Time Space Complexity Research Articles

Genetic electromagnetism-like mechanism based power system optimization research

To solve the problem of energy conservation with power system functioning, we researched intensively into the theory about hydrothermal power system energy-saving and the single-objective, multi-objective energy- saving regulation model building and optimizing approaches in this paper, surrounding the joint optimal regulation on hydrothermal power systems, in response to the complex space-time coupling between hydrothermal power systems with cascaded hydropower station, with a view to the rational and efficient utilization of hydropower resources and the saving of such non-renewable energy as coal. By building the compatibility conditions for hydropower station operation and the dynamic mathematical model of discarded water, a dynamic generating flow rate limit based optimal single-objective energy-saving regulation mathematical model for hydrothermal power systems is proposed. In response to the strong nonlinearity of built model, a genetic electromagnetism-like mechanism based energy-saving regulation model solution was proposed. This experimental study suggests that the genetic electromagnetism-like mechanism works in solving strongly nonlinear optimization problems. Thereby, power complemented with thermal power is an effective means to promote the power system efficiency and energy efficiency and to save non-renewable energy.

Explanation of Rotation Curves in Galaxies and Clusters of them, by Generalization of Schwarzschild Metric and Combination with MOND, eliminating Dark Matter

Schwarzschild Metric is the first and the most important solution of Einstein vacuum field equations. This is associated with Lorentz metric of flat spacetime and produces the relativistic potential (Φ) and the field strength (g) outside a spherically symmetric mass or a non-rotating black hole. It has many applications such as gravitational red shift, the precession of Mercury’s orbit, Shapiro time delay etc. However, it is inefficient to explain the rotation curves in large galaxies and clusters of them, causing the necessity for dark matter. On the other hand, Modified Newtonian Dynamics (MOND) has already explained these rotation curves in many cases, using suitable interpolating function (μ) in Milgrom’s Law. In this presentation, we initially produce a Generalized Schwarzschild potential and the corresponding Metric of spacetime, in order to be in accordance with any isotropic metric of flat spacetime (including Galilean Metric of spacetime which is associated with Galilean Transformation of spacetime). From this Generalized Schwarzschild potential (Φ), we calculate the corresponding field strength (g), which is associated with the interpolating function (μ). In this way, a new relativistic potential is obtained (let us call 2nd Generalized Schwarzschild potential) which describes the gravitational interaction at any distance and for any metric of flat spacetime. Thus, not only the necessity for Dark Matter is eliminated, but also MOND becomes a pure Relativistic Theory of Gravitational Interaction. Then, we pass to the case of flat spacetime with Lorentz metric (Minkowski space), because the experimental data have been extracted using the Relativistic Doppler Shift and the gravitational red shift of Classic Relativity (CR). Thus, we Explain the Rotation Curves in Galaxies (e.g. NGC 3198) and Clusters of them as well as the Solar system, eliminating Dark Matter. This relativistic potential and the corresponding metric of spacetime have been obtained by the light of Euclidean Closed Linear Transformations of Complex Spacetime endowed with the Corresponding Metric. Of course, may also be applied by scientists who prefer the hyperbolic geometry of Classic Relativity (CR).

Ensemble Fuzzy Clustering Using Cumulative Aggregation on Random Projections

Random projection is a popular method for dimensionality reduction due to its simplicity and efficiency. In the past few years, random projection and fuzzy c-means based cluster ensemble approaches have been developed for high-dimensional data clustering. However, they require large amounts of space for storing a big affinity matrix, and incur large computation time while clustering in this affinity matrix. In this paper, we propose a new random projection, fuzzy c-means based cluster ensemble framework for high-dimensional data. Our framework uses cumulative agreement to aggregate fuzzy partitions. Fuzzy partitions of random projections are ranked using external and internal cluster validity indices. The best partition in the ranked queue is the core (or base) partition. Remaining partitions then provide cumulative inputs to the core, thus, arriving at a consensus best overall partition built from the ensemble. Experimental results with Gaussian mixture datasets and a variety of real datasets demonstrate that our approach outperforms three state-of-the-art methods in terms of accuracy and space-time complexity. Our algorithm runs one to two orders of magnitude faster than other state-of-the-arts algorithms.

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic {mathfrak{o}}^{star }(4) symmetries

We construct firstly the complete list of five quantum deformations of D = 4 complex homogeneous orthogonal Lie algebra mathfrak{o}left(4;mathbb{C}right)cong mathfrak{o}left(3;mathbb{C}right)oplus mathfrak{o}left(3;mathbb{C}right) , describing quantum rotational symmetries of four-dimensional complex space-time, in particular we provide the corresponding universal quantum R-matrices. Further applying four possible reality conditions we obtain all sixteen Hopf-algebraic quantum deformations for the real forms of mathfrak{o}left(4;mathbb{C}right) : Euclidean mathfrak{o}(4) , Lorentz mathfrak{o}left(3, 1right) , Kleinian mathfrak{o}left(2, 2right) and quaternionic {mathfrak{o}}^{star }(4) . For mathfrak{o}left(3, 1right) we only recall well-known results obtained previously by the authors, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) as well as for the complex Lie algebra mathfrak{o}left(4;mathbb{C}right) we present new results.

Magnetohydrodynamic equations (MHD) generation code

A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.

Human mobility semantics analysis: a probabilistic and scalable approach

The popularity of smart mobile devices generated data, e.g., check-ins and geo-tagged status, offers new opportunity for better understanding human mobility regularity. Existing works on this problem usually resort to explicit frequency statistics models, such as association rules and sequential patterns, and rely on Euclidean distance to measure the spatial dependence. However, the noisiness and uncertainty natures of geospatial data hinder these methods’ application on human mobility in robust and intuitive way. Moreover, the mobility spatial data volume and accumulation speed challenge the traditional methods in efficiency, scalability, and time-space complexity aspects. In this context, we leverage full Bayesian sequential modeling, to revisit mobility regularity discovery from high level probabilistic semantic knowledge perspective, and to alleviate the inherent in mobility modeling and geo-data noisiness induced uncertainty. Specifically, the mobility semantics is embodied by virtue of underlying geospatial topics and topical transitions of mobility trajectories. A classic variational inference is derived to estimate posterior and predictive probabilities, and furthermore, the stochastic optimization is utilized to mitigate the costly computational overhead in message passing subroutine. The experimental results confirm that our approach not only reasonably recognizes the geospatial mobility semantic patterns, but also scales up well to embrace the massive spatial-temporal human mobility activity data.

Space–Time Evolution of the Low- and High-Frequency Intraseasonal Modes of the Indian Summer Monsoon

AbstractIn this study, rainfall estimates by the Tropical Rainfall Measuring Mission are used to understand the spatiotemporal structures of convection in the intraseasonal time scale and their intensity during the boreal summer over South Asia. A quantitative analysis on how these intraseasonal modes modulate the central Indian rainfall is also provided.Two dominant modes of variability with periodicities of 10–20 and 20–60 days are found, with the latter strongly modulated by sea surface temperature. The 20–60-day mode shows northward propagation from the equatorial Indian Ocean linked with eastward-propagating modes of convective systems over the tropics. The 10–20-day mode shows a complex space–time structure with a northwestward-propagating anomalous pattern emanating from the Indonesian coast. This pattern is found to be interacting with a structure emerging from higher latitudes propagating southeastward, the development of which is attributed to the vertical shear of the zonal wind. The two modes exhibit profound variability in their intensity on the interannual time scale and they contribute a comparable amount to the daily rainfall variability in a season. The intensity of the 20–60 and 10–20-day modes shows a significantly strong inverse and direct relationship with the all-India June–September rainfall, respectively.This study establishes that the probability of the occurrence of substantial rainfall over central India increases significantly if the two intraseasonal modes simultaneously exhibit positive anomalies over the region. The results presented in this paper will provide a pathway to understand, using observations and numerical model simulations, intraseasonal variability and its relative contribution to the Indian summer monsoon. It can also be used for model evaluation.

A spatiotemporal dengue fever early warning model accounting for nonlinear associations with hydrological factors: a Bayesian maximum entropy approach

Dengue fever is identified as one of the most widespread vector-borne diseases in the world. In the last decade, high incidence of dengue fever has been observed in southern Taiwan on an annual basis. There is an urgent need to develop a dengue fever early warning model for the area. Previous studies showed that dengue fever transmission has complex space–time dynamics highly depending upon the activities of human and vectors and their interactions, as well as hydrological processes. This study developed a 1-week-ahead dengue fever warning system in southern Taiwan considering weekly-based nonlinear temporal lagged associations between dengue cases and hydrological factors across space and time by investigating the disease database during 1998–2011. The proposed model is based on an integration of distributed lag nonlinear model and spatiotemporal dependence structure under an epistemic framework of Bayesian maximum entropy method. This study identified that minimum temperature and maximum 24-h rainfall are the most significant to dengue fever incidences. Their associations to dengue fever risks are presented with respect to both hydrological measurement levels and temporal lags. A nested spatiotemporal covariance of transmissions was used to account for the disease diffusion across space and time. Results show that the proposed approach can provide early warnings of the dengue fever occurrences in both initial and peak epidemic stages in 2012, and obtain the spatiotemporal distribution of dengue fever epidemics. These features can be useful for local governmental agencies to seek more effective strategies for dengue fever prevention and control.

Euclidean Closed Linear Transformations of Complex Spacetime and generally of Complex Spaces of dimension four endowed with the Same or Different Metric

Relativity Theory and the corresponding Relativistic Quantum Mechanics are the fundamental theories of physics. Special Relativity (SR) relates the frames of Relativistic Inertial observers (RIOs), through Linear Spacetime Transformation (LSTT) of linear spacetime. Classic Special Relativity uses real spacetime endowed with Lorentz metric and the frames of two RIOs with parallel spatial axes are always related through Lorentz Boost (LB). This cancels the transitive attribute in parallelism, when three RIOs are related, because LB is not closed transformation, causing Thomas Rotation. In this presentation, we consider closed LSTT of Complex Spacetime, so there is no necessity for spatial axes rotation and all the frames are chosen having parallel spatial axes. The solution is expressed by a 4x4 matrix (Λ) containing components of the complex velocity of one Observer wrt another and two functions depended by the metric of Spacetime. Demanding isometric transformation, it emerges a class of metrics that are in accordance with the closed LSTT and the transformation matrix contains one parameter ω depended by the metric of Spacetime. In case that we relate RIOs with steady metric, it emerges one steady number (ωI) depended by the metric of Spacetime of the specific SR. If ωI is an imaginary number, the elements of the Λ are complex numbers, so the corresponding spacetime is necessarily complex and there exists real Universal Speed (UI). The specific value ωI=±i gives Vossos transformation (VT) endowed with Lorentz metric (for gii=1) of complex spacetime and invariant spacetime interval (or equivalently invariant speed of light in vacuum), which produce the theory of Euclidean Complex Relativistic Mechanics (ECRMs). If ωI is a real number (ωI#0) the elements of the Λ are real numbers, so the corresponding spacetime is real, but there exist imaginary UI. The specific value ωI=0 gives Galileo Transformation (GT) with the invariant time, in which any other closed LSTT is reduced, if one RIO has small velocity wrt another RIO. Thus, we have infinite number of closed LSTTs, each one with the corresponding SR theory. In case that we relate accelerated observers with variable metric of spacetime, we have the case of General Relativity (GR). For being that clear, we produce a generalized Schwarzschild metric, which is in accordance with any SR based on this closed complex LSTT and Einstein equations. The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any linear space of dimension four endowed with steady or variable metric, whose elements (four- vectors) have spatial part (vector) with Euclidean metric.

The electron spin and spin magnetic moment in dual-4 d space-time Quantum mechanics

In dual-four-dimensional space-time quantum mechanics, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c，and frequency is ν0=E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1=ħ/mc，and frequency is ν1=E1/h. m0 and m is the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.

Effects of a scalar scaling field on quantum mechanics

This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces, both as structures, at different space time locations. Complex number structures and vector spaces at each location, are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. The lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region there are no restrictions on the field gradient.

Quantum deformations of D = 4 Euclidean, Lorentz, Kleinian and quaternionico⋆(4)symmetries in unifiedo(4;C)setting

We employ new calculational technique and present complete list of classical r-matrices for D=4 complex homogeneous orthogonal Lie algebra o(4;C), the rotational symmetry of four-dimensional complex space–time. Further applying reality conditions we obtain the classical r-matrices for all possible real forms of o(4;C): Euclidean o(4), Lorentz o(3,1), Kleinian o(2,2) and quaternionic o⋆(4) Lie algebras. For o(3,1) we get known four classical D=4 Lorentz r-matrices, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) we provide new results and mention some applications.

The complexity of interaction

In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and scheduled types, we certify concrete time, space and space-time complexity bounds for both sequential and parallel reductions of interaction-net programs by suitably assigning complexity potentials to typed nodes. The relevance of this approach is illustrated on archetypal programming examples. The provided analysis is precise, compositional and is, in theory, not restricted to particular complexity classes.

双4维时空量子力学描述中电子自旋、自旋磁矩

双4维时空量子力学描述中，微观客体的自旋是场物质球自身的转动。在自身参考系，场物质球的半径由静态康普顿动量m0c定义：R0=ħ/m0c，转动频率为：E0= hν0；在运动参考系，场物质球的半径由动态康普顿动量mc定义：R1= ħ/mc，转动频率为：E1= hν1。m，m0是微观客体的动、静质量。电子自旋S及自旋磁矩μs都可以通过场物质球模型来计算。若自身参考系就在复数空间，在闵氏4维时空观察转动场物质球的运动，生成双4维复数时空，形成场物质的波动运动，它就是德布罗意物质波。 In dual-four-dimensional quantum mechanism, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c, and frequency is ν0= E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1= ħ/mc, and frequency is ν1= E1/h. m0 and m are the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment μs both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four-dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.

Quantum Forces in a Relativistic Entangled "Space-Time" State in Complex Hamiltonian Dynamics

Based on complex quantum Hamilton-Jacobi theory and its natural complex spacetime configuration, we realized new states for both positive and negative values of energy and momentum, and we discuss this complex configuration in a relativistic entangled "space-time" state and the resultant 12 extra wave functions than the four solutions of Dirac equation for a free particle. Accordingly, we calculate the quantum forces between particles and antiparticles in a relativistic entangled "space-time" state.

Research of Dependent Tasks Scheduling Algorithm in Cloud Computing Environments

With the dependent relationship of tasks submitted by the users in the model of Cloud computing resources scheduling become stronger and stronger, it is worthy of studying how to optimize the scheduling strategy and algorithm to meet the different demands of the users, and it is absolutely importance. In this article, the author analysed the factors that will affect the entire task-sets execution firstly. Then proposed a new tasks scheduling model based on the original priority calculation method and the idea of redundant duplication of tasks. In the phase of tasks scheduling in the model, the execution results of all parent tasks of the subtask that being executing are considered. The costs of communication between task-sets has reduced by the method of redundant duplication of tasks, so that the execution time of some subtasks share be advanced, and the entire execution efficiency of task-sets can be increased. At the end of this article, from the comparative results of the space-time complexity of contrast algorithms and the algorithm proposed by the author during the process of processing dependent tasks, we can find that subtasks execution time can be advanced and the complete time of the whole task-set can be cut down to a certain extent

Vector graphics animation with time-varying topology

We introduce the Vector Animation Complex (VAC), a novel data structure for vector graphics animation, designed to support the modeling of time-continuous topological events. This allows features of a connected drawing to merge, split, appear, or disappear at desired times via keyframes that introduce the desired topological change. Because the resulting space-time complex directly captures the time-varying topological structure, features are readily edited in both space and time in a way that reflects the intent of the drawing. A formal description of the data structure is provided, along with topological and geometric invariants. We illustrate our modeling paradigm with experimental results on various examples.

A generalized Schrödinger equation via a complex Lagrangian of electrodynamics

In this paper we give a generalized form of the Schrödinger equation in the relativistic case, which contains a generalization of the Klein-Gordon equation. By complex Legendre transformation, the complex Lagrangian of electrodynamics produces a complex relativistic Hamiltonian H of electrodynamics, on the holomorphic cotangent bundle T′* M. By a special quantization process, a relativistic time dependent Schrödinger equation, in the adapted frames of (T′* M, H) is obtained. This generalized Schrödinger equation can be expressed with respect to the Laplace operator of the complex Hamilton space (T′*M, H). Finally, under some additional conditions on the proper time s of the complex space-time M and the time parameter t along the quantum state, by the method of separation of variables, we obtain two classes of solutions for the Schrödinger equation, one for the weakly gravitational complex curved space M, and the second in the complex space-time with Schwarzschild metric.

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space-time) states, the original version of EPR paradox can be discussed and the correct answer can be verified based on the strong rooted complex quantum Hamilton-Jacobi theory [2-27] and as another example we can use the negative energy states, to remove the Klein's paradox without the need of any further explanations or justifications like backwardly moving electrons. Finally, comparing the two approaches, we can point out to the existence of a connection between quantum Hamiltonian dynamics, standard quantum field theory, and Krein space quantization [28-43].

Partial synchronization and partial amplitude death in mesoscale network motifs.

We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of partial amplitude death and partial synchronization and are found to exist in large variety for all undirected networks of up to 5 nodes. The underlying concept is proved to be robust with respect to frequency mismatch and can also be extended to larger networks. In addition it directly links the stability of complete in-phase synchronization to only a small subset of topological eigenvalues of a network.