Central Path Research Articles

Development of an analyzing and tuning technology for improving circularity of cone-frustum motions of five-axis CNC machine tools

The machining of a cone frustum as specified on the ISO 10791-7 standard is a widely accepted test to evaluate the performance of five-axis machining centers. By measuring the cross-sectional circularity of the cone, the contouring accuracy of a five-axis CNC machine tool can be assessed. A reduction of circularity is directly related to the improvement of the contouring accuracy in circular motions. The contouring accuracy can also be assessed by measuring the circularity of the circular motion path described by the tool center point of a five-axis CNC machine tool. A better circular tool center path entails an enhancement on the circularity of the traversal sections of the cone frustum. The majority of CNC actuators are AC servomotors that are precisely controlled via two closed loops: one for position and one for velocity. The circular contouring accuracy of a five-axis CNC machine tool can be improved by adjusting the loop gains and time constant of the velocity loop integration. Although higher gains enable the servomotors to attain the desired positions faster, the resulting contouring accuracy may not be satisfactory. Furthermore, excessively high gains could cause vibrations. The objective of this research is to establish a frequency domain approach for tuning the control parameters for each motion axis such that their frequency responses are matched within a range of frequencies, reducing the circularity value of the cross sections of a cone frustum. Results demonstrate the effect of tuning the control loop parameters based on the frequency response of each axis. Case studies were conducted to determine the variation in the circularity value when the control parameters of each axis were tuned to obtain similar frequency responses to the linear and rotary axes within a frequency range. Rates of improvement greater than 80% were achieved after using the proposed method to tune the control parameters of each motion axis.

Simplified full Nesterov–Todd step infeasible interior-point algorithm for semidefinite optimization based on a kernel function

In this paper, we propose a new complexity analysis of the full Nesterov–Todd step infeasible interior-point algorithm for semidefinite optimization. With a specific feasibility step and the centering step induced by a well-known kernel function, the property of exponential convexity of the kernel function underlying the matrix barrier function is crucial in the analysis and enable us easily to estimate the proximity of iterates to center path. The analysis of the algorithm is simplified and the iteration bound obtained coincides with the currently best iteration bound for infeasible interior-point algorithm.

On total irregularity strength of caterpillar graphs with two leaves on each internal vertex

Let G(V, E) be a graph. A function f from to the set {1, 2, …, k} is said to be a totally irregular total k-labeling of G if the weights of any two different vertices x and y in V (G) satisfy where the weight wf(x) is the sum of label of x and labels of all edges incident to x, and the weights of any two different edges ux and vy in E(G) satisfy where the weight wf(ux) is obtained from the sum of: label of x, label of u and label of edge ux. The total irregularity strength of the graph G, denoted by ts(G), is the minimum number k for which G has a totally irregular total k-labeling. In this paper, we focus on a caterpillar graph with two leaves on each internal vertex T2n+p,q, where n is the number of leaves on each end vertex of the central path, p is the number of leaves connected to internal vertices, q is the number of vertices of the central path, p > 4 and q > 4. Firstly, we do some experiments for constructing a formula for totally irregular total k-labeling of the caterpillar graph T2n+p,q. Secondly, we determine the minimum number k which is ts of the caterpillar graph T2n+p,q. We obtain that and .

The influence of anode position and structure on cusped field thruster

A cusped field thruster is a kind of electric propulsion device using multi-stage cusped fields to realize plasma discharges and produce thrust. A previous study showed that plasma discharges in this thruster are non-uniform. In this work, a multi-annulus anode is used to measure the radial distribution of anode current density at different anode positions. The experimental results reveal that some electrons may reach the anode along the axis after they accelerate from the final cusp regardless of the anode positions. To further validate this idea and find out the mechanism of this central path along the axis, the central part of the anode is replaced with ceramics. This results in an increase in the total current with larger contributions at larger radii. The current oscillations also get larger. This brief letter is helpful to further understand the movement of electrons in cusped field thrusters and provide guidance on reducing the non-uniform degree of current density.

MODELS OF ROBOT’S WHEEL-MOVER BEHAVIOR ON FERROMAGNETIC SURFACES

The mobile robots which can move on complicated working surfaces play a significant role in the automation of various technological processes, in particular, ship repair, fire fighting, inspection of welding quality, rescue operations, etc. This work is a continuation of the authors’ investigation of the mobile robot’s moving on inclined and vertical ferromagnetic surfaces based on a magnetically operated wheel-mover. Special attention is paid to constructing magnetically operated wheel-mover with twelve legs and modeling of the robot’s wheel-mover behavior in different working modes including investigations of the wheel-mover center trajectory, behavior of control signals, etc. Geometrical dependences between a number of wheel-mover legs and deviation of the wheel center path from horizontal line are described. In the present article the modeling results for movement of the wheel-mover on both plain and non-plain surfaces are discussed. For this purpose, the mathematical model of the wheel-mover was created and analyzed and the results were verified using a simulation approach.

The shift orbits of the graded Kronecker modules

The Kronecker modules (or matrix pencils) are the representations of the n-Kronecker quiver K(n) (the quiver with two vertices, namely a sink and a source, and n arrows) over some fixed field. The universal cover of K(n) is the n-regular tree with bipartite orientation. The paper deals with the representations of the n-regular tree with bipartite orientation (thus with graded Kronecker modules). The simultaneous Bernstein-Gelfand-Ponomarev reflection at all sinks will be called the shift functor, and we consider the orbits under this shift functor. Whereas the length of a regular module growths exponentially when we apply the shift functor repeatedly, the radius of such a module growths just linearly. To any regular shift orbit, we attach a positive integer r (the minimal radius of the sink modules in the orbit) and the path in T(n) which starts at the center p of the sink modules in the orbit and ends at the center q of the source modules in the orbit. If r is even, then p has to be a sink, otherwise a source. We call this path the center path of the orbit (since the center of any module in the orbit lies on this path). If the center path of a shift orbit has length b, then the orbit contains precisely b flow modules, the remaining modules are sink modules and source modules. We use this division in order to index the regular graded Kronecker modules in a coherent way. Conversely, we show that given a positive integer r and a path in T(n) (starting at a sink iff r is even), there are regular shift orbits with these invariants.

An Arc Search Infeasible Interior-Point Algorithm for Symmetric Optimization Using a New Wide Neighborhood

In this paper, we propose an infeasible interior-point algorithm for symmetric optimization problems using a new wide neighborhood and estimating the central path by an ellipse. In contrast of most interior-point algorithms for symmetric optimization which search an $\varepsilon$ -optimal solution of the problem in a small neighborhood of the central path, our algorithm searches for optimizers in a new wide neighborhood of the ellipsoidal approximation of central path. The convergence analysis of the algorithm is shown and it is proved that the iteration bound of the algorithm is $O ( r\log\varepsilon^{-1} ) $ which improves the complexity bound of the recent proposed algorithm by Liu et al. (J. Optim. Theory Appl., 2013, https://doi.org/10.1007/s10957-013-0303-y ) for symmetric optimization by the factor $r^{\frac{1}{2}}$ and matches the currently best-known iteration bound for infeasible interior-point methods.

Does Capsular Laxity Lead to Microinstability of the Native Hip?

Background: Hip “microinstability” is commonly cited as the cause of symptoms that occur in the presence of translation of the femoral head away from conformity with the acetabular fossa. However, there is still no consistent objective criteria defining its presence and biomechanical basis. One hypothesis is that abnormal motion of the articular surfaces occurs because of capsular laxity, ultimately leading to clinical symptoms. Purpose: To determine the relationship between capsular laxity and abnormal rotation and translation of the hip. Study Design: Controlled laboratory study. Methods: Eight cadaveric hips were dissected down to the capsule and mounted in a customized multiaxial hip activity simulator. Each specimen was loaded with 5 N·m of internal and external rotational torque in full extension and 0°, 30°, 60°, and 90° of flexion. During testing, the relative position and rotation of the femur and the pelvis were monitored in real time with a 6-camera motion analysis system. The testing was repeated after capsular laxity was generated by placing a regular array of incisions (“pie crusting”) in the iliofemoral, pubofemoral, and ischiofemoral ligaments. Joint rotation and femoral head translation were calculated with specimen-specific models. A hip microinstability index was defined as the ratio between the length of the locus of the femoral head center and the radius of the femoral head during rotation from extension to 90° of flexion. Results: In intact hips, the components of femoral head translation were within 0.5 mm in positions close to neutral (<30° of flexion). Capsular modification led to significant increases in internal and external rotation (P < .01) and in the translation of the femoral head center at different positions (P < .05). Compared with intact hips, the femoral head was inferiorly displaced during external rotation and anteroinferiorly during internal rotation. The length of the locus of the femoral head center increased from 3.61 ± 1.30 mm to 5.35 ± 1.83 mm for external rotation (P < .05) and from 6.24 ± 1.48 mm to 8.21 ± 1.42 mm for internal rotation (P < .01). The correlations between rotational laxity and the total translation of the femoral head were not significant, with coefficients of 0.093 and 0.006 in external and internal rotation, respectively. In addition, the hip microinstability index increased from 0.40 ± 0.08 for intact hips to 0.55 ± 0.09 for modified hips (P < .01). Conclusion: The native hip approximates a concentric ball-and-socket joint within 30° of flexion; however, beyond 30° of flexion, the femoral head translation reached as high as 4 mm. Capsular laxity leads to microinstability of the hip, as indicated by significantly increased joint rotations and femoral head translations and an abnormal movement path of the femoral head center. However, there was no correlation between rotational laxity and the increase in femoral head translation. Clinical Relevance: Capsular laxity alters normal kinematics (joint rotation and femoral head translation) of the hip, potentially leading to abnormal femoral-acetabular contact and joint degeneration.

How to improve the comfort of Kesawan Heritage Corridor, Medan City

Comfort is indispensable to make a friendly neighborhood or city. Especially the comfort of the infrastructure in the corridor. People must be able to feel comfortable to act rationally in their physical environment. Existing infrastructure must able to support Kesawan as a historic district. Kesawan is an area that is filled with so many unique buildings. Without comfort, how good the existing buildings’ architecture cannot be enjoyed. It will also affect the identity of a region or city. The aim of this research is to re-design the public facilities from Kesawan corridor’s comfort aspect: orientation, traffic calming, vegetation, signage, public facilities (toilet, seating place, bus station, bins), information center, parking and pedestrian path. It will translate the design concept in the form of design criteria. This research uses qualitative methods. Some facilities in this corridor are unsuitable even some of them are not available. So, we need some improvements and additions to the existing facilities. It is expected that by upgrading the existing facilities, visitors who come to Kesawan will be able to enjoy more and able to make Medan city more friendly.

Prognostic value of CD56, ASCL1, and other biomarkers in small cell bladder cancer (SCBC).

452 Background: Increased DLL3 expression (exp) and small cell % (SC%) were found in prior analyses to predict worse outcomes in SCBC. Assessment of gene and protein exp of other Notch pathway and neuroendocrine (NE) markers, such as ASCL1 and CD56, can help with prognostication and treatment target identification in SCBC. Methods: Among 63 patients (pts) with biopsy-confirmed SCBC seen at Cleveland Clinic (1993-2015), 52 had tissue available for IHC analysis of tumor biomarkers: DLL3, PD-L1, ASCL1 and CD56. All pts had clinical and outcomes data, and had SC% quantified by central path review. A subset of 39 pts had gene exp analysis using HTG EdgeSeq OBP assay. Correlations among biomarkers, between biomarkers and pt characteristics as well as gene exp were assessed. Multivariate analyses (MVA) were used to identify predictors of overall (OS) and progression-free survival (PFS). Results: In the 52 pt cohort, median age was 71, 83% were men, 39% had LN+ disease, and 79% had SC% &gt; 50%. Protein exp ( &gt; 1% of tumor cells) of DLL3, PD-L1, ASCL1 and CD56 was noted in 68%, 30%, 52% and 81% of pts, respectively. ASCL1 protein exp correlated with protein exp of DLL3 (r = 0.73, p &lt; .0001), CD56 (r = 0.35, p = .01), and SC% (r = 0.34, p = .01) and correlated with gene exp of several Notch genes and NE markers: DLL3, DLL4, Notch1, CHGA (p &lt; .05 for all). CD56/NCAM1 protein exp correlated with DLL3 protein exp (r = 0.32, p = .02) and with SC% (r = 0.26, p = .06) and with gene exp of DLL4, Notch1, SYP and NCAM1 (p &lt; .05 for all). In MVA, increased CD56 protein exp ( &gt; 30%) was associated with shorter OS (HR: 2.23; 95%CI 1.06-4.70, p = .03) and PFS (HR: 2.07; 95%CI 1.02-4.20, p = .04). Pts with low protein exp of both CD56 (≤30%) and DLL3 (≤10%) had longer median OS (103.4 vs 18.4 months, p = .01) and PFS (92.2 vs 11.4 months, p = .02) relative to pts with high protein exp of either biomarker. Conclusions: Most SCBC tumors expressed CD56, and increased exp predicted shorter OS and PFS, findings similar to those reported for DLL3. Low concurrent exp of both CD56 and DLL3 proteins was associated with better outcomes. Strong correlation of CD56/NCAM1 gene and protein exp suggests that its regulation may be at the transcriptional level. Gene exp signature prognostic of outcomes is currently being pursued in SCBC.

Nonlinear transient analysis of hole-entry journal bearing with constant flow of micropolar fluids

The present work deals with study and analysis of a symmetric hybrid journal bearing compensated with constant flow valve restrictor operating with micropolar fluid from stability point of view. The effect of micropolar parameters on the stability of this journal bearing system is presented on the basis of nonlinear transient model. Finite element method has been used to solve modified Reynolds’ equation for the flow of micropolar fluid through the bearing. Computations are done for the static and dynamic characteristics of hole-entry hybrid journal bearing system. The stability characteristics in terms of critical mass of journal, threshold speed, and frequency of whirl are obtained for journal bearing system operating with Newtonian and micropolar fluids and are compared together. Paths of the journal center in the form of trajectories have also been plotted using the journal center coordinates obtained after solving nonlinear equation of motion by fourth-order Runge–Kutta method to find the stability margin of the considered bearing configuration more precisely and easily. Results indicate that micropolar effect causes significant increase in stability margin of the hybrid journal bearing system especially at higher loads. The results also indicate that lubricant flow through the bearing and type of lubricant should be decided in an appropriate manner for the stability of the constant flow valve compensated hybrid journal bearing system.

An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an "-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O ( p rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior- point algorithm for this class of mathematical problems.

A primal-dual interior-point algorithm for symmetric optimization based on a new method for finding search directions

We introduce an interior-point method for symmetric optimization based on a new method for determining search directions. In order to accomplish this, we use a new equivalent algebraic transformation on the centring equation of the system which characterizes the central path. In this way, we obtain a new class of directions. We analyse a special case of this class, which leads to the new interior-point algorithm mentioned before. Another way to find the search directions is using barriers derived from kernel functions. We show that in our case the corresponding direction cannot be deduced from a usual kernel function. In spite of this fact, we prove the polynomial complexity of the proposed algorithm.

Large-step interior-point algorithm for linear optimization based on a new wide neighbourhood

The interior-point algorithms can be classified in multiple ways. One of these takes into consideration the length of the step. In this way, we can speak about large-step and short-step methods, that work in different neighbourhoods of the central path. The large-step algorithms work in a wide neighbourhood, while the short-step ones determine the new iterates that are in a smaller neighbourhood. In spite of the fact that the large-step algorithms are more efficient in practice, the theoretical complexity of the short-step ones is generally better. Ai and Zhang introduced a large-step interior-point method for linear complementarity problems using a wide neighbourhood of the central path, which has the same complexity as the best short-step methods. We present a new wide neighbourhood of the central path. We prove that the obtained large-step primal–dual interior-point method for linear programming has the same complexity as the best short-step algorithms.

Detecting Shoot Beetle Damage on Yunnan Pine Using Landsat Time-Series Data

Tomicus yunnanensis and Tomicus minor have caused serious shoot damage in Yunnan pine forests in the Yunnan Province of China. However, very few remote sensing studies have estimated the shoot damage ratio (SDR). Thus, we used multi-date Landsat satellite imagery to quantify SDRs and assess the possibility of using spectral indices to determine the beetle outbreak time and spread direction. A new threshold-based classification method was proposed to identify damage levels (i.e., healthy, slightly to moderately infested, and severely infested forests) using time series of moisture stress index (MSI). Permanent plots and temporal field inspection data were both used as references for training and evaluation. Results show that a single threshold value can produce a total classification accuracy of 86.38% (Kappa = 0.80). Furthermore, time series maps detailing damage level were reconstructed from 2004 to 2016. The shoot beetle outbreak year was estimated to be 2013. Another interesting finding is the movement path of the geometric center of severe damage, which is highly consistent with the wind direction. We conclude that the time series of shoot damage level maps can be produced by using continuous MSI images. This method is very useful to foresters for determining the outbreak time and spread direction.

Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bounds are not computationally efficient and algorithms demonstrated efficiency in computation do not have a good or any polynomial bound. Todd raised a question in 2002: “Can we find a theoretically and practically efficient way to reoptimize?” This paper is an effort to close the gap. We propose two arc-search infeasible interior-point algorithms with infeasible central path neighborhood wider than all existing infeasible interior-point algorithms that are proved to be convergent. We show that the first algorithm is polynomial and its simplified version has a complexity bound equal to the best known complexity bound for all (feasible or infeasible) interior-point algorithms. We demonstrate the computational efficiency of the proposed algorithms by testing all Netlib linear programming problems in standard form and comparing the numerical results to those obtained by Mehrotra’s predictor-corrector algorithm and a recently developed more efficient arc-search algorithm (the convergence of these two algorithms is unknown). We conclude that the newly proposed algorithms are not only polynomial but also computationally competitive compared to both Mehrotra’s predictor-corrector algorithm and the efficient arc-search algorithm.

Study of Power Flow in an IPT System Based on Poynting Vector Analysis

This paper analyzes the power distribution and flow of an inductive power transfer (IPT) system with two coupled coils by using the Poynting vector. The system is modelled with a current source flowing through the primary coil, and a uniformly loaded secondary first, then the Poynting vector at an arbitrary point is analyzed by calculating the magnetic and electric fields between and around of the two coils. Both analytical analysis and numerical analysis have been undertaken to show the power distribution, and it has found that power distributes as a donut shape in three-dimensional (3D) space and concentrates along the edges in the proposed two-coil setup, instead of locating coaxially along the center path. Furthermore, power flow across the mid-plane between the two coils is analyzed analytically by the surface integral of the Poynting vector, which is compared with the input power from the primary and the output power to the secondary coil via coupled circuit theory. It has shown that for a lossless IPT system, the power transferred across the mid-plane is equal to the input and output power, which validates the Poynting vector approach. The proposed Poynting vector method provides an effective way to analyze the power distribution in the medium between two coupled coils, which cannot be achieved by traditional lumped circuit theories.

Dairy farmers’ business strategies in Central and Eastern Europe based on evidence from Lithuania, Poland and Slovenia

To evaluate market-oriented strategic decision-making by farmers in Central and Eastern Europe (CEE) farm development paths of dairy farmers in Slovenia, Poland and Lithuania were analysed. The influence of internal strengths and weaknesses, external opportunities and threats, and farmer goals on strategic choices and performance were explored. Principal component, hierarchical cluster and regression analyses were performed to test the conceptual framework. Seven strategic groups emerged with specific development paths, that is, Wait and see, Movers, Chain integrators, Specializers and Diversifiers. The latter two split into cooperative and independent groups. Maximisation of profit and sustainable farming ranked highest as farming goals. Availability of land and labour were weaknesses for all strategic groups in all countries. External opportunities and threats varied between countries and to a lesser degree between strategic groups. The Wait and see and Cooperating diversifier groups gave less optimistic scores than other strategic groups. The attitudes of CEE farmers towards the market and future Common Agricultural Policy remain more negative than those of a group of Western European farmers. The results of this study confirm that internal strengths and weaknesses, external opportunities and threats, together with farmers’ goals and strategies influence farmer performance, but independently of each other. Strategies do not appear to be a mediating variable between the internal and external environment of the farm and the performance of the farm. Policy makers, companies and extension workers should take the heterogeneity in strategic development into account when dealing with these and similar groups of farms.

Log-Barrier Interior Point Methods Are Not Strongly Polynomial

We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by constructing a family of linear programs with $3r+1$ inequalities in dimension $2r$ for which the number of iterations performed is in $\Omega(2^r)$. The total curvature of the central path of these linear programs is also exponential in $r$, disproving a continuous analogue of the Hirsch conjecture proposed by Deza, Terlaky and Zinchenko. Our method is to tropicalize the central path in linear programming. The tropical central path is the piecewise-linear limit of the central paths of parameterized families of classical linear programs viewed through logarithmic glasses. This allows us to provide combinatorial lower bounds for the number of iterations and the total curvature, in a general setting.

Canal Transportation and Centering Ability of ProTaper and SafeSider in Preparation of Curved Root Canals: A CBCT Evaluation.

Introduction:Maintaining the original central canal path is an important parameter in efficient root canal preparation. Instruments causing minimal changes in original canal path are preferred for this purpose. This study sought to compare canal transportation and centering ability of ProTaper and SafeSider instruments in curved mesiobuccal root canals of mandibular first molars using cone beam computed tomography (CBCT). Methods and Materials :In this experimental study, 30 mesiobuccal root canals of extracted human mandibular first molars with 20° to 40° curvature were randomly divided into two groups (n=15). After mounting in putty, preoperative CBCT scans were obtained of teeth. Root canals in group A were shaped using S1, S2, F1 and F2 of ProTaper system. Root canals in group B were instrumented to size 25 using SafeSider system according to the manufacturers’ instructions. Postoperative CBCT scans were then obtained. The distance between the external root surface and internal canal wall was measured at the mesial and distal at 1, 3 and 7 mm from the apex. The values measured on primary and secondary CBCT scans were compared to assess possible changes in original central canal path and canal transportation. Data were compared using the t-test and repeated measure ANOVA. Results:ProTaper and SafeSider were significantly different in terms of canal transportation and centering ability, and ProTaper was significantly superior to SafeSider in this respect (P<0.001). Conclusion:ProTaper (in contrast to SafeSider) is well capable of maintaining the original central canal path with the least amount of transportation.