Numbers Of Ones Research Articles

Twisted cubic and point-line incidence matrix in $$\mathrm {PG}(3,q)$$

We consider the structure of the point-line incidence matrix of the projective space $$\mathrm {PG}(3,q)$$ connected with orbits of points and lines under the stabilizer group of the twisted cubic. Structures of submatrices with incidences between a union of line orbits and an orbit of points are investigated. For the unions consisting of two or three line orbits, the original submatrices are split into new ones, in which the incidences are also considered. For each submatrix (apart from the ones corresponding to a special type of lines), the numbers of lines through every point and of points lying on every line are obtained. This corresponds to the numbers of ones in columns and rows of the submatrices.

Stochastic Analysis and Optimal Design of Majority Systems

Majority systems, whose correct operation usually requires a specific number of components, are ubiquitous and have been used in various critical infrastructures. To capture a deeper understanding, we consider several types of majority systems, i.e., consecutive (i.e., linear and circular ones) and symmetrical systems. Moreover, to enhance the accuracy and efficiency of reliability evaluation, stochastic analysis architectures are proposed: input signal probabilities of any distributions can be addressed efficiently with the adoption of non-Bernoulli sequences, consisting of random permutations of fixed numbers of ones and zeros. Via propagating the sequences within constructed stochastic architectures, we can derive the system reliability. Moreover, various benchmarks are analyzed through stochastic analysis, and we also compare the corresponding results with those obtained using other approaches. Though the accuracy of stochastic analysis is largely affected by the employed sequence length, an acceptable accuracy can be attained with the adoption of a reasonable sequence length. In this line, the optimal design is also investigated for different implementations.

A Stochastic Approach for the Analysis of Dynamic Fault Trees With Spare Gates Under Probabilistic Common Cause Failures

A redundant system usually consists of primary and standby modules. The so-called spare gate is extensively used to model the dynamic behavior of redundant systems in the application of dynamic fault trees (DFTs). Several methodologies have been proposed to evaluate the reliability of DFTs containing spare gates by computing the failure probability. However, either a complex analysis or significant simulation time are usually required by such an approach. Moreover, it is difficult to compute the failure probability of a system with component failures that are not exponentially distributed. Additionally, probabilistic common cause failures (PCCFs) have been widely reported, usually occurring in a statistically dependent manner. Failure to account for the effect of PCCFs overestimates the reliability of a DFT. In this paper, stochastic computational models are proposed for an efficient analysis of spare gates and PCCFs in a DFT. Using these models, a DFT with spare gates under PCCFs can be efficiently evaluated. In the proposed stochastic approach, a signal probability is encoded as a non-Bernoulli sequence of random permutations of fixed numbers of ones and zeros. The component's failure probability is not limited to an exponential distribution, thus this approach is applicable to a DFT analysis in a general case. Several case studies are evaluated to show the accuracy and efficiency of the proposed approach, compared to both an analytical approach and Monte Carlo (MC) simulation.

A Data Driven Runs Test to Identify First Order Positive Markovian Dependence

We propose a data driven test to identify first order positive Markovian dependence in a Bernoulli sequence, based on a combination of two runs tests: a well known runs test for the same purpose conditional on the numbers of ones in the sequence, and a modified runs test independent of the number of ones. We give analytic expressions for the exact distribution of the modified runs test statistic and for its power; also we built an algorithm to calculate it explicitly. To compare the power of the tests, we calculated these for some values of the proportion of ones and the success probability. We show that there are some intervals for the success probability in which the new runs test surpasses the power of the conditional test, and that the data driven test improves the power of the two runs tests, when they are considered separately.

Hierarchy and Adaptive Size Particle Swarm Optimization Algorithm for Solving Geometric Constraint Problems

Geometric constraint problems are equivalent to a series of nonlinear equations which are constraint-meeting. Thus, it is a significant issue to improve solving efficiency of the nonlinear equations. This paper proposes Hierarchy and Adaptive Size Particle Swarm Optimization (HASPSO) algorithm for solving geometric constraint problems, and its aim is to greatly improving solving efficiency. This is the basic idea: according to individual extremum, making a comparison between each particle and its members in the direct next hierarchy, then based on transmission principle, taking the best particle’s personal optimal position as its own to do subsequent iterations. Meanwhile, it depends on the natural principle of Fibonacci sequence, by simulating biological reproduction behavior, to make the algorithm adaptively expand its population size from a single individual to appropriate numbers of ones for subsequent hierarchies. If a particle still has not found precision-meeting optimal solution after a T times of iterations, then our approach judge whether the particle is new reproduced individual before the iterations, if so, it continues next T times of iterations, otherwise it produces one new individual in its direct next hierarchy, and reinitializes its position and velocity. HASPSO is able to rank population based on the form of adaptively increasing size by degrees. Theoretical Analysis and experiment show that compared with traditional particle swarm optimization (PSO) algorithm, it can make solution efficiency greatly improved and is an effective method for solving geometric constraint problems.

A molecular solution to the hitting-set problem in DNA-based supercomputing

Assume that there exists a collection C of subsets of a finite set S, and a positive integer K ⩽ ∣ S∣, and we need to know whether there is a subset S′ ⊆ S with ∣ S′∣ ⩽ K such that S′ contains at least one element of each subset in C. In other words, S′ is the subset that intersects every subset in C and is called the hitting-set. In this paper, a DNA-based algorithm is proposed to solve the small hitting-set problem. A small hitting-set is a hitting-set with the smallest K value, i.e., the hitting-set with the smallest number of elements. Furthermore, another algorithm is introduced to find the number of ones from 2 n combinations and minimum numbers of ones represents the small hitting-set since K is expected to be as small as possible. The complexity of the proposed DNA-based algorithm is discussed, in terms of time complexity, volume complexity, numbers of test tube used and the longest library strand in solution space. Finally, the simulated experiment is applied to verify the correctness of our proposed DNA-based algorithm, in order to solve the well-known hitting-set problem.

Possible numbers of ones in the squares of 0–1 matrices with a given rank

For a symmetric 0–1 matrix A, we give the number of ones in A 2 when rank(A) = 1, 2, and give the maximal number of ones in A 2 when rank(A) = k (3 ≤ k ≤ n). The sufficient and necessary condition under which the maximal number is achieved is also obtained. For generic 0–1 matrices, we only study the cases of rank 1 and rank 2.

Imprimitive matrices of zeros and ones with extremal numbers of ones

In [X. Zhan, Extremal numbers of positive entries of imprimitive nonnegative matrices, Linear Algebra Appl. 424 (2007) 132–138], Zhan determined the maximum and minimum numbers of positive entries of irreducible nonnegative matrices. In this paper, we characterize the irreducible ( 0 , 1 ) matrices with the maximum and minimum numbers of positive entries.

Possible numbers of ones in 0–1 matrices with a given rank

We determine the possible numbers of ones in a 0–1 matrix with given rank in the generic case and in the symmetric case. There are some unexpected phenomena. The rank 2 symmetric case is subtle.

An Analysis of Te-Scattering From a Multiangular Groove in a Ground Plane

The 2D problem of H-polarized plane wave scattering by a multiangular groove engraved in a perfect conducting plane is investigated. The domain product technique is used to construct solution of the problem in the interior of the channel. The sought-for fields inside and outside the cavity are expressed in terms of the Mathieu function expansions. The problem is reduced to solving system of infinite matrix equations of the second kind with respect to expension coefficients. The validity and efficiency of the approach is checked and confirmed for the well-studied case of a rectangular groove. Illustrative examples dealing with arbitrary cavities are presented. The approach is efficient in the range of cavity size variation from several hundredths of wavelength to several numbers of ones.