Differentiation and quality estimation of Cordyceps with infrared spectroscopy

Heretofore, a scientific and systemic method for differentiation and quality estimation of a well-known Chinese traditional medicine, ‘Cordyceps’, has not been established in modern market. In this paper, Fourier-transform infrared spectroscopy (FTIR) and two-dimensional correlation infrared spectroscopy (2D-IR) are employed to propose a method for analysis of Cordyceps. It has presented that IR spectra of real Cordyceps of different origins and counterfeits have their own macroscopic fingerprints, with discriminated shapes, positions and intensities. Their secondary derivative spectra can amplify the differences and confirm the potentially characteristic IR absorption bands 1400–1700 cm⁻¹ to be investigated in 2D-IR. Many characteristic fingerprints are discovered in 2D-IR spectra in the range of 1400–1700 cm⁻¹ and hetero 2D spectra of 670–780 cm⁻¹ × 1400–1700 cm⁻¹. The different fingerprints display different chemical constitutes. Through the three steps, different Cordyceps and their counterfeits can be discriminated effectively and their qualities distinctly display. Successful analysis of eight Cordyceps capsule products has proved the practicability of the method, which can also be applied to the quality estimation of other Chinese traditional medicines.     

An upper bound for Cubicity in terms of Boxicity

An axis-parallel b-dimensional box is a Cartesian product R₁×R₂×?×R_b where each R_i (for 1≤i≤b) is a closed interval of the form [a_i,b_i] on the real line. The boxicity of any graph G, is the minimum positive integer b such that G can be represented as the intersection graph of axis-parallel b-dimensional boxes. A b-dimensional cube is a Cartesian product R₁×R₂×?×R_b, where each R_i (for 1≤i≤b) is a closed interval of the form [a_i,a_i+1] on the real line. When the boxes are restricted to be axis-parallel cubes in b-dimension, the minimum dimension b required to represent the graph is called the cubicity of the graph (denoted by ). In this paper we prove that , where n is the number of vertices in the graph. We also show that this upper bound is tight.Some immediate consequences of the above result are listed below:

1.

Planar graphs have cubicity at most 3⌈log₂n⌉.

2.

Outer planar graphs have cubicity at most 2⌈log₂n⌉.

3.

Any graph of treewidth tw has cubicity at most (tw+2)⌈log₂n⌉. Thus, chordal graphs have cubicity at most (ω+1)⌈log₂n⌉ and circular arc graphs have cubicity at most (2ω+1)⌈log₂n⌉, where ω is the clique number.

The above upper bounds are tight, but for small constant factors.     

Color-bounded hypergraphs, II: Interval hypergraphs and hypertrees

A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set E={E₁,…,E_m}, together with integers s_i and t_i (1≤s_i≤t_i≤|E_i|) for i=1,…,m. A vertex coloring φ is feasible if the number of colors occurring in edge E_i satisfies s_i≤|φ(E_i)|≤t_i, for every i≤m.In this paper we point out that hypertrees-hypergraphs admitting a representation over a (graph) tree where each hyperedge E_i induces a subtree of the underlying tree-play a central role concerning the set of possible numbers of colors that can occur in feasible colorings. We also consider interval hypergraphs and circular hypergraphs, where the underlying graph is a path or a cycle, respectively. Sufficient conditions are given for a ‘gap-free’ chromatic spectrum; i.e., when each number of colors is feasible between minimum and maximum. The algorithmic complexity of colorability is studied, too.Compared with the ‘mixed hypergraphs’-where ‘D-edge’ means (s_i,t_i)=(2,|E_i|), while ‘C-edge’ assumes (s_i,t_i)=(1,|E_i|−1)-the differences are rather significant.     

Invariant measures for interval maps with critical points and singularities

We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an ergodic invariant probability measures which is absolutely continuous with respect to Lebesgue measure.     

Jump-preserving surface reconstruction from noisy data

A new local smoothing procedure is suggested for jump-preserving surface reconstruction from noisy data. In a neighborhood of a given point in the design space, a plane is fitted by local linear kernel smoothing, giving the conventional local linear kernel estimator of the surface at the point. The neighborhood is then divided into two parts by a line passing through the given point and perpendicular to the gradient direction of the fitted plane. In the two parts, two half planes are fitted, respectively, by local linear kernel smoothing, providing two one-sided estimators of the surface at the given point. Our surface reconstruction procedure then proceeds in the following two steps. First, the fitted surface is defined by one of the three estimators, i.e., the conventional estimator and the two one-sided estimators, depending on the weighted residual means of squares of the fitted planes. The fitted surface of this step preserves the jumps well, but it is a bit noisy, compared to the conventional local linear kernel estimator. Second, the estimated surface values at the original design points obtained in the first step are used as new data, and the above procedure is applied to this data in the same way except that one of the three estimators is selected based on their estimated variances. Theoretical justification and numerical examples show that the fitted surface of the second step preserves jumps well and also removes noise efficiently. Besides two window widths, this procedure does not introduce other parameters. Its surface estimator has an explicit formula. All these features make it convenient to use and simple to compute.     

Stochastic monotonicity of the MLE of exponential mean under different censoring schemes

In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE) of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the result for the exponential competing risks model with censoring.     

Optimal Estimator for Distributed Anonymous Observers

In this paper, we consider a distributed estimation problem in which multiple observations of a signal process are combined via the maximum function for the decision making. A key result established is that, under suitable technical conditions, the optimal decision function can be implemented by means of thresholds. A natural question is how to determine the optimal threshold value. We propose here an algorithm for threshold adjustment by means of training sequences. The algorithm is a variation of the Kiefer-Wolfowitz algorithm with expanding truncations and randomized differences. A result of the paper is to establish the convergence of the algorithm if the variance of observation noises is small enough.     

An improved standardized time series Durbin–Watson variance estimator for steady-state simulation

We discuss an improved jackknifed Durbin–Watson estimator for the variance parameter from a steady-state simulation. The estimator is based on a combination of standardized time series area and Cramér–von Mises estimators. Various examples demonstrate its efficiency in terms of bias and variance compared to other estimators.     

LP narrowing: A new strategy for finding all solutions of nonlinear equations

An efficient algorithm is proposed for finding all solutions of systems of n nonlinear equations. This algorithm is based on interval analysis and a new strategy called LP narrowing. In the LP narrowing strategy, boxes (n-dimensional rectangles in the solution domain) containing no solution are excluded, and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques. Since the LP narrowing is very powerful, all solutions can be found very efficiently. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 5000-50,000 nonlinear equations in practical computation time.     

Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model

In order to reduce computational burden and improve the convergence rate of identification algorithms, an auxiliary model based multi-innovation stochastic gradient (AM-MISG) algorithm is derived for the multiple-input single-output systems by means of the auxiliary model identification idea and multi-innovation identification theory. The basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm, and then to derive the AM-MISG algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length. The simulation example shows that the proposed algorithms work quite well.