Central Path Research Articles

Shennan Road and the modernization of Shenzhen architecture

Shenzhen exemplifies the rapid development of urban planning and construction in China. Over the last 40 years, many representative urban spaces and buildings have been built on Shennan Road, the city's main east–west thoroughfare, which has witnessed the formation of a multicenter structural layout and the miraculous expansion of the city. Many iconic buildings were designed by Hong Kong or foreign architects. The continuous development along Shennan Road not only symbolizes the fruits of the reform and opening up policies of Shenzhen and even China, but also reflects the modern architectural history in Shenzhen. This study uses historical research methods to review the changes in the urban fabric and the design trends, as seen in representative buildings along Shennan Road in different periods. In addition to the transition path of the city center, the unique role of streets and buildings in the development of the urban structure is analyzed, and other urban functions and symbolic meanings are identified. This work contributes to the history and theory of the modernization of contemporary Chinese architecture.

Shennan Road and the Modernization of Shenzhen Architecture

Shenzhensetsanexampleforrapiddevelopmentofurbanplanningandconstruction.It was the starting point of the most massive city-construction movement in contemporary China. In less than 40 years, many representative urban space and buildings on the mainmast-west highway—-ShennanRoad,have witnessed the for mation of the banded multi-center structural layout and the miraculous expansion of the city. Many of those iconic buildings are designed by Hong Kong or foreign architects. With the continuous development of the length and width of Shennan road, its broad and prosperous image is not only a symbol of the fruits of reform and opening up in Shenzhen or even China, but also contains the growth history of Shenzhen’s architectural modernization. This paper reviews and summarizes the changes of the urban fabric and the design trend of representative buildings along with the Shennan Road in different periods by the historical research methods. Combined with the transfer path of the city center, this study analyzes what kind of unique role the street and buildings act as in the developmentofurbanstructureinShenzhen,and expound what other urban functions and symbolic meaning they have. In the context of globalization, this article discusses how do the buildings designed by foreign architects change our city,thedrivenfactors behind the phenomenon of the design trend change. This research can make a supplement to the history and theory of the modernization of contemporary Chinese architecture.

A primal-dual interior-point method based on a new kernel function for linear complementarity problem

In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.

Parametric analysis of semidefinite optimization

ABSTRACTIn this paper, we study parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function. We study the behaviour of the optimal partition and optimal set mapping on a so-called nonlinearity interval. Furthermore, we investigate the sensitivity of the approximation of the optimal partition in a nonlinearity interval, which has been recently studied by Mohammad-Nezhad and Terlaky. The approximation of the optimal partition was obtained from a bounded sequence of interior solutions on, or in a neighbourhood of the central path. We derive an upper bound on the distance between the approximations of the optimal partitions of the original and perturbed problems. Finally, we examine the theoretical bounds by way of experimentation.

The Chow Form of a Reciprocal Linear Space

A reciprocal linear space is the image of a linear space under coordinatewise inversion. These fundamental varieties describe the analytic centers of hyperplane arrangements and appear as part of the defining equations of the central path of a linear program. Their structure is controlled by an underlying matroid. This provides a large family of hyperbolic varieties, recently introduced by Shamovich and Vinnikov. Here we give a definite determinantal representation to the Chow form of a reciprocal linear space. One consequence is the existence of symmetric rank-one Ulrich sheaves on reciprocal linear spaces. Another is a representation of the entropic discriminant as a sum of squares. For generic linear spaces, the determinantal formulas obtained are closely related to the Laplacian of the complete graph and generalizations to simplicial matroids. This raises interesting questions about the combinatorics of hyperbolic varieties and connections with the positive Grassmannian.

Rat Retrosplenial Cortical Involvement in Wayfinding Using Visual and Locomotor Cues.

The retrosplenial cortex (RSC) has been implicated in wayfinding using different sensory cues. However, the neural mechanisms of how the RSC constructs spatial representations to code an appropriate route under different sensory cues are unknown. In this study, rat RSC neurons were recorded while rats ran on a treadmill affixed to a motion stage that was displaced along a figure-8-shaped track. The activity of some RSC neurons increased during specific directional displacements, while the activity of other neurons correlated with the running speed on the treadmill regardless of the displacement directions. Elimination of visual cues by turning off the room lights and/or locomotor cues by turning off the treadmill decreased the activity of both groups of neurons. The ensemble activity of the former group of neurons discriminated displacements along the common central path of different routes in the track, even when visual or locomotor cues were eliminated where different spatial representations must be created based on different sensory cues. The present results provide neurophysiological evidence of an RSC involvement in wayfinding under different spatial representations with different sensory cues.

An interior point method for $$P_{*}(\kappa )$$-horizontal linear complementarity problem based on a new proximity function

Kernel functions play an important role in the design and complexity analysis of interior point algorithms for solving convex optimization problems. They determine both search directions and the proximity measure between the iterate and the central path. In this paper, we introduce a primal-dual interior point algorithm for solving \(P_*(\kappa ) \)-horizontal linear complementarity problems based on a new kernel function that has a trigonometric function in its barrier term. By using some simple analysis tools, we present some properties of the new kernel function. Our analysis shows that the algorithm meets the best known complexity bound i.e., \(O\left( (1+2\kappa )\sqrt{n}\log n\log \frac{n}{\varepsilon }\right) \) for large-update methods. Finally, we present some numerical results illustrating the performance of the algorithm.

Deep-learning–assisted automatic digitization of applicators in 3D CT image-based high-dose-rate brachytherapy of gynecological cancer

PurposeApplicator digitization is one of the most critical steps in 3D high-dose-rate brachytherapy (HDRBT) treatment planning. Motivated by recent advances in deep-learning, we propose a deep-learning–assisted applicator digitization method for 3D CT image-based HDRBT. This study demonstrates its feasibility and potential in gynecological cancer HDRBT. Methods and MaterialsOur method consisted of two steps. The first step used a U-net to segment applicator regions. We trained the U-net using two-dimensional CT images with a tandem-and-ovoid (T&O) applicator and corresponding applicator mask images. The second step applied a spectral clustering method and a polynomial curve fitting method to extract applicator central paths. We evaluated the accuracy, efficiency, and robustness of our method in different scenarios including other T&O cases that were not used in training, a T&O case scanned with cone-beam CT, and Y-tandem and cylinder-applicator cases. ResultsIn test cases with a T&O applicator, average 3D Dice similarity coefficient between automatic and manual segmented applicator regions was 0.93. Average distance between tip positions and average Hausdorff distance between applicator channels determined by our method and manually were 0.64 mm and 0.68 mm, respectively. Although trained only using CT images of T&O cases, our tool can also digitize Y-tandem, cylinder applicator, and T&O applicator scanned in cone-beam CT with error of tip position and Hausdorff distance <1 mm. Computation time was ∼15 s per case. ConclusionsWe have developed a deep-learning–assisted applicator digitization tool for 3D CT image–based HDRBT of gynecological cancer. The achieved accuracy, efficiency, and robustness made our tool clinically attractive.

Strong Stubborn Set Pruning for Star-Topology Decoupled State Space Search

Analyzing reachability in large discrete transition systems is an important sub-problem in several areas of AI, and of CS in general. State space search is a basic method for conducting such an analysis. A wealth of techniques have been proposed to reduce the search space without affecting the existence of (optimal) solution paths. In particular, strong stubborn set (SSS) pruning is a prominent such method, analyzing action dependencies to prune commutative parts of the search space. We herein show how to apply this idea to star-topology decoupled state space search, a recent search reformulation method invented in the context of classical AI planning.&#x0D; Star-topology decoupled state space search, short decoupled search, addresses planning tasks where a single center component interacts with several leaf components. The search exploits a form of conditional independence arising in this setting: given a fixed path p of transitions by the center, the possible leaf moves compliant with p are independent across the leaves. Decoupled search thus searches over center paths only, maintaining the compliant paths for each leaf separately. This avoids the enumeration of combined states across leaves.&#x0D; Just like standard search, decoupled search is adversely affected by commutative parts of its search space. The adaptation of strong stubborn set pruning is challenging due to the more complex structure of the search space, and the resulting ways in which action dependencies may affect the search. We spell out how to address this challenge, designing optimality-preserving decoupled strong stubborn set (DSSS) pruning methods. We introduce a design for star topologies in full generality, as well as simpler design variants for the practically relevant fork and inverted fork special cases. We show that there are cases where DSSS pruning is exponentially more effective than both, decoupled search and SSS pruning, exhibiting true synergy where the whole is more than the sum of its parts. Empirically, DSSS pruning reliably inherits the best of its components, and sometimes outperforms both.

A precise mathematical model for geometric modeling of wire rope strands structure

Based on the Frenet frame, this paper proposes a general mathematical spiral model with an arbitrary smooth space curve as the center path, which can accurately build complex skeleton lines of wire rope strands. From the aspect of geometry, all the wires are spatial cylinders and must meet the actual geometric requirements: 1. The center cylinder is tangent or separated from the spiral cylinder; 2. The adjacent spiral cylinders do not overlap each other. For requirement 1, Costello’ conclusion is referenced and extended universally to suit an arbitrary smooth space central curve case with rigorous proofs. For requirement 2, the overlapping problem is described as obtaining the minimum distance between the two adjacent spatial path curves, which is deduced by a novel cross section method (SCM) with rigorous proofs and solved by the General Particle Swarm Optimization (PSO) algorithm. Based on the above models, the geometric modeling of wire rope strands procedure is proposed and implemented on the platforms of MATLAB and SolidWorks. Validations are conducted through geometric graphical representations, compared with those from some previous researches. For the simple straight strand case, when the number of spiral cylinders and spiral radius are given, the critical relationship between the ratio of spiral wire radius to spiral radius and the spiral angle is firstly obtained, which can be a precise dimension design reference of simple straight strand for eliminating initial geometric overlap. Further, to show the advance, some precise graphical examples of complex wire rope strands like independent wire rope core (IWRC) and multilayered rope are presented. The wire rope strands geometric modeling method proposed in this paper is precise enough averting initial geometric overlap between the wires for the benefit of subsequent mechanical computation accuracy and efficiency.

An arc-search predictor-corrector infeasible-interior-point algorithm for P∗(κ)-SCLCPs

In this paper, we propose a new arc-search predictor-corrector infeasible-interior-point algorithm for linear complementarity problems over symmetric cones with the Cartesian P∗(κ)-property (P∗(κ)-SCLCP). The proposed algorithm is based on a wide neighborhood of the central path and searches the optimizers along the ellipses that approximate the entire the central path. The algorithm uses a commutative class of search directions, which includes the Nesterov-Todd direction and the xs and sx directions. To the best of our knowledge, this is using a new strategy in the complexity analysis; we improve the theoretical complexity bound of an arc-search infeasible-interior-point method for P∗(κ)-SCLCP. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.

On the convergence analysis of arc search interior point methods for LCPs

Following the central-path, as a guide line to optimal solution of mathematical problems, is one of the main difficulty of interior-point methods in practice. These iterative methods, follow the central path step by step to get close enough to the optimal solution of underlying problem. Based on estimating the central path by an ellipse, we propose an infeasible interior-point method for linear complementarity problem. In each iteration, the algorithm follows the ellipsoidal approximation of the central-path to find an $$\varepsilon $$ -approximate solution of the problem. We prove that under certain conditions the proposed algorithm is well-defined and the generated points by the algorithm converge to an $$\varepsilon $$ -approximate solution of the linear complementarity problem.

A corrector\u2013predictor interior-point method with new search direction for linear optimization

We introduce a feasible corrector–predictor interior-point algorithm (CP IPA) for solving linear optimization problems which is based on a new search direction. The search directions are obtained by using the algebraic equivalent transformation (AET) of the Newton system which defines the central path. The AET of the Newton system is based on the map that is a difference of the identity function and square root function. We prove global convergence of the method and derive the iteration bound that matches best iteration bounds known for these types of methods. Furthermore, we prove the practical efficiency of the new algorithm by presenting numerical results. This is the first CP IPA which is based on the above mentioned search direction.

MODEL ELABORATION LIKELIHOOD DALAM PEMBENTUKAN PERSONAL BRANDING PITA’S LIFE DI YOUTUBE CHANNEL

Abstrack This study aims to describe the formation of the personal pranding Pita 's Life vlog on youtube through the analysis of Model Elaboration Likelihood. From this research, it is expected to provide input and advice to the Youtuber to better display content that is better and not detrimental to themselves and others, so as to produce a positive outlook on their personal. The type of research used in this research is qualitative descriptive using the content analysis design. The use of the content analysis method was carried out in this study because the source of the data produced was verbal communication from the vlog of the Ribbon which was then re-identified in writing. The population used in this study was 64 'Pita's Life vlog shows from July to November 2018. The sample used in this study was the Pita Vlog show which only aired a life of 20 husbands and children. This research proves that the formation of the Pita 's Life vlog personal branding on Youtube can be analyzed using the Model Elabation Likelihood. This is because both the central line and peripheral lines in the Elaboration Likelihood Model are both processes in forming the Ribbon personal branding. In the central path, it shows that the arguments uttered by the Pita contain positive things. The argument expressed by Pita is also supported by its quality as a source of messages that appears to have ethos, attractions and power on peripheral lines, so both the argumentation and quality of the Ribbon as a communicator make Pita's vlog show an interesting show to be watched by the public. Keyword : Elaboration Likelihood Model, Personal Branding, Youtub e Cha nnel DOI : https://doi.org/10.26905/nomosleca.v5i1.2985

A New Search Direction for Full-Newton Step Interior-Point Method in -HLCP

In this article, a full-Newton step feasible interior-point algorithm for -horizontal linear complementarity problems is proposed that uses a new method for identifying search directions. The method is based on a simple equivalent form of the centering equations of the system which defines the central path. The theoretical complexity of the new algorithm is derived which coincides with the best-known iteration bound for -horizontal linear complementarity problems.

Autonomous Vehicles: Autodriver Algorithm and Vehicle Dynamics

A given road can be expressed mathematically in a global (or world) coordinate frame. Following the road can be substituted by following the loci of its curvature center and turning at the right circle of curvature. Considering that a vehicle in motion is always in turn about an instantaneous rotation center relative to the ground, an autonomous vehicle capable of following a given path by coinciding the rotation center of vehicle at every moment on the curvature center of the road could be designed. The dynamic reactions of the vehicle influence its path of motion and make its rotation center to depart from the desired path of the curvature center of the road. In this study, the Autodriver algorithm control strategy to front-wheel-steering vehicles has been developed and a control loop is introduced to compensate the present errors generated by the differences of the desired locating on the road and the real position of the vehicle.

Three-dimensional path of the body centre of mass during walking in children: an index of neural maturation.

Few studies have investigated the kinematic aspects of the body centre of mass motion, that is, its three-dimensional path during strides and their changes with child development. This study aimed to describe the three-dimensional path of the centre of mass in children while walking in order to disentangle the effect of age from that of absolute forward speed and body size and to define preliminary pediatric normative values. The three-dimensional path of the centre of mass during walking was compared across healthy children 5–6− years (n = 6), 7–8 years (n = 6), 9–10 years (n = 5), and 11–13 years of age (n = 5) and healthy adults (23–48 years, n = 6). Participants walked on a force-sensing treadmill at various speeds, and height normalization of speed was conducted with the dimensionless Froude number. The total length and maximal lateral, vertical, and forward displacements of the centre of mass path were calculated from the ground reaction forces during complete strides and were scaled to the participant’s height. The centre of mass path showed a curved figure-of-eight shape. Once adjusted for speed and participants’ height, as age increased, there was a decrease in the three-dimensional parameters and in the lateral displacement, with values approaching those of adults. At each step, lateral redirection of the centre of mass requires brisk transient muscle power output. The base of support becomes relatively narrower with increasing age. Skilled shortening of the lateral displacement of the centre of mass may therefore decrease the risk of falling sideways. The three-dimensional path of the centre of mass may represent maturation of neural control of gait during growth.

On the identification of the optimal partition for semidefinite optimization

The concept of the optimal partition was originally introduced for linear optimization and linear complementarity problems and subsequently extended to semidefinite optimization. For linear optimization and sufficient linear complementarity problems, from a central solution sufficiently close to the optimal set, the optimal partition and a maximally complementary optimal solution can be identified in strongly polynomial time. In this paper, we consider the identification of the optimal partition of semidefinite optimization, for which we provide an approximation from a bounded sequence of solutions on, or in a neighborhood of the central path. Using bounds on the magnitude of the eigenvalues, we identify the subsets of eigenvectors of the interior solutions whose accumulation points are orthonormal bases for the subspaces of the optimal partition. The magnitude of the eigenvalues of an interior solution is quantified using a condition number and an upper bound on the distance of an interior solution to the optimal set. We provide a measure of proximity of the approximation obtained from the central solutions to the true optimal partition of the problem.

A primal-dual interior-point algorithm with arc-search for semidefinite programming

We propose a wide neighborhood primal-dual interior-point algorithm with arc-search for semidefinite programming. In every iteration, the algorithm constructs an ellipse and searches an $$\varepsilon $$ -approximate solution of the problem along the ellipsoidal approximation of the central path. Assuming a strictly feasible starting point is available, we show that the algorithm has the iteration complexity bound $$O\left( n^{\frac{3}{4}}\log \frac{{X^{0}}\bullet {S}^{0}}{\varepsilon }\right) $$ for the Nesterov–Todd direction, which is similar to that of the corresponding algorithm for linear programming. The numerical results show that our algorithm is efficient and promising.

Optimized choice of parameters in interior-point methods for linear programming

In this work, we propose a predictor–corrector interior point method for linear programming in a primal–dual context, where the next iterate is chosen by the minimization of a polynomial merit function of three variables: the first is the steplength, the second defines the central path and the third models the weight of a corrector direction. The merit function minimization is performed by restricting it to constraints defined by a neighborhood of the central path that allows wide steps. In this framework, we combine different directions, such as the predictor, the corrector and the centering directions, with the aim of producing a better one. The proposed method generalizes most of predictor–corrector interior point methods, depending on the choice of the variables described above. Convergence analysis of the method is carried out, considering an initial point that has a good practical performance, which results in Q-linear convergence of the iterates with polynomial complexity. Numerical experiments using the Netlib test set are made, which show that this approach is competitive when compared to well established solvers, such as PCx.