Minimum Stretch Research Articles

Complexity of the multiobjective minimum weight minimum stretch spanner problem

In this paper, we take an in-depth look at the complexity of a hitherto unexplored multiobjective minimum weight minimum stretch spanner problem; or in short multiobjective spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied minimum t-spanner problem. This multiobjective approach allows to find solutions that offer a viable compromise between cost and utility—a property that is usually neglected in singleobjective optimization. Thus, the MSp can be a powerful modeling tool when it comes to, e.g., the planning of transportation or communication networks. This holds especially in disaster management, where both responsiveness and practicality are crucial. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if P≠NP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{P}} \ e \ extbf{NP}$$\\end{document}, the set of extreme points cannot be computed in output-polynomial time, for instances with unit costs and arbitrary graphs. Furthermore, we consider the directed versions of the cases above.

NP-полнота задачи построения графа с минимальным коэффициентом непрямолинейности

In this paper, we consider the problem of constructing a planar connected weighted graph on a given set of points in such a way that the sum of the shortest paths between all pairs of vertices is the minimum possible. In other words, the problem of constructing a graph with a minimum stretch factor. The euclidean distance between the ends is taken as the weight of the edge. It is proved that such a problem is NP-complete. This problem arises when planning transport networks, since it is the stretch factor of the graph of the transport network that directly indicates the level of overrun of transport, which should be as small as possible in order to minimize the resources spent. But since this problem is NP-complete, a heuristic algorithm for solving the problem under consideration is proposed, which is based on sorting some simple paths and has a recursive character. This algorithm always builds a triangulation, since only in this class of graphs is it possible to solve the problem. A number of experiments have been carried out on the statistical study of the stretch factor of the triangulation constructed as a result of the operation of the above algorithm on randomly generated points. Experiments show that the losses are about 1.5–7.8% , and for real cities this parameter is about 30%.

Volumetric versus distortional deformation in rat lungs.

There are several lung diseases that lead to alterations in regional lung mechanics, including acute respiratory distress syndrome. Such alterations can lead to localized underventilation of the affected areas resulting in the overdistension of the surrounding healthy regions. They can also lead to the surrounding alveoli expanding unevenly or distorting. Therefore, the quantification of the regional deformation in the lungs offers insights into identifying the regions at risk of lung injury. Although few recent studies have developed image processing techniques to quantify the regional volumetric deformation in the lung from dynamic imaging, the presence and extent of distortional deformation in the lung, and its correlation with volumetric deformation, remain poorly understood. In this study, we present a method that uses the four-dimensional displacement field obtained from image registration to quantify both regional volumetric and distortional deformation in the lung. We used dynamic computed tomography scans in a healthy rat over the course of one respiratory cycle in free breathing. Non-rigid image registration was performed to quantify voxel displacement during respiration. The deformation gradient was calculated using the displacement field and its determinant was used to quantify regional volumetric deformation. Regional distortion was calculated as the ratio of maximum to minimum principal stretches using the isochoric part of the Cauchy green tensor. We found an inverse correlation between volumetric strains and distortion indicating that poorly expanding alveoli tend to experience larger distortion. The combination of regional volumetric strains and distortion may serve as high-fidelity biomarkers to identify the regions at risk of most adverse lung injuries.

Microvascular anastomosis of the human lacrimal gland: a concept study towards transplantation of the human lacrimal gland

IntroductionSevere aqueous tear deficiency is caused by primary or secondary main lacrimal gland insufficiency. The transplantation of a human lacrimal gland could become a potential treatment option to provide physiological tears with optimal properties. To this end, we performed an ex vivo study to develop a surgical strategy that would ensure a vascular supply for a lacrimal gland transplant using microvascular techniques.Material and methodsFive cadaver heads were used to perform a lateral orbitotomy in order to identify the vascular pedicle and the lacrimal gland itself. The principal feasibility and the time of the required surgical steps for an intraorbital microvascular re-anastomosis of the human lacrimal gland were documented. Patency and potential leakage of the anastomosis were tested with hematoxylin intraoperatively. Postoperatively, routine histological, as well as scanning electron microscopy (SEM) of the gland and vascular anastomosis, were performed.ResultsThe vascular pedicle of all five glands could be isolated over a minimum stretch of at least 1 cm, severed, and successfully reanastmosed microsurgically. Time for arterial anatomization (n = 4) was 23 ± 7 min and 22 ± 3 min for the vein (p = 0.62). The total time for the entire microvascular anastomosis was 46 ± 9 min. All anastomosis were patent upon testing. SEM revealed well-aligned edges of the anastomosis with tight sutures in place.ConclusionOur study demonstrates as proof of principle the feasibility of intraorbital microvascular re-anastomosis of a human lacrimal gland within the presumed window of ischemia of this tissue. This should encourage orbital surgeons to attempt lacrimal gland transplantation in humans in vivo.

Molecular biology of the cell

Molecular biology of the cell

Constraining pterosaur launch: range of motion in the pectoral and pelvic girdles of a medium-sized ornithocheiraean pterosaur

Abstract Launch is the most energetically expensive part of flight and is considered a limiting factor in the size of modern flyers. Pterosaurs reached significantly larger sizes than modern flyers and are proposed to have launched either bipedallly or quadrupedally. We investigated the ability of a medium-sized ornithocheiraean pterosaur to assume the poses required to launch bipedally or quadrupedally. We applied range of motion (ROM) mapping methodology to the pectoral and pelvic girdles to identify viable poses at varying levels of appendicular cartilage based on the extant phylogenetic bracket. The ROMs were constrained by novel triangulated minimum stretch methodology, used to identify the restraining tissue ROM. Our study indicates that a medium-sized ornithocheiraean could assume the poses required to use a quadrupedal launch and, with an additional 10° of hindlimb abduction, a bipedal launch, although further analysis is required to determine whether sufficient muscular power and leverage was available to propel the animal into the air.

General variable neighborhood search for the minimum stretch spanning tree problem

General variable neighborhood search for the minimum stretch spanning tree problem

Minimum Stretch Spanning Tree Problem in Operations on Trees

The minimum stretch spanning tree problem for a connected graph [Formula: see text] is to find a spanning tree [Formula: see text] of [Formula: see text] such that the maximum distance in [Formula: see text] between two adjacent vertices of [Formula: see text] is minimized, where the minimum value is called the tree-stretch of [Formula: see text]. This paper presents the tree-stretch of a graph constructed by the Cartesian product of two trees. This result is a generalization of the result for the grid graphs obtained by Lin and Lin (L. Lin, Y. Lin, The minimum stretch spanning tree problem for typical graphs, Acta Mathematicae Applicatae Sinica, English Series, 37(3) (2021) 510–522). Then, we give the tree-stretch of the [Formula: see text]-th power of a tree.

Characterization of the structural configuration and tensile properties of medical bandages

Bandages are a group of medical textiles that are available in various types for use in different applications such as wound dressing, compression therapy, treatment of burns, cramps, and sprains. In the present research, the structural and tensile characteristics of various medical bandages produced by different companies have been compared. According to the results, different bandages commercially sold under the same category demonstrate quite varied tensile properties, depending on their structure and constructional parameters. Consequently, compression bandages of the same type produced under different trade names would exert various amount of pressure to the body under constant stretch. In other word, various amount of stretch must be applied to different compression bandages to achieve and maintain the required pressure. Hence, to obtain better treatment outcomes, it is essential to provide the required information about the features of each medical bandage for the consumers. Furthermore, it was observed that the knitted compression bandages due to their higher stiffness (elastic modulus) provide higher pressure under minimum stretch in comparison with woven samples. Moreover, incorporation of higher number of stretch yarns to the bandage structure as well as using tighter structure increases the stiffness of the bandage, and in turn enhances the power of the bandage to cling on the limb for a longer period of time, in case of compression bandages.

The Minimum Stretch Spanning Tree Problem for Typical Graphs

With applications in communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The problem has been proved NP-hard and fixed-parameter polynomial algorithms have been obtained for some special families of graphs. In this paper, we concentrate on the optimality characterizations for typical classes of graphs. We determine the exact formulae for the complete k-partite graphs, split graphs, generalized convex graphs, and several planar grids, including rectangular grids, triangular grids, and triangulated-rectangular grids.

Optimization of spanning tree stretch and congestion for graphs

In spanning tree optimization of graphs, there are two important criteria, namely, dilation (stretch) and congestion. This gives rise to two combinatorial optimization problems as follows. The minimum stretch spanning tree problem is to find a spanning tree of a graph such that the maximum distance of all embedded edges in the tree is minimized. The minimum congestion spanning tree problem is to find a spanning tree of a graph such that the maximum number of overlapped edges for all embedded edges in the tree is minimized. These problems bring us two graph-theoretic parameters, tree stretch and tree congestion. In this paper we mainly study the structural properties of tree stretch and tree congestion, including the duality of fundamental cycle and fundamental cocycle, extremal property, lower and upper bounds, optimality characterization, and optimal value computation.

Mechanical stimuli for left ventricular growth during pressure overload.

The mechanical stimulus (i.e. stress or stretch) for growth occurring in the pressure-overloaded left ventricle (LV) is not exactly known. To address this issue, we investigate the correlation between local ventricular growth (indexed by local wall thickness) and the local acute changes in mechanical stimuli after aortic banding. LV geometric data were extracted from 3D echo measurements at baseline and 2 weeks in the aortic banding swine model (n = 4). We developed and calibrated animal-specific finite element (FE) model of LV mechanics against pressure and volume waveforms measured at baseline. After the simulation of the acute effects of pressure-overload, the local changes of maximum, mean and minimum myocardial stretches and stresses in three orthogonal material directions (i.e., fiber, sheet and sheet-normal) over a cardiac cycle were quantified. Correlation between mechanical quantities and the corresponding measured local changes in wall thickness was quantified using the Pearson correlation number (PCN) and Spearman rank correlation number (SCN). At 2 weeks after banding, the average septum thickness decreased from 10.6 ± 2.92mm to 9.49 ± 2.02mm, whereas the LV free-wall thickness increased from 8.69 ± 1.64mm to 9.4 ± 1.22mm. The FE results show strong correlation of growth with the changes in maximum fiber stress (PCN = 0.5471, SCN = 0.5111) and changes in the mean sheet-normal stress (PCN= 0.5266, SCN = 0.5256). Myocardial stretches, however, do not have good correlation with growth. These results suggest that fiber stress is the mechanical stimuli for LV growth in pressure-overload.

Optimality computation of the minimum stretch spanning tree problem

Abstract The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices of G is minimized, where the minimum value is called the tree-stretchof G. There has been extensive study on the algorithmic aspects, such as the NP-hardness and fixed-parameter solvability. We are concerned in this paper with the computation of exact tree-stretch for given graph families. We relate an optimization approach of computing lower and upper bounds. This approach is applied to several typical graph families, such as the hypercubes Qn, the graph products Km × Kn, Pm × Kn, Cm × Cn, Pm × Cn, Pm × Pn, and Km × Cn.

The Minimum Stretch Spanning Tree Problem for Hamming Graphs and Higher-Dimensional Grids

The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a graph invariant σ(G), called the tree-stretch of G. The problem has been proved NP-hard. In this paper we present a general approach to determine the exact values σ(G) for a series of typical graphs arising from communication networks, such as Hamming graphs and higher-dimensional grids (including hypercubes).

Constitutive modeling of the cyclic dissipation in thin and thick rubber specimens

AbstractA thermo‐viscoelastic‐damage constitutive model, in accordance with the thermodynamic principles, is proposed to describe the cyclic dissipation in rubbers. The general form of the model can be represented by a thermal branch responsible for the stress‐free thermal expansion joined to parallel mechanical multi‐branches responsible for the cyclically damaged‐elastic response and the inelastic effects, i.e. fatigue‐induced stress‐softening and hysteresis. The viscoelastic and damage dissipations contributing to heat build‐up are considered in the model formulation using the internal state variable theory. The model is identified and verified using experimental observations on stress‐softening, hysteresis and dissipative heating obtained on rubber flat specimens containing different amounts of carbon‐black and cyclically loaded under different minimum stretch levels. The model is then used to predict damage and thermal patterns in thick specimens involving different triaxial stress states in the median cross‐section.

Strain geometry, microstructure and metamorphism in the dextral transpressional Mubarak Shear Belt, Central Eastern Desert, Egypt

Mubarak shear belt provides an opportunity to investigate quantitative finite strain (Rs), proportions of pure shear and simple shear components, sense of shear indicators, subhorizontal to steeply plunging mineral lineations, in a dextral transpressional zone. The structural style of the Mubarak shear belt is consistent with dextral transpression within the Central Eastern Desert where dextral and reverse shear have developed simultaneously with the regional foliation. The high strain zone of the Mubarak shear belt is characterized by steeply dipping foliation with sub-horizontal stretching lineation (simple shear) surrounded by thrust imbrications with slightly plunging stretching lineations. Strain estimates from the Mubarak shear belt are used to determine how pure and simple shear components of deformation are partitioned. The axial ratios in XZ sections range from 1.16 to 2.33 with the maximum stretch, S X , ranges from 1.06 to 1.48. The minimum stretch, S Z , ranges from 0.65 to 0.92 indicating a moderate variation in vertical shortening. Volcaniclastic metasediments and metagabbros were subjected to prograde low-grade regional metamorphism in the range of greenschist to lower amphibolite facies (450–650°C at 2–4 kbar). Medium pressure (6–8 kbar at 530°C) was estimated from the high strain zone within the dextral strike-slip shear zones. Retrograde metamorphism occurred at a temperature range of 250–280°C. There is a trend towards decreasing the ratio of 100Mg/(Mg + Fetot + Mn) away from the high strain zone of the Mubarak shear belt. Integrated strain and temperature estimates indicate that the simple shear (non-coaxial) components of deformation played a significant role in formation and exhumation of the Mubarak shear belt during the accumulation of finite strain and consequently during progressive transpression and thrusting.

On Minimum Average Stretch Spanning Trees in Grid Graphs

A minimum average stretch spanning tree of a graph is a spanning tree that minimizes the average stretch. We present a necessary-and-sufficient condition for a spanning tree to be a minimum average stretch spanning tree (mast) in grid graphs and provide a linear-time algorithm to construct an mast.

Experimental investigation and theoretical modelling of induced anisotropy during stress-softening of rubber

The Mullins effect refers to a stress-softening phenomenon of rubber-like materials during cyclic loading. Anisotropy of the material behaviour is generally observed after stretching. In this paper, a large set of original suitable experiments are reported to characterise this effect under several deformation conditions. Then, a phenomenological model is derived to capture the anisotropic distribution. For that, the affine micro-sphere model (Miehe et al., 2004) is amended with a directional network alteration in order to describe anisotropy. The alteration process, involving the breakage and the slippage of the links embedded in the macromolecular network, is modelled by the evolution of the average number of monomer segments per chain during stretching. The average chain length and the chain density are incrementally described by functions to allow both softening and stiffening, depending to the maximum and the minimum stretch rates and levels endured in each direction. The good capacity of the model to reproduce experimental observations validates the above assumptions.

Complexity of Routing in Store-and-Forward LEO Satellite Networks

In this letter, we analyze the effect of the mobility of satellites on routing in store-and-forward low earth orbit (LEO) satellite networks, and the NP-hard proofs are given for the minimum path stretch schedule (MIN-PSS), maximum path contraction schedule (MAX-PCS), and maximum constant path schedule (MAX-CPS) problems. These conclusions theoretically prove the routing intractability in store-and-forward LEO satellite networks.

Context as Combinatory Conditionality of Word Meaning's Actualization

The article touches upon the problem of identifying the term ‘context’. Within Combinatory Linguistics that is the area of linguistics studying syntagmatic properties of language units and their combinatory potential of special importance is the concept ‘context’ denoting the minimum stretch of speech necessary and sufficient to determine which of the possible meanings of a polysemantic word is used. Moreover, the article deals with the problem of distinguishing the concepts of ‘context’ and ‘compatibility’. In accordance with the theory of Combinatory Linguistics context is a condition and combinatory conditionality of a language unit in actualization of its lexical meaning, while compatibility is a property of language units to be combined with each other forming units of a higher level.