Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem

The k-means problem has been paid much attention for many applications. In this paper, we define the uncertain constrained k-means problem and propose a (1+ϵ)-approximate algorithm for the problem. First, a general mathematical model of the uncertain constrained k-means problem is proposed. Second, the random sampling properties of the uncertain constrained k-means problem are studied. This paper mainly studies the gap between the center of random sampling and the real center, which should be controlled within a given range with a large probability, so as to obtain the important sampling properties to solve this kind of problem. Finally, using mathematical induction, we assume that the first j−1 cluster centers are obtained, so we only need to solve the j-th center. The algorithm has the elapsed time O((1891ekϵ2)8k/ϵnd), and outputs a collection of size O((1891ekϵ2)8k/ϵn) of candidate sets including approximation centers.

A First Approach to Closeness Distributions

Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller distributions are likely to be similar to one another. In this paper we provide an information geometric approach on how to incorporate this information and see that it allows us to reinterpret some already existing models. Our proposal relies on providing a formal definition of what it means to be close. We provide an example on how this definition can be actioned for multinomial distributions. We use the results on multinomial distributions to reinterpret two already existing hierarchical models in terms of closeness distributions.

DEVELOPMENT OF INSTRUMENTAL MODULE FOR OUTWARD IRREGULAR POLISHING WITH ACTIVATING LUBRICATING-COOLING LIQUIDS (LCL )

Quality of superficial layer of details of machines, qualificatory them operating descriptions in most cases are formed at polishing. This process is characterized high thermal tension and large probability of appearance in the superficial layers of the polished details of defects as прожогов and микротрещин, reducing their operating properties. One of ways of decline of thermal tension of process of polishing and improvement of quality of the polished details are the use of rational charts of treatment and application of effective compositions of lubricating-cooling liquids (LCL). For realization of these terms the instrumental module of collapsible diamond-impregnated for the round outward polishing, using the methods of irregular treatment, is in-process worked out, providing a serve LCL in the zone of cutting and her activating in кавитационных attachments. His construction allows to improve penetration LCL in the zone of contact of diamond-impregnated with a purveyance, that results in reduction of теплонапряженности process and improvement of quality of surface at the increase of the productivity of treatment. The effect of the irregular polishing is got with admission LCL through abrasive bars and interval between them.

A Time-Interleaved Statistically-Driven Two-Step Flash ADC for High-Speed Wireline Applications

This paper presents a statistically-driven two-step flash sub-analog-to-digital converter (ADC) to construct the high-speed time-interleaved ADC in wireline communication applications. The comparators in the flash sub-ADC are divided into the large probability first stage and the small probability second stage to take advantage of the nonuniform probability distribution of the input signal. At the first step of operation, the large probability first stage is activated while the small probability second stage is suspended. If the input signal is beyond the input range of the first stage, the segment selection signal will trigger proper segment in the second stage. Feed-forward equalization is proposed to manipulate the probability distribution of the ADC input signal. A possible implementation of the proposed ADC as well as the modulation and equalization scheme is presented to comply with the IEEE 802.3ap 10[Formula: see text]G Ethernet standard. In the case of a PAM-4 pseudorandom signal, the proposed solution achieves [Formula: see text] reduction on the average number of activated comparators compared to a conventional flash ADC.

THE ABSOLUTE POSITIVE PARTIAL TRANSPOSE PROPERTY FOR RANDOM INDUCED STATES

In this paper, we first obtain an algebraic formula for the moments of a centered Wishart matrix, and apply it to obtain new convergence results in the large dimension limit when both parameters of the distribution tend to infinity at different speeds. We use this result to investigate APPT (absolute positive partial transpose) quantum states. We show that the threshold for a bipartite random induced state on Cd = Cd1 ⊗ Cd2, obtained by partial tracing a random pure state on Cd ⊗ Cs, being APPT occurs if the environmental dimension s is of order s0 = min (d1, d2)3 max (d1, d2). That is, when s ≥ Cs0, such a random induced state is APPT with large probability, while such a random states is not APPT with large probability when s ≤ cs0. Besides, we compute effectively C and c and show that it is possible to replace them by the same sharp transition constant when min (d1, d2)2 ≪ d.

Asymmetrical Gating with Application on Maneuvering Target Tracking

A new asymmetrical gate with application in target tracking is proposed. Proposed gate has asymmetric shape that has large probability of target detection in the gate and has more advantages compared with elliptical gate. The gate is defined as the region in which the tracked target is expected to exist and just observation vectors in the gate are used as target detection. An analytical method to compute optimal size of gate is proposed and recursive estimation of asymmetric parameters of gate are studied. Comparison between proposed gate and conventional elliptical gate showed the efficiency of the proposed method in maneuvering target tracking applications and simulation results showed the proficiency of the proposed method.

A Chi-Square Distribution Based Steady-State Data Judgment Criterion

The acquisition of steady-state data is the premise for optimizing the boiler combustion parameters. Assuming the measuring parameters obey the Gaussion distribution, this paper uses the large-probability distribution interval to approximate the variation range of random variable, constructs appropriate working condition matrix whose column quadratic sum approximately obeys the Chi-square distribution, and then obtains the Chi-square distribution based steady-state data judgment criterion. The judgment threshold of this criterion could be self-adaptive. This judgment criterion has been validated by an experiment.

A New Chaos Optimization Algorithm and its Application

In order to avoid blind searching before reducing the searching space of optimized variable and enhance searching efficiency in chaos optimization algorithm, a new mutative scale chaos optimization algorithm, Probability Chaos Optimization Algorithm (PCOA) was proposed. The current searching space is searched according to large probability and the origin space is searched according to small probability. Though the searching space is shrunk prematurely, the global optimal point can be found because the origin space is still searched according to small probability, which can overcome the shortcoming of losing the global optimal points owing to prematurely shrinking the searching space of the optimized variables in conventional mutative scale chaos optimization algorithm. The simulation results prove the validity of the algorithm.

A New Solution for the Return Period of a Sea Storm in Which the Largest Wave Height Exceeds a Fixed Threshold

A new analytical solution for the return period of a sea storm in which the largest wave height exceeds a fixed threshold is obtained, by applying the Boccotti’s Equivalent Triangular Storm (ETS) model. An expression is then given for the probability that a wave, which is both higher than a fixed threshold and the highest of its own storm, will occur during a sea storm with a given intensity (the storm intensity being the maximum significant wave height during the storm). In the applications it is shown that the new solution has a simpler form than the Boccotti’s original one (two integrals to solve numerically, compared with the four integrals of the Boccotti’s solution), and that they give identical results. Finally it is achieved that the extreme waves of given height H, with large probability will occur in a sea storm with maximum significant wave height Hs max close to 0.5H.