Non-negative Values Research Articles

Characteristics of the GLLE Family of Lifetime Distributions, and Applications

ABSTRACT. A Generalized Log-Logistic (GLL) family of lifetime distributions is one in which any pair of distributions are related through a GLL transformation, for some (non-negative) value of the transformation parameter (the odds function of the second distribution is the power of the odds function of the first distribution). We consider GLL families generated from an exponential distribution. We derive some useful characteristics of these distributions; moreover, we discuss the hazard rates and Kullback-Leibler divergence, then illustrate the usefulness of this distribution family by fitting real data sets.

Matrix Factorization and Prediction for High-Dimensional Co-Occurrence Count Data via Shared Parameter Alternating Zero Inflated Gamma Model

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word–word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item–item or user–item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize these data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item–item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to find the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

Static output feedback control for positive 2D discrete systems in Roesser model

Abstract This paper investigates the output stabilization problem for multi-input multi-output positive 2D systems described by a linear discrete-time Roesser system. This kind of systems have the property that the horizontal and vertical states take non-negative values whenever the initial boundaries are non-negative. Conditions for the existence of desired static output feedback controllers guaranteeing the resultant closed-loop system to be positive and asymptotically stable are obtained. Also, the synthesis of static output feedback controllers, including the requirement of positivity of the controllers, is solved. These results are then extended to the case of uncertain plants. All of the proposed conditions are expressed in terms of Linear Programming, which can be easily verified by using standard numerical software. Finally, several numerical examples are included to illustrate the validity and the effectiveness of the developed results.

Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor

Abstract We investigate bound entanglement in three-qubit mixed states which are diagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these states is detected using entanglement witnesses and the analysis focuses on states exhibiting positive partial transpose (PPT). We then compare the detection capabilities of optimal linear and nonlinear entanglement witnesses. In theory, both linear and nonlinear witnesses produce non-negative values for separable states and negative values for some entangled GHZ diagonal states with PPT, indicating the presence of entanglement. Our experimental results reveal that in cases where linear entanglement witnesses fail to detect entanglement, nonlinear witnesses are consistently able to identify its presence. Optimal linear and nonlinear witnesses were generated on an IBM quantum computer and their performance was evaluated using two bound entangled states (Kay and Kye states) from the literature, and randomly generated entangled states in the GHZ diagonal form. Additionally, we propose a general quantum circuit for generating a three-qubit GHZ diagonal mixed state using a six-qubit pure state on the IBM quantum processor. We experimentally implemented the circuit to obtain expectation values for three-qubit mixed states and compute the corresponding entanglement witnesses.

Fair division with two-sided preferences

We study a fair division setting in which participants are to be fairly distributed among teams, where not only do the teams have preferences over the participants as in the canonical fair division setting, but the participants also have preferences over the teams. We focus on guaranteeing envy-freeness up to one participant (EF1) for the teams together with a stability condition for both sides. We show that an allocation satisfying EF1, swap stability, and individual stability always exists and can be computed in polynomial time, even when teams may have positive or negative values for participants. When teams have nonnegative values for participants, we prove that an EF1 and Pareto optimal allocation exists and, if the valuations are binary, can be found in polynomial time. We also show that an EF1 and justified envy-free allocation does not necessarily exist, and deciding whether such an allocation exists is computationally difficult.

Fair Shares: Feasibility, Domination, and Incentives

We consider fair allocation of indivisible goods to n equally entitled agents. Every agent i has a valuation function vi from some given class of valuation functions. A share s is a function that maps [Formula: see text] to a nonnegative value. A share is feasible if for every allocation instance, there is an allocation that gives every agent i a bundle that is acceptable with respect to vi, one of value at least her share value [Formula: see text]. We introduce the following concepts. A share is self-maximizing if reporting the true valuation maximizes the minimum true value of a bundle that is acceptable with respect to the report. A share s ρ-dominates another share [Formula: see text] if [Formula: see text] for every valuation function. We initiate a systematic study of feasible and self-maximizing shares and a systematic study of ρ-domination relation between shares, presenting both positive and negative results. Funding: The research of M. Babaioff is supported in part by a Golda Meir Fellowship. The research of U. Feige is supported in part by the Israel Science Foundation [Grant 1122/22].

SIMULATION OF RELIABILITY, RELIABILITY INDEX, PROBABILITY DENSITY FUNCTION AND FAILURE FUNCTIONS FROM WEIBULL DISTRIBUTION FOR ENGINEERING APPLICATIONS

In modelling and simulating future rainfall for a selected location, the probability distributions have been established to be an effective tool. In this study, the different methods utilised in the estimation of the probability distributions’ parameters were evaluated and presented using Weibull's two parameters. Different estimator methods (mean rank, median rank, symmetric, graphical, least square, empirical, maximum likelihood, general probability, modified maximum likelihood, Mabchour, alternative maximum likelihood, equivalent energy, moment expression, Lysen and Moment methods) were used to determine probability density function, reliability, reliability index and failure functions of rainfall data from Maiduguri. The performances of these different methods were compared probability density function, reliability, reliability index and failure functions of Weibull two parameters. The study revealed that the values of probability distribution dimensionless shape variables were between 1.0193 and 4.205, and probability distribution scale factor constants were between 0.302 and 7.254. These values are all positive (non-negative values or less than zero) values. It was established that there were significant differences (F108, 1728 was 162.1976 and the probability (p) was zero) between the individual reliabilities and Weibull estimators (F15, 1620 was 14928.98 and probability was zero) at a 95 % confidence level (p less than 0.05). It was concluded that caution must be taken in the utilization of general probability, equivalent energy, Alternative Maximum Likelihood Method and moment expression methods in any engineering applications to prevent failure of devices or infrastructure.

Selecting Pedal Load for Lower-Limb Rehabilitation Based on the Combination of Muscle Synergy and Fourier Series

This paper introduces a new lower-limb rehabilitation machine that meets the rehabilitation needs of hemiplegic patients. First, a left–right independent rotary pedal mechanism was selected to facilitate rehabilitation and adapt to the user’s physical condition. Then, a half model of the lower-limb rehabilitation machine is designed and manufactured with ergonomics in mind. As analytical tools, we combine non-negative matrix factorization and non-negative double singular value decomposition to calculate muscle synergy of the walking muscle surface electromyography (sEMG) signal, and use cosine similarity to evaluate the similarity between walking and pedaling activities. By comparing the results of the walking and pedaling experiments, the effectiveness of pedaling in gait rehabilitation is revealed. To further improve the similarity between walking and pedaling, double integration of the sEMG signal is introduced, and the relationship between load input and rotation angle is described for the first time using Fourier series. The results of the experiment confirmed that more than half of the 10 subjects performed pedaling exercises similar to walking using Fourier series loading compared to pedaling exercises with normal constant loading. This loading parameter may have the potential to improve rehabilitation efficiency for many subjects compared to the usual exercise.

Structure based transmission estimation in single image dehazing

The single image dehazing (SID) is challenging because of ill-posed characteristic, since there exist multiple possible dehazed images for a single hazy image due to multiple possible values of transmission. The SID is solved using scattering model, which requires computation of two parameters (transmission and atmospheric light) for its solution. The existing methods have presented priors and techniques to estimate transmission with limited focus on structure of the transmission. This paper proposes a lower bound on transmission using structural measure. The proposed lower bound is utilized to estimate the value of transmission, while preserving structural. Further, a quality control parameter is introduced to ensure non-negative value of the transmission for images with brighter objects than atmospheric light. The accuracy and efficiency of the proposed method is established by comparing with renowned SID methods using benchmark datasets.

Novel consensus framework on discrete-time positive multi-agent systems

This paper investigates the consensus of discrete-time positive multi-agent systems. A framework on the consensus of positive multi-agent systems is constructed. By introducing a finite point and a self-feedback term, a novel consensus protocol is proposed to drive all states to common nonnegative finite values. An improved error model is established for positive multi-agent systems. Based on the consensus error model, the consensus of the agents is transformed into the stability of the error systems. Under the proposed consensus protocol and the new consensus error model, the consensus of agents is realized. A copositive Lyapunov function is chosen to derive the consensus of the multi-agent systems. Such a consensus approach is extended for time-delay multi-agent systems. All positivity and consensus conditions can be solved by virtue of linear programming. The main novelties of this paper lie in that: (i) A novel consensus error model is established, (ii) A finite value consensus is achieved, and (iii) Linear programming-based conditions are presented for the consensus design. Finally, two illustrated examples are given to verify the validity of the theoretical findings.

A Discrete Version of the Half-Logistic Distribution Based on the Mimicking of the Probability Density Function

We introduce a count distribution obtained as a discrete analogue of the continuous half-logistic distribution. It is derived by assigning to each non-negative integer value a probability proportional to the corresponding value of the density function of the parent model. The main features of this new distribution, in particular related to its shape, moments, and reliability properties, are described. Parameter estimation, which can be carried out resorting to different methods including maximum likelihood, is discussed, and a numerical comparison of their performances, based on Monte Carlo simulations, is presented. The applicability of the proposed distribution is proved on two real datasets, which have been already fitted by other well-established count distributions. In order to increase the flexibility of this counting model, a generalization is finally suggested, which is obtained by adding a shape parameter to the continuous one-parameter half-logistic and then applying the same discretization technique, based on the mimicking of the density function.

Uncertainty Regularized Evidential Regression

The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific activation functions must be employed to enforce non-negative values, which is a constraint that compromises model performance by limiting its ability to learn from all samples. This paper provides a theoretical analysis of this limitation and introduces an improvement to overcome it. Initially, we define the region where the models can't effectively learn from the samples. Following this, we thoroughly analyze the ERN and investigate this constraint. Leveraging the insights from our analysis, we address the limitation by introducing a novel regularization term that empowers the ERN to learn from the whole training set. Our extensive experiments substantiate our theoretical findings and demonstrate the effectiveness of the proposed solution.

Preserving non-negative porosity values in a bi-phase elasto-plastic material under Terzaghi’s effective stress principle

Poromechanics is a well-established field of continuum mechanics which seeks to model materials with multiple phases, usually a stiff solid phase and fluid phases of liquids or gases. Applications are widespread particularly in geomechanics where Terzaghi’s effective stress is widely used to solve engineering soil mechanics problems. This approach assumes that the solid phase is incompressible, an assumption that leads to many advantages and simplifications without major loss of fidelity to the real world. Under the assumption of finite (as opposed to infinitesimal) strains, the poromechanics of two- or bi-phase materials gains complexity and while the compressible solid phase case has received attention from researchers, the incompressible case has received less. For the finite strain - incompressible solid phase case there is a fundamental issue with standard material models, in that for some loadings solid skeleton mass conservation is violated and negative Eulerian porosities are predicted. While, to the authors’ best knowledge, acknowledgement of this essential problem has been disregarded in the literature, an elegant solution is presented here, where the constraint on Eulerian porosity can be incorporated into the free energy function for a material. The formulation is explained in detail, soundly grounded in the laws of thermodynamics and validated on a number of illustrative examples.

Learning-augmented maximum flow

We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since these were unknown at the time of learning). We present an algorithm that, given an m-edge flow network and a predicted flow, computes a maximum flow in O(mη) time, where η is the ℓ1 error of the prediction, i.e., the sum over the edges of the absolute difference between the predicted and optimal flow values. Moreover, we prove that, given an oracle access to a distribution over flow networks, it is possible to efficiently PAC-learn a prediction minimizing the expected ℓ1 error over that distribution. Our results fit into the recent line of research on learning-augmented algorithms, which aims to improve over worst-case bounds of classical algorithms by using predictions, e.g., machine-learned from previous similar instances. So far, the main focus in this area was on improving competitive ratios for online problems. Following Dinitz et al. (2021) [6], our results are among the firsts to improve the running time of an offline problem.

A new chaos function development through the combination of Circle map and MS map

Digital data protection is very important to prevent manipulation of digital data by unauthorized parties. Reliable techniques for securing digital data are needed, safe and fast. One technique is to use cryptography. One of the cryptographic techniques that can be used to encode digital data is to use the chaos function. We propose in this paper a new chaos function which is a composition of Circle map and MS map functions. This function has chaotic nature and the result of which is named the MSI-Circle map. The sensitivity and randomness tests of the MSI-Circle map function are carried out using a bifurcation diagram, Lyapunov exponent, and NIST test suites. The analysis result of the bifurcation diagram shows that the MSI-Circle map has a good density at the value of r ∈ (−∞,−3] ∪ [3,−∞]. Lyapunov exponent has a non-negative value at x0 = 0.4, r = 3.8, Ω = 0.5, λ = 2.1, K = 4 which is the domain xn ∈ (0, 1) and parameter values r, Ω, λ and K are any real numbers. The results of the NIST randomness level test show that the MSI-Circle map function passed all the randomness test of 16 NIST tests.

The exponential non-uniform bound on the half-normal approximation for the number of returns to the origin

This research explored the number of returns to the origin within the framework of a symmetric simple random walk. Our primary objective was to approximate the distribution of return events to the origin by utilizing the half-normal distribution, which is chosen for its appropriateness as a limit distribution for nonnegative values. Employing the Stein's method in conjunction with concentration inequalities, we derived an exponential non-uniform bound for the approximation error. This bound signifies a significant advancement in contrast to existing bounds, encompassing both the uniform bounds proposed by Döbler <sup>[<span class="xref"><a href="#b1" ref-type="bibr">1</a></span>]</sup> and polynomial non-uniform bounds presented by Sama-ae, Chaidee, and Neammanee <sup>[<span class="xref"><a href="#b2" ref-type="bibr">2</a></span>]</sup>, and Siripraparat and Neammanee <sup>[<span class="xref"><a href="#b3" ref-type="bibr">3</a></span>]</sup>.

Non-Negative Universal Differential Equations With Applications in Systems Biology

Universal differential equations (UDEs) leverage the respective advantages of mechanistic models and artificial neural networks and combine them into one dynamic model. However, these hybrid models can suffer from unrealistic solutions, such as negative values for biochemical quantities. We present non-negative UDE (nUDEs), a constrained UDE variant that guarantees non-negative values. Furthermore, we explore regularisation techniques to improve generalisation and interpretability of UDEs.

SVD entanglement entropy

In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the Rényi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence.

The critical polynomial of a graph

Let G be a connected graph on n vertices with adjacency matrix AG. Associated to G is a polynomial dG(x1,…,xn) of degree n in n variables, obtained as the determinant of the matrix MG(x1,…,xn), where MG=Diag(x1,…,xn)−AG. We investigate in this article the set VdG(r) of non-negative values taken by this polynomial when x1,…,xn≥r≥1. We show that VdG(1)=Z≥0. We show that for a large class of graphs one also has VdG(2)=Z≥0. When VdG(2)≠Z≥0, we show that for many graphs VdG(2) is dense in Z≥0. We give numerical evidence that in many cases, the complement of VdG(2) in Z≥0 might in fact be finite. As a byproduct of our results, we show that every graph can be endowed with an arithmetical structure whose associated group is trivial.

Scaled consensus for second-order multi-agent systems subject to communication noise with stochastic approximation-type protocols

This work is dedicated to the leaderless/leader-following stochastic scaled consensus issue of second-order stochastic multi-agent systems (SMASs) in a noisy environment. Scaled consensus represents that the ratios among agents asymptotically tend to designated constants rather than the common convergence value. To lessen the influence of communication noise, some stochastic approximation protocols with time-varying gain are designed for our underlying system, where the time-varying gain remove the restriction of nonnegative value. Compared with the existing consensus results with communication noise, the major challenge is that the introduction of time-varying gain results in the inapplicability of Lyapunov-based technique. To cope with it, a state decomposition method is utilized, and a series of sufficient necessary conditions are set up for interacting agents with constant velocity and zero velocity if the topology includes a spanning tree. Furthermore, it is conducted that the consensus and bipartite consensus can be seen as two special cases of our work. Finally, the validity of our results is demonstrated by a simulation example.