State Transition Matrix Approach Research Articles

Correlations and Fractality in Sentence-Level Sentiment Analysis Based on VADER for Literary Texts

We perform a sentence-level sentiment analysis study of different literary texts in English language. Each text is converted into a series in which the data points are the sentiment value of each sentence obtained using the sentiment analysis tool (VADER). By applying the Detrended Fluctuation Analysis (DFA) and the Higuchi Fractal Dimension (HFD) methods to these sentiment series, we find that they are monofractal with long-term correlations, which can be explained by the fact that the writing process has memory by construction, with a sentiment evolution that is self-similar. Furthermore, we discretize these series by applying a classification approach which transforms the series into a one on which each data point has only three possible values, corresponding to positive, neutral or negative sentiments. We map these three-states series to a Markov chain and investigate the transitions of sentiment from one sentence to the next, obtaining a state transition matrix for each book that provides information on the probability of transitioning between sentiments from one sentence to the next. This approach shows that there are biases towards increasing the probability of switching to neutral or positive sentences. The two approaches supplement each other, since the long-term correlation approach allows a global assessment of the sentiment of the book, while the state transition matrix approach provides local information about the sentiment evolution along the text.

Electromagnetic characterization of strong-coupled Omega-type bianisotropic metamaterials using the state transition matrix method

A feasible extraction procedure is proposed to retrieve the diagonal tensor elements of the permittivity and permeability, and the magnetoelectric coupling coefficient of Omega-type biansiotropic metamaterials (MMs). The procedure is based on the state transition matrix approach and uses non-iterative closed-form expressions between constitutive parameters and scattering (S-) parameters to achieve such determination using S-parameters for normal incidence and oblique incidence of TE and TM modes (a desirable feature from practical point of view). S-parameter simulations of a bianisotropic MM slab constructed by edge-coupled resonators are performed using a 3D electromagnetic simulator program and used to validate the proposed procedure and compare its accuracy against previously developed extraction procedures. The effects of incidence angle, S-parameters' noise, and dimensional variations (fabrication tolerances) on the extracted parameters of the examined MM slab are investigated.

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.

Orbital dispersion and Earth-impact probability analysis for fragmented asteroids

This paper describes the orbital dispersion problem for a fragmented asteroid in an elliptical orbit. The use of a state transition matrix derived from the general relative equation of motion for an elliptical orbit is emphasized in this paper. The state transition matrix is used to propagate the orbital dispersion. The Earth-impact probability is then computed to obtain a measure of the likelihood of impact with the Earth after the asteroid is fragmented with a high-energy fragmentation method. The state transition matrix approach is also compared with numerical integration approaches that use the two-body equation and the general relative equations of motion. The computational efficiency of such a state transition matrix approach is verified with accuracy equal to the numerical integration approaches. The employed state transition matrix, known as the Cochran, Lee and Jo (CLJ) state transition matrix, is also evaluated for the numerous fragments with data from the burst.

Effects of Anisotropy of Ferrite Coating On the Radiation Characteristics of a Cylindrical Conductor Excited By Elementary Sources

In this paper, radiation characteristics of an arbitrarily oriented source in an anisotropic multilayered cylindrical structure are investigated by using the state transition matrix approach. Full wave transversal field equations in spectral domain are derived for anisotropic medium in cylindrical coordinates. These expressions are formed into a set of linear first order differential equations. The solution at each layer is expressed in terms of the state transition matrices which are evaluated numerically. Fields are matched at the interfaces. Far fields are evaluated asymptotically by using the steepest descents method. Numerical results are presented for a conducting cylinder coated with an anisotropic ferrite excited by Hertzian dipole. The effects of changing the bias magnetic field of the ferrite and the other medium parameters on the radiation characteristics are examined. Beam scanning, beam splitting, pattern shaping, beamwidth adjustment and control on cross polarized component can be obtained by varying the medium parameters.

Simulation of power electronic circuits containing nonlinear inductances

Power electronic circuits which contain nonlinear inductances are described by a set of nonlinear state equations. The author presents a sampled-data model for the circuit from which a set of linear state equations can be formulated. In the sampled-data model, the nonlinear inductor is modeled by an ideal sampler, a variable gain, and a clamp. The state variables for the circuit are updated during the simulation using a three-step procedure. One step involves the solution of the linear state equations using a technique such as the state transition matrix approach. Two additional steps are employed to account for the effects of the ideal sampler, variable gain, and clamp.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simulation of power converter devices with nonlinear elements

This paper presents a technique for modeling and simulating power converters which contain nonlinear elements such as saturable inductors. Each nonlinear element is modeled by an ideal sampler, a variable gain, and a clamp. A state variable is added for each nonlinearity. A homogeneous state model is then formulated for the power converter. This state model is solved using a state transition matrix ap proach. A jump matrix J is utilized to account for the ideal sampler operations.

Simulation of AC spacecraft power systems

A technique is presented for modeling and simulating AC spacecraft power systems by combining all component models into an overall system model. Each component in the spacecraft power system is treated as a two-port network. A state model is written for each two-port network with the port voltages as the inputs. Each component state model is solved independently using the state transition matrix approach and assuming that its inputs are constant. The inputs to all components are then calculated using network analysis principles. As an example, a 20 kHz system is simulated using this approach, and the results are compared with those of a SPICE2 simulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>