Orbit Weighting Scheme in the Context of Vector Space Information Retrieval

This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schemes like tf-idf and BM25.These conventional methods often struggle with accurately capturing document relevance,leading to inefficiencies in both retrieval performance and index size management.OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space,emphasizing term relationships and distribution patterns overlooked by existing models.Our research focuses on evaluating OWS’s impact on model accuracy using Information Retrieval metrics like Recall,Precision,InterpolatedAverage Precision(IAP),andMeanAverage Precision(MAP).Additionally,we assessOWS’s effectiveness in reducing the inverted index size,crucial for model efficiency.We compare OWS-based retrieval models against others using different schemes,including tf-idf variations and BM25Delta.Results reveal OWS’s superiority,achieving a 54%Recall and 81%MAP,and a notable 38%reduction in the inverted index size.This highlights OWS’s potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS’s capabilities in information retrieval methodologies.

Motion and Special Relativity in Complex Spaces

A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M4 model for special relativity (SR) to complex C4 space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C4 one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M4 real space-time can be recovered. This means all the SR theory is preserved in the real subspace M4 of the space-time C4 while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C4 model to the C3 “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C3 alone. On the other hand, the complex time defined within the C3 theory is interpreted and modeled by the single separate C1 complex plane. The possibility for application of the C3 model to quantum mechanics is suggested. As such, the model C3 seems to have unifying abilities for application to different physical theories.

Word Embeddings and Semantic Spaces in Natural Language Processing

One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse of dimensionality, a problem which plagues NLP in general given that the feature set for learning starts as a function of the size of the language in question, upwards of hundreds of thousands of terms typically. As such, much of the research and development in NLP in the last two decades has been in finding and optimizing solutions to this problem, to feature selection in NLP effectively. This paper looks at the development of these various techniques, leveraging a variety of statistical methods which rest on linguistic theories that were advanced in the middle of the last century, namely the distributional hypothesis which suggests that words that are found in similar contexts generally have similar meanings. In this survey paper we look at the development of some of the most popular of these techniques from a mathematical as well as data structure perspective, from Latent Semantic Analysis to Vector Space Models to their more modern variants which are typically referred to as word embeddings. In this review of algoriths such as Word2Vec, GloVe, ELMo and BERT, we explore the idea of semantic spaces more generally beyond applicability to NLP.

Meteoroid and Space Debris Risk Assessment for Satellites Orbiting the Earth/Moon

Interplanetary meteoroids and space debris can impact satellites orbiting the Earth or spacecraft traveling to the Moon.Targeting China Space Station(CSS),7 satellites selected from the constellation of Beidou Navigation Satellite System Phase III(BDS-3),and 3 spacecraft orbiting the Moon,we have adopted in the paper the Meteoroid Engineering Model 3,Divine-Staubach meteoroid environment model,and Jenniskens-McBride meteoroid steam model to analyze the meteoroid environment with the mass range of 10–6~10 g.Orbital Debris Engineering Model 3.1 space debris model is used to analyze the orbital debris environment faced by these satellites.The flux of space debris with a size larger than 100μm is compared with that of the meteoroids.The results show that the space debris flux encountered by China Space Station is much higher than that of the meteoroids with sizes in the above range.And quite the opposite,the meteoroids flux impacting the 7 satellites from the BDS-3 is higher.Upon adopting the double-layer Whipple protection measure,the catastrophic collision flux of these satellites encountering meteoroids is about 10–6 times of that without protection,or even less,implying that the Whipple protection effectively guarantees the safety of the satellites in orbit.Besides,it is also found that the flux of the high-density meteoroid population encountered by each satellite is greater than that of the low-density population,whereas the impact velocity is lower for each satellite.These results can aid the orbit selection and the protection design for satellites and spacecraft.

State Space Modeling and Implementation of a New Transformer Based Multilevel Inverter Topology with Reduced Switch Count

This paper presents a new transformer based multilevel inverter, with a novel pulse width modulation scheme to achieve seven-level inverter output voltage. The proposed inverter switching pattern consists of three fundamental frequency sinusoidal reference signals with an offset value, and one high frequency triangular carrier signal. This switching scheme has been implemented using an 8-bit Xilinx SPARTAN-3E field programmable gate array based controller. In addition, the state space model of the proposed inverter is developed. The significant features of the proposed topology are: reduction of the power switch count and the gate drive power supply unit, the provision of a galvanic isolation between load and sources by a centre tap transformer. An exhaustive comparison has been made of the existing multilevel inverter topologies and the proposed topology. The performances of the proposed topology with resistive, resistive-inductive loads are simulated in a MATLAB environment and validated experimentally on a laboratory prototype.

Traffic condition estimation with pre-selection space time model

A pre-selection space time model was proposed to estimate the traffic condition at poor-data-detector,especially non-detector locations.The space time model is better to integrate the spatial and temporal information comprehensibly.Firstly,the influencing factors of the "cause nodes" were studied,and then the pre-selection "cause nodes" procedure which utilizes the Pearson correlation coefficient to evaluate the relevancy of the traffic data was introduced.Finally,only the most relevant data were collected to compose the space time model.The experimental results with the actual data demonstrate that the model performs better than other three models.

Locating Error Considering Dimensional Errors Modeling for Multistation Manufacturing System

Multistation machining process is widely applied in contemporary manufacturing environment. Modeling of variation propagation in multistation machining process is one of the most important research scenarios. Due to the existence of multiple variation streams, it is challenging to model and analyze variation propagation in a multi-station system. Current approaches to error modeling for multistation machining process are not explicit enough for error control and ensuring final product quality. In this paper, a mathematic model to depict the part dimensional variation of the complex multistation manufacturing process is formulated. A linear state space dimensional error propagation equation is established through kinematics analysis of the influence of locating parameter variations and locating datum variations on dimensional errors, so the dimensional error accumulation and transformation within the multistation process are quantitatively described. A systematic procedure to build the model is presented, which enhances the way to determine the variation sources in complex machining systems. A simple two-dimensional example is used to illustrate the proposed procedures. Finally, an industrial case of multistation machining part in a manufacturing shop is given to testify the validation and practicability of the method. The proposed analytical model is essential to quality control and improvement for multistation systems in machining quality forecasting and design optimization.

Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

Design Criterion for Fixture Layout Based on the State Space Model in M ultistation Assembly Processes

The fixture layout is crucial to assure the product quality in a multistation assembly process （MAP）. A well-designed fixture layout will make the final product＇s variability be insensitive to the fixture variation inputs. As the basis of the fixture layout design, the design criterion plays an important role in the effectiveness of a solution and the optimization efficiency. In this paper, an effective and efficient design criterion is proposed for the fixture layout with a fixed reference point （FRP） in an MAP. First of all, a state space model for the individual port＇s variation propagation and accumulation is developed, which is the mathematical foundation of the proposed criterion. Then, based on this model, a novel design criterion used to evaluate the performance of the fixture layout is proposed for the fixture layout with an FRP. Finally, a method extracted from the proposed design criterion is developed for quick fixture layout design. A four-station assembly process is used to validate the effectiveness and efficiency of the proposed models and methods.

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on singleoscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.

Quantum-dot Semiconductor Optical Amplifiers in State Space Model

A state space model(SSM) is derived for quantum-dot semiconductor optical amplifiers(QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA′s static and dynamic characteristics with high accuracy.

The rough representation and measurement of quotient structure in algebraic quotient space model

Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.

Space station short-term mission planning using ontology modelling and time iteration

This paper studies the problem of the space station short-term mission planning, which aims to allocate the executing time of missions effectively, schedule the corresponding resources reasonably and arrange the time of the astronauts properly. A domain model is developed by using the ontology theory to describe the concepts, constraints and relations of the planning domain formally, abstractly and normatively. A method based on time iteration is adopted to solve the short-term planning problem. Meanwhile, the resolving strategies are proposed to resolve different kinds of conflicts induced by the constraints of power, heat, resource, astronaut and relationship. The proposed approach is evaluated in a test case with fifteen missions, thirteen resources and three astronauts. The results show that the developed domain ontology model is reasonable, and the time iteration method using the proposed resolving strategies can successfully obtain the plan satisfying all considered constraints.

A Generalized State Space Average Model for Parallel DC-to-DC Converters

The high potentiality of integrating renewable energies,such as photovoltaic,into a modern electrical microgrid system,using DC-to-DC converters,raises some issues associated with controller loop design and system stability.The generalized state space average model(GSSAM)concept was consequently introduced to design a DC-to-DC converter controller in order to evaluate DC-to-DC converter performance and to conduct stability studies.This paper presents a GSSAM for parallel DC-to-DC converters,namely:buck,boost,and buck-boost converters.The rationale of this study is that modern electrical systems,such as DC networks,hybrid microgrids,and electric ships,are formed by parallel DC-to-DC converters with separate DC input sources.Therefore,this paper proposes a GSSAM for any number of parallel DC-to-DC converters.The proposed GSSAM is validated and investigated in a time-domain simulation environment,namely a MATLAB/SIMULINK.The study compares the steady-state,transient,and oscillatory performance of the state-space average model with a fully detailed switching model.

Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models

This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a non-linear model. On the basis of the error definition,this paper puts forward a new adjustment criterion, SGPE.Last,this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.

Modeling and Analysis of Pulse Skip Modulation

The state space average model and the large signal models of Pulse Skip Modulation （PSM） mode are given in this paper. Farther more, based on these models and simulations of PSM converter circuits, the analysis of the characteristics of PSM converter is described in this paper, of which include efficiency, frequency spectrum analysis, output voltage ripple, response speed and interference rejection capability. Compared with PWM control mode, PSM converter has high efficiency, especially with fight loads, quick response, good interference rejection and good EMC characteristic. Improved PSM slightly, it could be a kind of good independent regulating mode during the whole operating process for a DC-DC converter. Finally, some experimental results are also presented in this paper.

Deviation Diagnosis and Analysis of Hull Flat Block Assembly Based on a State Space Model

Dimensional control is one of the most important challenges in the shipbuilding industry. In order to predict assembly dimensional variation in hull flat block construction, a variation stream model based on state space was presented in this paper which can be further applied to accuracy control in shipbuilding. Part accumulative error, locating error, and welding deformation were taken into consideration in this model, and variation propagation mechanisms and the accumulative rule in the assembly process were analyzed. Then, a model was developed to describe the variation propagation throughout the assembly process. Finally, an example of fiat block construction from an actual shipyard was given. The result shows that this method is effective and useful.

A Novel Formal Theory for Security Protocol Analysis of Denial of Service Based on Extended Strand Space Model

Denial of Service Distributed Denial of Service （DOS） attack, especially （DDoS） attack, is one of the greatest threats to Internet. Much research has been done for it by now, however, it is always concentrated in the behaviors of the network and can not deal with the problem exactly. In this paper, we start from the security of the protocol, then we propose a novel theory for security protocol analysis of Denial of Service in order to deal with the DoS attack. We first introduce the conception of weighted graph to extend the strand space model, then we extend the penetrator model and define the goal of anti-DoS attack through the conception of the DoS-stop protocol, finally we propose two kinds of DoS test model and erect the novel formal theory for security protocol analysis of Denial of Service. Our new formal theory is applied in two example protocols. It is proved that the Internet key exchange （IKE） easily suffers from the DoS attacks, and the efficient DoS- resistant secure key exchange protocol （JFK） is resistant against DoS attack for the server, respectively.

Bilateral shear strength of rectangular frame column based on simplified space truss-arch model

To investigate the bilateral shear strength of rectangular frame column subjected to oblique horizontal load, we presented a simplified space truss-arch model developed from unilateral truss-arch model. Main parameters in the new model were the cross-sectional area, transverse reinforcement raito, axial load, and material strength of the column. The reduction coefficient of concrete sterength owing to the severe cracking of column was also introduced in the model. Finally, 14 specimens under oblique horizontal load were tested to verified the feasibility and applicability of the space truss-arch model.

Description of the Nature Using the Models Developed in Euclidean Space

In elucidating the laws of matter motion, it is necessary also to take into account the subjective human possibilities to think and construct models. These possibilities are restricted to the framework of Euclidean space. No problems could arise during the development of the laws of classical science. However, it was established later on that in some areas it was rather difficult to describe the motion of the matter in terms of Euclidean models. In these cases, researchers either introduce a space of higher dimensionality, use complex numbers, or make some deformations of our habitual Euclidean space. Those were exactly the cases for which the pseudo-Euclidean, Hilbertian, reciprocal, micro-Euclidean and other spaces were proposed. Humans are able to think only in terms of Euclidean space. So, to provide a correct description of unusual motion of matter, the necessity arises to transform the information into the understandable Euclidean space. The operators suitable for these purposes are Lorentz transformations, Schrodinger equation, the integral transformations of Fourier and Weierstrass, etc. The features of information transformations between different spaces are illustrated with the examples from the areas of X-ray structural analysis and quantum physics.