Dimensional Paths Research Articles

A Two-Layer Heterogeneous Ant Colony System With Applications in Part-Picking Planning

Abstract The tape carrier packaging machine with multiple sucking discs is designed for modern, high-speed packaging production line, which is an important part of the electronic manufacturing process. The efficiency of the part-picking can directly affect the efficiency of the packaging production line. The problem involves at least three coupled sub-problems: the number of picking rounds, the matching relationship between the parts and sucking discs, and the picking order. Because the actual industrial production requires real-time or soft real-time scheduling, the challenge is how to efficiently solve this multi-dimensional combinatorial optimization problem within a fairly limited time. The existing advanced algorithms such as the genetic algorithm and the simulated annealing algorithm usually require complex and time-consuming encoding and decoding while solving this problem. In contrast, the ant colony algorithm has advantages in the convergence rate and parallel computing, especially for searching high dimensional paths in dynamic environments. In order to further improve the comprehensive performance of the ant colony algorithm in solving multi-dimensional coupled optimization problems in extremely limited time, we propose a novel two-layer heterogeneous ant colony system based on three strategies: (1) a bottom-up two-layer solution framework to decouple the original tightly coupled problem into a loosely coupled problem composed of two sub-problems; (2) a candidate cluster augmentation strategy based on the Delaunay triangulation to improve the diversity and quality of the clusters; (3) a co-evolution between a pair of heterogeneous colonies by mixing the high-quality pheromone properly as well as a co-evolution based on the prior knowledge. Finally, through a large set of comparisons, the average picking efficiency of Two-layer Heterogeneous Ant Colony System improved by the three proposed strategies is 13–16% higher than that of other popular heuristic algorithms.

Technological improvement rates and recent innovation trajectories in automated advanced composites manufacturing technologies: A patent-based analysis

The importance of advanced composites in industries such as aerospace, defense, automotive, clean energy, and hydrogen has grown at a fast pace and is expected to keep enlarging its strategic importance. Using objective patent-based methodologies, this paper estimates the yearly performance improvement rates and traces the most recent technological trajectories of Automated Tape Laying (ATL), Automated Fiber Placement (AFP) and Additive Manufacturing (AM) for advanced composites. For each technology, a set of representative patents is retrieved. A robust predictor based on the centrality of patents within the citation network is used to estimate yearly performance improvement rates. A knowledge persistence algorithm is applied to trace the most important technological trajectories. Results show that ATL (13.0%) and AFP (9.3%) are improving faster than milling technology (3.4%), a high grade metal technology, which indicates that composites applications should continue to grow relative to metal based components. AM for advanced composites is improving at a substantially faster rate (31.5%) suggesting potential to penetrate further as a viable solution in the advanced manufacturing landscape. ATL and AFP trajectories show developments mainly targeted to increase process productivity and reliability. Productivity increases are fostered primarily by innovations in automatic inspection, tow/tape heating, and material dispensing. Improvements over tow/tape cutting and steering systems and closed-loop control of operations contribute to reliability increase. AM appears to be evolving from cartesian motion to robotic arms machines. These allow for deposition over three dimensional paths which greatly increase component design freedom and mechanical properties further fostering AM's penetration.

Developing a Three Dimensional (3D) Elastoplastic Constitutive Model for Soils Based on Unified Nonlinear Strength (UNS) Criterion

To achieve versatility, a unified nonlinear strength (UNS) criterion is put forward for capturing the complicated strength behaviors exhibited by geomaterials under three dimensional (3D) stress paths. The UNS criterion, widely covering meridian planes and octahedral planes, can serve for describing the nonlinear strength behaviors exhibited by soils, as well as confirm how the intermediate principal stress affects the strength of different materials. Based on UNS strength criterion, an elastoplastic constitutive model is presented, with the purpose of predicting the strength as well as deformation behavior exhibited by soils under 3D stress conditions. Besides, although the proposed model is extremely simple, it is fit for predicting the results of true triaxial tests in related literature with the help of the UNS criterion, and meanwhile can confirm how intermediate principal stress affects material strength and material deformation when the stresses are different.

Lava flow hazard map of Piton de la Fournaise volcano

Abstract. Piton de la Fournaise, situated on La Réunion island (France), is one of the most active hot spot basaltic shield volcanoes worldwide, experiencing at least two eruptions per year since the establishment of the volcanological observatory in 1979. Eruptions are typically fissure-fed and form extensive lava flow fields. About 95 % of some ∼ 250 historical events (since the first confidently dated eruption in 1708) have occurred inside an uninhabited horseshoe-shaped caldera (hereafter referred to as the Enclos), which is open to the ocean on its eastern side. Rarely (12 times since the 18th century), fissures have opened outside of the Enclos, where housing units, population centers, and infrastructure are at risk. In such a situation, lava flow hazard maps are a useful way of visualizing lava flow inundation probabilities over large areas. Here, we present the up-to-date lava flow hazard map for Piton de la Fournaise based on (i) vent distribution, (ii) lava flow recurrence times, (iii) statistics of lava flow lengths, and (iv) simulations of lava flow paths using the DOWNFLOW stochastic numerical model. The map of the entire volcano highlights the spatial distribution probability of future lava flow invasion for the medium to long term (years to decades). It shows that the most probable location for future lava flow is within the Enclos (where there are areas with up to 12 % probability), a location visited by more than 100 000 visitors every year. Outside of the Enclos, probabilities reach 0.5 % along the active rift zones. Although lava flow hazard occurrence in inhabited areas is deemed to be very low (< 0.1 %), it may be underestimated as our study is only based on post-18th century records and neglects older events. We also provide a series of lava flow hazard maps inside the Enclos, computed on a multi-temporal (i.e., regularly updated) topography. Although hazard distribution remains broadly the same over time, some changes are noticed throughout the analyzed periods due to improved digital elevation model (DEM) resolution, the high frequency of eruptions that constantly modifies the topography, and the lava flow dimensional characteristics and paths. The lava flow hazard map for Piton de la Fournaise presented here is reliable and trustworthy for long-term hazard assessment and land use planning and management. Specific hazard maps for short-term hazard assessment (e.g., for responding to volcanic crises) or considering the cycles of activity at the volcano and different event scenarios (i.e., events fed by different combinations of temporally evolving superficial and deep sources) are required for further assessment of affected areas in the future – especially by atypical but potentially extremely hazardous large-volume eruptions. At such an active site, our method supports the need for regular updates of DEMs and associated lava flow hazard maps if we are to be effective in keeping up to date with mitigation of the associated risks.

Molecular dynamics simulations of oxide ion migration in La2Ga3O7.5 with completely ordered interstitial oxide ions

Molecular dynamics simulations were performed on metastable La2Ga3O7.5 melilite ceramics, which were synthesized previously by direct crystallization of an under-cooled melt. La2Ga3O7.5 possesses the theoretically maximum content of interstitial oxide ions featuring complete ordering but ~3 orders of magnitude lower oxide ion conductivities compared with disordered La1·54Sr0.46Ga3O7.27 within 573–773 ​K. One dimensional diffusion paths of interstitial oxide ion was identified in La2Ga3O7.5 based on the molecular dynamics simulations, which shows that the interstitial oxide ions can migrate from the pentagonal ring containing GaO5 pyramid unit to its neighboring pentagonal ring free of interstitial oxide ion mainly along the a axis through a synergic mechanism involving continuous breaking and reformation of Ga2O8 units assisted by rotation and deformation of GaOn polyhedra and knock-on process between interstitial and framework oxygen atoms. Such constrained dimensionality on the diffusion paths arising from the confining effect for a large number of oxygen interstitials in the highly relaxed and ordered melilite superstructure accounts for the lower oxide ion conductivity in La2Ga3O7.5.

POLITICAL ETHNICITY AND MUSLIMS AROUND THE WORLD A SOCIOLOGICAL PERSPECTIVE

Political ethnicity has remained a core analytical aspect for individuals, politicians, and scholars regarding their substantial roles in society, economy, politics, and religion. Under some extensive measures, the study of ethnic politics is not as new as it seems. Eventually, the politics revolving around the state arena started from the advent of the imperial rules of empires vesting towards the voyage of obtaining substantial interest and economic gain, which surprisingly oriented the turmoil of class differences and other racial and religious conflicts over the decades. Furthermore, the concept of ethnic politics has often changed its dimensional paths with the unification of revolutionary, ethnic groups, which conjugates into never-ending movements with incessant consequences. Wherever ethnic politics tend to exist, world politics' climax drifts apart because a humanitarian approach does not just infer superficial societal changes. There is a common assumption, and the West's misconception is effective than the East, and Muslims are not much advanced as they often exhibit incapacity. Unlike other ideologies and civilizations, Islam, from its very start, acknowledged the sociopolitical rights and obligations of people. The view of Islam for individuals is the total submission to Allah's need, not subjugation to people's will. The study focusses on the issues of Muslim political ethnicities around the world in the sociological point of view.

Homing tactics of Weddell seals in the Antarctic fast-ice environment

Most activities of Weddell seals (Leptonychotes weddellii) occur during under-ice dives that extend hundreds to thousands of meters and require the seals to hold their breath for 15 min or more. In the fast-ice environment of Antarctica, holes in the ice where seals can surface to breathe are scarce. Consequently, seals must return to a previous breathing hole or locate a new one to avoid drowning; how they navigate underwater with such precision is not known. This study individually displaced ten seals, each fitted with an archival data logger, to unfamiliar locations and analyzed the three dimensional paths of voluntary dives to test eight predictions under four hypothesized way-finding tactics: geomagnetic sensitivity, path integration, pilotage, and hydrodynamic trail following. Analyses of dive tracks provided strong evidence that Weddell seals primarily used pilotage via visible, overhead features to return home during individual dives under ice cover. Upon release at an unfamiliar location, long-distance diving began only after a period of short-distance diving. Outbound paths of dives progressively increased in distance from home. Homeward paths were remarkably straight and oriented directly toward home, or they traveled to a frequented route then turned toward home. Seventy-five percent of the frequented routes were directly below known linear disturbances in the snow on the top of the sea ice. There was little evidence that seals used geomagnetic or hydrodynamic cues, nor that homing ability was hindered by low light levels (twilight). These results contribute to a growing body of literature indicating that animals can learn to use artificial, and sometimes ephemeral landmarks to guide their movements. How Weddell seals are able to dive during polar winter, with only starlight and moonlight to illuminate landmarks, remains unknown.

Landscape inferred from gene expression data governs pluripotency in embryonic stem cells

Embryonic stem cells (ESCs) can differentiate into diverse cell types and have the ability of self-renewal. Therefore, the study of cell fate decisions on embryonic stem cells has far-reaching significance for regenerative medicine and other biomedical fields. Mathematical models have been used to study emryonic stem cell differentiation. However, the underlying mechanisms of cell differentiation and lineage reprogramming remain to be elucidated. Especially, how to integrate the computational models with quantitative experimental data is still challenging. In this work, we developed a data-constrained modelling approach, and established a model of mouse embryonic stem cells. We used the truncated moment equations (TME) method to quantify the potential landscape of the ESC network. We identified two attractors on the landscape, which represent the embryonic stem cell (ESC) state and differentiated cell (DC) state, respectively, and quantified high dimensional biological paths for differentiation and reprogramming process. Through identifying the optimal combinations of gene targets based on a landscape control strategy, we offered some predictions about the key regulatory factors that govern the differentiation and reprogramming in ESCs.

The 2I/E model: Integrating temporal comparisons into the internal/external frame of reference model.

The 2I/E model is an extension of Marsh’s (1986) classical internal/external frame of reference (I/E) model. Whereas the classical I/E model describes the formation of academic self-concept by the joint operation of social (external) and dimensional (internal) comparisons, the 2I/E model integrates temporal comparisons as an additional internal comparison process. In the 2I/E model, paths from achievement levels to self-concepts in the same subject are assumed to represent social comparisons, paths from achievement levels to self-concepts in another subject are assumed to represent dimensional comparisons, and paths from achievement changes to self-concepts in the same subject are assumed to represent temporal comparisons. The present research validated the 2I/E model in six empirical studies with a total of more than 20,000 students. Generally, there were strong positive social comparison paths, moderate negative dimensional comparison paths, and small positive temporal comparison paths. Furthermore, the relations of the 2I/E model were replicated with both grades and standardized test scores as achievement indicators (Study 1 and Study 2). Dimensional comparison effects were stronger between dissimilar subjects, like math and German, than between similar subjects, like German and English (Study 2 and Study 3). Also, the relations of the 2I/E model were shown when prior self-concepts were controlled for (Study 4). Overall, the 2I/E model seems to have the potential to enrich future theory and research on self-concept formation and comparison processes. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

Vertically aligned nanostructured FeOOH@MnO2 core shell electrode with better areal capacitance

Present work focuses on hydrothermal preparation of FeOOH@MnO2 core shell as a vertically aligned 1-D nanostructure and improvement in electrochemical charge storage by utilizing MnO2 nanostructure as an active electrode material and vertically aligned FeOOH nanorods for one dimensional electron transfer paths. A FeOOH@MnO2 core shell thin film electrode gives maximum capacitance of 0.252 Fcm−2 for the applied current density of 1 mAcm−2 and maintains 99.5% capacitance retention for 2000 charge discharge cycles at 5 mAcm−2 that attributes to better capacitive charge storage in the material. Assembled solid state symmetric electrochemical capacitor of FeOOH@MnO2 electrode yields maximum of 0.05 mWhcm−2 energy density with power delivery of 1.5 mWcm−2.

Time dispersion in quantum mechanics

In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum effects along the time axis to be of order an attosecond. Such effects are not ruled out by current experiments. But they are large enough to be detected with current technology, if sufficiently specific predictions can be made. To supply such we use path integrals. The only change required is to generalize the usual three dimensional paths to four. We predict a large variety of testable effects. The principal effects are additional dispersion in time and full equivalence of the time/energy uncertainty principle to the space/momentum one. Additional effects include interference, diffraction, and entanglement in time. The usual ultraviolet divergences do not appear: they are suppressed by a combination of dispersion in time and entanglement in time. The approach here has no free parameters; it is therefore falsifiable. As it treats time and space with complete symmetry and does not suffer from the ultraviolet divergences, it may provide a useful starting point for attacks on quantum gravity.

A deterministic walk on the randomly oriented Manhattan lattice

Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic walk is then started at the origin and at each step moves diagonally to the nearest vertex in the direction of the horizontal and vertical lines of the present location. This definition can be generalized, in a natural way, to larger dimensions, but we mainly focus on the two dimensional case. In this context the process localizes on two vertices at all large times, almost surely. We also provide estimates for the tail of the length of paths, when the walk is defined on the two dimensional lattice. In particular, the probability of the path to be larger than $n$ decays sub-exponentially in $n$. It is easy to show that higher dimensional paths may not localize on two vertices but will still eventually become periodic, and are therefore bounded.

Existence and continuity of the flow constant in first passage percolation

We consider the model of i.i.d. first passage percolation on $\mathbb{Z} ^d$, where we associate with the edges of the graph a family of i.i.d. random variables with common distribution $G$ on $ [0,+\infty ]$ (including $+\infty $). Whereas the time constant is associated to the study of $1$-dimensional paths with minimal weight, namely geodesics, the flow constant is associated to the study of $(d-1)$-dimensional surfaces with minimal weight. In this article, we investigate the existence of the flow constant under the only hypothesis that $G(\{+\infty \} ) < p_c(d)$ (in particular without any moment assumption), the convergence of some natural maximal flows towards this constant, and the continuity of this constant with regard to the distribution $G$.

Significantly improved electrical and interlaminar mechanical properties of carbon fiber laminated composites by using special carbon nanotube pre-dispersion mixture

High electrical conductivity through thickness direction is an indispensable prerequisite for the application of laminated composites in the aircraft. The epoxide (butyl glycidyl ether) functionalized multiwall carbon nanotube (MWCNT-BGE) was prepared and then reacted with epoxy resin to form a new type of pre-dispersion mixture. Subsequently, the MWCNT-BGE/epoxy pre-dispersion mixture was transferred to the interlayer of carbon fiber/epoxy composite laminates by well-designed spraying technique, and the relevant micro-morphology and size distribution were quantitatively analyzed. The results showed that the three dimensional continuous conductive paths can be built and maintained across the interlayer of composite laminates through the incorporation of fluffy and network-like MWCNT-BGE/epoxy pre-dispersion mixture. A remarkable increase of 283% can be realized in the through-thickness electrical conductivity after spraying pre-dispersion mixture with a concentration of 0.5wt%. Further, the incorporation of pre-dispersion mixture can efficiently enhance the interlaminar shear strength of carbon fiber composite laminates simultaneously.

Convergence to equilibrium for a directed (1+d)-dimensional polymer

We consider a flip dynamics for directed (1+d)-dimensional lattice paths with length L. The model can be interpreted as a higher dimensional version of the simple exclusion process, the latter corresponding to the case d=1. We prove that the mixing time of the associated Markov chain scales like L^2\log L up to a d-dependent multiplicative constant. The key step in the proof of the upper bound is to show that the system satisfies a logarithmic Sobolev inequality on the diffusive scale L^2 for every fixed d, which we achieve by a suitable induction over the dimension together with an estimate for adjacent transpositions. The lower bound is obtained with a version of Wilson's argument for the one-dimensional case. Keywords: exclusion process, adjacent transpositions, logarithmic Sobolev inequality, mixing time

Pathwise Taylor expansions for random fields on multiple dimensional paths

In this paper we establish the pathwise Taylor expansions for random fields that are “regular” in terms of Dupire’s path-derivatives [6]. Using the language of pathwise calculus, we carry out the Taylor expansion naturally to any order and for any dimension, which extends the result of Buckdahn et al. (2011). More importantly, the expansion can be both “forward” and “backward”, and the remainder is estimated in a pathwise manner. This result will be the main building block for our new notion of viscosity solution to forward path-dependent PDEs corresponding to (forward) stochastic PDEs in our accompanying paper Buckdahn et al. [4].

Encapsulated within graphene shell silicon nanoparticles anchored on vertically aligned graphene trees as lithium ion battery anodes

Silicon has been regarded as one of the most promising anode material for the next generation lithium ion battery. Unfortunately, the structure damage caused by the volume change of silicon and the continual interfacial reaction due to the electrolyte remain two major challenges. Here, we design a novel kind of in-situ growth binder-free silicon-based anodes. The adaptable silicon nanoparticles were encapsulated in graphene nanosheets (SiNPs@GNS). Simultaneously, the SiNPs@GNS composites anchored on vertically aligned graphene trees with loose intersecting leaves (GrTr). In the resulting samples, the GNS shells, as adaptable sealed wraps, could synergistically accommodate the volume change of the wrapped SiNPs, thus effectively avoiding the direct contact between encapsulated silicon and the electrolyte and enabling the interfacial and structural stabilization of encapsulated SiNPs during cycling. The GrTrs directly grown on current collector act as supporters of SiNPs, which ensure their dispersion uniformity and supply three dimensional short transportation paths for both Li ions and electrons. The in-situ growth of SiNPs@GNS–GrTr composites were proximately used as anodes in LIBs without adhesives and other complex brushing processes of the active material. The composite material exhibits a high capacity (1528mAhg−1 at 150mA/g), relatively good cycle stability (88.6% after 50 cycles), and fast charge/discharge rate (412mAhg−1 at 8A/g). The uniquely designed structure of the composites, which provide an ultra-thin, flexible GNS shell to accommodate the changes in volume, introduces large efficient areas, good conductivity, three dimensional transportation paths for both Li ions and electrons, and contributes to its excellent performance.

Quantifying Cell Fate Decisions for Differentiation and Reprogramming of a Human Stem Cell Network: Landscape and Biological Paths

Cellular reprogramming has been recently intensively studied experimentally. We developed a global potential landscape and kinetic path framework to explore a human stem cell developmental network composed of 52 genes. We uncovered the underlying landscape for the stem cell network with two basins of attractions representing stem and differentiated cell states, quantified and exhibited the high dimensional biological paths for the differentiation and reprogramming process, connecting the stem cell state and differentiated cell state. Both the landscape and non-equilibrium curl flux determine the dynamics of cell differentiation jointly. Flux leads the kinetic paths to be deviated from the steepest descent gradient path, and the corresponding differentiation and reprogramming paths are irreversible. Quantification of paths allows us to find out how the differentiation and reprogramming occur and which important states they go through. We show the developmental process proceeds as moving from the stem cell basin of attraction to the differentiation basin of attraction. The landscape topography characterized by the barrier heights and transition rates quantitatively determine the global stability and kinetic speed of cell fate decision process for development. Through the global sensitivity analysis, we provided some specific predictions for the effects of key genes and regulation connections on the cellular differentiation or reprogramming process. Key links from sensitivity analysis and biological paths can be used to guide the differentiation designs or reprogramming tactics.

A Combinatorial Proof of the Recurrence for Rook Paths

Let $a_n$ count the number of $2$-dimensional rook paths $\mathcal{R}_{n,n}$ from $(0,0)$ to $(2n,0)$. Rook paths $\mathcal{R}_{m,n}$ are the lattice paths from $(0,0)$ to $(m+n,m-n)$ with allowed steps $(x,x)$ and $(y,-y)$ where $x,y\in\mathbb{N}^{+}$. In answer to the open question proposed by M. Erickson et al. (2010), we shall present a combinatorial proof for the recurrence of $a_n$, i.e., $(n+1)a_{n+1}+9(n-1)a_{n-1}=2(5n+2)a_n$ with initial conditions $a_0=1$ and $a_1=2$. Furthermore, our proof can be extended to show the recurrence for the number of multiple Dyck paths $d_n$, i.e., $(n+2)d_{n+1}+9(n-1)d_{n-1}=5(2n+1)d_n$ with $d_0=1$ and $d_1=1$, where $d_n=\mathcal{N}_n(4)$ and $\mathcal{N}_n(x)$ is Narayana polynomial.

Hölder-Continuous Rough Paths by Fourier Normal Ordering

We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf algebra of decorated rooted trees (in connection with the Chen or multiplicative property) and of the Hopf shuffle algebra (in connection with the shuffle or geometric property). H\"older continuity is proved by using Besov norms. The method is well-suited in particular in view of applications to probability theory (see the companion article \cite{Unt09} for the construction of a rough path over multidimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or \cite{Unt09ter} for a short survey in that case).