Search

Text processing tasks commonly grapple with the challenge of high dimensionality. One of the most effective solutions to this challenge is to preprocess text data through feature selection methods. Feature selection can select the most advantageous features for subsequent operations (e.g., classification) from the native feature space of the text. This process effectively trims the feature space's dimensionality, enhancing subsequent operations' efficiency and accuracy. This paper proposes a straightforward and efficient filter feature selection method based on document-term matrix unitization (DTMU) for text processing. Diverging from previous filter feature selection methods that concentrate on scoring criteria definition, our method achieves more optimal feature selection by unitizing each column of the document-term matrix. This approach mitigates feature-to-feature influence and reinforces the role of the weighting proportion within the features. Subsequently, our scoring criterion subtracts the sum of weights for negative samples from positive samples and takes the absolute value. We conduct numerical experiments to compare DTMU with four advanced filter feature selection methods: max–min ratio metric, proportional rough feature selector, least loss, and relative discrimination criterion, along with two classical filter feature selection methods: Chi-square and information gain. The experiments are performed on four ten-thousand-dimensional feature space datasets: b o o k , d v d , m u s i c , m o v i e and two thousand-dimensional feature space datasets: i m d b , a m a z o n _ c e l l s , sourced from Amazon product reviews and movie reviews. Experimental findings demonstrate that DTMU selects more advantageous features for subsequent operations and achieves a higher dimensionality reduction rate than those of the other six methods used for comparison. Moreover, DTMU exhibits robust generalization capabilities across various classifiers and dimensional datasets. Notably, the average CPU time for a single run of DTMU is measured at 1.455 s. • This paper offers DTMU, a filter feature selection method enhancing feature quality via unitization for improved properties. • DTMU is notably user-friendly, involving only two straightforward steps. • This paper substantiates, through numerical experiments, that DTMU stands as an advanced and effective method. [ABSTRACT FROM AUTHOR]

This paper presents a cost-effective and efficient closed-loop calibration method to enhance the absolute positioning accuracy of industrial robots. The method utilizes an economical and highly accurate set of simple measurement devices, including a device mounted on the robot's end effector and a spherical constraint device positioned within the robot's workspace. A novel local area measurement method is employed for the spherical constraint device, effectively converting position errors into the errors in the sphere center position of the constraint device. Furthermore, the error model considers both kinematic parameter deviations of the robot itself as well as those of the measurement device, along with non-kinematic errors caused by link self-weight. The closed-loop calibration model relies on position constraints, enabling identification and compensation of all error parameters using Levenberg Marquardt method after substituting measured data. The effectiveness of this proposed method is demonstrated through simulation and experimentation. In simulations, average position error reduces from 8.249 mm to 0.8384 mm, while absolute mean difference in sphere center positions obtained using our measurement equipment decreases from 1.206 mm to 0.1027 mm. Significant reductions in both position error and difference in sphere center position are indicated after calibration. This proves that the absolute mean value of the sphere center position difference can be used as the basis for judging the size of the robot's end position error. Experimental results show that absolute mean difference in sphere center position decreases from 0.4319 mm to 0.02869 mm, leading to substantial improvement in overall positioning accuracy. • Calibration model incorporates both kinematic and non-kinematic deviation. • Local area measurement data effectively reflects the robot's end position error. • Closed-loop calibration method exhibits robustness in the presence of noise. [ABSTRACT FROM AUTHOR]

The spectral radius ρ (A) is the maximum absolute value of the eigenvalues of a matrix A. In this paper, we establish some relationship between the spectral radius of a symmetric matrix and its principal submatrices, i.e., if A is partitioned as a 2 × 2 block matrix A = ( 0 A 12 A 21 A 22 ) , then ρ (A) 2 ≤ ρ 2 2 + θ ⁎ , where θ ⁎ is the largest real root of the equation μ 2 = (x − ν) 2 (ρ 2 2 + x) and ρ 2 = ρ (A 22) , μ = ρ (A 12 A 22 A 21) , ν = ρ (A 12 A 21). Furthermore, the results are used to obtain several upper bounds of the spectral radius of graphs, which strengthen or improve some known results. [ABSTRACT FROM AUTHOR]

In this paper, Mg 2.3 Y 0.1 Ni + x wt.% graphene (x = 1, 3, 5, 7) composite hydrogen storage alloys were fabricated by mechanical ball milling of Mg 2.3 Y 0.1 Ni alloy powder and graphene. The experimental results show that the phases of the composite alloy consist mainly of Mg 2 Ni, Mg, MgNi 2 and Ni 3 Y phases, and graphene tends to be distributed at the edges of the alloy, increasing the phase boundary resulting from the contact between the C-boundary and the Mg 2.3 Y 0.1 Ni alloy, providing more channels for the diffusion of H 2. In which 7 wt.% of graphene is added, the gestation period of the composite alloy completely disappears. And the ball-milled alloy with 3 wt.% graphene at different temperatures has the highest hydrogen uptake in 2 min and the highest hydrogen release in 10 min. At 573 K, the composite alloy has a hydrogen absorption capacity of 3.251 wt.% H 2 in 2 min and reaches 90.21% of the maximum hydrogen absorption, while it is able to release 3.389 wt.% H 2 in 10 min and reaches 99.04% of the maximum hydrogen release. And the composite alloy with 3 wt.% graphene has the smallest dehydrogenation activation energy. The absolute value of the enthalpy change is reduced from 60.1 kJ/mol to 54.8 kJ/mol, and the desorption enthalpy change is reduced from 73.4 kJ/mol to 67.5 kJ/mol. • Addition of graphene increases the phase boundary of the composite alloy. • Graphene lowers the reaction barrier of the alloy with hydrogen. • Graphene improves the kinetics of hydrogen absorption/release of the alloy. • Graphene reduces the thermodynamic stability of composite alloys. [ABSTRACT FROM AUTHOR]

Let M n be the space of real matrices of order n. The sign-real spectral radius ξ : M n → R + , introduced in a 1997 paper by S.M. Rump, intervenes for instance in the problem of estimating the componentwise distance to singularity. The function ξ has also a bearing in the analysis of generalized absolute value equations and linear complementarity problems. Although ξ is not a norm, it is at least absolutely homogeneous and continuous. Furthermore, ξ is invariant under transposition, permutation similarity, and a few other linear isomorphisms on M n. A matrix A ∈ M n is called sign-real expansive if ξ (A) ≥ 1. Let Ω n be the set of such matrices. The purpose of this work is to discover new properties of the function ξ and to explore in detail the structure of the set Ω n. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph. The Seidel energy of G , denoted by E s (G) , is the sum of absolute values of all Seidel eigenvalues of G. A complete r -partite graph with n vertices is called r -partite Turán graph, denoted by T (n , r) , if the number of vertices of each part is either ⌊ n r ⌋ or ⌈ n r ⌉. In 2021, Tian et al. proposed a problem that for any edge e of Turán graph T (n , r) with r ≥ 4 , does there exist a sufficiently large integer n 0 such that E s (T (n , r)) < E s (T (n , r) − e) whenever n ≥ n 0 . In this paper, we prove that the Seidel energy of T (n , 5) of order n ≥ 5 is always increased when an edge is deleted. [ABSTRACT FROM AUTHOR]

The stress state of a fault plane influences the mode of sliding and characteristics of slide behaviour. Existing researchers have mainly focused on studying the effect of shear stiffness on fault behaviour under the constant normal load (CNL) boundary conditions. However, the impact of the normal stiffness effect of deep faults on fault sliding stability and seismic source parameters remains uncertain. Addressing the issue, this paper conducts friction tests on granite-simulated faults under the constant normal stiffness (CNS) boundary conditions. It analyzes the impact of normal stiffness on the mechanical behaviour of fault sliding. The results of this paper demonstrate the following findings: (1) Under both normal boundary conditions, various sliding modes occur, including creep-slip, chaotic stick-slip, regular inclusion chaotic stick-slip, and regular stick-slip. (2) The normal stiffness effect reduces the duration of creep-slip and chaotic stick-slip behaviour and decreases the frequency of regular inclusion chaotic stick-slip behaviour. (3) Shear stress and normal stress of the regular stick-slip mode exhibit periodic changes under the CNS boundary conditions. (4) Compared to the CNL boundary conditions, the CNS boundary conditions show a larger shear stress drop and a positive correlation between the normal stress drop and normal stiffness. (5) The CNS boundary conditions result in larger shear stiffness, the absolute value of stick-slip stiffness, characteristic sliding displacement, and fracture energy compared to the relevant seismic source parameters of the CNL boundary conditions. These parameters display positive correlations with normal stiffness. The stick-slip period and normal stiffness initially decrease and then increase, while the normal displacement drop and normal stiffness display a negative correlation trend. These analyses provide comprehensive insights into the mechanical characteristics of fault-slip behaviour and can contribute to improving models and predictions related to fault-sliding behaviour and seismic activity. • We discover a new fault-slip pattern known as regular inclusion chaotic stick-slip. • The normal stiffness effect shortens the duration of fault-slip behaviour. • Under CNS condition, the shear and normal stress exhibit synchronous changes. • The values of seismic source parameters tend to be larger for the CNS condition. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to solve tensor absolute value equation by using preconditioned techniques and the inexact fixed point iteration method. For an existing preconditioner, we present a new inexact fixed point iteration method for solving tensor absolute value equation. Theoretically, we give the convergence of the proposed method. Numerically, we show the efficiency of the proposed method by two numerical examples. [ABSTRACT FROM AUTHOR]

Rapidly populating renewable energy sources and storage units at the distribution system, made it crucial to monitor the system in real-time. This necessity brings new challenges and business opportunities for the distribution system operator (DSO). DSO requires situational awareness on the system via several analyses, most of which rely on correct system topology. However, switch statuses of the distribution system may not be telemetered or transferred correctly to the DSO, despite having several switching actions daily. This paper proposes a state estimation based method for distribution systems with limited number of measurements to detect and identify topology error. The method is applicable with both conventional SCADA and/or PMU measurements. Weighted Least Absolute Values (WLAV) state estimator is employed because of its robustness against inaccurate measurements or bad data. The computational performance of the proposed method is comparable with that of the WLAV state estimator, and hence applicable in practical applications. • High performance algorithm for distribution system topology error detection. • Performing in the presence of limited number of field measurements. • Reduced uncertainty using the Weighted Least Absolute Value (WLAV) state estimator. [ABSTRACT FROM AUTHOR]

• A disturbance simulation model of tooth-flexible body residual film-soil based on DEM-MBD was established. • The flow characteristics of film-soil was studied using DEM-MBD simulation methods. • A film picking test bench was established to verify the reliability of the simulation model. • The cross-sectional shape of soil was used to verify the accuracy of DEM simulation models. • The mechanical properties and tensile performance of the residual film were analyzed. The residual film in the cotton cultivation layer will seriously affect cotton cultivation, and mechanized recycling of residual film is currently the best way to solve this problem. To improve the recovery effect of the chain tooth tillage layer residual film recovery machine, a bionic elastic tooth was designed in this paper. Furthermore, DEM-MBD coupling multibody dynamics was used as the research method to study the bionic elastic tooth-residual film-soil interactive disturbance. A DEM-MBD simulation model for predicting the film lifting effect of a film lifting device has been established. And the DEM-MBD simulation model was used to optimize the design parameters of the film lifting device by studying the film lifting effect of the elastic teeth. The absolute value of the maximum curvature at the tip of the elastic tooth (A), the angle between the midline of the power wheel and the ground plane (B), and the spacing of the elastic teeth (C) were used as the influencing factors. The optimal solution parameters (A = 0.03, B = 54°, C = 83 mm) were obtained. The field test's film picking and disturbance rate was 91.27 %, the error with the simulation results (89.69 %) was 1.8 %, which verified the accuracy of the simulation results and the superiority of the optimized parameters. The recovery rates of residual film under soil compaction conditions of 600 kPa, 800 kPa, and 1000 kPa were 91.25 %, 90.94 %, and 90.89 % (Verified the strong adaptability of the device). This study can provide a theoretical research basis and test methods for the design optimization of touching parts. [ABSTRACT FROM AUTHOR]

• A composite fringe pattern based on a spatial orthogonal frequency multiplexing is meticulously crafted, incorporating ample spatial and temporal information and providing neural network with the theoretical basis for learning the required mapping correspondence. • An end-to-end network is designed to achieve pixel-wise prediction of absolute phase values, utilizing a nested strategy and the concept of centralized information interaction. • A diverse dataset comprising numerous scenes is collected, wherein high-precision ground truths are computed using standard N -step phase-shifting and multi-frequency temporal phase unwrapping methods. • A seven-map training loss calculation strategy is adopted to instruct training process. • The first qualitative experiment proves the superiority of our method over alternative four methods. The second quantitative evaluation and respectively validates its capability in high dynamic range 3D measurement and in precise 3D measurement. The pursuit of precise and efficient 3D shape measurement has long been a focal point within the fringe projection profilometry (FPP) domain. However, achieving precise 3D reconstruction for isolated objects from a single fringe image remains a challenging task in the field. In this paper, a deep learning-based frequency-multiplexing (FM) composite-fringe projection profilometry (DFCP) is proposed, where an end-to-end absolute phase retrieval network (APR-Net) is trained to directly recover the absolute phase map from a FM composite fringe pattern. The obtained absolute phase map exhibits exceptional precision and is devoid of spectrum crosstalk or leakage disturbance typically encountered in traditional FM techniques. APR-Net is intricately crafted, incorporating a nested strategy along with the concept of centralized information interaction. A diverse dataset encompassing various scenarios and free from spectrum aliasing is assembled to guide the training process. A seven-map loss calculation scheme is employed to guide the training process, of which the efficacy is proved through ablation experiments. In the first qualitative experiment, DFCP demonstrates comparable phase accuracy to ground truths with 47 fewer projected images, outperforming other three methods with mean absolute phase errors of 0.0052 rad, 0.1761 rad, 0.0169 rad, and 0.0139 rad. The second qualitative experiment and the quantitative evaluation respectively prove DFCP's capability in high dynamic range 3D measurement and in precise 3D measurement, with sphere diameter errors of 0.0780 mm and 0.0726 mm, and a spherical centroid distance error of 0.0555 mm. [ABSTRACT FROM AUTHOR]

In order to enhance the texture and particle retention capabilities of the anti-abrasive seal layer, this paper focuses on the interlocking pattern between the seal and the particles of the pavement, and for the first time considers the base pavement texture, the particle size of the seal, and the amount of seal particles as design variables. The study investigates the relationship between these factor variables and response variables such as texture loss and mass loss. An optimization of the plan design was conducted using the I-optimization method in the mixture design of Design Expert software. The study involved a long-term wear test of 20,000 wear cycles on anti-abrasive seals. The response surfaces corresponding to each response variable were calculated using RSM (response surface method), thereby providing design solutions with high wear-resistant performance. Finally, the rationality and scientific nature of the optimized solutions were verified using three-dimensional texture indices, preliminarily elucidating the texture characteristics of the high wear-resistant performance. The results indicate that combinations of 0.7 kg/m² aggregate usage, 0.8 mm-1.0 mm texture depth, 0.6 mm-1.18 mm aggregate particle size, and 0.75 kg/m² aggregate usage, 1.2 mm-1.3 mm texture depth, 0.3 mm-0.6 mm aggregate particle size experienced the least quality and TD loss. The general texture characteristics of high wear-resistant seal layers include a small Sq value (Sq less than 1.8), a moderate Ssk value (Ssk approximately 0), and a slightly higher Sku value (Sku greater than 3). However, if Ssk is not close to zero (and the absolute value of Ssk is too large), even higher Sku values can result in increased large losses. • The durability of the seal layer is enhanced by improving the interlock between particles and aggregates. • RSM is used to optimize the design of sealing parameters such as aggregate size, aggregate amount, and base texture. • The height distribution of particles is assessed through the kurtosis and skewness measurements in three-dimensional texture analysis. • Recommendations are made regarding the appropriate matching of the base texture with the particle size and quantity. [ABSTRACT FROM AUTHOR]

In the paper, the mechanical properties of uniaxial tensile sintered nano-silver components were investigated by molecular dynamics method, and the effects of sintering pressure and temperature on them were analyzed. The sintered body was obtained by sintering three adjacent cubes, and the sintered nano-silver component under uniaxial tension was cut from the existing sintered body. The results show that the potential energy decreases while the kinetic energy has a jump. The higher the sintering pressure, the earlier the nano-silver sintering begins. Temperature has little effect on sintering time. When sintered nano-silver components are uniaxial tensile, the greater the sintering pressure, the greater the rising absolute value of the potential energy, and the greater the yield stress. When the sintering temperature is 250 °C, the variation of potential energy is large and the yield stress is high. The paper aims to supplement and guide the mechanical properties of sintered nano-silver. • The mechanical properties of sintered nano-silver components were simulated. • Uniaxial tension rather than sintering process is analyzed. • The influence of sintering pressure and temperature on it was investigated. • The greater the sintering pressure, the greater the yield stress. • When the sintering temperature is 250 °C, the yield stress is high. [ABSTRACT FROM AUTHOR]

Many problems in scientific computing and engineering fields lead to the solution of generalized absolute value equations (GAVE). In this paper, by simultaneously splitting both coefficient matrices in the differential and non-differential parts of the GAVE, a modified Newton-based matrix splitting (MNMS) iteration method is proposed. The MNMS iteration method not only covers the well-known generalized Newton iteration method as well as the recent proposed modified Newton-based iteration method and the Newton-based matrix splitting iteration method for solving the GAVE, but also results in a series of relaxation versions that are very flexible in real applications. Convergence properties of the MNMS iteration method are studied in detail when the coefficient matrices are positive definite matrices and H + -matrices. Finally, three numerical examples are presented to show the feasibility and effectiveness of the proposed MNMS iteration method. [ABSTRACT FROM AUTHOR]

The current standard in China does not specify the standard test method for determining Poisson's ratio, and the Poisson's ratio used in pavement design is often roughly fixed, which can result in large errors in the calculations and analysis of road structure. In this paper, the research on different test methods for Poisson's ratio is carried out and the non-linear characteristics of tensile and compressive Poisson's ratio on pavement materials under different influencing factors are analyzed. The results indicate that the absolute value of the ratio between transverse rebound strain and longitudinal rebound strain under 50% of the maximum destructive load can objectively characterize the mechanical properties of Poisson's ratio, and it is the optimal measurement method for Poisson's ratio in asphalt pavement materials. The Poisson's ratio of two pavement materials both decreases with the increase of loading rate and gradually tends to a constant value. Cement dosage and temperature are the most significant factors affecting the tensile and compressive Poisson's ratio of cement stabilized crushed stone and asphalt mixture, respectively. Specifically, when cement dosage increases by 1%, the Poisson's ratio of cement stabilized crushed stone decreases by approximately 10%, and the temperature has a significant influence on the difference in tension and compression for Poisson's ratio of asphalt mixture (up to 40%). The asphalt content corresponding to the minimum Poisson's ratio is basically consistent with the optimal asphalt content obtained by the Marshall volume method. Based on these, a quantification value-taking model is established of the tensile and compressive Poisson's ratios of typical asphalt pavement materials varying with multiple factors. The research results can serve as a reference for the scientific value-taking of pavement structural design parameters considering the different mechanical characteristics of materials in tension and compression. • The scientific and reasonable measuring method of Poisson's ratio was established. • The quantitative model of Poisson's ratio affected by many factors was established. • The Poisson's ratio increases with loading speed and gradually tends to stabilize. • The optimum asphalt content mixture by Marshall method has minimum Poisson's ratio [ABSTRACT FROM AUTHOR]

Engine performance models are used in various fields, such as operation optimization, control, and diagnosis. In order to effectively apply an engine performance model in these fields, a high level of prediction accuracy is required. When improving the accuracy of an engine model through performance adaptation using measurement data, it is important to functionalize the component adaptation factors calculated at each measurement point to enable them to be utilized at other operating points. A method of curve fitting to find the adaptation factor for a single performance parameter was previously used to functionalize the component adaptation factor. In this paper, machine learning techniques are newly applied to functionalize component adaptation factors for several parameters, including engine operation characteristics, and their effectiveness is analyzed. The prediction accuracy of the adapted model for a two-spool mixed-flow turbofan engine is compared based on the fan exit total pressure, high-pressure compressor (HPC) exit static pressure, exhaust gas temperature (EGT), and high-pressure spool speed. For an engine model adapted using the existing functionalization method, the average absolute value of the relative errors in the fan exit total pressure, HPC exit static pressure, EGT, and high-pressure spool speed in the validation dataset were 2.91 %, 2.20 %, 5.32 %, and 1.84 %, respectively, whereas for an engine model adapted using the proposed machine learning-based functionalization method, these errors were 0.70 %, 1.00 %, 2.56 %, and 0.26 %, respectively, under the same conditions. As a result, it was confirmed that the performance prediction accuracy of the engine model adapted using the proposed method was improved compared to the existing method. [ABSTRACT FROM AUTHOR]

Precision current detection is essential in smart power switches. In this paper, a current-sensing amplifier with symmetric topology is presented, which adopts the chopping technique to improve sensing accuracy. This design offers four advantages at the same time. Firstly, the rail-to-rail complementary differential pairs are achieved to obtain a full input voltage swing, and the Class AB output stage is incorporated to increase the slew rate. Secondly, symmetric topology with the current shunt source provides moderate gain enhancement without extra power consumption and further increases the gain bandwidth product. Thirdly, the chopping technique is applied to achieve a significant reduction in the amplifier's input offset without an extra low pass filter. Fourthly, the constant G M -C biasing circuit is introduced to improve the robustness of system response and current sensing accuracy under process variations. The four advantages can be substantiated through the application of a 0.5-μm BCD technology process, with multiple simulation results, including frequency responses and current sensing accuracy in process corners and temperature variations. The mismatch Monte-Carlo and noise analyses are also conducted with the chopper on or off. Chip experimental results show that the current sensing error is within ±1.6 % from 0.01 A to 3 A load current. Furthermore, multiple tests have been conducted to determine the absolute values of the input offset voltages, ranging between 20 μV and 50 μV, which is a relatively small amount to vastly improve the sensing accuracy. [ABSTRACT FROM AUTHOR]

For layered models with a low-velocity half-space, Rayleigh waves can exhibit inversely dispersive patterns and thus are advantageous for providing useful information on the seismic properties of such structures. However, the calculation of dispersion curves usually encounters some difficulties such as root skipping or numerical instability due to the presence of leaky modes. The full-wavefield method and spectral element method can offer better solutions but at the cost of a significant computational effort. For practical applications, most researchers treat the zeros of the real part of the secular function as an approximation to the leaky modes, which may lead to relatively large errors that cannot be ignored. Instead, in this paper, we propose a simple and efficient method to approximate the leaky mode based on the local minima of the absolute value of the secular function. Compared with the dispersion curve generated from the real part of the secular function, the proposed method can provide a more accurate approximation. We further apply a new efficient Monte Carlo search technique to two synthetic datasets and a permafrost example. Results show that our forward and inverse methods are effective, efficient, and robust. Moreover, our numerical experiments indicate that the modified Thomson-Haskell method is more suitable for calculating leaky modes compared with the fast delta method and the generalized reflection/transmission method, and that the inversion results are less sensitive to the effect of the limited spread length on the measured dispersion curves. The present study emphasizes the high efficiency of the proposed method in imaging permafrost structures and foundation features of buildings or roads. • A fast solver for calculating the apparent modes due to a low-velocity half-space. • The modified Thomson-Haskell method is more suitable for calculating the leaky modes. • Application for imaging permafrost structures. [ABSTRACT FROM AUTHOR]

In this paper, the tracking control problem of the uncertain control system is studied in the frame of uncertainties estimation and compensation. To eliminate the influence of external disturbances and internal uncertainties on the control system, the error-driven nonlinear extended state observer (EDN-ESO), whose gain is set as an increasing function with respect to the absolute value of estimation error of the system output, is proposed to improve the estimation performance for the "total disturbance". Next, both the estimation error of proposed ESO and the tracking error of system output are proven to be bounded by selecting the lower bound and variation range of ESO's bandwidth. Moreover, the convergence of the estimation error as well as the tracking error to zero is proven under certain conditions. Finally, the proposed design method is applied to the air–fuel ratio control system of gasoline engines, and the experimental results show that the proposed EDN-ESO can effectively adjust the observer gain, so as to enhance the tracking performance. • A novel error-driven nonlinear ESO is designed to achieve faster response of ESO. • The stability of the proposed ESO and the closed-loop system are both proven. • The AFR experiment shows that the proposed method can enhance the tracking effect. [ABSTRACT FROM AUTHOR]

Let Γ = (G , σ) be a signed graph. The spectral radius of Γ is the largest absolute value of its adjacency eigenvalues. In this paper we identify the real numbers which are limit points of spectral radii of signed graphs. This is one of the two aspects of a problem in spectral graph theory known as the Hoffman program, implemented here for signed graphs. [ABSTRACT FROM AUTHOR]

• Stable and homogeneous of droplets for the aqueous two-phase system is achieved. • Neck evolution of water-in-water droplets in flow-focusing devices is self-similar. • Four flow patterns were observed and analyzed. • Formation process of droplet includes slow and fast squeezing, and pinch-off stages. • Evolution regulations of droplet neck interface in three stages were described. In ATPS, the ultra-low interfacial tension makes the stable generation of droplets very difficult. In this paper, the stable and homogeneous preparation of ATPS droplets is achieved over a wide range of flow rates, and the self-similarity analysis and formation dynamics of the droplets are studied. Formation of ATPS droplets show good self-similarity. The generation process of ATPS droplets can be divided into slow squeezing, fast squeezing and rapid pinch-off stages. In the slow squeezing stage, the dimensionless minimum neck width w m / w c is linear with the time, and the absolute value of the slope increases with the capillary number of continuous phase Ca c. In the rapid squeezing and rapid pinch-off stages, the w m / w c satisfies the power-law relationship with time, and the absolute value of the power-law indexes decrease with increasing Ca c , and the pre-exponential factor of pinch-off stage increases with increasing Ca c. [ABSTRACT FROM AUTHOR]