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.

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.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

INTERVAL ADJUSTABLE ENTROPY ALGORITHM FOR A CLASS OF UNCONSTRAINED DISCRETE MINIMAX PROBLEMS

In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient.

Interval Algorithm for Inequality Constrained Discrete Minimax Problems

An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form this problem to unconstrained optimization. Second, the interval extensions of the penalty functions and the test rules of region deletion are discussed. At last, we design an interval algorithm with the bisection rule of Moore. The algorithm provides bounds on both the minimax value and the localization of the minimax points of the problem. Numerical results show that algorithm is reliable and efficiency.

Moved Score Confidence Intervals for Means of Discrete Distributions

Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means;for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.

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.

Risk of bias and reporting practices in studies comparing VO2max responses to sprint interval vs.continuous training:A systematic review and meta-analysis

Background:It remains unclear whether studies comparing _(max)imal oxygen uptake(VO_(2max))response to sprint interval training(SIT)vs.moderate-intensity continuous training(MICT)are associated with a high risk of bias and poor reporting quality.The purpose of this study was to evaluate the risk of bias and quality of reporting in studies comparing changes in VO_(2max) between SIT and MICT.Methods:We conducted a comprehensive literature search of 4 major databases:AMED,CINAHL,EMBASE,and MEDLINE.Studies were excluded if participants were not healthy adult humans or if training protocols were unsupervised,lasted less than 2 weeks,or utilized mixed exercise modalities.We used the Cochrane Collaboration tool and the CONSORT checklist for non-pharmacological trials to evaluate the risk of bias and reporting quality,respectively.Results:Twenty-eight studies with 30 comparisons(3 studies included 2 SIT groups)were included in our meta-analysis(n=360 SIT participants:body mass index(BMI)=25.9±3.7 kg/m^(2),baseline VO_(2max)=37.9±8.0 mL/kg/min;n=359 MICT participants:BMI=25.5±3.8 kg/m^(2),baseline VO_(2max)=38.3±8.0 mL/kg/min;all mean±SD).All studies had an unclear risk of bias and poor reporting quality.Conclusion:Although we observed a lack of superiority between SIT and MICT for improving VO_(2max)(weighted Hedge’s g=0.004,95%con-fidence interval(95%CI):-0.08 to 0.07),the overall unclear risk of bias calls the validity of this conclusion into question.Future studies using robust study designs are needed to interrogate the possibility that SIT and MICT result in similar changes in VO_(2max).

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.

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.

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

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.

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.