Multidimensional Phase Space Research Articles

Multidimensional phase space methods for mass measurements and decay topology determination

Collider events with multi-stage cascade decays fill out the kinematically allowed region in phase space with a density that is enhanced at the boundary. The boundary encodes all available information as regards the spectrum and is well populated even with moderate signal statistics due to this enhancement. In previous work, the improvement in the precision of mass measurements for cascade decays with three visible and one invisible particles was demonstrated when the full boundary information is used instead of endpoints of one-dimensional projections. We extend these results to cascade decays with four visible and one invisible particles. We also comment on how the topology of the cascade decay can be determined from the differential distribution of events in these scenarios.

Potential for optimizing the Higgs boson CP measurement in H→ττ decays at the LHC including machine learning techniques

We investigate potential for measuring CP state of the Higgs boson in the H to tau tau$ decay with consecutive tau-lepton decays in channels: tau^+- to rho^+- nu_tau and tau^+- to a1^+- nu_tau combined. Subsequent decays rho^+- to pi^+- pi^0, a1^+- to rho^0 pi^+- and rho^0 to pi^+ pi^- are taken into account. We will explore extensions of the method, where acoplanarity angle for the planes build on the visible decay products, pi^+- pi^0 of tau^+- to pi^pm pi^0 nu_tau, was used. The angle is sensitive to transverse spin correlations, thus to parity. We show, that in the case of the cascade decays of tau to a1 nu, information on the CP state of Higgs can be extracted from the acoplanarity angles as well. Because in the cascade decay a1^+- to rho^0 pi^pm,rho^0 to pi^+ pi^- up to four planes can be defined, up to 16 distinct acoplanarity angles are available for H \to tau tau to a1^+ a1^- nu nu decays. These acoplanarities carry in part supplementary but also correlated information. It is thus cumbersome to evaluate an overall sensitivity. We investigate sensitivity potential of such analysis, by developing and implementing model in the Machine Learning (ML) techniques. We quantify possible improvements when multi-dimensional phase-space of outgoing decay products directions is used, instead of 1-dimensional projections i.e. the acoplanarity angles. We do not take into account ambiguities resulting from detector uncertainties or background contamination, we concentrate on usefulness of ML methods and tau to 3pi nu decays for Higgs boson parity measurement.

Multiple sources and multiple measures based traffic flow prediction using the chaos theory and support vector regression method

Abstract This study proposes a multiple sources and multiple measures based traffic flow prediction algorithm using the chaos theory and support vector regression method. In particular, first, the chaotic characteristics of traffic flow associated with the speed, occupancy, and flow are identified using the maximum Lyapunov exponent. Then, the phase space of multiple measures chaotic time series are reconstructed based on the phase space reconstruction theory and fused into a same multi-dimensional phase space using the Bayesian estimation theory. In addition, the support vector regression (SVR) model is designed to predict the traffic flow. Numerical experiments are performed using the data from multiple sources. The results show that, compared with the single measure, the proposed method has better performance for the short-term traffic flow prediction in terms of the accuracy and timeliness.

Investigations of fission characteristics and correlation effects

We review the experimental results on the P-even and P-odd angular correlations of fission fragments in the fission of the 235U and 239Pu nuclei induced by unpolarized and polarized resonance neutrons, and on the TRI and ROT effects in the ternary and binary fission of actinides induced by polarized thermal neutrons. Also reported are the measured yields of prompt and delayed neutrons per fission event. The experimental data are analyzed within a novel theoretical framework developed by the JINR—RNC KI Collaboration, whereby the reduction of the multidimensional phase space of fission fragments to the JπK-channel space is consistently validated and the role of resonance interference in the observed correlation effects is revealed.

MULTIPLE TIME-SCALES NONLINEAR PREDICTION OF RIVER FLOW USING CHAOS APPROACH

River flow prediction is important in determining the amount of water in certain areas to ensure sufficient water resources to meet the demand. Hence, an analysis and prediction of multiple time-scales data for daily, weekly and 10-day averaged time series were performed using chaos approach. An analysis was conducted at the Tanjung Tualang station, Malaysia. This method involved the reconstruction of a single variable in a multi-dimensional phase space. River flow prediction was performed using local linear approximation. The prediction result is close to agreement with a high correlation coefficient for each time scale. The analysis suggests that the presence of low dimensional chaos as an optimal embedding dimension exists when the inverse method is adopted. In addition, a comparison of the prediction performance of chaos approach, autoregressive integrated moving average (ARIMA), artificial neural network (ANN), support vector machine (SVM) and least squares support vector machines (LSSVM) were performed. The comparative analysis shows that all methods provide comparable predictions. However, chaos approach provides a simpler means of analysis since it only use a scalar time series (river flow data). Therefore, the relevant authorities may use this prediction result for the creation of a water management system for local benefit.

On the potential of multivariate techniques for the determination of multidimensional efficiencies

Differential measurements of particle collisions or decays can provide stringent constraints on physics beyond the Standard Model of particle physics. In particular, the distributions of the kinematical and angular variables that characterise heavy meson multibody decays are non-trivial and can be used to probe this new physics. In the era of high luminosity opened by the advent of the Large Hadron Collider and of Flavor Factories, differential measurements are less and less dominated by statistical precision and require a precise determination of efficiencies that depend simultaneously on several variables and do not factorise in these variables. This article is a reflection on the potential of multivariate techniques for the determination of such multidimensional efficiencies. We carried out two case studies showing that multivariate techniques, such as neural networks, can determine and correct for the distortions introduced by reconstruction and selection criteria in the multidimensional phase space of the decays \( B^{0}\rightarrow K^{*0}(\rightarrow K^{+}\pi^{-})\mu^{+}\mu^{-}\) and \( D^{0}\rightarrow K^{-}\pi^{+} \pi^{+}\pi^{-}\), at the price of a minimal analysis effort. We conclude that this method can already be used for measurements which statistical precision does not yet reach the percent level. With more sophisticated machine learning methods, the aforementioned potential is very promising.

Метод многомерных фазовых пространств в оценке хаотической динамики тремора в условиях статических нагрузок

The article presents the feasibility of application of the method of multidimensional phase spaces, based on the methods of calculating the quasi-attractor parameters as a quantitative measure of the chaotic dynamics of the tremor. The measure is used in two-dimensional quasi-attractor phase space. The quasi-attractor square is used for the identification of the actual changes in the parameters of the functional state of the organism with no load and under static loads. Specifically, the static load provides the threefold increasing of the area of quasi-attractor (from 0.31 to 0.99 cu under load of 300 g). This is a quantitative measure of the body´s reaction to changes. It was proved that calculation of quasi-attractor parameters demonstrated at three phase space more statistical stable picture then two dimensional quasi-attractors.

Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles.

The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.

Bridging the Gap between Computation and Experiments in GPCRs

GPCRs transduce extracellular signals to intracellular downstream pathway via their ability to dynamically change their orientation to different functional conformations. While kinetic experiments such as correlation spectroscopy or Forster resonance energy transfer can observe projected kinetics and provide information about population distributions, the main limitation is that it only probes a few structural coordinates simultaneously and therefore, few timescales can be uniquely extracted. Such data may suggest simple models that fit with the few states accessible in the experiment. Currently, the only technique that can access dynamics and structure simultaneously in atomistic detail is MD simulation. In contrast to kinetic experiments, MD simulations often reveal highly complex dynamics with many discrete states and multiple timescales. This creates a challenge when reconciling simple models gleaned from experiments to the complex, multidimensional phase space revealed from MD simulations. We use dynamical fingerprinting, a statistical framework that visualizes kinetic features from both simulation and experiment in terms of peaks with specific amplitude and timescale, to identify the residues that are most strongly coupled to distinct activation pathways and suggest labeling sites for future kinetic experiments.

Characterizing the signature of flame flashback precursor through recurrence analysis.

In this paper, it is shown that prior to flashback, small dynamical changes appear in the system. These changes appear as a drift in the recurrence plots and are found to be associated with a gradual increase in the determinism and recurrence rate. Thus, this study indicates that precursors to flame flashback exist and can be detected in the multidimensional phase space reconstructed from pressure measurements acquired during flashback. This observation could have broad academic as well as industrial implications.

Beyond the continuum: a multi-dimensional phase space for neutral-niche community assembly.

Neutral and niche processes are generally considered to interact in natural communities along a continuum, exhibiting community patterns bounded by pure neutral and pure niche processes. The continuum concept uses niche separation, an attribute of the community, to test the hypothesis that communities are bounded by pure niche or pure neutral conditions. It does not accommodate interactions via feedback between processes and the environment. By contrast, we introduce the Community Assembly Phase Space (CAPS), a multi-dimensional space that uses community processes (such as dispersal and niche selection) to define the limiting neutral and niche conditions and to test the continuum hypothesis. We compare the outputs of modelled communities in a heterogeneous landscape, assembled by pure neutral, pure niche and composite processes. Differences in patterns under different combinations of processes in CAPS reveal hidden complexity in neutral-niche community dynamics. The neutral-niche continuum only holds for strong dispersal limitation and niche separation. For weaker dispersal limitation and niche separation, neutral and niche processes amplify each other via feedback with the environment. This generates patterns that lie well beyond those predicted by a continuum. Inferences drawn from patterns about community assembly processes can therefore be misguided when based on the continuum perspective. CAPS also demonstrates the complementary information value of different patterns for inferring community processes and captures the complexity of community assembly. It provides a general tool for studying the processes structuring communities and can be applied to address a range of questions in community and metacommunity ecology.

Стохастическая и хаотическая оценка динамики параметров сердечно-сосудистой системы человека при трансширотных перемещениях.

Using the methods of statistical analysis and methods of multidimensional phase spaces (analysis and calculation of the volume of quasi-attractors matrices mezhattraktornyh distances) studied the behavior of the state vector of the body girls (for example, the behavior of the parameters of the cardiovascular system) with transshirotnyh movements. The differences in the assessment of the dynamic behavior of the parameters of the cardio-vascular system, namely the decrease in quasi-attractors indicates good revitalizing effect two-week stay in a boarding house young children oilman. Analysis matrices mezhattraktonyh distances showed that the motion of chaotic and stochastic centers at latitude movements somewhat different girls: mezhattraktornye distance when driving chaotic center upon arrival to rest down, after a two-week vacation, it becomes even more, to return to the city of Surgut is similar to the results for the arrival at rest, indicating the lack of formation of the girls adaptive mechanisms, as well as a significant tension of regulatory processes and the degree of mismatch of functional systems at transshirotnyh movements.

Возможности стохастики и теории хаоса в обработке миограмм

In studies using the method of multi-dimensional phase space. In the study and modeling of complex biological objects (complexity) there is the possibility of introducing traditional physical methods in biological research and new methods based on chaos theory, self-organization. The paper shows the feasibility of applying the method of multi-dimensional phase space as a quantitative measure for the evaluation of chaotic dynamics on the example of the muscles (flexor of the little finger). As a measure of the state of the neuromuscular system of the person (weak muscle tension and strong, almost the maximum force) used quasi-attractors volumes of multidimensional phase space. This enables identification of the actual measurements of the parameters of the functional state with weak muscles (p = 5th Dan) and strong (P = 10 daN) static stress. Was built timebase signal obtained with myograph and were built autocorrelation function A (t) signal. In the end analysis of the biomechanical system based on a comparison of volume quasi-attractor, as well as on the basis of analysis of the Shannon entropy N. kzvaziattraktora volume displacement at low load is slightly less than the same amount of displacement under a heavy load of flexor muscles of the little finger, just as the values of the Shannon entropy at a heavy load is increased as compared with the values obtained by the weak muscle load.

Анализ миограмм с позиций стохастики и теории хаоса-самоорганизации

The paper shows the feasibility of applying the method of multi-dimensional phase space as a quantitative measure for the evaluation of chaotic dynamics on the example of the muscles (flexor of the little finger). The method of multi-dimensional phase space was used. In the study and modeling of complex biological objects (complexity) there is the possibility of introducing traditional physical methods in biological research and new methods based on the chaos theory and self-organization. As a measure of the state of the neuromuscular system of the person (weak muscle tension and strong, almost the maximum force), the authors used quasi-attractors volumes of multidimensional phase space. This enables identification of the actual measurements of the parameters of the functional state with weak muscles (Fi = 5 daN) and strong (Fi = 10 daN) static stress. The authors built a timebase signal received from the electromyograph
 
 and the autocorrelation function A(t) of signal. A biomechanical analysis of the state of the system is carried out on the basis of comparison of the volume VG quasi attractor, as well as on the basis of the analysis of the Shannon entropy E. Volume of quasi attractor VG displacements under low load is slightly less than the same volume displacement VG with strong exertion of the muscles of the flexor of the little finger, exactly the same as the values of the Shannon entropy under a heavy load increases compared to the values obtained under low load the muscles.

Kernel density estimation of a multidimensional efficiency profile

Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data samples, whereas if the kernel width is large, boundaries and narrow structures tend to be smeared. Here, an approach to correct for such effects, is proposed that uses an approximate density to describe narrow structures and boundaries. The approach is shown to be well suited for the description of the efficiency shape over a multidimensional phase space in a typical particle physics analysis. An example is given for the five-dimensional phase space of the Λ0b → D0pπ− decay.

Оценка состояния параметров нервно-мышечного кластера в условиях дозированной физической нагрузки

Parameters of neuromuscular system at the unexercised and trained examinees from a position of the theory of chaos and self-organization are studied. Essential distinction between two studied groups (the trained and unexercised students) is established. Dynamics of involuntary micro-movements of extremities (fingers of hands) in a person as reaction to the dosed physical activity is shown in change of parameters of quasiattractors of characteristics of a tremor. Dynamics of increase in volumes of quasiattractors of a vector of organism state in the unexercised students is revealed. The new technique of research of a control system by movements of a person by means of the analysis of characteristics of a tremor of an extremity in the conditions of physical activity is stated. Practical possibility of application of the method of multidimensional phase spaces of involuntary micro-movement in the assessment of reaction of neuromuscular system of the person on dynamic physical activity is shown. As a measure of state of human neuromuscular system (to loading and after loading) the authors use the quasiattractors of movement of state vector of system in two-dimensional phase space of states.

Состояние функциональных систем организма человека по данным математического моделирования возрастных особенностей

In this paper the relevance of the study of age features of the organism on the basis of modern biophysical approaches and mathematical modeling is justified. The study purpose was to establish the patterns of behavior parameters of quasi-attractors of cardiovascular system in the pupils of the Surgut schools in the multidimensional phase space of states. The results of monitoring surveys in 2038 persons with the use conventional and new synergetic approaches were used and treated mathematically. The importance of mathematical modeling for obtaining objective information proved. It is established that there is a predominance of activity of the parasympathetic nervous system, regardless of the time of year and profile of education, more expressed age stability body systems in the pupils of gymnasium compared with a secondary school. The authors have identified nine times greater severity of seasonal changes of the vegetative-vascular regulation in the pupils of secondary school in comparison with the pupils of gymnasium on the basis of the dynamics of their quasi-attractors.

Collisional relaxation: Landau versus Dougherty operator

A detailed comparison between the Landau and the Dougherty collision operators has been performed by means of Eulerian simulations, in the case of relaxation toward equilibrium of a spatially homogeneous field-free plasma in three-dimensional velocity space. Even though the form of the two collisional operators is evidently different, we found that the collisional evolution of the relevant moments of the particle distribution function (temperature and entropy) are similar in the two cases, once an ‘ad hoc’ time rescaling procedure has been performed. The Dougherty operator is a nonlinear differential operator of the Fokker-Planck type and requires a significantly lighter computational effort with respect to the complete Landau integral; this makes self-consistent simulations of plasmas in presence of collisions affordable, even in the multi-dimensional phase space geometry.

Возрастная эволюция организма человека как движение квазиаттракторов

Today the formalization of the description of the evolving system doesn’t exist in biology. But if a biosystem is described by a state vector x=x(t)=(x1, x2, …, xm)T in multidimensional phase space, notions of speed and acceleration for the description of quasi-attractor’s motion can be introduced. Vector x(t) moves constantly and chaotically inside the quasi-attractor, i.e. dx/dt≠0 is constant. With age these quasi-attractors show translational motion in phase space for which the model as an dx/dt=(a-bx)x is created and speed V=dx/dt and acceleration a=dV/dt are determined for evolution of biosystems. The current paper presents concrete examples of age-related changes of quasi-attractor’s parameters (two-dimensional phase space) that should be considered as an evolution of vector of cardiorespiratory system in six-dimensional phase space. Models of such dynamics are discussed according to quasi-attractor’s parameters that allow to calculating speed and acceleration of evolution in some integrative values.

Defining the Flora Family: Orbital properties, reflectance properties and age

The Flora family resides in the densely populated inner main belt, bounded in semimajor axis by the ν6 secular resonance and the Jupiter 3:1 mean motion resonance. The presence of several large families that overlap dynamically with the Floras (e.g., the Vesta, Baptistina, and Nysa-Polana families), and the removal of a significant fraction of Floras via the nearby ν6 resonance complicates the Flora family’s distinction in both proper orbital elements and reflectance properties. Here we use orbital information from the Asteroids Dynamic Site (AstDyS), color information from the Sloan Digital Sky Survey (SDSS), and albedo information from the Wide-field Infrared Survey Explorer (WISE) to obtain the median orbital and reflectance properties of the Floras by sampling the core of the family in multidimensional phase space. We find the median Flora SDSS colors to be a∗=0.126±0.007 and i-z=-0.037±0.007; the median Flora albedo is pV=0.291±0.012. These properties allow us to define ranges for the Flora family in orbital and reflectance properties, as required for a detailed dynamical study. We use the young Karin family, for which we have an age determined via direct backward integration of members’ orbits, to calibrate the Yarkovsky drift rates for the Flora family without having to estimate the Floras’ material properties. The size-dependent dispersion of the Flora members in semimajor axis (the “V” plot) then yields an age for the family of 950-170+200My, with the uncertainty dominated by the uncertainty in the material properties of the family members (e.g., density and surface thermal properties). We discuss the effects on our age estimate of two independent processes that both introduce obliquity variations among the family members on short (My) timescales: (1) the capture of Flora members in spin–orbit resonance, and (2) YORP-driven obliquity variation through YORP cycles. Accounting for these effects does not significantly change this age determination.