Parameter dependence and outcome dependence in dynamical models for state vector reduction

We apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous state vector reduction. We show that in the nonlinear model there is a set of realizations of the stochastic process that drives the state vector reduction for which parameter independence is violated for parallel spin components in the EPR-Bohm setup. Such a set has an appreciable probability of occurrence ( 1/2). On the other hand, the linear model exhibits only extremely small parameter dependence effects. We investigate some specific features of the models and we recall that, as has been pointed out recently, if one wants to be able to speak of definite outcomes (or equivalently of possessed objective elements of reality) at finite times, one has to slightly change the criteria for their attribution to physical systems. The concluding section is devoted to a detailed discussion of the difficulties which one meets when one tries to take, as a starting point for the formulation of a relativistic theory, a nonrelativistic scheme which exhibits parameter dependence. Here we derive a theorem which identifies the precise sense in which the occurrence of parameter dependence forbids a genuinely relativistic generalization. Finally we show how the appreciable parameter dependence of the nonlinear model gives rise to problems with relativity, while the extremely weak parameter dependence of the linear model does not give rise to any difficulty, provided one takes into account the appropriate criteria for the attribution of definite outcomes.Work supported in part by the Trieste Section of the INFN.     

Relativistic dynamical reduction models: General framework and examples

The formulation of a relativistic theory of state-vector reduction is proposed and analyzed, and its conceptual consequences are elucidated. In particular, a detailed discussion of stochastic invariance and of local and nonlocal aspects at the level of individual systems is presented.     

Groups as dynamical models

Felix Klein classified geometries by their group structure. It is pointed out that a similar program has been in place for particle physics and canonical quantum mechanics.Colloquim in celebration of Lawrence Biedenharn's seventieth birthday.     

Weighing neutrinos in dynamical dark energy models

正The discovery of neutrino oscillation indicates that neutrinos have masses and each flavor state is actually a superposition of three mass states with masses m_1,m_2,and m_3.However,the neutrino oscillation experiments are not able to measure the absolute masses of neutrinos,but can only measure the squared mass differences between the neutrino mass eigenstates—The solar and reactor experiments gave Δm~2_(21)? 7.5×10~(-5), and the atmospheric and accelerator beam experiments gave|?m~2_(31)|?2.5×10~(-3),which indicates that there are two possible mass orders,i.e.,the normal hierarchy (NH) with m_1m_2?m_3 and the inverted hierarchy(IH) with m_3 ? m_1 m_2.     

Frequency dependence of phase-synchronization time in nonlinear dynamical systems

It has been found recently that the averaged phase-synchronization time between the input and the output signals of a nonlinear dynamical system can exhibit an extremely high sensitivity to variations in the noise level. In real-world signal-processing applications, sensitivity to frequency variations may be of considerable interest. Here we investigate the dependence of the averaged phase-synchronization time on frequency of the input signal. Our finding is that, for typical nonlinear oscillator systems, there can be a frequency regime where the time exhibits significant sensitivity to frequency variations. We obtain an analytic formula to quantify the frequency dependence, provide numerical support, and present experimental evidence from a simple nonlinear circuit system.     

Idealized freeze-out in relativistic fluid dynamical models

Freeze-out of particles across a three-dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for space-like and time-like freeze-out surfaces, taking into account conservation laws across the freeze-out discontinuity. Generally the conservation laws lead to a change of temperature, baryon density and flow velocity at freeze-out.     

Estimating statistics for detecting determinism using global dynamical models

Classification of time series using a dynamical system ansatz is potentially powerful, however assessing performance for noisy experimental data is problematic. Here, we develop a rigorous statistical framework for calculating classification probabilities using global dynamical models, and analytically derive some asymptotic properties. We illustrate the method numerically by attempting to detect “determinism” in a noisy data set.     

Identifiability and observability analysis for experimental design in nonlinear dynamical models

Dynamical models of cellular processes promise to yield new insights into the underlying systems and their biological interpretation. The processes are usually nonlinear, high dimensional, and time-resolved experimental data of the processes are sparse. Therefore, parameter estimation faces the challenges of structural and practical nonidentifiability. Nonidentifiability of parameters induces nonobservability of trajectories, reducing the predictive power of the model. We will discuss a generic approach for nonlinear models that allows for identifiability and observability analysis by means of a realistic example from systems biology. The results will be utilized to design new experiments that enhance model predictiveness, illustrating the iterative cycle between modeling and experimentation in systems biology.     

Cellular automata and nonlinear dynamical models

A point of view is pursued in which cellular automata (CA) are viewed as a laboratory to investigate nonlinear dynamics. We introduce an irreversible cellular automaton (ICA) with minimal coupling which exhibit class 4 behavior. Periodic structures (phases) are studied along with their stability properties. We observe topological conserved quantities and introduce a classification of structures via a topological number. Time reversal invariant cellular automata (TRCA) are also investigated; we discuss stability of phases and use a concept of local entropy to measure the growth of chaos in slightly perturbed phases. A classification of approach to chaos into 3 classes is proposed for TRCA.     

On algebraic models of dynamical systems

We describe a universal algebraic model which, being read appropriately, yields (periodic and infinite) discrete dynamical systems, as well as their continuous limits, which cover all differential scalar Lax systems. For this model we give: Two different constructions of an infinity of integrals; modified equations; deformations; infinitesimal automorphisms. The basic tools are supplied by symbolic calculus and the abstract Hamiltonian formalism.     

Solitons in models with dynamical spontaneous symmetry breaking

An approximate quasi-classical method for the investigation of solitons appearing at quantum level is described. The existence of the soliton in the model with Yukawa coupling in two-dimensional space-time is established with the help of this method. The existence of solitons in the Georgi-Glashow type model with dynamical spontaneous symmetry breaking is shown.     

Energy dependence of non-linear dynamical features in e^＋e^- collisions

A study of the d.ynamical fluctuation properties at various c.m.energies in e~ e~- collisions is performed using the Monte Carlo method.The results suggest that,after the normalized factorial moments of 3-dimensional phase space are analyzed using an isotropical phase space partition,the NFM describing non- linear dynamical properties show a power-law scaling,i.e.,the dynamical fluctuations in higher dimensional phase space are isotropic.For c.m.energies s~(1/2)≤80 GeV,the scaling exponentsφ_q increase rapidly with the c.m.energy and for c.m.energies s~(1/2)>80 GeV,theφ_q gradually saturate.     

State and parameter estimation in stochastic dynamical models

This paper derives generalized maximum likelihood estimates of state and model parameters of a stochastic dynamical model. In contrast to previous studies, the change in background distribution due to changes in model parameters is taken into account. An ensemble approach to solving the maximum likelihood estimates is proposed. An exact solution for the ensemble update based on a square root Kalman Filter is derived. This solution involves a two step procedure in which an ensemble is first produced by a standard ensemble Kalman Filter, and then “corrected” to account for parameter estimation, thereby allowing a user to take advantage of an existing ensemble filter. The solution is illustrated with simple, low-dimensional stochastic dynamical models and shown to work well and outperform augmentation methods for estimating stochastic parameters.     

Estimation of noise levels for models of chaotic dynamical systems

We investigate how far it is possible to identify and separate dynamical noise from measurement noise in observed nonlinear time series. Using Bayesian methods, we derive estimates for the two noise levels, and find that, given a good model of the dynamics, these can give accurate results even if the dynamical noise level is orders of magnitude smaller than the measurement noise level, whereas a simple calculation of root mean square error badly understates the dynamical noise. We argue that this allows better estimates of the underlying dynamical time series, and so better predictions of its future and of its fundamental dynamical properties.     

Nonlinear dynamical wave structures of Zoomeron equation for population models

The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevé approach method (PPAM). When the variables appearing in the exact solutions take specific values, the solitary wave solutions will be easily obtained. The realized results prove the efficiency of this technique.     

Dimension reduction method for ODE fluid models

We develop a new dimension reduction method for large size systems of ordinary differential equations (ODEs) obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large-size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of smoothed particle hydrodynamic ODEs describing single-phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single-phase flow driven by the periodic body force and for the two-phase flows, the higher-order (the first- and second-order) deconvolutions were necessary to obtain a sufficiently accurate solution.     

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.     

平面超薄准直器件的参数依赖性

该文设计了一具有高效强指向性的平面超薄人工结构,当平面声波垂直入射到该结构时,若中心狭缝处产生的Fabry-Perot(F-P)共振和两侧类亥姆霍兹凹槽的共振频率耦合时,会产生一具有高度指向性的准直声束。通过对结构两侧的凹槽阵列的作用、凹槽周期D和凹槽数量r的探讨,发现凹槽阵列可将散射声波转换成声表面波,大大提高了透射效率,同时结构的共振频率、声透射率和准直效果与D、r的变化关系不大,说明对该结构准直效应产生影响的是F-P共振频率和类亥姆霍兹共振器共振频率,与布拉格散射无关。这一发现有助于在降低结构尺寸的同时仍保持结构的有效性,为后续指向性器件的应用提供了理论依据。     

Lattice dynamical models of adaptive spatio-temporal phenomena

We describe the rich spectrum of spatio-temporal phenomena emerging from a class of models incorporating adaptive dynamics on a lattice of nonlinear (typically chaotic) elements. The investigation is based on extensive numerical simulations which reveal many novel dynamical phases, ranging from spatio-temporal fixed points and cycles of all orders, to parameter regimes displaying marked scaling properties (as manifest in distinct 1/f spectral characteristics and power law distributions of spatial quantities).     

Beam-energy and system-size dependence of dynamical net charge fluctuations

We present measurements of net charge fluctuations in Au + Au collisions at ?{s_NN }\sqrt {s_{NN} } = 19.6, 62.4, 130, and 200 GeV, Cu + Cu collisions at ?{s_NN }\sqrt {s_{NN} } = 62.4, 200 GeV, and p + p collisions at ?s\sqrt s = 200 GeV using the net charge dynamical fluctuations measure ν+ −,dyn. The dynamical fluctuations are non-zero at all energies and exhibit a rather modest dependence on beam energy. We find that at a given energy and collision system, net charge dynamical fluctuations violate 1/N _ch scaling, but display approximate 1/N _part scaling. We observe strong dependence of dynamical fluctuations on the azimuthal angular range and pseudorapidity widths.