The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it (...) has a polynomial-space lower bound for the domains of type , and has a #P lower bound for the domains of type. (shrink)

The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it (...) has a polynomial-space lower bound for the domains of type, and has a #P lower bound for the domains of type. (shrink)

Individuals vary in the way they navigate through space. Some take novel shortcuts, while others rely on known routes to find their way around. We wondered how and why there is so much variation in the population. To address this, we first compared the trajectories of 368 human subjects navigating a virtual maze with simulated trajectories. The simulated trajectories were generated by strategy-based path planning algorithms from robotics. Based on the similarities between human trajectories and different strategy-based simulated trajectories, (...) we found that there is a variation in the type of strategy individuals apply to navigate space, as well as variation within individuals on a trial-by-trial basis. Moreover, we observed variation within a trial when subjects occasionally switched the navigation strategies halfway through a trajectory. In these cases, subjects started with a route strategy, in which they followed a familiar path, and then switched to a survey strategy, in which they took shortcuts by considering the layout of the environment. Then we simulated a second set of trajectories using five different but comparable artificial maps. These trajectories produced the similar pattern of strategy variation within and between trials. Furthermore, we varied the relative cost, that is, the assumed mental effort or required timesteps to choose a learned route over alternative paths. When the learned route was relatively costly, the simulated agents tended to take shortcuts. Conversely, when the learned route was less costly, the simulated agents showed preference toward a route strategy. We suggest that cost or assumed mental effort may be the reason why in previous studies, subjects used survey knowledge when instructed to take the shortest path. We suggest that this variation we observe in humans may be beneficial for robotic swarms or collections of autonomous agents during information gathering. (shrink)

Individuals vary in the way they navigate through space. Some take novel shortcuts, while others rely on known routes to find their way around. We wondered how and why there is so much variation in the population. To address this, we first compared the trajectories of 368 human subjects navigating a virtual maze with simulated trajectories. The simulated trajectories were generated by strategy-based path planning algorithms from robotics. Based on the similarities between human trajectories and different strategy-based simulated trajectories, (...) we found that there is a variation in the type of strategy individuals apply to navigate space, as well as variation within individuals on a trial-by-trial basis. Moreover, we observed variation within a trial when subjects occasionally switched the navigation strategies halfway through a trajectory. In these cases, subjects started with a route strategy, in which they followed a familiar path, and then switched to a survey strategy, in which they took shortcuts by considering the layout of the environment. Then we simulated a second set of trajectories using five different but comparable artificial maps. These trajectories produced the similar pattern of strategy variation within and between trials. Furthermore, we varied the relative cost, that is, the assumed mental effort or required timesteps to choose a learned route over alternative paths. When the learned route was relatively costly, the simulated agents tended to take shortcuts. Conversely, when the learned route was less costly, the simulated agents showed preference toward a route strategy. We suggest that cost or assumed mental effort may be the reason why in previous studies, subjects used survey knowledge when instructed to take the shortest path. We suggest that this variation we observe in humans may be beneficial for robotic swarms or collections of autonomous agents during information gathering. (shrink)

This paper presents an integrated approach to plan smooth path for robots docking in unknown environments with obstacles. To determine the smooth collision-free path in obstacle environment, a tree structure with heuristic expanding strategy is designed as the foundation of path planning in this approach. The tree employs 3D Dubins curves as its branches and foundation for path feasibility evaluation. For the efficiency of the tree expanding in obstacle environment, intermediate nodes and collision-free branches are determined (...) inspired by the elastic band theory. A feasible path is chosen as the shortest series of branches that connects to the docking station after the sufficient expansion of the tree. Simulation results are presented to show the validity and feasibility of the proposed approach. (shrink)

Over the previous three decades, the area of computer networks has progressed significantly, from traditional static networks to dynamically designed architecture. The primary purpose of software-defined networking is to create an open, programmable network. Conventional network devices, such as routers and switches, may make routing decisions and forward packets; however, SDN divides these components into the Data plane and the Control plane by splitting distinct features away. As a result, switches can only forward packets and cannot make routing decisions; the (...) controller makes routing decisions. OpenFlow is the communication interface between the switches and the controller. It is a protocol that allows the controller to identify the network packet’s path across the switches. This project uses the SDN environment to implement the firefly optimization algorithm to determine the shortest path between two nodes in a network. The firefly optimization algorithm was implemented using Ryu control. The results reveal that using the firefly optimization algorithm improves the selected short path between the source and destination. (shrink)

Islamic building codes require mosques to face Mecca. The further Islam spreads, the more apt are believers to fall into a quandary. X faces Y only when the front of X is closer to Y than any other side of X. So the front of the mosque should be oriented along a shortest path to Mecca. Which way is that? Does the path to Mecca tunnel through the earth? Or does the path follow the surface of (...) the earth? (shrink)

In computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, (...) eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. This book introduces a set of concepts in solving problems computationally such as Growth of Functions; Backtracking; Divide and Conquer; Greedy Algorithms; Dynamic Programming; Elementary Graph Algorithms; Minimal Spanning Tree; Single-Source Shortest Paths; All Pairs Shortest Paths; Flow Networks; Polynomial Multiplication, to ways of solving NP-Complete Problems, supported with comprehensive, and detailed problems and solutions, making it an ideal resource to those studying computer science, computer engineering and information technology. (shrink)

This paper investigates the Generalized Traveling Salesman Problem (GTSP), which is an extension of the well-known Traveling Salesman Problem (TSP), and it searches for an optimal tour in a clustered graph, such that every cluster is visited exactly once. In this paper, we describe a novel Memetic Algorithm (MA) for solving efficiently the GTSP. Our proposed MA has at its core a genetic algorithm (GA), completed by a Chromosome Enhancement Procedure (CEP), which is based on a TSP solver and the (...) Shortest Path (SP) algorithm and for improving the convergence characteristics of the GA, a Local Search (LS) operation is applied for the best chromosomes in each generation. We tested our algorithm on a set of well-known instances from the literature and the achieved results prove that our novel memetic algorithm is highly competitive against the existing solution approaches from the specialized literature. (shrink)

Through structural analysis of 8-year tag networks from online knowledge-sharing platforms, this study finds that, with the scale of tag networks growing quickly, the growth trend of number edges indicates that tag network follows densification law. The clustering coefficient and the average shortest path of the network show that the rapid growth of network size does not bring about the compartmentalization of the knowledge network, and the degree distribution of tag networks shows a truncated power-law distribution. According to (...) the structural characteristics of the tag network, this study proposes a tag network model based on the BA model. Based on the preference attachment, the triadic closure mechanism is employed to construct the edges between the old nodes, which revises the limitation that the BA model only connects edges between old and new nodes. The results show that the simulation model matches the actual tag network structure well. The generation mechanism of the tag network model provides a reference for understanding the knowledge construction process of the online knowledge-sharing platform to a certain extent. (shrink)

Background and PurposeTranscranial direct current stimulation is an emerging non-invasive neuromodulation technique for focal epilepsy. Because epilepsy is a disease affecting the brain network, our study was aimed to evaluate and predict the treatment outcome of cathodal tDCS by analyzing the ctDCS-induced functional network alterations.MethodsEither the active 5-day, −1.0 mA, 20-min ctDCS or sham ctDCS targeting at the most active interictal epileptiform discharge regions was applied to 27 subjects suffering from focal epilepsy. The functional networks before and after ctDCS were (...) compared employing graph theoretical analysis based on the functional magnetic resonance imaging data. A support vector machine prediction model was built to predict the treatment outcome of ctDCS using the graph theoretical measures as markers.ResultsOur results revealed that the mean clustering coefficient and the global efficiency decreased significantly, as well as the characteristic path length and the mean shortest path length at the stimulation sites in the fMRI functional networks increased significantly after ctDCS only for the patients with response to the active ctDCS. Our prediction model achieved the mean prediction accuracy of 68.3% after the nested cross validation. The mean area under the receiver operating curve was 0.75, which showed good prediction performance.ConclusionThe study demonstrated that the response to ctDCS was related to the topological alterations in the functional networks of epilepsy patients detected by fMRI. The graph theoretical measures were promising for clinical prediction of ctDCS treatment outcome. (shrink)

This article shows the organization of distance learning, particularly the idea of b-learning, combining the accomplishment of classes carried on in the traditional way and via computers. The authors present learning activities related to complementary education herein. Some of these course types may be successfully adapted to an e-learning background. The models and structure of the university virtual environment for distance learning are described. These illustrate a new approach to creating a virtual space for medical and technical studies where e-learning (...) courses are created to be used for distance education, which allows students to be taught more effectively. The projected virtual courses for different groups of students ensure individualization of students’ work, which could be a relevant element for creating the shortest path of development of professional competencies. This paper further includes a brief overview of technologies used to build interactive elements into learning mate- rials. The authors present the use of interactive elements in medical education based on examples of certain selected games and animations. (shrink)

Why bother to praise mathematics when you claim, as Alain Badiou does, that philosophy is first and foremost a metaphysics of happiness, or else it’s not worth an hour of trouble? What possible relationship can there be between mathematics and happiness? That is precisely the issue at stake in this dialogue, which serves as a very accessible introduction to what mathematics is and an exploration of the crucial influence it has always exerted on the greatest philosophers. Far from the thankless, (...) pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness. (shrink)

For almost the whole of the first half of the nineteenth century, philosophy at Moscow University was subjected to fierce persecution at the hands of the authorities. Their aim was, evidently, to smother in the cradle any manifestation of freethinking among students, the thinking part of Russian society. It was no coincidence that philosophy was chosen as the target of persecution, because the study of this science could lead by the shortest path to reflections concerning man's place in (...) the world, the role of the social sciences, the just or unjust nature of the existing state order in Russia, and so on. What would a student who got carried away by, for instance, Socrates's ideal of inner freedom or Spinoza's pantheistic system become? For a classical police state, which imperial Russia was, that was intolerable. One need merely recall that Chaadaev, Herzen, and many other rebels had at some time studied at the university. Russia's rulers clearly had no need of such people. (shrink)

We pursue an account of merging through the use of geodesic semantics, the semantics based on the length of the shortest path on a graph. This approach has been fruitful in other areas of belief change such as revision and update. To this end, we introduce three binary merging operators of propositions defined on the graph of their valuations and we characterize them with a finite set of postulates.

The energy hole is a severe problem for underwater acoustic distributed networks in that it affects the normal operations of the network and shortens the network’s life span. To deal with this problem, a loop-free routing control technique is proposed in this paper. The classical shortest-path routing control method is used to generate multiple disjointed routing tables. The residual energy of the nodes and the changing information of the uplink/downlink matrix are added to the data frames for distribution. (...) The source node specifies the routing path to transmit the data frames based on the changing information, and the relay nodes route the data frames strictly according to the routing path designated by the source node. Besides, the energy consumption of the relay node is saved by replying to the pseudo-ACK frame. Simulation experiments are implemented in four typical scenarios, and the results reflect that the proposed technique could extend the network’s life span by approximately 10% when compared to other mature techniques. Besides, it has no other negative effects on the normal operations of the network. (shrink)

The application of machine learning touches all activities of human behavior such as computer network and routing packets in LAN. In the field of our research here, emphasis was placed on extracting weights that would affect the speed of the network's response and finding the best path, such as the number of nodes in the path and the congestion on each path, in addition to the cache used for each node. Therefore, the use of these elements in (...) building the neural network is worthy, as is the exploitation of the feed forwarding and the backpropagation in the neural network in order to reach the best prediction for the best path. The goal of the proposed neural network is to minimize the network time delay within the optimization of the packet paths being addressed in this study. The shortest path is considered as the key issue in routing algorithm that can be carried out with real time of path computations. Exploiting the gaps in previous studies, which are represented in the lack of training of the system and the inaccurate prediction as a result of not taking into consideration the hidden layers' feedback, leads to great performance. This study aims to suggest an efficient algorithm that could help in selecting the shortest path to improve the existing methods using weights derived from packet ID and to change neural network iteration simultaneously. In this study, the design of the efficient neural network of appropriate output is discussed in detail including the principles of the network. The findings of the study revealed that exploiting the power of computational system to demonstrate computer simulation is really effective. It is also shown that the system achieved good results when training the neural network system to get 2.4% time delay with 5 nodes in local LAN. Besides, the results showed that the major features of the proposed model will be able to run in real time and are also adaptive to change with path topology. (shrink)

This paper deals primarily with countable, simple, connected graphs and the following two conditions which are trivially satisfied if the graphs are finite: (a) there is an edge-recognition algorithm, i.e., an effective procedure which enables us, given two distinct vertices, to decide whether they are adjacent, (b) there is a shortest path algorithm, i.e., an effective procedure which enables us, given two distinct vertices, to find a minimal path joining them. A graph $G = \langle\eta, \eta\rangle$ with (...) η as set of vertices and η as set of edges is an α-graph if it satisfies (a); it is an ω-graph if it satisfies (b). G is called r.e. (isolic) if the sets ν and η are r.e. (isolated). While every ω-graph is an α-graph, the converse is false, even if G is r.e. or isolic. Several basic properties of finite graphs do not generalize to ω-graphs. For example, an ω-tree with more than one vertex need not have two pendant vertices, but may have only one or none, since it may be a 1-way or 2-way infinite path. Nevertheless, some elementary propositions for finite graphs $G = \langle\nu, \eta\rangle$ with $n = \operatorname{card}(\nu), e = \operatorname{card}(\eta)$ , do generalize to isolic ω-graphs, e.g., n - 1 ≤ e ≤ n(n - 1)/2. Let N and E be the recursive equivalence types of ν and η respectively. Then we have for an isolic α-tree $G = \langle\nu, \eta\rangle: N = E + 1$ iff G is an ω-tree. The theorem that every finite graph has a spanning tree has a natural, effective analogue for ω-graphs. The structural difference between isolic α-graphs and isolic ω-graphs will be illustrated by: (i) every infinite graph is isomorphic to some isolic α-graph; (ii) there is an infinite graph which is not isomorphic to any isolic ω-graph. An isolic α-graph is also called a twilight graph. There are c such graphs, c denoting the cardinality of the continuum. (shrink)

ObjectiveTo explore alterations in white matter network topology in de novo Parkinson's disease patients with rapid eye movement sleep behavior disorder.Materials and MethodsThis study included 171 de novo PD patients and 73 healthy controls recruited from the Parkinson's Progression Markers Initiative database. The patients were divided into two groups, PD with probable RBD and PD without probable RBD, according to the RBD screening questionnaire. Individual structural network of brain was constructed based on deterministic fiber tracking and analyses were performed using (...) graph theory. Differences in global and nodal topological properties were analyzed among the three groups. After that, post hoc analyses were performed to explore further differences. Finally, correlations between significant different properties and RBDSQ scores were analyzed in PD-pRBD group.ResultsAll three groups presented small-world organization. PD-pRBD patients exhibited diminished global efficiency and increased shortest path length compared with PD-npRBD patients and HCs. In nodal property analyses, compared with HCs, the brain regions of the PD-pRBD group with changed nodal efficiency were widely distributed mainly in neocortical and paralimbic regions. While compared with PD-npRBD group, only increased Ne in right insula, left middle frontal gyrus, and decreased Ne in left temporal pole were discovered. In addition, significant correlations between Ne in related brain regions and RDBSQ scores were detected in PD-pRBD patients.ConclusionsPD-pRBD patients showed disrupted topological organization of white matter in the whole brain. The altered Ne of right insula, left temporal pole and left middle frontal gyrus may play a key role in the pathogenesis of PD-RBD. (shrink)

An analogy between the evolution of organisms and some complex computational problems (cryptosystem cracking, determination of the shortest path in a graph) is considered. It is shown that in the absence of a priori information about possible species of organisms such a problem is complex (is rated in the class NP) and cannot be solved in a polynomial number of steps. This conclusion suggests the need for re-examination of evolution mechanisms. Ideas of a deterministic approach to the evolution (...) are discussed. (shrink)

We consider a special case of heuristics, namely numeric heuristic evaluation functions, and their use in artificial intelligence search algorithms. The problems they are applied to fall into three general classes: single-agent path-finding problems, two-player games, and constraint-satisfaction problems. In a single-agent path-finding problem, such as the Fifteen Puzzle or the travelling salesman problem, a single agent searches for a shortest path from an initial state to a goal state. Two-player games, such as chess and checkers, (...) involve an adversarial relationship between two players, each trying to win the game. In a constraint-satisfaction, problem, such as the 8-Queens problem, the task is to find a state that satisfies a set of constraints. All of these problems are computationally intensive, and heuristic evaluation functions are used to reduce the amount of computation required to solve them. In each case we explain the nature of the evaluation functions used, how they are used in search algorithms, and how they can be automatically learned or acquired. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:400 KANT'S MISREPRESENTATIONS OF HUME'S PHILOSOPHY OF MATHEMATICS IN THE PROLEGOMENA In 1783, Immanuel Kant published the following reflections upon the philosophy of mathematics of David Hume, words which have colored all subsequent interpretations of the letter's work: Hume being prompted to cast his eye over the whole field of a priori cognitions in which human understanding claims such mighty possessions (a calling he felt worthy of a philosopher) (...) heedlessly severed from it a whole, and indeed its most valuable, province, namely, pure mathematics ; for he imagined its nature or, so to speak, the state constitution of this empire depended on totally different principles, namely, on the law of contradiction alone; and although he did not divide judgments in this manner formally and universally as I have done here, what he said was equivalent to this: that mathematics contains only analytical, but metaphysics synthetical, a priori propositions. In this he was mistaken, and the mistake had a decidedly injurious effect upon his whole conception. But for this, he would have extended his question concerning the origin of our synthetical judgments far beyond the metaphysical concept of causality and included in it the possibility of mathematics a priori also, for this latter he must have assumed to be equally synthetical. And then he could not have based his metaphysical propositions on mere experience without subjecting the axioms of mathematics equally to experience, a thing which he was far too acute to do. The good company in which metaphysics would thus have been brought would have saved it from the danger of a contemptuous illtreatment, or the thrust intended for it must have reached mathematics, which was and could not have been Hume's intention. Thus that acute 401 man could have been led into considerations which must needs be similar to those that now occupy us, but would have gained inestimably by his inimitably elegant style. In other words, Hume failed to notice that mathematics, despite its a priori character, is synthetic. It was thus easy for him to conclude that all a priori judgments are analytic, and that therefore metaphysics (conceived of as synthetic ¿ priori judgments) is impossible. Now what considerations led Kant himself to the opposite conclusion, that mathematics is synthetic despite being a priori? Let's consider Kant's own words in a typical passage: Just as little is any principle of geometry analytical. That a straight line is the shortest path between two points is a synthetical proposition. For my concept of straight contains nothing of quantity, but only a quality. The concept 'shortest' is therefore altogether additional and cannot be obtained by any analysis of the concept 'straight line.' Here, too, intuition must come to aid us. It alone makes the synthesis possible. I should like the reader now to compare the following passage from Hume's Treatise of Human 2 Nature, Book I, Part II, Section IV: 'Tis true, mathematicians pretend they give an exact definition of a right line, when they say, it is the shortest way betwixt two points. But in the first place, I observe, that this is more properly the discovery of one of the properties of a right line, than a just definition of it. For I ask any one, if upon mention of a right line he thinks not immediately on such a particular appearance, and if 'tis not by accident only that he considers this property? A right line can be comprehended alone; but this definition is unintelligible 402 without a comparison with other lines, which we conceive to be more extended. In common life 'tis establish 'd as a maxim, that the streightest way is always the shortest; which wou'd be as absurd as to say, the shortest way is always the shortest, if our idea of a right line was not different from that of the shortest way betwixt two points. Style and terminology apart, I defy the reader to distinguish between these two arguments and their conclusions. Hume argues that 'The shortest distance between two points is a straight line' is no definition; furthermore he says almost explicitly that 'There is a longer distance between two points than a straight line... (shrink)

Under “the Belt and Road” initiative, China promoted cooperation between domestic enterprises and international ports vigorously, which brought back fruitful results, while the rational selection of strategic pivots ports and the optimization of the layout of the port network are important guarantees to a further promotion to the economic development of “the Belt and Road” ports and give full play to the driving and radiation role of strategic pivots ports. On the basis of constructing a network of 155 ports in (...) the world, according to the number of ports crossed by the shortest path and betweenness centrality in the network, this paper uses K-Medoids clustering algorithm to train the strategic importance of ports and verifies the reliability of the analysis results. On this basis, the joint coverage analysis of strategically important ports is carried out, 17 ports are identified as strategic pivots ports of the global port network, and, finally, based on the two attributes of “the Belt and Road” and “Chinese enterprise participation” of strategic pivots ports, the leading role of strategic pivots ports in geographical location, path coverage, development potential, cooperation stability, and control is analyzed, and instructive suggestions are put forward. (shrink)

This article examines the communication networks within and between science and technology studies (STS) and the history of science. In particular, journal relatedness data are used to analyze some of the structural features of their disciplinary identities and relationships. The results first show that, although the history of science is more than half a century older than STS, the size of the STS network is more than twice that of the history of science network. Further, while a majority of the (...) journals in the STS network are connected by weak ties, about half of the history of science network consists of strong ties. The history of science network is thus more cohesive than the STS network. The relatively strong cohesion within the history of science network is associated with comparatively high degrees of intra-disciplinary communication, but comparatively weak ties to only a few related disciplines. The analysis also shows that very few members of the history of science cliques are situated on the shortest path between both specialties. Moreover, given the relatively impermeable nature of the history of science network, the latter partially depends on STS to reach some of the neighboring disciplines. (shrink)

This paper presents an axiomatization of a class of set-theoretic conditional operators using minimization of the geodesic distance defined as the shortest path generated by the accessibility relation on a frame. The objective of this modeling is to define conditioning based on a notion of similarity generated by degrees of indistinguishability.

We introduce a path-based measure of convexity to be used in assessing the compactness of legislative districts. Our measure is the probability that a district will contain the shortest path between a randomly selected pair of its' points. The measure is defined relative to exogenous political boundaries and population distributions.

What is the relationship between complexity in the world and complexity in the mind? Intuitively, increasingly complex objects and events should give rise to increasingly complex mental representations (or perhaps a plateau in complexity after a certain point). However, a counterintuitive possibility with roots in information theory is an inverted U-shaped relationship between the “objective” complexity of some stimulus and the complexity of its mental representation, because excessively complex patterns might be characterized by surprisingly short computational descriptions (e.g., if they (...) are represented as having been generated “randomly”). Here, we demonstrate that this is the case, using a novel approach that takes the notion of “description” literally. Subjects saw static and dynamic visual stimuli whose objective complexity could be carefully manipulated, and they described these stimuli in their own words by giving freeform spoken descriptions of them. Across three experiments totaling over 10,000 speech clips, spoken descriptions of shapes (Experiment 1), dot-arrays (Experiment 2), and dynamic motion-paths (Experiment 3) revealed a striking quadratic relationship between the raw complexity of these stimuli and the length of their spoken descriptions. In other words, the simplest and most complex stimuli received the shortest descriptions, while those stimuli with a “medium” degree of complexity received the longest descriptions. Follow-up analyses explored the particular words used by subjects, allowing us to further explore how such stimuli were represented. We suggest that the mind engages in a kind of lossy compression for overly complex stimuli, and we discuss the utility of such freeform responses for exploring foundational questions about mental representation. (shrink)

Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be (...) in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Of Diversities and Comparisons...Sor-hoon TanEncyclopedia of Chinese Philosophy. Edited by Antonio S. Cua. New York and London: Routledge, 2003. Pp. 1,020.Encyclopedias can be useful in teaching philosophy when students need some reading that sets out the basics on a key topic in a few pages without their getting lost in too many complex details or being misled by oversimplifications. They can also be edifying for the philosophy teacher and (...) scholar—providing reliable, up-to-date information on topics that lie in their field but that are not part of their working knowledge. For these reasons, those working in Chinese philosophy will welcome the publication of the Encyclopedia of Chinese Philosophy. The 187 entries cover a variety of subject areas such as "Moral Philosophy" and "Philosophy of language"; Confucianism in different periods and countries, Daoism, Mohism, Legalism, the school of names, Buddhism, and Marxism in China; philosophical trends in post-Mao China, Taiwan, and overseas; key concepts such as dao (the way), fa (law, standards), liyi fenshu (principle and manifestations), and quanli (rights); texts such as the Huainanzi and the Wenzi; and thinkers from Laozi and Confucius to Hu Shih and Mou Zongsan.Instead of more numerous short entries, this encyclopedia has opted for fewer entries of greater length—the Preface tells us that entries on important thinkers and philosophical topics typically range from five thousand to nine thousand words in length, and a quick check reveals that even the shortest entry is at least two pages long (more than one thousand words). This format allows authors to explore the philosophical issues at some depth, and expound even complex arguments in detail. The connections between different concepts, thinkers, texts, philosophical theories, and development that stretch across different periods and territories can be delineated more clearly in a single entry. There is a danger of duplication with this format, as some texts and concepts may be covered in several articles; for example, most of "Confucianism: Constructs of Classical Thought" is on what the author identifies as six key texts of Classical Confucianism: the Analects, Mencius, Xunzi, Yizhuan, Zhongyong (Doctrine of the mean), and Daxue (Great Learning). The sections on Mencius and Xunzi (pp. 66-67) merely introduce a small part of what is discussed in much greater depth and detail in the entries on these two thinkers (pp. 440-448 and 821-829). The Zhongyong and Daxue also have their own entries, and "Confucianism: Confucius" (p. 61) contains an entire section on the Analects.As it turns out, the duplication is less than expected. Pei-jung Fu, author of "Confucianism: Constructs of Classical Thought," implicitly questions Xunzi's Confucian pedigree, beginning his discussion with "Xunzi professed to be an advocate of Confucianism" (p. 67). Such doubt is clearly not shared by A. S. Cua, who authored [End Page 111] the entry on "Xunzi," introducing the thinker as "an important exponent of classical Confucianism" (p. 821). Cua also does not share Fu's view that "the real issue between Mencius and Xunzi lies in their concepts of heaven (tian)" (p. 67). Fu and the author of the entry on the Zhongyong translate key terms in the texts differently: Fu discusses "five ethical codes" and "three comprehensive virtues" (p. 68) while Yanming An calls them "five universal paths" and "three universal virtues" (p. 890). Such differences can be either thought provoking or confusing (especially when unaccompanied by Chinese characters or even pinyin), depending on the reader. The sections on the Analects in "Confucianism: Confucius" and "Confucianism: Constructs of Classical Thought" have hardly anything in common; the first examines it as an account of how Confucius lives as an exemplar remembered by his students, while the latter discusses its content, focusing on ren and li, as well as on Confucius' religious concerns. While concepts such as ren and li are frequently discussed, the different ways in which authors employ them and the different characteristics, contexts, and philosophical stakes they pay attention to enrich one's understanding of the many dimensions of these concepts even as similarities in diverse entries reinforce certain aspects and perspectives.One comes across disagreements to various degrees on common or related topics among different entries. While... (shrink)

Two experiments are reported that evaluated survey learning of youth with DS and typically developing children (TD) matched on Mental Age (MA). In Experiment 1, the experimenter navigated participants through a novel virtual environment along a circuitous path, beginning and ending at a target landmark (i.e., a door). Then, the participants were placed at a pre-specified location in the environment and instructed to navigate to the same door using the shortest possible path from their current location. They (...) completed the task three times: once after being shown the environment one time, once after three exposures, and once after five exposures. Results indicated that the participants with DS exhibited significantly less skill at identifying the shortcut than did the TD participants. In Experiment 2, participants learned two overlapping routes through a simple environment. Following acquisition, they were tested on several measures of survey knowledge: finding a shortcut, identifying the direction of landmarks not currently visible from their location in the environment, and recognizing a bird’s-eye representation of the overall environment. The results of Experiment2 indicated that the participants with DS were at least as good as the TD participants on all of our measures of survey learning. Hence, we concluded that people with DS can acquire some survey knowledge when they learn a simple environment. However, the performance of both groups was relatively poor in Experiment 2, indicating a need to consider identifying the mechanisms underlying the poor performance on wayfinding of people with DS. Identifying the underlying mechanisms, is a logical first step in devising methods of enhancing environmental learning of people with DS. (shrink)

This study aimed to explore practices and strategies that have successfully reduced time-to-proficiency of the workforce in large multinational organisations and develop a model based on them. The central research question of this study was: How can organisations accelerate time-to-proficiency of employees in the workplace? The study addressed three aspects: the meaning of accelerated proficiency, as seen by business leaders; the business factors driving the need for shorter time-to-proficiency and benefits accrued from it; and practices and strategies to shorten time-to-proficiency (...) of the workforce. 85 participants (n=85) from 7 countries who represented 10 economic sectors, 20 business sectors and 28 industry groups contributed 66 successful bounded project cases. A qualitative research approach was used. Data were collected through in-depth interviews with project leaders and by collecting additional project case documents. Data were analysed using thematic analysis to identify the themes in the data. Matrix analysis was then used to perform within-case and cross-case analysis to compare the project cases. 11 overarching themes were developed from the data analysis, out of which two overarching themes explained the characteristics of job-role proficiency and accelerated proficiency, while three overarching themes described the magnituide and scale of time-to-proficiency business problem, business drivers for accelerating proficiency and business benefits of reduced time-to-proficiency. Six overarching themes revealed the business practices employed by organisations to reduce time-to-proficiency: (1) Defining business-driven proficiency measures in terms of expected business outcomes from a job role; (2) Developing a proficiency reference map of all the inputs, conditions and roadblocks that determine or influence how required business outcomes are being produced in a job role; (3) Sequencing an efficient proficiency path of activities and experiences ordered to produce the desired business outcomes in the shortest possible time; (4) Manufacturing accelerated contextual experiences by leveraging on-the-job opportunities or training interventions in a compressed time-frame; (5) Promoting an active emotional immersion through engagements, consequences, stakes, feedback and proficiency assessments; and (6) Setting up a proficiency eco-system, providing timely support to performers while doing the job such as enabling job environment, highly involved manager, structured mentoring from experts, purposeful social connectivity with peers, leveraging subject matter experts and on-demand performance support systems. Organisations orchestrated these six business practices as an input-output-feedback system to reduce time-to-proficiency of the workforce. A conceptual model (Accelerated Proficiency Model) was developed representing interactions among six business-level practices/processes as a closed-loop system to explain the concept and process of accelerated proficiency in the workplace. These practices were implemented through a set of twenty-four strategies proven successful in various contexts. The strategies employed were much beyond the boundaries of conventional training interventions. The job itself acted as the primary mechanism to accelerate proficiency. A two-level hierarchical framework (6/24 framework of strategies) was also constructed in the form of a checklist consisting of six practices and twenty-four strategies for practitioners. Overall, the findings of this research study contribute significantly to the body of knowledge on accelerated proficiency. In particular, the conceptual model and the framework developed in this study can be implemented across a range of contexts, business sectors, job types and settings to reduce time-to-proficiency of the workforce. (shrink)

This paper analyses the particular composition of the last book of the Quaestiones Convivales and puts it in relation to the remaining eight books. The particularity of the 9th book can be seen at different levels. The prologue is the shortest one and has no educational goals in contrast to all preceding ones. There are more questions - 15 instead of 10 - and all of them belong to the same symposion. Accordingly there is a stable constellation of participants (...) instead of a permanent changing of characters. In this particular structure the last book should be placed near to the classical symposia of Plato and Xenophon, while the first eight books have a strong proximity to the problemata literature. A close look at the content shows an interesting development: There is no friendly conversation at the beginning, but disconnected and chaotic discussions, so the symposiarch Ammonios and other participants like Plutarch have to apply all their knowledge on symposia to achieve a friendly atmosphere. There are no programmatic discourses on symposia but a display of all necessary skills. Therefore the last book of the Quaestiones Convivales can be seen as a last examination for the reader and an opportunity to polish his learned symposiac skills. The dramatic time of this last symposion is set in the young days of Plutarch, when he was a student in Athens. He is one of the young participants, his master Ammonios is the host.While Ammonios plays the role of an alter Socrates, Plutarch as his pupil acts as a symposiast-to-be. In this way Plutarch illustrates in this last book the first step of his path to knowledge and presents himself as a worthy successor of Ammonios in sympotic competence. (shrink)

The earth, the abode of the only form of intelligent life in the universe of which we are aware, is a minor member of a system of nine planets, 40 or so moons and about 100 billion asteroids orbiting around the Sun, an average-size member of the 100-billion-star community making up our galaxy, the Milky Way. It is the third planet to the Sun, which it orbits, following an almost circular elliptical path maintaining an average distance of 1.5×108 km, (...) with the longest and the shortest radii now being 1.53×108 km and 1.47×10 km respectively (Fig. 1). This orbit is subject to changes in its “eccentricity” (i.e., in how much it deviates from a circle) with periods of 105 and 4×10 years5 years (Fig. 2A). In addition, the elliptical orbit itself slowly rotates as shown in Fig. 2B, in what we call the precession. (shrink)

This piece, included in the drift special issue of continent. , was created as one step in a thread of inquiry. While each of the contributions to drift stand on their own, the project was an attempt to follow a line of theoretical inquiry as it passed through time and the postal service(s) from October 2012 until May 2013. This issue hosts two threads: between space & place and between intention & attention . The editors recommend that to experience the (...) drifiting thought that attention be paid to the contributions as they entered into conversation one after another. This particular piece is from the BETWEEN INTENTION & ATTENTION thread: Jeremy Fernando, Sitting in the Dock of the bay, watching... * R.H. Jackson, Reading Eyes * Gina Rae Foster, Nyctoleptic Nomadism: The Drift/Swerve of Knowing * Bronwyn Lay, Driftwood * Patricia Reed, Sentences on Drifitng * David Prater, drift: a way * * * * The gaze drifts where the stare dares not. The gaze is attentive while the stare is intent. Dériver : Equally to drift and/or to derive. —When drifting then, something must be taken along. Something must be derived from the drift. Something of oneself must always become other. Incorporating the other, incorporating oneself as other. Je est un autre , Rimbaud disait; 1 this in his last letter to Georges Izambard, a final correspondence to a former mentor and friend, from whom he was drifting away, having derived much. The drift is a control incomplete. To drift is to come closer and closer, but to always be turning away, pulling apart, pulling oneself apart. It is parabolic in the sense that it is always eluding a formerly established intent. Of all axes, it never finds room to rest. Filling new spaces, always changing places, ever escaping the Cartesian; the indubitable pinpointing of position. It is never pinned down. Love together what we will be apart. Once together, we will drift apart. Il le faut . Attention is held; it traces the path. It follows each point which traces the arc, the line, the swerve. It is not concerned with the figure being drawn, but rather the movement between one point and the next. The smallest movement. The clinamen of De Rerum Natura is the smallest of swerves, it is nothing more than the minimum — nec plus quam minimum . Michel Serres says of the clinamen , that it is an absurdity — a logical, geometrical, mechanical, physical absurdity. 'The clinamen, from here (its state of absurdity), finds refuge in subjectivity; it passes from the world to the soul, from the physical to the metaphysical, from the theory of inert bodies in freefall to the theory of the free movements of the living.' 2 So this swerve is something of the mind and something of the body, both in action, rather than a body which is merely acted upon. Swerve, however, has a connotation of suddenness. It is a movement which is made to avoid an otherwise inevitable impact. Drift, on the other hand, is the unleashing of something which is then allowed to follow a more complex series of forces. These forces now come from within as well as without. It is no longer tethered; now following tides, winds, flows or pitched slopes, now acting on its own. We are not atoms in freefall. Our attention long ago pulled us from this precipitous descent. We now live, ourselves, as one of the many forces. In the drift, as with the gaze, there is an ease. ‘Ease is the proper name of this unrepresentable space.’ It is the space nearest, the next, the neighboring space. To occupy this space requires a turn, a shift or a drift. It cannot be reached by proceeding straight ahead. ‘..the space adjacent, the empty place where each can move freely, in a semantic constellation where spatial proximity borders on opportune time (ad-agio, moving at ease) and convenience borders on the correct relation.’ 3 Intention always seeks to straighten this line, to make it less complex, to isolate the point of departure and the desired destination. It believes there can be two points and, between them, there must be a straight line. Can there be? Maybe. Must there be? Never. Straight lines may exist, but they can never be followed to the finish. After leaving this point, we will never reach that one without being buffeted at least a little — at least the least. One foot in front of the other, this is a very restrictive dance, less even than a two-step. Straight lines lead only to lost intentions, being the shortest and quickest way to get there. When attention drifts it slowly turns away from the intended target, leaving it for something which pulls the attention away. Now we are for a moment free; all at once we can pivot, now we can waltz. Drifting along the page, deriving from what is seen. Reading is seeing; the movement of the eyes as they drift. Reading in the eyes what has been seen, what has been derived from the act of reading. Reading eyes drift back and forth down the page, now and then jump back and forth, up to the top, one word, back down, quickly a few pages back, now gaze out towards the horizon. When attention drifts it is the gaze that follows. Our attention is not restricted to the path the words follow, but links them together; deriving what is to be seen, rather than read. La philosophie fait voir . ‘Thus, philosophers speak through proverbs, and demonstrate. They connect their imaginations with foreign rings, flown into famous tombs.’ 4 Now drifting off to sleep, dreams come as unintended visions. To dream is pure drift, vision without an object, gazing into the dark, reading the unknown of the night. NOTES: Arthur Rimbaud, Poésies (Paris: Bibliothéque de Cluny, 1958), 57. Michel Serres, La Naissance de la Physique (Paris: Les Editions de Minuit, 1977), 10. Translation courtesy of R.H. Jackson. Giorgio Agamben, The Coming Community (Minneapolis: University of Minnesota, 1993), 25. Louis Aragon, Une Vague des Rêves (Paris: Editions Seghers, 2006), 10. Translation courtesy of R.H. Jackson.  . (shrink)

The earth, the abode of the only form of intelligent life in the universe of which we are aware, is a minor member of a system of nine planets, 40 or so moons and about 100 billion asteroids orbiting around the Sun, an average-size member of the 100-billion-star community making up our galaxy, the Milky Way. It is the third planet to the Sun, which it orbits, following an almost circular elliptical path maintaining an average distance of 1.5×108 km, (...) with the longest and the shortest radii now being 1.53×108 km and 1.47×10 km respectively (Fig. 1). This orbit is subject to changes in its “eccentricity” (i.e., in how much it deviates from a circle) with periods of 105 and 4×10 years5 years (Fig. 2A). In addition, the elliptical orbit itself slowly rotates as shown in Fig. 2B, in what we call the precession. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Of Diversities and Comparisons...Sor-hoon TanEncyclopedia of Chinese Philosophy. Edited by Antonio S. Cua. New York and London: Routledge, 2003. Pp. 1,020.Encyclopedias can be useful in teaching philosophy when students need some reading that sets out the basics on a key topic in a few pages without their getting lost in too many complex details or being misled by oversimplifications. They can also be edifying for the philosophy teacher and (...) scholar—providing reliable, up-to-date information on topics that lie in their field but that are not part of their working knowledge. For these reasons, those working in Chinese philosophy will welcome the publication of the Encyclopedia of Chinese Philosophy. The 187 entries cover a variety of subject areas such as "Moral Philosophy" and "Philosophy of language"; Confucianism in different periods and countries, Daoism, Mohism, Legalism, the school of names, Buddhism, and Marxism in China; philosophical trends in post-Mao China, Taiwan, and overseas; key concepts such as dao (the way), fa (law, standards), liyi fenshu (principle and manifestations), and quanli (rights); texts such as the Huainanzi and the Wenzi; and thinkers from Laozi and Confucius to Hu Shih and Mou Zongsan.Instead of more numerous short entries, this encyclopedia has opted for fewer entries of greater length—the Preface tells us that entries on important thinkers and philosophical topics typically range from five thousand to nine thousand words in length, and a quick check reveals that even the shortest entry is at least two pages long (more than one thousand words). This format allows authors to explore the philosophical issues at some depth, and expound even complex arguments in detail. The connections between different concepts, thinkers, texts, philosophical theories, and development that stretch across different periods and territories can be delineated more clearly in a single entry. There is a danger of duplication with this format, as some texts and concepts may be covered in several articles; for example, most of "Confucianism: Constructs of Classical Thought" is on what the author identifies as six key texts of Classical Confucianism: the Analects, Mencius, Xunzi, Yizhuan, Zhongyong (Doctrine of the mean), and Daxue (Great Learning). The sections on Mencius and Xunzi (pp. 66-67) merely introduce a small part of what is discussed in much greater depth and detail in the entries on these two thinkers (pp. 440-448 and 821-829). The Zhongyong and Daxue also have their own entries, and "Confucianism: Confucius" (p. 61) contains an entire section on the Analects.As it turns out, the duplication is less than expected. Pei-jung Fu, author of "Confucianism: Constructs of Classical Thought," implicitly questions Xunzi's Confucian pedigree, beginning his discussion with "Xunzi professed to be an advocate of Confucianism" (p. 67). Such doubt is clearly not shared by A. S. Cua, who authored [End Page 111] the entry on "Xunzi," introducing the thinker as "an important exponent of classical Confucianism" (p. 821). Cua also does not share Fu's view that "the real issue between Mencius and Xunzi lies in their concepts of heaven (tian)" (p. 67). Fu and the author of the entry on the Zhongyong translate key terms in the texts differently: Fu discusses "five ethical codes" and "three comprehensive virtues" (p. 68) while Yanming An calls them "five universal paths" and "three universal virtues" (p. 890). Such differences can be either thought provoking or confusing (especially when unaccompanied by Chinese characters or even pinyin), depending on the reader. The sections on the Analects in "Confucianism: Confucius" and "Confucianism: Constructs of Classical Thought" have hardly anything in common; the first examines it as an account of how Confucius lives as an exemplar remembered by his students, while the latter discusses its content, focusing on ren and li, as well as on Confucius' religious concerns. While concepts such as ren and li are frequently discussed, the different ways in which authors employ them and the different characteristics, contexts, and philosophical stakes they pay attention to enrich one's understanding of the many dimensions of these concepts even as similarities in diverse entries reinforce certain aspects and perspectives.One comes across disagreements to various degrees on common or related topics among different entries. While... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Of Diversities and Comparisons...Sor-hoon TanEncyclopedia of Chinese Philosophy. Edited by Antonio S. Cua. New York and London: Routledge, 2003. Pp. 1,020.Encyclopedias can be useful in teaching philosophy when students need some reading that sets out the basics on a key topic in a few pages without their getting lost in too many complex details or being misled by oversimplifications. They can also be edifying for the philosophy teacher and (...) scholar—providing reliable, up-to-date information on topics that lie in their field but that are not part of their working knowledge. For these reasons, those working in Chinese philosophy will welcome the publication of the Encyclopedia of Chinese Philosophy. The 187 entries cover a variety of subject areas such as "Moral Philosophy" and "Philosophy of language"; Confucianism in different periods and countries, Daoism, Mohism, Legalism, the school of names, Buddhism, and Marxism in China; philosophical trends in post-Mao China, Taiwan, and overseas; key concepts such as dao (the way), fa (law, standards), liyi fenshu (principle and manifestations), and quanli (rights); texts such as the Huainanzi and the Wenzi; and thinkers from Laozi and Confucius to Hu Shih and Mou Zongsan.Instead of more numerous short entries, this encyclopedia has opted for fewer entries of greater length—the Preface tells us that entries on important thinkers and philosophical topics typically range from five thousand to nine thousand words in length, and a quick check reveals that even the shortest entry is at least two pages long (more than one thousand words). This format allows authors to explore the philosophical issues at some depth, and expound even complex arguments in detail. The connections between different concepts, thinkers, texts, philosophical theories, and development that stretch across different periods and territories can be delineated more clearly in a single entry. There is a danger of duplication with this format, as some texts and concepts may be covered in several articles; for example, most of "Confucianism: Constructs of Classical Thought" is on what the author identifies as six key texts of Classical Confucianism: the Analects, Mencius, Xunzi, Yizhuan, Zhongyong (Doctrine of the mean), and Daxue (Great Learning). The sections on Mencius and Xunzi (pp. 66-67) merely introduce a small part of what is discussed in much greater depth and detail in the entries on these two thinkers (pp. 440-448 and 821-829). The Zhongyong and Daxue also have their own entries, and "Confucianism: Confucius" (p. 61) contains an entire section on the Analects.As it turns out, the duplication is less than expected. Pei-jung Fu, author of "Confucianism: Constructs of Classical Thought," implicitly questions Xunzi's Confucian pedigree, beginning his discussion with "Xunzi professed to be an advocate of Confucianism" (p. 67). Such doubt is clearly not shared by A. S. Cua, who authored [End Page 111] the entry on "Xunzi," introducing the thinker as "an important exponent of classical Confucianism" (p. 821). Cua also does not share Fu's view that "the real issue between Mencius and Xunzi lies in their concepts of heaven (tian)" (p. 67). Fu and the author of the entry on the Zhongyong translate key terms in the texts differently: Fu discusses "five ethical codes" and "three comprehensive virtues" (p. 68) while Yanming An calls them "five universal paths" and "three universal virtues" (p. 890). Such differences can be either thought provoking or confusing (especially when unaccompanied by Chinese characters or even pinyin), depending on the reader. The sections on the Analects in "Confucianism: Confucius" and "Confucianism: Constructs of Classical Thought" have hardly anything in common; the first examines it as an account of how Confucius lives as an exemplar remembered by his students, while the latter discusses its content, focusing on ren and li, as well as on Confucius' religious concerns. While concepts such as ren and li are frequently discussed, the different ways in which authors employ them and the different characteristics, contexts, and philosophical stakes they pay attention to enrich one's understanding of the many dimensions of these concepts even as similarities in diverse entries reinforce certain aspects and perspectives.One comes across disagreements to various degrees on common or related topics among different entries. While... (shrink)

Name der Zeitschrift: Internationales Jahrbuch für philosophische Anthropologie Jahrgang: 7 Heft: 1 Seiten: 245-258.

This chapter provides a historical account of the transformation of pregnancy through philosophical theory and legal practice. What has remained seemingly consistent across history, though, is the lack of rights a pregnant woman can enjoy. Whilst it may manifest differently across time and place, unfortunately misogynistic attitudes persist, and this is reflected in the continual degrading of the gestator (and gestation), which is reinforced by certain philosophical theorising and technological advancement. We thus urge caution in making philosophical claims about the (...) epistemic transformation in pregnancy, given the epistemic (and other) injustices already faced by pregnant people. We recognise that there are transformations that occur because of pregnancy, but we argue that there ought not be with respect to the pregnant person's autonomy, agency, and control over their bodies. Through an analysis of legal cases, we can see that the practice falls out of line with the theory regarding how pregnant people are treated. But perhaps it is both the theory and the practice that need to change so as to bring them in line. How we theorise about pregnancy is intertwined with our cultural views, our technological advancements, and our medical and legal practices, requiring multi-disciplinary study for a more holistic overview. In this chapter, we contribute to this endeavour by bringing some such strands together, regarding the transformation that pregnancy is, that pregnancy makes, and that pregnancy has had historically, in philosophy, and in legal practice. (shrink)