Extended simple regions have been the focus of recent developments in philosophical logic, metaphysics, and philosophy of physics. However, only a handful of works provides a rigorous characterization of an extended simple region. In particular, a recent paper in this journal defends a definition based on an extrinsic notion of least distance. Call it the Least Distance proposal. This paper provides the first assessment of it. It argues that Least Distance faces difficulties and drawbacks. The paper then goes on to (...) suggest a different proposal, the Diameter proposal that is able to handle such drawbacks and difficulties. (shrink)

We classify countable metrically homogeneous graphs of diameter 3.

We classify countable metrically homogeneous graphs of diameter 3.

This paper addresses the issues related to designing and estimating the strength of solid-alloy elements in the deforming broaches of significant diameter (exceeding 150 mm) for the developed process of discrete broaching. The tool limit condition was assessed based on two strength criteria: the specific potential energy of shape change and the maximum tangent stresses. Numerical modeling using the finite element method has made it possible to derive the distribution of equivalent stresses in the tool elements and the contact stresses (...) at the surface of the contact between a solid-alloy insert and the body, which enabled the analysis of tool strength under loading. The simulation was performed under a single normal load, which ensured the versatility of the calculation for any contact pressure values. We have derived formulae to calculate the acceptable contact pressure depending on unit load. The effect of the insert protrusion height over the body on the strength of tool elements has been established. We have derived engineering dependences that determine the required magnitude of insert protrusion over the body depending on the ultimate load. An example of calculating the strength of a prefabricated deforming element in the machining of a sleeve made from gray modified cast iron of hardness HB230 has been considered. Our calculations have shown that the deforming element designed for the new technological process corresponds to the conditions of strength, provided the ratio h1/h=0.15 is maintained (where h1 is the insert height above the body, h is the insert height). The results obtained could be used in engineering calculations when designing the prefabricated tool for discrete deformation, as well as to assess the strength of prefabricated tools, such as cutters, core drills, reamers, when refining external loads. (shrink)

ABSTRACTMany of our emotions arise in social contexts, as we interact with and learn about others. What is not yet clear, however, is how such emotions unfold when we either react to others or attempt to regulate our emotions. To address this issue, 30 healthy volunteers reacted to or reappraised positive or negative information that was paired with neutral faces. While they were doing this task, we assessed pupillary responses. We also asked participants to provide ratings of accountability and experienced (...) emotion. Findings indicated that appraised accountability increased in response to emotional information, and changes in accountability were associated with commensurate changes in valence reports and increased pupil diameter. During reappraisal, accountability and emotion decreased, but pupil diameter increased. The findings highlight the importance of accountability appraisals during the generation and regulation of emotional reactions to others, while also documenting pupillary increases during emot... (shrink)

There is increasing interest in how the pupil dynamics of the eye reflect underlying cognitive processes and brain states. Problematic, however, is that pupil changes can be due to non-cognitive factors, for example luminance changes in the environment, accommodation and movement. In this paper we consider how by modeling the response of the pupil in real-world environments we can capture the non-cognitive related changes and remove these to extract a residual signal which is a better index of cognition and performance. (...) Specifically, we utilize sequence measures such as fixation position, duration, saccades, and blink-related information as inputs to a deep recurrent neural network (RNN) model for predicting subsequent pupil diameter. We build and evaluate the model for a task where subjects are watching educational videos and subsequently asked questions based on the content. Compared to commonly-used models for this task, the RNN had the lowest errors rates in predicting subsequent pupil dilation given sequence data. Most importantly was how the model output related to subjects' cognitive performance as assessed by a post-viewing test. Consistent with our hypothesis that the model captures non-cognitive pupil dynamics, we found (1) the model's root-mean square error was less for lower performing subjects than for those having better performance on the post-viewing test, (2) the residuals of the RNN (LSTM) model had the highest correlation with subject post-viewing test scores and (3) the residuals had the highest discriminability (assessed via area under the ROC curve, AUC) for classifying high and low test performers, compared to the true pupil size or the RNN model predictions. This suggests that deep learning sequence models may be good for separating components of pupil responses that are linked to luminance and accommodation from those that are linked to cognition and arousal. (shrink)

In so-called garden-path jokes, an initial semantic representation is violated, and semantic revision reestablishes a coherent representation. 48 jokes were manipulated in three conditions: (i) a coherent ending, (ii) a joke ending, and (iii) a discourse-incoherent ending. A reading times study ( N = 24) and three studies with recordings of ERP and pupil changes ( N = 21, 24, and 24, respectively) supported the hypothesized cognitive processes. Jokes showed increased reading times of the final word compared to coherent endings. (...) ERP data mainly indicated semantic integration difficulties (N400). Larger pupil diameters to joke endings presumably reflect emotional responses. ERP evidence for increased discourse processing efforts and emotional responses, as assumed to be reflected in modulations of the late left anterior negativity (LLAN) and in an enhanced late frontal positivity (fP600), respectively, remains however incomplete. Processing of incoherent endings was also accompanied by increased reading times, a stronger and sustained N400, and context-sensitive P600 effects. Together, these findings provide evidence for a sequential, non-monotonic, and incremental discourse comprehension of garden-path jokes. (shrink)

This note is motivated by Whitehead’s researches in inclusion-based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead’s definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to avoid (...) such a drawback. Moreover, since such a notion enables us to define a metric in the set of points, our proposal looks to be a good starting point for a foundation of the geometry metrical in nature (as proposed, for example, by L.M. Blumenthal). (shrink)

Recent brain imaging studies using functional magnetic resonance imaging (fMRI) have implicated insula and anterior cingulate cortices in the empathic response to another’s pain. However, virtually nothing is known about the impact of the voluntary generation of compassion on this network. To investigate these questions we assessed brain activity using fMRI while novice and expert meditation practitioners generated a loving-kindness-compassion meditation state. To probe affective reactivity, we presented emotional and neutral sounds during the meditation and comparison periods. Our main hypothesis (...) was that the concern for others cultivated during this form of meditation enhances affective processing, in particular in response to sounds of distress, and that this response to emotional sounds is modulated by the degree of meditation training. The presentation of the emotional sounds was associated with increased pupil diameter and activation of limbic regions (insula and cingulate cortices) during meditation (versus rest). During meditation, activation in insula was greater during presentation of negative sounds than positive or neutral sounds in expert than it was in novice meditators. The strength of activation in insula was also associated with self-reported intensity of the meditation for both groups. These results support the role of the limbic circuitry in emotion sharing. The comparison between meditation vs. rest states between experts and novices also showed increased activation in amygdala, right temporo-parietal junction (TPJ), and right posterior superior temporal sulcus (pSTS) in response to all sounds, suggesting, greater detection of the emotional sounds, and enhanced mentation in response to emotional human vocalizations for experts than novices during meditation. Together these data indicate that the mental expertise to cultivate positive emotion alters the activation of circuitries previously linked to empathy and theory of mind in response to emotional stimuli.. (shrink)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt:...earth. r' = radius of moon, or other body. P = moon's horizontal parallax = earth's angular semidiameter as seen from the moon. f = moon's angular semidiameter. Now = P (in circular measure), r'-r = r (in circular measure);.'. r: r':: P: P', or (radius of earth): (radios of (...) moon):: (moon's parallax): (moon's semidiameter). Examples. 1. Taking the moon's horizontal parallax as 57', and its angular diameter as 32', find its radius in miles, assuming the earth's radius to be 4000 miles. Here moon's semidiameter = 16';.-. 4000::: 57': 16';.-. r = 400 16 = 1123 miles. 2. The sun's horizontal parallax being 8"8, and his angular diameter 32V find his diameter in miles. ' Am. 872,727 miles. 3. The synodic period of Venus being 584 days, find the angle gained in each minute of time on the earth round the sun as centre. Am. l"-54 per minute. 4. Find the angular velocity with which Venus crosses the sun's disc, assuming the distances of Venus and the earth from the sun are as 7 to 10, as given by Bode's Law. Since (fig. 50) S V: VA:: 7: 3. But Srhas a relative angular velocity round the sun of l"-54 per minute (see Example 3); therefore, the relative angular velocity of A V round A is greater than this in the ratio of 7: 3, which gives an approximate result of 3"-6 per minute, the true rate being about 4" per minute. Annual ParaUax. 95. We have already seen that no displacement of the observer due to a change of position on the earth's surface could apparently affect the direction of a fixed star. However, as the earth in its annual motion describes an orbit of about 92 million miles radius round the sun, the different positions in space from which an observer views the fixed stars from time to time throughout the year must be separated... (shrink)

In his Brouillon Project on conic sections, Girard Desargues studies the notion of traversale, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of polar, a concept that emerged in the beginning of 19th century. In this article we shall study in great detail the developments around that notion in the middle part of the Brouillon project. We shall in particular show, using the notes added by Desargues after the first draft (...) was written, how here arises a new theory, that of the polarity associated to a conic section. We shall show that besides a natural correspondance between points and lines, Desargues has understood that a conic induces on every line in its plane an involution, and how he progressively handles the considerable conceptual difficulties he has to deal with when trying to explain clearly his novative ideas. (shrink)

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it is necessary that (...) particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

A common and disabling consequence of stroke is the difficulty in processing contralesional space (i.e., hemispatial neglect). According to paper-and-pencil tests, neglect remits or stabilizes in severity within a few months after a brain injury. This arbitrary temporal limit, however, is at odds with neglect’s well-known dependency on task-sensitivity. The present study tested the hypothesis that the putative early resolution of neglect might be due to the insensitivity of testing methods rather than to the lack of spontaneous recovery at later (...) stages. A right hemisphere stroke patient was studied longitudinally for 3 years. According to paper-and-pencil tests the patient showed no symptom of hemispatial neglect 1 month post stroke. Awareness of spatially lateralized visual targets was then assessed by means of computer-based single- and dual-tasks requiring an additional top-down deployment of attention for the parallel processing of visual or auditory stimuli. Errorless performance at computer-based tasks was reached at month 12 and maintained until month 29 after stroke. A bottom-up manipulation was then implemented by reducing target diameter. Following this change, more than 50% of contralesional targets were omitted, mostly under dual-tasking. At months 40 and 41 the same task revealed a significant (but not complete) reduction in the number of contralesional omissions. Ipsilesional targets were, in contrast, still errorless detected. The coupling of a bottom-up (target change) and a top-down (dual-tasking) manipulation revealed the presence of a long-lasting spontaneous recovery from contralesional spatial awareness deficits. In contrast, neither manipulation was effective when implemented separately. After having excluded the potential confound of practice effects, it was concluded that not only the presence but also the time course of hemispatial neglect strongly depends on the degree of attentional engagement required by the task. (shrink)

In the middle part of his Brouillon Project on conics, Girard Desargues develops the theory of the traversale, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the Brouillon Project, is devoted to the last part of the text, in which Desargues puts his theory (...) of the traversal into practice by giving a very elegant tratment of the classical theory of parameters and foci. This will lead us to show that Desargues’ proofs can only be understood if one accepts that he reasons in a resolutely projective framework, completely assimilating elements at infinity to those at finite distance in his proofs. (shrink)

n the pioneering days of radio, my grandfather's job was to lecture to young engineers who were joining Marconi's company. To illustrate that any complex wave form can be broken down into summed simple waves of different frequencies (important in both radio and acoustics), he took wheels of different diameters and attached them with pistons to a clothesline. When the wheels went round, the clothesline was jerked up and down, causing waves of movement to snake along it. The wriggling (...) clothesline was a model of a radio wave, giving the students a more vivid picture of wave summation than mathematical equations could ever have done. (shrink)

We hypothesise that the sarcolemma of an actively growing myofibre has different properties to the sarcolemma of a mature adult myofibre. Such fundamentally different properties have clinical consequences for the onset, and potential therapeutic targets, of various skeletal muscle diseases that first manifest either during childhood (e.g. Duchenne muscular dystrophy, DMD) or after cessation of the main growth phase (e.g. dysferlinopathies). These characteristics are also relevant to the selection of both tissue culture and in vivo models employed to study such (...) myopathies and the molecular regulation of adult myofibres. During growth, multinucleated myofibres increase enormously in size and volume with dramatic increases in length (up to ∼600 mm). This is in striking contrast with most mononucleated cells such as fibroblasts, that remain at a relatively small size (∼10–20 µm diameter). The consequences of a dynamic, expanding sarcolemma during growth, compared with that of an adult myofibre of a fixed length, are discussed with respect to various aspects of muscle biology. (shrink)

In order to solve the problem of unsmooth and inefficient human-computer interaction process in the information age, a method for human-computer interaction intention prediction based on electroencephalograph signals and eye movement signals is proposed. This approach is different from previous methods where researchers predict using data from human-computer interaction and a single physiological signal. This method uses the eye movements and EEG signals that clearly characterized the interaction intention as the prediction basis. In addition, this approach is not only tested (...) with multiple human-computer interaction intentions, but also takes into account the operator in different cognitive states. The experimental results show that this method has some advantages over the methods proposed by other researchers. In Experiment 1, using the eye movement signal fixation point abscissa Position X, fixation point ordinate Position Y, and saccade amplitude to judge the interaction intention, the accuracy reached 92%, In experiment 2, only relying on the pupil diameter, pupil size and fixed time, fixed time of eye movement signals can not achieve higher accuracy of the operator’s cognitive state, so EEG signals are added. The cognitive state was identified separately by combining the screened EEG parameters Rα/β with the eye movement signal pupil diameter and fixation time, with an accuracy of 91.67%. The experimental combination of eye movement and EEG signal features can be used to predict the operator’s interaction intention and cognitive state. (shrink)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...) an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

Platonic myth meets American noir in this haunting series of philosophical images, from gigantic ferris wheels to offshore drilling rigs. It has been said that Plato, Nietzsche, and Giordano Bruno gave us the three great mythical presentations of serious philosophy in the West. They have spawned few imitators, as philosophers have generally drifted toward a dry, scholarly tone that has become the yardstick of professional respectability. In this book, Graham Harman tries to restore myth to its central place in the (...) discipline. In Chapter One, the narrator considers the motion of a Ferris wheel of many miles in diameter, which generates disasters and other events in its endless revolutions. In Chapter Two, he moves from the Chesapeake Bay to the depths of Hell, where he observes the show trial of pre-Socratic thinkers. In Chapter Three, the narrator encounters a battered steam calliope in India that may summon tsunamis, solar flares, and other catastrophic forces. In Chapter Four, he tries to explain reports of a ghostly boat in Japanese waters. In Chapter Five, he discusses causation on an offshore drilling platform. And in Chapter Six, amidst a deadly Paris hailstorm, he proposes a theory of objects without relations. (shrink)

In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

A classical point electron radiates when it accelerates. However, there are classical electron models with extended charge distributions which can accelerate and/or deform without radiating. Can a model be contrived that will undergo radiationless motion while accelerating (on the average) over a distance large compared to its size? The answer is no: we prove that the “center” of the electron is always closer than the electron “diameter” to a fictitious point undergoing constant-velocity motion, if the electron's motion is radiationless.

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated , was (...) to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

A fundamental aspect of biological systems is their spatial organization. In development, regeneration and repair, directional signals are necessary for the proper placement of the components of the organism. Likewise, pathogens that invade other organisms rely on directional signals to target vulnerable areas. It is widely understood that chemical gradients are important directional signals in living systems. Less well recognized are electrical fields, which can also provide directional information. Small, steady electrical fields can directly guide cell movement and growth and (...) can generate chemical gradients of charged macromolecules against the leveling action of diffusion. At the site of a lesion in an ion‐transporting epithelium, for example, a substantial electrical field is instantly generated and may extend over many cell diameters. There are numerous other situations in which relatively long‐range electrical fields have been shown to exist naturally. Recently, there has been substantial progress in identifying specific processes that are controlled, to some extent, by these endogenous electrical fields. This review highlights these recent data and discusses possible mechanisms by which the fields might affect biological processes. BioEssays 25:759–766, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1752 edition. Excerpt:... to which the original Exclusion had been owing, the Points of two short and slender Hairs appear'd protruding themselves from its oval Surface. The thicker butoblong Bodies, from whose Extremities these grew, next forc'd themselves out, and it was evident to a-'n accustom'd Eye, that they were (...) the Antennze of a two wing'd Fly; next presented themselves the anterior Surfaces of two chequeffd Orbs, which were plainly the complex Eyes of anlnsect' of the same Species, separated by a plain Portion of a Forehead; and soon after the whole Head. This was no sooner all in View, than it swell'd to a Diameter equal to twice the Measure of that of the Breast. lt might have appear'd from the first, that the Head was growing under the Eye of the Observer, from the Extremity of the Thorax, but tho' a more rational Enquiry could not but produce for its Answer, that it was only now thrust forth out of the Cavity of the Breast in which it had before been lodg'd; it yet appear'd singular after this sudden Change in Size to conceive how a Thing should have been till that Moment lodg'd in a Cavityz not equal to half its own Diameter. P a The The Head was now entire and in its Place, and the Legs were firm, and supported the Body well, but the Wings did not yet appear. On examining the Place where they were to be expacted, I discover'd two irregular Protuberances of a wrinkled Surface, and considerably large, and under them the two oblong Pedicies which we see supporting the Balls under the Wings of all the two wing'd Flies. It was evident from this, that the Protuberances at the two Sides of the Base of the Thorax were the very Wings in their folded State, and this was soon prov'd by their expanding. The Wings in all this Race of Creatures are the last Part... (shrink)

Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly (...) accepted formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers. (shrink)

We want to build tiny gnat-sized robots, a millimeter or two in diameter. They will be cheap, disposable, totally sefcontained autonomous agents able to do useful things in the world. This paper consists of two parts. The first describes why we want to build them. The second is a technical outline of how to go about it. Gnat robots are going to change the world.

Axons are the longest cellular structure reaching over a meter in the case of human motor axons. They have a relatively small diameter and contain several cytoskeletal elements that mediate both material and information exchange within neurons. Recently, a novel type of axonal plasticity, termed axonal radial contractility, has been unveiled. It is represented by dynamic and transient diameter changes of the axon shaft to accommodate the passages of large organelles. Mechanisms underpinning this plasticity are not fully understood. Here, we (...) first summarised recent evidence of the functional relevance for axon radial contractility, then discussed the underlying structural basis, reviewing nanoscopic evidence of the subtle changes. Two models are proposed to explain how actomyosin rings are organised. Possible roles of non‐muscle myosin II (NM‐II) in axon degeneration are discussed. Finally, we discuss the concept of periodic functional nanodomains, which could sense extracellular cues and coordinate the axonal responses. Also see the video abstract here: https://youtu.be/ojCnrJ8RCRc. (shrink)

Summary Tycho Brahe's lunar theory, mostly the work of his assistant Christian Longomontanus, published in the Progymnasmata (1602), was the most advanced and accurate lunar theory yet developed. Its principal innovations are: the introduction of equant motion for the first inequality in order to separate the determination of direction and distance; a more accurate limit for the second inequality although requiring a more complex calculation; additional inequalities of the variation and, in place of the annual inequality in Tycho's earlier theory, (...) a reduction in the equation of time; in the latitude theory a variation of the inclination of the orbital plane and an inequality of the motion of the nodes; a reduction in the range of variation of distance, parallax, and apparent diameter. Some of these were already present in Tycho's earlier lunar theory (1599), but all were changed in notable ways. Twenty years later Longomontanus published a modified version of the lunar theory in Astronomia Danica (1622), for the purpose of facilitating the calculation through new correction tables, and also explained his reasons for parts of the theory in the Progymnasmata. This paper is a technical study of both lunar theories. (shrink)

Successful athletic performance requires precision in many respects. A batter stands behind home plate awaiting the arrival of a ball that is less than three inches in diameter and moving close to 100 mph. His goal is to hit it with a ba­­t that is also less than three inches in diameter. This impressive feat requires extraordinary temporal and spatial coordination. The sweet spot of the bat must be at the same place, at the same time, as the ball. A (...) basketball player must keep a ball bouncing as she speeds from one end of the court to another, evading defensive players. She may never break pace as she lifts from the ground, throwing the ball fifteen feet toward a hoop that is eighteen inches in diameter. One task facing a psychologist involves explaining how the body does such things within the sometimes very demanding spatial and temporal constraints that a given task imposes. Part of the goal of this chapter is to sketch the commitments of an embodied approach to such an explanation. We shall see that an embodied account of motor skills draws concepts that depart radically from more traditional cognitivist theories of motor activity. Similarly, because an embodied approach to cognition introduces new ways to understand the human capacity for social interaction, it also promises to shed new light on how athletes coordinate their actions with each other. (shrink)

Let M be a smooth, compact manifold of dimension n ≥ 5 and sectional curvature | K | ≤ 1. Let Met (M) = Riem(M)/Diff(M) be the space of Riemannian metrics on M modulo isometries. Nabutovsky and Weinberger studied the connected components of sublevel sets (and local minima) for certain functions on Met (M) such as the diameter. They showed that for every Turing machine T e , e ∈ ω, there is a sequence (uniformly effective in e) of homology (...) n-spheres {P k e } k ∈ ω which are also hypersurfaces, such that P k e is diffeomorphic to the standard n-sphere S n (denoted P k e ≈ diff S n ) iff T e halts on input k, and in this case the connected sum N k e =M ♯ P k e ≈ diff M , so N k e ∈ Met(M), and N k e is associated with a local minimum of the diameter function on Met(M) whose depth is roughly equal to the settling time σ e (k) of T e on inputs y i } ∈ ω of c.e. sets so that for all i the settling time of the associated Turing machine for A i dominates that for A i + 1 , even when the latter is composed with an arbitrary computable function. From this, Nabutovsky and Weinberger showed that the basins exhibit a "fractal" like behavior with extremely big basins, and very much smaller basins coming off them, and so on. This reveals what Nabutovsky and Weinberger describe in their paper on fractals as "the astonishing richness of the space of Riemannian metrics on a smooth manifold, up to reparametrization." From the point of view of logic and computability, the Nabutovsky-Weinberger results are especially interesting because: (1) they use c.e. sets to prove structural complexity of the geometry and topology, not merely undecidability results as in the word problem for groups, Hilbert's Tenth Problem, or most other applications; (2) they use nontrivial information about c.e. sets, the Soare sequence {A i } i ∈ ω above, not merely G öodel's c.e. noncomputable set K of the 1930's; and (3) without using computability theory there is no known proof that local minima exist even for simple manifolds like the torus T 5 (see §). (shrink)

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.