Convexity and Positivity of Bivariate Quadratic Bézier Surfaces over a Rectangle

With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.

Determinants of Persistent Sputum Smear Positivity after Intensive Phase Chemotherapy among Patients with Tuberculosis at Rhodes Chest Clinic, Nairobi, Kenya

The prevalence of TB in sub-Sahara Africa has been reported as 511 per 100,000 populations and a mortality of 74 per 100,000 in year 2009. In the same period, incidence was estimated at 350 cases per 100,000. In this regard, the health system requires strengthening to respond to the rising cases of infection, drug resistance and quality of life lost while continuing to seek interventions that improve adherence to medication and case detection among those infected. Methods: This study sought to determine factors that are associated with sputum positivity after intensive phase of chemotherapy in people with tuberculosis. It was a retrospective case-control study conducted in Rhodes chest clinic, a City Council health unit in Nairobi that specializes in treatment of chest infections. The participants were sampled from clinic attendants who had completed two months of intensive phase TB chemotherapy and met inclusion criteria. Results: Seventy participants of whom 25 (36%) were sputum positive at the end of two (2) months intensive phase were included in the study. Skipping medication doses was significantly associated with sputum positivity (p = 0.01). Patients who were sputum positive at the end of the two-month period were more likely to have taken longer time before seeking treatment compared to those who were sputum negative by median (IQR) 8 (3 - 12) and 4 (3 - 8) weeks respectively although this difference was not significant (p = 0.09). Patients who had not disclosed their infection status had a two-fold possibility of remaining sputum positive at the end of intensive phase. Conclusion: Early diagnosis and treatment of TB, and adherence to medication were important factors that affect sputum conversion during intensive phase of TB treatment. Therefore, public health practitioners should advise patients to seek prompt diagnosis and treatment of signs and symptoms of tuberculosis.

The Role of Photographs and Time Lag on Positivity Ratings of Vaca­tion and Weekend Memories

Two studies examined the question of whether photograph taking of an event influences the positivity of the evaluations of the event at a later point in time.Memories of photographed events yielded higher positivity ratings than memories that were not photographed.Although we expected fading of positivity ratings to occur more slowly over a period of two months for memories of photographed events,we found faster affect fading for those memories in Study 2 instead.The findings of the two studies support the idea that taking photographs of events sustains the affective reconstruction of autobiographical memories,regardless of whether these events are special,such as vacation memories,or more mundane,such as memories of the past weekend.

Total Positivity of UE Spline Basis

A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.

Positivity-Preserving Numerical Methods for Belousov-Zhabotinsky Reaction

The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.

Towards Positivity:A Large-Scale Diachronic Sentiment Analysis of the Humanities and Social Sciences in China

With its rising number of publications and expanding international collaborations,China's humanities and social sciences(HSS)research is displaying its potential for global prominence.Researchers have been exploring the development of China's HSS from different perspectives.However,the examinations from the perspective of sentiment analysis are scanty.Our aim is then to examine the sentiment features in Chinese HSS academic writing,by analyzing a large-scale corpus with over 275 million characters and with a time span from 2000 to 2020.Considering that most studies only focused on abstracts,we examined both the abstracts and the full texts,as well as a direct comparison between them.We found that Chinese HSS academic writing has evolved to be more positively biased in the past two decades,showing an upward trend in the use of positive words and a slight downward trend in the use of negative words.However,the upward trend of positive words in the full texts is not that clear,resembling a fluctuating pattern.Regarding the comparison,the abstracts are more likely to use positive words while the full texts tend to use more negative words.These phenomena can be explained with the social cognitive theory,in that they may be shaped by a joint force of the nature of human beings,the nature of language,the particular socio-cultural background in China and the features of the academic genre.

hh-transforms of Positivity Preserving Semigroups and Associated Markov Processes

The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-associated with a pair of special standard processes which are in weak duality.

Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.

Positivity and Stability of Fractional-Order Linear Time-Delay Systems

This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems(FOLTDSs)which are composed of N(N≥2)subsystems.Firstly,a sufficient and necessary condition is given to ensure the positivity of FOLTDSs.The solutions of the studied systems are obtained by using the Laplace transform method,and it can be observed that the positivity of FOLTDSs is completely determined by the series of matrices and independent of the magnitude of time-delays.Secondly,a theorem is given to prove the asymptotic stability of positive FOLTDSs.By considering the monotonicity and asymptotic properties of systems with constant time-delay,it is further shown that the asymptotic stability of positive FOLTDSs is independent of the time-delay.Next,a state-feedback controller,whose gain matrix is derived by resolving a linear programming question,is designed such that the state variables of the systems are nonnegative and asymptotically convergent.When the order of the FOLTDSs is greater than one,by utilizing a proposed property of Caputo derivative,a sufficient condition for the positivity of FOLTDS is presented.Finally,simulation examples are presented to verify the validity and practicability of the theoretical analysis.

A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography

This paper presents an improved well-balanced Godunov-type 2-D finite volume model with structured grids to simulate shallow flows with wetting and drying fronts over an irregular topography. The intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for the water depth is implemented to resolve the stationary or wet/dry fronts. The bed slope source term is discretized using a central difference method to capture the static flow state over the irregular topography. Second-order accuracy in space is achieved by using the slope limited linear reconstruction method. With the proposed method, the model can avoid the partially wetting/drying cell problem and maintain the mass conservation. The proposed model is tested and verified against three theoretical benchmark tests and two experimental dam break flows. Further, the model is applied to predict the maximum water level and the flood arrival time at different gauge points for the Malpasset dam break event. The predictions agree well with the numerical results and the measurement data published in literature, which demonstrates that with the present model, a well-balanced state can be achieved and the water depth can be nonnegative when the Courant number is kept less than 0.25.

Patients with Prolonged Positivity of SARS-CoV-2 RNA Benefit from Convalescent Plasma Therapy:A Retrospective Study

Convalescent plasma therapy has been implemented in a few cases of severe coronavirus disease 2019.No report about convalescent plasma therapy in treating patients with prolonged positivity of SARS-CoV-2 RNA has been published.In this study,we conducted a retrospective observational study in 27 patients with prolonged positivity of SARS-CoV-2 RNA,the clinical benefit of convalescent plasma therapy were analyzed.q RT-PCR test of SARS-CoV-2 RNA turned negative(B 7 days)in a part of patients(early negative group,n=15)after therapy,others(late negative group,n=12)turned negative in more than 7 days.Pulmonary imaging improvement was confirmed in 7 patients in early negative group and 8 in late negative group after CP therapy.Viral load decreased in early negative group compared with late negative group at day 3,5,7 after implementing convalescent plasma therapy.Patients in early negative group had a shorter median length of hospital stay.In conclusion,convalescent plasma therapy might help eliminate virus and shorten length of hospital stay in patients with prolonged positivity of SARS-CoV-2 RNA.

Collaborative positioning for swarms:A brief survey of vision,LiDAR and wireless sensors based methods

As positioning sensors,edge computation power,and communication technologies continue to develop,a moving agent can now sense its surroundings and communicate with other agents.By receiving spatial information from both its environment and other agents,an agent can use various methods and sensor types to localize itself.With its high flexibility and robustness,collaborative positioning has become a widely used method in both military and civilian applications.This paper introduces the basic fundamental concepts and applications of collaborative positioning,and reviews recent progress in the field based on camera,LiDAR(Light Detection and Ranging),wireless sensor,and their integration.The paper compares the current methods with respect to their sensor type,summarizes their main paradigms,and analyzes their evaluation experiments.Finally,the paper discusses the main challenges and open issues that require further research.

Method for determining the position of landslide slip-surface with a typical inclinometric curves

In the actual monitoring of deep hole displacement,the identification of slip surfaces is primarily based on abrupt changes observed in the inclinometric curve.In conventional identification methods,inclinometric curves exhibiting indications of sliding can be categorized into three types:B-type,D-type,and r-type.The position of the slip surface is typically determined by identifying the depth corresponding to the point of maximum displacement mutation.However,this method is sensitive to the interval of measurement points and the observation scale of the coordinate axes and suffers from unclear sliding surfaces and uncertain values.Based on the variation characteristics of these diagonal curves,we classified the landslide into three components:the sliding body,the sliding interval,and the immobile body.Moreover,three different generalization models were established to analyze the relationships between the curve form and the slip surface location based on different physical indicators such as displacement rate,relative displacement,and acceleration.The results show that the displacement rate curves of an r-type slope exhibit a clustering feature in the sliding interval,and by solving for the depth of discrete points within the step phase,it is possible to determine the location of the slip surface.On the other hand,D-type slopes have inflection points in the relative displacement curve located at the slip surface.The acceleration curves of B-type slopes exhibit clustering characteristics during the sliding interval,while the scattered acceleration data demonstrate wandering characteristics.Consequently,the slip surface location can be revealed by solving the depth corresponding to the maximum acceleration with cubic spline interpolation.The approach proposed in this paper was applied to the monitoring data of a landslide in Yunnan Province,China.The results indicate that our approach can accurately identify the slip surface location and enable computability of its position,thereby enhancing applicability and reliability of the deep-hole displacement monitoring data.

Effects of the initiation position on the damage and fracture characteristics of linear-charge blasting in rock

To study the effects of the initiation position on the damage and fracture characteristics of linear-charge blasting, blasting model experiments were conducted in this study using computed tomography scanning and three-dimensional reconstruction methods. The fractal damage theory was used to quantify the crack distribution and damage degree of sandstone specimens after blasting. The results showed that regardless of an inverse or top initiation, due to compression deformation and sliding frictional resistance, the plugging medium of the borehole is effective. The energy of the explosive gas near the top of the borehole is consumed. This affects the effective crushing of rocks near the top of the borehole, where the extent of damage to Sections Ⅰ and Ⅱ is less than that of Sections Ⅲ and Ⅳ. In addition, the analysis revealed that under conditions of top initiation, the reflected tensile damage of the rock at the free face of the top of the borehole and the compression deformation of the plug and friction consume more blasting energy, resulting in lower blasting energy efficiency for top initiation. As a result, the overall damage degree of the specimens in the top-initiation group was significantly smaller than that in the inverse-initiation group. Under conditions of inverse initiation, the blasting energy efficiency is greater, causing the specimen to experience greater damage. Therefore, in the engineering practice of rock tunnel cut blasting, to utilize blasting energy effectively and enhance the effects of rock fragmentation, using the inverse-initiation method is recommended. In addition, in three-dimensional(3D) rock blasting, the bottom of the borehole has obvious end effects under the conditions of inverse initiation, and the crack distribution at the bottom of the borehole is trumpet-shaped. The occurrence of an end effect in the 3D linear-charge blasting model experiment is related to the initiation position and the blocking condition.

Influence of High-Pressure Induced Lattice Dislocations and Distortions on Thermoelectric Performance of Pristine SnTe

As a sister compound of PbTe, SnTe possesses the environmentally friendly elements. However, the pristine SnTe compounds suffer from the high carrier concentration, the large valence band offset between the L and Σpositions and high thermal conductivity. Using high-pressure and high-temperature technology, we synthesized the pristine SnTe samples at different pressures and systemically investigated their thermoelectric properties.High pressure induces rich microstructures, including the high-density dislocations and lattice distortions, which serve as the strong phonon scattering centers, thereby reducing the lattice thermal conductivity. For the electrical properties, pressure reduces the harmful high carrier concentration, due to the depression of Sn vacancies.Moreover, pressure induces the valence band convergence, reducing the energy separation between the L and Σpositions. The band convergence and suppressed carrier concentration increase the Seebeck coefficient. Thus, the power factors of pressure-sintered compounds do not deteriorate significantly under the condition of decreasing electrical conductivity. Ultimately, for a pristine SnTe compound synthesized at 5 GPa, a higher ZT value of 0.51 is achieved at 750 K, representing a 140% improvement compared to the value of 0.21 obtained using SPS. Therefore, the high-pressure and high-temperature technology is demonstrated as an effectively approach to optimize thermoelectric performance.

Encroachment drives facilitation at alpine shrublines

Ongoing encroachment is driving recent alpine shrubline dynamics globally,but the role of shrub-shrub interactions in shaping shrublines and their relationships with stem density changes remain poorly understood.Here,the size and age of shrubs from 26 Salix shrubline populations along a 900-km latitudinal gradient(30°-38°N)were measured and mapped across the eastern Tibetan Plateau.Point pattern analyses were used to quantify the spatial distribution patterns of juveniles and adults,and to assess spatial associations between them.Mean intensity of univariate and bivariate spatial patterns was related to biotic and abiotic variables.Bivariate mark correlation functions with a quantitative mark(shrub height,basal stem diameter,crown width)were also employed to investigate the spatial relationships between shrub traits of juveniles and adults.Structural equation models were used to explore the relationships among conspecific interactions,patterns,shrub traits and recruitment dynamics under climate change.Most shrublines showed clustered patterns,suggesting the existence of conspecific facilitation.Clustered patterns of juveniles and conspecific interactions(potentially facilitation)tended to intensify with increasing soil moisture stress.Summer warming before 2010 triggered positive effects on population interactions and spatial patterns via increased shrub recruitment.However,summer warming after2010 triggered negative effects on interactions through reduced shrub recruitment.Therefore,shrub recruitment shifts under rapid climate change could impact spatial patterns,alter conspecific interactions and modify the direction and degree of shrublines responses to climate.These changes would have profound implications for the stability of alpine woody ecosystems.

Cryptic divergences and repeated hybridizations within the endangered “living fossil” dove tree(Davidia involucrata) revealed by whole genome resequencing

The identification and understanding of cryptic intraspecific evolutionary units(lineages) are crucial for planning effective conservation strategies aimed at preserving genetic diversity in endangered species.However, the factors driving the evolution and maintenance of these intraspecific lineages in most endangered species remain poorly understood. In this study, we conducted resequencing of 77 individuals from 22 natural populations of Davidia involucrata, a “living fossil” dove tree endemic to central and southwest China. Our analysis revealed the presence of three distinct local lineages within this endangered species, which emerged approximately 3.09 and 0.32 million years ago. These divergence events align well with the geographic and climatic oscillations that occurred across the distributional range.Additionally, we observed frequent hybridization events between the three lineages, resulting in the formation of hybrid populations in their adjacent as well as disjunct regions. These hybridizations likely arose from climate-driven population expansion and/or long-distance gene flow. Furthermore, we identified numerous environment-correlated gene variants across the total and many other genes that exhibited signals of positive evolution during the maintenance of two major local lineages. Our findings shed light on the highly dynamic evolution underlying the remarkably similar phenotype of this endangered species. Importantly, these results not only provide guidance for the development of conservation plans but also enhance our understanding of evolutionary past for this and other endangered species with similar histories.

Gates joint locally connected network for accurate and robust reconstruction in optical molecular tomography

Optical molecular tomography(OMT)is a potential pre-clinical molecular imaging technique with applications in a variety of biomedical areas,which can provide non-invasive quantitative three-dimensional(3D)information regarding tumor distribution in living animals.The construction of optical transmission models and the application of reconstruction algorithms in traditional model-based reconstruction processes have affected the reconstruction results,resulting in problems such as low accuracy,poor robustness,and long-time consumption.Here,a gates joint locally connected network(GLCN)method is proposed by establishing the mapping relationship between the inside source distribution and the photon density on surface directly,thus avoiding the extra time consumption caused by iteration and the reconstruction errors caused by model inaccuracy.Moreover,gates module was composed of the concatenation and multiplication operators of three different gates.It was embedded into the network aiming at remembering input surface photon density over a period and allowing the network to capture neurons connected to the true source selectively by controlling three different gates.To evaluate the performance of the proposed method,numerical simulations were conducted,whose results demonstrated good performance in terms of reconstruction positioning accuracy and robustness.

An improved particle filter indoor fusion positioning approach based on Wi-Fi/PDR/geomagnetic field

The existing indoor fusion positioning methods based on Pedestrian Dead Reckoning(PDR)and geomagnetic technology have the problems of large initial position error,low sensor accuracy,and geomagnetic mismatch.In this study,a novel indoor fusion positioning approach based on the improved particle filter algorithm by geomagnetic iterative matching is proposed,where Wi-Fi,PDR,and geomagnetic signals are integrated to improve indoor positioning performances.One important contribution is that geomagnetic iterative matching is firstly proposed based on the particle filter algorithm.During the positioning process,an iterative window and a constraint window are introduced to limit the particle generation range and the geomagnetic matching range respectively.The position is corrected several times based on geomagnetic iterative matching in the location correction stage when the pedestrian movement is detected,which made up for the shortage of only one time of geomagnetic correction in the existing particle filter algorithm.In addition,this study also proposes a real-time step detection algorithm based on multi-threshold constraints to judge whether pedestrians are moving,which satisfies the real-time requirement of our fusion positioning approach.Through experimental verification,the average positioning accuracy of the proposed approach reaches 1.59 m,which improves 33.2%compared with the existing particle filter fusion positioning algorithms.

A semantic vector map-based approach for aircraft positioning in GNSS/GPS denied large-scale environment

Accurate positioning is one of the essential requirements for numerous applications of remote sensing data,especially in the event of a noisy or unreliable satellite signal.Toward this end,we present a novel framework for aircraft geo-localization in a large range that only requires a downward-facing monocular camera,an altimeter,a compass,and an open-source Vector Map(VMAP).The algorithm combines the matching and particle filter methods.Shape vector and correlation between two building contour vectors are defined,and a coarse-to-fine building vector matching(CFBVM)method is proposed in the matching stage,for which the original matching results are described by the Gaussian mixture model(GMM).Subsequently,an improved resampling strategy is designed to reduce computing expenses with a huge number of initial particles,and a credibility indicator is designed to avoid location mistakes in the particle filter stage.An experimental evaluation of the approach based on flight data is provided.On a flight at a height of 0.2 km over a flight distance of 2 km,the aircraft is geo-localized in a reference map of 11,025 km~2using 0.09 km~2aerial images without any prior information.The absolute localization error is less than 10 m.