Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme

In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme(MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol.We conduct a comprehensive analysis of the improved protocol's performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.

Book Announcement of L. Celentano, Robust Tracking Controllers Design with Generic References for Continuous and Discrete Uncertain Linear SISO Systems, LAP LAMBERT Academic Publishing, 2012

In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.

Techniques of Discrete Function Transfers into Continuous Function in Practice

One confusing question over a long period of time is how transfer the discrete function transfers into continuous function. Recently the issue has been resolved but some details of the transformation process will be introduced in the paper. The correlation coefficients of 100,000 values are established from the two groups of data with the range between -1 and 1, creating a histogram from these correlation coefficient values known as “the probability mass function.” The coefficient values are brought into the discrete distribution function, so that transfers into the discrete cumulative function, next converted into a continuous cumulative function, next which is differentiated to get the density function, so that it is easy to being research analysis. A model will be established during the process of the conversion what the medium is “the least squares algorithm.” Finally, when the integral of the area within the range of the density function equals to 1, this implies that the transformation complete succeeds from the discrete function to the continuous function.

Discrete Spectra and Continuous Spectrum of the BarotropicQuasi-Geostrophic Model-A Calculation ofMeteorological Data

Atmospheric disturbances at 300 hPa are decomposed into normal modes, referred as discrete—spectrum disturbances which can propagate freely in the observed zonal mean flow, and non—modal transient disturbances, referred as continuous—spectrum disturbances which are continuously sheared and eventually absorbed by the zonal flow. It is shown that normal modes represent only a small fraction of the observed atmospheric disturbances, while continuous—spectrum disturbances represent the majority of observed disturbances, even when the basic flow is unstable. Daily variabilities of the observed continuous—spectrum disturbances are presented. They are shown to follow the results of wave—packet theory. Calculations suggest that there are abundant sources to excite continuous—spectrum disturbances in the atmosphere.

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.

Is Nature Fundamentally Continuous or Discrete, and How Can These Two Different But Very Useful Conceptions Be Fully Reconciled?

Our contention is that reality is actually analog, but at a critical limit, when the Octonian gravity condition kicks in, for a time it is made to appear discrete. This is due to an initial phase transition just at the start of the big bang. Our second consideration is that symmetry breaking models, i.e. the Higgs boson, are in themselves not appropriate or necessary for the formation of particles with mass just before Octonionic gravity which could arise in pre-Planckian physics models without a potential. Finally, the necessity of potentials for pre-Octonionic gravity physics can be circumvented via judicious use of Scherrer k essence physics.

Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk

The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.

CONTINUOUS AND DISCRETE N-CONVEX APPROXIMATIONS

We show that the best L_p-approximant to continuous functions by n-convex functions is the limit of discrete n-convex approximations.The techniques of the proof are then used to show the existence of near interpolants to discrete n-convex data by continuous n-convex functions if the data points are close.

Transitioning from Discrete to Continuous Distribution Mathematica vs. Excel —An Example

Frequencies of the repeated integers of the first n digits of e.g. π utilizing commercial software are listed. The discrete distribution is utilized to evaluate its statistical moments. The distribution is fitted with a polynomial generating a continuous replica of the former. Its statistical moments are evaluated and compared to the former. The procedure clarifies the mechanism transiting from discrete to a continuous domain. Applying Mathematica the fitted polynomial is replaced with an interpolated function with controlled smoothing factor refining the quality of the fit and its corresponding moments. Knowledge learned assists in the understanding of the standard procedure calculating moments of e.g. Maxwell-Boltzmann continuous distribution in kinetic Theory of gases.

Relative navigation for satellite formation flight using a continuous-discrete converted measurement Kalman filter

The present paper develops an approach of relative orbit determination for satellite formation flight.Inter-satellite measurements by the onboard devices of the satellite were chosen to perform this relative navigation,and the equations of relative motion expressed in the Earth Centered Inertial frame were used to eliminate the assumption of the circular reference orbit.The relative orbit estimation was achieved through a continuous-discrete converted measurement Kalman filter design,in which the measurements were transformed to the inertial frame to avoid the linearization error of the observation equation.In addition,the situation of the coarse measurement period(only microwave radar measurements are available)existing was analyzed.The numerical simulation results verify the validity of the navigation approach,and it has been proved that this approach can be applied to the formation with an elliptical reference orbit.

Robust stability test for 2-D continuous-discrete systems with interval parameters

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.

Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair

Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics.

NEW SET OF OPERATOR-VALUED BESSEL FUNCTIONS,THE HOLOMORPHIC DISCRETE SERIES AND ITS ANALYTIC CONTINUATION

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A branch-and-bound algorithm for discrete multi-factor portfolio optimization model

In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.

Gravitational Space-Time Quantization for Charged Wormholes and the Diophantine Uncertainty Relation

This research work proceeds from the assumption, which was still considered by Einstein, that the quantization of gravity does not require additional external procedures: quantum phenomena can be a consequence of the properties of the universal gravitational interaction, which maps any physical field upon the space-time geometry. Therefore, an attempt is made in this research work to reduce the quantization of physical fields in GRT to the space-time quantization. Three reasons for quantum phenomena are considered: Partition of space-time into a set of unconnected Novikov’s R- and T-domains impenetrable for light paths;the set is generated by the invariance of Einstein’s equations with respect to dual mappings;The existence of electric charge quanta of wormholes, which geometrically describe elementary particles in GRT. This gives rise to a discrete spectrum of their physical and geometric parameters governed by Diophantine equations. It is shown that the fundamental constants (electric charge, rest masses of an electron and a proton) are interconnected arithmetically;The existence of the so-called Diophantine catastrophe, when fluctuations in the values of physical constants tending to zero lead to fluctuations in the number of electric charges and the number of nucleons at the wormhole throats, which tend to infinity, so that the product of the increments of these numbers by the increment of physical constants forms a relation equivalent to the uncertainty relation in quantum mechanics. This suggests that space-time cannot but fluctuate, and, moreover, its fluctuations are bounded from below, so that all processes become chaotic, and the observables become averaged over this chaos.

Free vibration of a sagged cable with attached discrete elements

An algorithm is presented to analyze the free vibration in a system composed of a cable with discrete elements, e.g., a concentrated mass, a translational spring, and a harmonic oscillator. The vibrations in the cable are modeled and analyzed with the Lagrange multiplier formalism. Some fragments of the investigated structure are modeled with continuously distributed parameters, while the other fragments of the structure are modeled with discrete elements. In this case, the linear model of a cable with a small sag serves as a continuous model, while the elements, e.g., a translational spring, a concentrated mass, and a harmonic oscillator, serve as the discrete elements. The method is based on the analytical solutions in relation to the constituent elements, which, when once derived, can be used to formulate the equations describing various complex systems compatible with an actual structure. The numerical analysis shows that, the method proposed in this paper can be successfully used to select the optimal parameters of a system composed of a cable with discrete elements, e.g., to detune the frequency resonance of some structures.

Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

Mental Illness Disorder Diagnosis Using Emotion Variation Detection from Continuous English Speech

Automatic recognition of human emotions in a continuous dialog model remains challenging where a speaker’s utterance includes several sentences that may not always carry a single emotion.Limited work with standalone speech emotion recognition(SER)systems proposed for continuous speech only has been reported.In the recent decade,various effective SER systems have been proposed for discrete speech,i.e.,short speech phrases.It would be more helpful if these systems could also recognize emotions from continuous speech.However,if these systems are applied directly to test emotions from continuous speech,emotion recognition performance would not be similar to that achieved for discrete speech due to the mismatch between training data(from training speech)and testing data(from continuous speech).The problem may possibly be resolved if an existing SER system for discrete speech is enhanced.Thus,in this work the author’s existing effective SER system for multilingual and mixed-lingual discrete speech is enhanced by enriching the cepstral speech feature set with bi-spectral speech features and a unique functional set of Mel frequency cepstral coefficient features derived from a sine filter bank.Data augmentation is applied to combat skewness of the SER system toward certain emotions.Classification using random forest is performed.This enhanced SER system is used to predict emotions from continuous speech with a uniform segmentation method.Due to data scarcity,several audio samples of discrete speech from the SAVEE database that has recordings in a universal language,i.e.,English,are concatenated resulting in multi-emotional speech samples.Anger,fear,sad,and neutral emotions,which are vital during the initial investigation of mentally disordered individuals,are selected to build six categories of multi-emotional samples.Experimental results demonstrate the suitability of the proposed method for recognizing emotions from continuous speech as well as from discrete speech.

Continuous and Discrete Similarity Coefficient for Identifying Essential Proteins Using Gene Expression Data

Essential proteins play a vital role in biological processes,and the combination of gene expression profiles with Protein-Protein Interaction(PPI)networks can improve the identification of essential proteins.However,gene expression data are prone to significant fluctuations due to noise interference in topological networks.In this work,we discretized gene expression data and used the discrete similarities of the gene expression spectrum to eliminate noise fluctuation.We then proposed the Pearson Jaccard coefficient(PJC)that consisted of continuous and discrete similarities in the gene expression data.Using the graph theory as the basis,we fused the newly proposed similarity coefficient with the existing network topology prediction algorithm at each protein node to recognize essential proteins.This strategy exhibited a high recognition rate and good specificity.We validated the new similarity coefficient PJC on PPI datasets of Krogan,Gavin,and DIP of yeast species and evaluated the results by receiver operating characteristic analysis,jackknife analysis,top analysis,and accuracy analysis.Compared with that of node-based network topology centrality and fusion biological information centrality methods,the new similarity coefficient PJC showed a significantly improved prediction performance for essential proteins in DC,IC,Eigenvector centrality,subgraph centrality,betweenness centrality,closeness centrality,NC,PeC,and WDC.We also compared the PJC coefficient with other methods using the NF-PIN algorithm,which predicts proteins by constructing active PPI networks through dynamic gene expression.The experimental results proved that our newly proposed similarity coefficient PJC has superior advantages in predicting essential proteins.

The Full Potential of Continuous System Simulation Modelling

Continuous System Simulation (CSS) is a powerful way to study the behaviour of differential-algebraic equation models. Differential-algebraic equation modelling goes back to Newton and works well for models of e.g. physical systems where stochasticity plays almost no role, and where only a single attribute of an object is studied over time. However, when results from a deterministic CSS model are compared with results from a Discrete Event Simulation (DES) model, they are often inconsistent. The reasons behind this CSS-DES inconsistency are nowadays well understood. In this paper, we demonstrate that a CSS model can contain both continuous state variables (compartments) that change continuously over time and discrete state variables (also compartments) that model discrete entities and change by integer amounts. In both cases, the time-slicing method is used to advance time. Furthermore, stochasticity can and should play the same role in CSS as it does in DES. This paper first explains how a well-defined conceptual model can be stepwise transformed in a consistent way into a CSS model. These transformation steps provide insights into how to construct a consistent CSS model. In short, this is about preserving uncertainties, attributes and dynamic properties. An additional benefit of this approach is that continuous and discrete sub-models can interact within the same model, without having to combine different types of simulation languages, types of time handling and incongruent concepts. To facilitate the use and understanding of stochastic CSS, this paper is also intended to serve as a guide to performing consistent CSS modelling and simulation. Furthermore, an open source tool for collecting and analyzing the outputs from a stochastic CSS model and analyzing and presenting the results in statistical form is also developed and made available to the reader.