Markov decision processes (MDPs) with compact action set. Since, for a general compact multichain model, the optimality equation system may have no solution, and also a policy iteration algorithm may yield a suboptimal policy rather than an optimal one, we concentrate only on a special case of multichain models in this paper, where we assume that the classifications of states are fixed identically rather than varying with policies. By using the concept of performance potentials, the existence of solutions to the optimality equation system is established, and then a potential-based policy iteration algorithm is supposed to solve this system. In addition, the optimality convergence, for recurrent classes, of the algorithm has been proved. Finally, a numerical example is provided.

Forward Λ production and nuclear stopping power ind+Aucollisions atsNN=200GeV

We report the measurement of {lambda} and {lambda} yields and inverse slope parameters in d+Au collisions at {radical}(s{sub NN})=200 GeV at forward and backward rapidities (y={+-}2.75), using data from the STAR forward time projection chambers. The contributions of different processes to baryon transport and particle production are probed exploiting the inherent asymmetry of the d+Au system. Comparisons to model calculations show that baryon transport on the deuteron side is consistent with multiple collisions of the deuteron nucleons with gold participants. On the gold side, HIJING-based models without a hadronic rescattering phase do not describe the measured particle yields, while models that include target remnants or hadronic rescattering do. The multichain model can provide a good description of the net baryon density in d+Au collisions at energies currently available at the BNL Relativistic Heavy Ion Collider, and the derived parameters of the model agree with those from nuclear collisions at lower energies.

Molecular orientation ordering in surface layers of polymer films

The spontaneous ordering of fragments of chain molecules near the surface in polymer films is described in terms of the multichain model that allows for local intra-and interchain orientational interactions of chain segments and for transverse fluctuation of their orientation in the approximation of strong planar-orientation order in the layers. Chain packing in the plane-ordered state is impossible unless the interchain interaction parameter has a value of b = 2K 2/k B T > b c. The value of b c decreases with a growth in chain rigidity (parameter a = 2K 1/k B T). The calculated dependence of the limiting values of the quadrupole orientation order parameter S 0 on the length of the Kuhn statistical segment A = 2a reasonably well describes the experimental data obtained in a study of polymer-homolog (polysaccharide) films by means of the tilted polarized-beam technique at an interchain interaction parameter of b = 1.75. The monolayer thickness (d ≅ 10 mn) is films of some polysaccharides was calculated from the fit of the theoretical to the experimental dependences of the orientational order parameter and the birefringence on the number of layers.

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.

Combining object and feature dynamics in probabilistic tracking

Objects can exhibit different dynamics at different spatio-temporal scales, a property that is often exploited by visual tracking algorithms. A local dynamic model is typically used to extract image features that are then used as inputs to a system for tracking the object using a global dynamic model. Approximate local dynamics may be brittle—point trackers drift due to image noise and adaptive background models adapt to foreground objects that become stationary—and constraints from the global model can make them more robust. We propose a probabilistic framework for incorporating knowledge about global dynamics into the local feature extraction processes. A global tracking algorithm can be formulated as a generative model and used to predict feature values thereby influencing the observation process of the feature extractor, which in turn produces feature values that are used in high-level inference. We combine such models utilizing a multichain graphical model framework. We show the utility of our framework for improving feature tracking as well as shape and motion estimates in a batch factorization algorithm. We also propose an approximate filtering algorithm appropriate for online applications and demonstrate its application to tasks in background subtraction, structure from motion and articulated body tracking.