Negative Entries Research Articles

Application of 3D printing technology combined with PBL teaching model in teaching clinical nursing in congenital heart surgery: A case-control study.

We aimed to explore the application of three-dimensional (3D) printing technology with problem-based learning (PBL) teaching model in clinical nursing education of congenital heart surgery, and to further improve the teaching quality of clinical nursing in congenital heart surgery. In this study, a total of 132 trainees of clinical nursing in congenital heart surgery from a grade-A tertiary hospital in 2019 were selected and randomly divided into 3D printing group or traditional group. The 3D printing group was taught with 3D printed heart models combined with PBL teaching technique, while the traditional group used conventional teaching aids combined with PBL technique for teaching. After the teaching process, the 2 groups of nursing students were assessed and surveyed separately to evaluate the results. Compared to the traditional group, the theoretical scores, clinical nursing thinking ability, self-evaluation for comprehensive ability, and teaching satisfaction from the questionnaires filled by the 3D printing group were all higher than the traditional group. The difference was found to be statistically significant (P < .05). Our study has shown the 3D printing technology combined with the PBL teaching technique in the clinical nursing teaching of congenital heart surgery achieved good results.

Identification of high-yielding wheat genotypes resistant to Pyrenophora tritici-repentis (tan spot)

Tan spot, caused by Pyrenophora tritici-repentis, is a major foliar disease of wheat in Kazakhstan. This study evaluated 103 winter wheat genotypes for tan spot resistance and high-productivity traits in the field in two years. Entries were also characterized using the molecular marker Xfcp623, indicative of Tsn1 gene conferring sensitivity to Ptr ToxA. The proportion of entries insensitive to Ptr ToxA was relatively high (71%). Forty-eight entries with the lowest tan spot severity in the field were confirmed to be insensitivity to Ptr ToxA in the molecular screening. Entries which were resistant under field conditions had similar level of seedling resistance. Principal component analysis biplots showed, that all spike productivity traits were highly correlated. Days to heading (DH) and tan spot severity, as well as the normalized difference vegetation index and DH were strongly correlated. Thousand kernels weight (TKW) and plant height were highly correlated and both were negatively correlated with DH and tan spot severity, indicating that taller cultivars tended to be more resistant. The Xfcp623 negative entries had lower disease severity (by about 40%), flowered up to 2 days later than entries with Tsn1 and had significantly more spikelets per spike, number of grains per spike, TKW and grain weight/spike. The results of the study will be important for increasing the efficiency of breeding based on the elimination of the genotypes with dominant allele Tsn1. Of the 103 entries evaluated, 28 can be directly used in breeding programs to improve tan spot resistance and productivity of winter wheat.

Generalized lattice-point visibility in ℕk

It is a well-known result that the proportion of lattice points visible from the origin is given by $\frac{1}{\zeta(2)}$, where $\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s}$ denotes the Riemann zeta function. Goins, Harris, Kubik and Mbirika, generalized the notion of lattice point visibility by saying that for a fixed $b\in\mathbb{N}$, a lattice point $(r,s)\in\mathbb{N}^2$ is $b$-visible from the origin if no other lattice point lies on the graph of a function $f(x)=mx^b$, for some $m\in\mathbb{Q}$, between the origin and $(r,s)$. In their analysis they establish that for a fixed $b\in\mathbb{N}$, the proportion of $b$-visible lattice points is $\frac{1}{\zeta(b+1)}$, which generalizes the result in the classical lattice point visibility setting. In this short note we give an $n$-dimensional notion of $\bf{b}$-visibility that recovers the one presented by Goins et. al. in $2$-dimensions, and the classical notion in $n$-dimensions. We prove that for a fixed ${\bf{b}}=(b_1,b_2,\ldots,b_n)\in\mathbb{N}^n$ the proportion of ${\bf{b}}$-visible lattice points is given by $\frac{1}{\zeta(\sum_{i=1}^nb_i)}$. Moreover, we propose a $\bf{b}$-visibility notion for vectors $\bf{b}\in \mathbb{Q}_{>0}^n$, and we show that by imposing weak conditions on those vectors one obtains that the density of ${\bf{b}}=(\frac{b_1}{a_1},\frac{b_2}{a_2},\ldots,\frac{b_n}{a_n})\in\mathbb{Q}_{>0}^n$-visible points is $\frac{1}{\zeta(\sum_{i=1}^nb_i)}$. Finally, we give a notion of visibility for vectors $\bf{b}\in (\mathbb{Q}^{*})^n$, compatible with the previous notion, that recovers the results of Harris and Omar for $b\in \mathbb{Q}^{*}$ in $2$-dimensions; and show that the proportion of $\bf{b}$-visible points in this case only depends on the negative entries of $\bf{b}$.

Scaled Simplex Representation for Subspace Clustering.

The self-expressive property of data points, that is, each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering (SC) methods. Most self-expressive methods usually construct a feasible affinity matrix from a coefficient matrix, obtained by solving an optimization problem. However, the negative entries in the coefficient matrix are forced to be positive when constructing the affinity matrix via exponentiation, absolute symmetrization, or squaring operations. This consequently damages the inherent correlations among the data. Besides, the affine constraint used in these methods is not flexible enough for practical applications. To overcome these problems, in this article, we introduce a scaled simplex representation (SSR) for the SC problem. Specifically, the non-negative constraint is used to make the coefficient matrix physically meaningful, and the coefficient vector is constrained to be summed up to a scalar to make it more discriminative. The proposed SSR-based SC (SSRSC) model is reformulated as a linear equality-constrained problem, which is solved efficiently under the alternating direction method of multipliers framework. Experiments on benchmark datasets demonstrate that the proposed SSRSC algorithm is very efficient and outperforms the state-of-the-art SC methods on accuracy. The code can be found at https://github.com/csjunxu/SSRSC.

A novel consensus learning approach to incomplete multi-view clustering

Multi-view data may lose some instances in real applications. Most existing methods for clustering such incomplete multi-view data still have at least one of the following limitations: 1) The common relations among data points across all views are ignored. 2) The complementary multi-view information of original data representation is not well exploited. 3) Arbitrary incomplete scenarios or data with negative entries cannot be handled. To address these limitations, in this paper, we propose a novel Consensus Learning approach to Incomplete Multi-view Clustering (CLIMC). Specifically, a low-dimensional consensus representation is introduced to exploit complementary multi-view information from the original feature representation of available instances by integrating index matrices into matrix factorization. In addition, by combining self-representation, index matrices, and consensus term, a consensus similarity graph is leveraged to explore the underlying cross-view relations among data points. Further, the key of the proposed CLIMC is that the consensus representation is correlated with the similarity graph by a graph Laplacian regularization. Consequently, the compactness of the low-dimensional representation and the accuracy of similarity degree of the graph are reciprocally promoted. Extensive experiments on several multi-view datasets demonstrate the effectiveness of CLIMC over state-of-the-arts.

A characterization of trace-zero sets realizable by compensation in the SNIEP

The symmetric nonnegative inverse eigenvalue problem (SNIEP) is the problem of characterizing all possible spectra of entry-wise nonnegative symmetric matrices of given dimension. A list of real numbers is said to be symmetrically realizable if it is the spectrum of some nonnegative symmetric matrix. One of the most general sufficient conditions for realizability is so-called C-realizability, which amounts to some kind of compensation between positive and negative entries of the list. In this paper we present a combinatorial characterization of C-realizable lists with zero sum, together with explicit formulas for C-realizable lists having at most four positive entries. One of the consequences of this characterization is that the set of zero-sum C-realizable lists is shown to be a union of polyhedral cones whose faces are described by equations involving only linear combinations with coefficients 1 and −1 of the entries in the list.

On existence and uniqueness of a carrying simplex in Kolmogorov differential systems

This paper deals with global asymptotic behaviour of the dynamics for N-dimensional competitive Kolmogorov differential systems of equations . A theory based on monotone dynamical systems was well established by Hirsch (1988 Nonlinearity 1 51–71). One of his theorems is outstanding and states the existence of a co-dimension 1 compact invariant submanifold Σ that attracts all the nontrivial orbits under certain assumptions and, in practice, under the condition that the system is totally competitive (all N 2 entries of the Jacobian matrix Df are negative). The submanifold Σ has been called carrying simplex since then and the theorem has been well accepted with many hundreds of citations. In this paper, we point out that the requirement of total competition is too restrictive and too strong; we prove the existence and uniqueness of a carry simplex under the assumption of strong internal competition only (i.e. N diagonal entries of Df are negative), a much weaker condition than total competition. Thus, we improve the theorem significantly by dramatic cost reduction from requiring N 2 to N negative entries of Df. As an example of applications of the main result, the existence and global attraction (repulsion) of a heteroclinic limit cycle for three-dimensional systems is discussed and two concrete examples are given to demonstrate the existence of such heteroclinic cycles.

±1-Matrices with Vanishing Permanent

The problem of finding (−1, 1)-matrices with vanishing permanent was posed by Edward Wang in 1974. This paper states and proves bounds on the number of negative entries in a matrix with zero permanent and minimal number of negative entries among all matrices of the same equivalence class. Then representatives of every equivalence class of matrices with zero permanent are found for n ≤ 5. Bibliography: 20 titles.

Gaussian Binomial Coefficients with Negative Arguments

Loeb showed that a natural extension of the usual binomial coefficient to negative (integer) entries continues to satisfy many of the fundamental properties. In particular, he gave a uniform binomial theorem as well as a combinatorial interpretation in terms of choosing subsets of sets with a negative number of elements. We show that all of this can be extended to the case of Gaussian binomial coefficients. Moreover, we demonstrate that several of the well-known arithmetic properties of binomial coefficients also hold in the case of negative entries. In particular, we show that Lucas' Theorem on binomial coefficients modulo $p$ not only extends naturally to the case of negative entries, but even to the Gaussian case.

Anchors Bring Ease: An Embarrassingly Simple Approach to Partial Multi-View Clustering

Clustering on multi-view data has attracted much more attention in the past decades. Most previous studies assume that each instance appears in all views, or there is at least one view containing all instances. However, real world data often suffers from missing some instances in each view, leading to the research problem of partial multi-view clustering. To address this issue, this paper proposes a simple yet effective Anchorbased Partial Multi-view Clustering (APMC) method, which utilizes anchors to reconstruct instance-to-instance relationships for clustering. APMC is conceptually simple and easy to implement in practice, besides it has clear intuitions and non-trivial empirical guarantees. Specifically, APMC firstly integrates intra- and inter- view similarities through anchors. Then, spectral clustering is performed on the fused similarities to obtain a unified clustering result. Compared with existing partial multi-view clustering methods, APMC has three notable advantages: 1) it can capture more non-linear relations among instances with the help of kernel-based similarities; 2) it has a much lower time complexity in virtue of a noniterative scheme; 3) it can inherently handle data with negative entries as well as be extended to more than two views. Finally, we extensively evaluate the proposed method on five benchmark datasets. Experimental results demonstrate the superiority of APMC over state-of-the-art approaches.

Living With Neuroendocrine Tumors: Assessment of Quality of Life Through a Mobile Application.

PURPOSETo understand the quality of life (QoL) for patients with neuroendocrine tumors (NETs) through comparison of QoL questionnaires and symptom tracking as well as journaling via the Carcinoid NETs Health Storylines mobile application (app).PATIENTS AND METHODSThis was a 12-week prospective, observational study of US patients with NET who were taking long-acting somatostatin analogs. National Institutes of Health Patient-Reported Outcomes Measurement Information System (PROMIS) and European Organisation for Research and Treatment of Cancer (EORTC) questionnaires were administered three times. Patients also monitored symptoms, mood, bowel movements, food, activity, and sleep, and they journaled in their app, which was coded by theme and sentiment for qualitative analysis.RESULTSOf the 120 patients with NET, 78% were women (mean age, 57 years); 76% had gastroenteropancreatic NETs, and 88% had metastases. Lanreotide depot and octreotide long-acting release (LAR) were used by 41% and 59%, respectively. The most common symptoms at baseline were fatigue (76.7%), diarrhea (62.5%), abdominal discomfort (64.1%), and trouble sleeping (57.5%). The majority completed five of six survey assessments (median, 5; mean, 5.1) and tracked four symptoms in the app (median, 4; mean, 5.5); the average frequency was 41.6 days for each symptom (median, 43; mean, 41.6; range, 1 to 84 days [12 weeks]). Without treatment change, most EORTC-assessed physical symptoms decreased from baseline to midpoint (eg, 59.3% at baseline v 33% at midpoint reported “quite a bit” or “very much” diarrhea; P = .002). App-based symptom tracking revealed large day-to-day variation, but weekly averages correlated well with survey scores. Journal entries showed that more patients made predominantly negative unsolicited entries about their injection experience with octreotide LAR compared with lanreotide (13 of 17 v two of 13; P < .001).CONCLUSIONPatients with NET experience a large symptom burden that varies daily. A decrease in physical symptoms on QoL surveys suggests an effect from daily app-based monitoring or journaling, which may reduce recall bias and benefit the patient’s experience of symptoms.

English

A 0/1-simplex is the convex hull of n+1 affinely independent vertices of the unit n-cube In. It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute 0/1-simplices in In can be represented by 0/1-matrices P of size n × n whose Gramians G = P⊤P have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part D of the transposed inverse P−⊤ of P is doubly stochastic and has the same support as P. In fact, P has a fully indecomposable doubly stochastic pattern. The negative part C of P−⊤ is strictly row-substochastic and its support is complementary to that of D, showing that P−⊤ = D−C has no zero entries and has positive row sums. As a consequence, for each facet F of an acute 0/1-facet S there exists at most one other acute 0/1-simplex Ŝ in In having F as a facet. We call Ŝ the acute neighbor of S at F. If P represents a 0/1-simplex that is merely nonobtuse, the inverse of G = P⊤P is only weakly diagonally dominant and has nonpositive off-diagonal entries. These matrices play an important role in finite element approximation of elliptic and parabolic problems, since they guarantee discrete maximum and comparison principles. Consequently, P−⊤ can have entries equal to zero. We show that its positive part D is still doubly stochastic, but its support may be strictly contained in the support of P. This allows P to have no doubly stochastic pattern and to be partly decomposable. In theory, this might cause a nonobtuse 0/1-simplex S to have several nonobtuse neighbors Ŝ at each of its facets. In this paper, we study nonobtuse 0/1-simplices S having a partly decomposable matrix representation P. We prove that if S has such a matrix representation, it also has a block diagonal matrix representation with at least two diagonal blocks. Moreover, all matrix representations of S will then be partly decomposable. This proves that the combinatorial property of having a fully indecomposable matrix representation with doubly stochastic pattern is a geometrical property of a subclass of nonobtuse 0/1-simplices, invariant under all n-cube symmetries. We will show that a nonobtuse simplex with partly decomposable matrix representation can be split in mutually orthogonal simplicial facets whose dimensions add up to n, and in which each facet has a fully indecomposable matrix representation. Using this insight, we are able to extend the one neighbor theorem for acute simplices to a larger class of nonobtuse simplices.

Products of Generalized Stochastic Matrices With Applications to Consensus Analysis in Networks of Multiagents With Delays.

Product theory of stochastic matrices provides a powerful tool in the consensus analysis of discrete-time multiagent systems. However, the classic theory cannot deal with networks with general coupling coefficients involving negative ones, which have been discussed only in very few papers due to the technicalities involved. Motivated by these works, here we developed some new results for the products of matrices which generalize that of the classical stochastic matrices by admitting negative entries. Particularly, we obtained a generalized version of the classic Hajnal inequality on this generalized matrix class. Based on these results, we proved some convergence results for a class of discrete-time consensus algorithms with time-varying delays and general coupling coefficients. At last, these results were applied to the analysis of a class of continuous-time consensus algorithms with discrete-time controller updates in the existence of communication/actuation delays.

Preprocessed Compressive Adaptive Sense and Search Algorithm

To address the performance degradation due to the cancellation of positive and negative entries of adaptive compressed sensing algorithms, we propose a simple adaptive sensing and group testing algorithm for sparse signals. The algorithm, termed “preprocessed compressive adaptive sense and search”, divides the input signal into two equal-length subsignals that include only non-positive or non-negative entries through a nonlinear preprocessing process and subsequently generates adaptive sensing and group testing. The proposed algorithm is computationally less intensive than non-adaptive compressed sensing and requires only klog(n/k) measurements to recover a k-sparse signal of dimension n. A theoretical guarantee for signal recovery is provided, and the provided numerical examples demonstrate a better recovery performance than non-adaptive sensing and compressive adaptive sense and search algorithms for the same signal-to-noise ratio.

Simultaneous construction of dual Borgen plots. II: Algorithmic enhancement for applications to noisy spectral data

AbstractBorgen plots are low‐dimensional representations of the set of all nonnegative factorizations of spectral data matrices. Classical Borgen plots are limited to nonnegative data and can be constructed for the spectral factor or for the concentration profiles. In the first part of this paper, a simultaneous construction of the two dual Borgen plots is presented, which intensively exploits the underlying duality principles. The second part introduces algorithmic enhancements which make the simultaneous Borgen plot construction possible for noisy experimental data matrices which can contain small negative matrix entries. The new method is tested for FT‐IR spectral data from the Rhodium catalyzed hydroformylation process. The results are compared to those by the FACPACK‐implementation of the polygon inflation method.

Signed countings of types B and D permutations and t,q-Euler numbers

It is a classical result that the parity-balance of the number of weak excedances of all permutations (derangements, respectively) of length n is the Euler number En, alternating in sign, if n is odd (even, respectively). Josuat-Vergès obtained a q-analog of the results respecting the number of crossings of a permutation. One of the goals in this paper is to extend the results to the permutations (derangements, respectively) of types B and D, on the basis of the joint distribution in statistics excedances, crossings and the number of negative entries obtained by Corteel, Josuat-Vergès and Kim.Springer numbers are analogous Euler numbers that count the alternating permutations of type B, called snakes. Josuat-Vergès derived bivariate polynomials Qn(t,q) and Rn(t,q) as generalized Euler numbers via successive q-derivatives and multiplications by t on polynomials in t. The other goal in this paper is to give a combinatorial interpretation of Qn(t,q) and Rn(t,q) as the enumerators of the snakes with restrictions.

Correlation Matrices with the Perron Frobenius Property

This paper investigates conditions under which correlation matrices have a strictly positive dominant eigenvector. The sufficient conditions, from the Perron-Frobenius theorem, are that all the matrix entries are positive. The conditions for a correlation matrix with some negative entries to have a strictly positive dominant eigenvector are examined. The special structure of correlation matrices permits obtaining of detailed analytical results for low dimensional matrices. Some specific results for the $n$-by-$n$ case are also derived. This problem was motivated by an application in portfolio theory.

Image regularization by nonnegatively constrained Conjugate Gradient

In the image reconstruction context the nonnegativity of the computed solution is often required. Conjugate Gradient (CG), used as a reliable regularization tool, may give solutions with negative entries, particularly when large nearly zero plateaus are present. The active constraints set, detected by projection onto the nonnegative orthant, turns out to be largely incomplete leading to poor effects on the accuracy of the reconstructed image. In this paper an inner-outer method based on CG is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constraints set. This method appears to be especially suitable for the reconstruction of images having large nearly zero backgrounds. The numerical experimentation validates the effectiveness of the proposed method when compared to other strategies for nonnegative reconstruction.

Launching and controlling Gaussian beams from point sources via planar transformation media

Based on operations prescribed under the paradigm of Complex Transformation Optics (CTO) [1-5], it was recently shown in [5] that a complex source point (CSP) can be mimicked by a parity-time ($\mathcal{PT}$) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to non-symmetric complex coordinate transformations as put forth in [6] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed {\it outside} the slab as well [6]. By making use of the extra degrees of freedom (real and imaginary part of the coordinate transformation) provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization of Gaussian-like beams. We illustrate how beam properties such as peak amplitude and waist location can be controlled by a proper choice of (complex-valued) CTO Jacobian elements. In particular, the beam waist location may be moved bidirectionally by allowing for negative entries in the Jacobian (equivalent to inducing negative refraction effects). These results are then interpreted in light of the ensuing CSP location.

Population Models with Projection Matrix with Some Negative Entries - A Solution to the Natchez Paradox

The research was supported by the National Research Foundation of South Africa under Grant NN. 00317.