A model is proposed that deals with the observed collinearities (spatial, temporal and quantitative) of Hox gene expression during pattern formation along the primary and secondary axes of vertebrates. In particular, in the proximodistal axis of the developing limb, it is assumed that a morphogen gradient is laid down with its source at the distal tip of the bud. The extracellular signals in every cell of the morphogenetic field are transduced and uniformly amplified so that molecules are produced in the (...) nucleus with appropriate physicochemical properties. These molecules can exert a concentration‐dependent force on the Hox cluster. It is assumed that, before activation, the Hox cluster is packaged as an elongated rigid body inside the chromatin and is covered by a coat that prevents the transcription factors reaching the genes of the cluster. The transcription factors are confined to the interchromatin domain and their density decreases with their distance from the chromatin surface. A gradual increase in the extracellular morphogen concentration causes a corresponding increase in the number of the nuclear molecules and the resulting bigger force pushes the Hox cluster toward the interchromatin domain. The step‐by‐step translocations of the Hox cluster initiate the consecutive exposure of genes to their transcription factors. The model explains how gene activation is triggered and it describes spatial, temporal and quantitative collinearities at the initial stages of gene expression. Some recent experiments of Hox deletions and duplications are accounted for by the model. BioEssays 26:189–195, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Collinearity or correspondence between the contours of the inducing figure to allow `contour continuation' or `figure completion' were, according to G. Kanizsa, the necessary conditions for producing anomalous surfaces or contours. Since Kanizsa's early work various hypotheses have been advanced to explain the phenomenon, but very few examples of anomalous contours that do not satisfy the above conditions have been reported. When two small white discs (1 cm in diameter) are set on a larger black disc in slow rotation, (...) the two discs, after some observation time, will appear as the extremities of a rigid cylinder displaced in depth. The surface of the cylinder, under dim illumination, appears as a whitish transparent surface. However, when the two discs are substituted by a circle and a semicircle of the same size, a clear anomalous contour appears to form the cylinder, even under clear light conditions and when the colours are reversed; i.e., black circles on white disc. The anomalous contours are not apparent when the configuration is stationary. I will demonstrate how the anomalous contours of a stereokinetic cylinder can be obtained even without the “interruption” of the lines in the semicircle. (shrink)

It is not understood how the numbers and identities of vertebrae are controlled during mammalian development. The remarkable robustness and conservation of segmental numbers may suggest the digital nature of the underlying process. The study proposes a mechanism that allows cells to obtain and store the segmental information in digital form, and to produce a pattern of chromatin accessibility that in turn regulates Hox gene expression specific to the metameric segment. The model requires that a regulatory element be present such (...) that the number of occurrences of the motif between two consecutive Hox genes equals the number of segments under the control of the anterior gene. This is true for the recently discovered hydroxyl radical cleavage 3bp-periodic (HRC3) motif, associated with histone modifications and developmental genes. The finding not only allows the correct prediction of the numbers of segments using only sequence information, but also resolves the 40-year-old enigma of the function of temporal and spatial collinearity of Hox genes. The logic of the mechanism is illustrated in the attached animated video. How different aspects of the proposed mechanism can be tested experimentally is also discussed. (shrink)

The history of biochemistry and molecular biology is replete with examples of erroneous theories that persisted for considerable lengths of time before they were rejected. This paper examines patterns of dissolution of three such erroneous hypotheses: The idea that nucleic acids are tetrads of the four nucleobases (‘the tetranucleotide hypothesis’); the notion that proteins are collinear with their encoding genes in all branches of life; and the hypothesis that proteins are synthesized by reverse action of proteolytic enzymes. Analysis of these (...) cases indicates that amassed contradictory empirical findings did not prompt critical experimental testing of the prevailing theories nor did they elicit alternative hypotheses. Rather, the incorrect models collapsed when experiments that were not purposely designed to test their validity exposed new facts. (shrink)

Marr (1982) may have been one of the rst vision researchers to insist that in modeling vision it is important to separate the location of visual features from their type. He argued that in early stages of visual processing there must be “place tokens” that enable subsequent stages of the visual system to treat locations independent of what specic feature type was at that location. Thus, in certain respects a collinear array of diverse features could still be perceived as a (...) line, and under certain conditions could function as such in perceptual phenomena like the Poggendorf illusion. (shrink)

We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle's dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle's elementary magnetic dipole moment. As consistency checks, we calculate (...) the overall system's energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system's Belinfante-Rosenfeld energy-momentum tensor. (shrink)

In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond (...) to pure orthogeometries, irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. (shrink)

I explore the viability of a Galilean relational theory of space-time—a theory that includes a three-place collinearity relation among its stock of basic relations. Two formal results are established. First, I prove the existence of a class of dynamically possible models of Newtonian mechanics in which collinearity is uninstantiated. Second, I prove that the dynamical properties of Newtonian systems fail to supervene on their Galilean relations. On the basis of these two results, I argue that Galilean relational space-time (...) is too weak of a structure to support a relational interpretation of classical mechanics. (shrink)

This paper compares two 3D logical diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron and the nested tetrahedron. Geometric properties such as collinearity and central symmetry are examined from a cognitive perspective, focussing on diagram design principles such as congruence/isomorphism and apprehension.

We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields.

We distinguish between the roles played by spatial attention and conscious intention in terms of their impact on the processing of segmentation signals, like discontinuities in lines, associated with the act of scrutinizing. We showed previously that the processing of discontinuities in lines can be activated. This is evidenced by an impairment in the detection of a gap between parallel elements when it follows a gap between collinear elements in the same location and orientation. This effect is no longer observed (...) if attention is divided between two gaps in the first stimulus. The results from this study show that focusing attention on a gap between collinear elements is not enough to observe a modulation, consistently with the need to integrate, rather than to separate, collinear elements in usual conditions. The modulation is sensitive to the conscious expectations of subjects, suggesting that an intention can trigger modulations that spatial attention cannot. (shrink)

Cognitive reserve postulates that individual differences in task performance can be attributed to differences in the brain’s ability to recruit additional networks or adopt alternative cognitive strategies. Variables that are descriptive of lifetime experience such as socioeconomic status, educational attainment, and leisure activity are common proxies of CR. CR is mostly studied using neuroimaging techniques such as functional MRI in which case individuals with a higher CR were observed to activate a smaller brain network compared to individuals with a lower (...) CR, when performing a task equally effectively, and electroencephalography where a particular EEG component that reflects the attention and working memory load, has been targeted. Despite the contribution of multiple factors such as age, education, working, leisure, and household activities in CR formation, most neuroimaging studies, and those using EEG in particular, focus on formal education level only. The aim of the current EEG study is to investigate how the P300 component, evoked in response to an oddball paradigm, is associated with other components of CR besides education, such as working and leisure activity in older adults. We have used hereto a recently introduced CR index questionnaire that quantifies both professional and leisure activities in terms of their cognitive demand and number of years practiced, as well as a data-driven approach for EEG analysis. We observed complex relationships between CRIq subcomponents and P300 characteristics. These results are especially important given that, unlike previous studies, our measurements do not require active use of the same executive function and, thus, render our results free of a collinearity bias. (shrink)

We prove that the null ideal restricted to a non-null set of reals could be isomorphic to a variety of sigma ideals. Using this, we show that the following are consistent: (1) There is a non-null subset of plane each of whose non-null subsets contains three collinear points. (2) There is a partition of a non-null set of reals into null sets, each of size [Formula: see text], such that every transversal of this partition is null.

We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, ‘points’ and ‘lines’ , containing three individual constants, A0, A1, A2, standing for three non-collinear points, two binary operation symbols, φ and ι, with φ = l to be interpreted as ‘[MATHEMATICAL SCRIPT SMALL L] is the line joining A and B’ , and ι = P to be interpreted as [MATHEMATICAL SCRIPT SMALL L]P is the point of intersection of (...) g and h , and two binary operation symbols, π1 and —2, with πi = g to be interpreted as ‘g is one of the two limiting paralle lines from P to [MATHEMATICAL SCRIPT SMALL L]. (shrink)

A series of experiments was performed in which subjects indicated whether two four-dot patterns were the same, although possibly viewed from different directions, or different, paired at random. Analyses of responses times and error rates suggest that the subjects' performance in this affine matching task is based on non-accidental properties such as convexity, parallelism, collinearity, and proximity, rather than on real affine invariants such as the ratio of triangular areas.

This comment is offered in response to Hansen's "A Multidimensional Scale for Measuring Business Ethics: A Purification and Refinement". Five issues arising from Hansen's purification and refinement efforts are addressed. These include the issues of parsimony, predictive validity, collinearity, reliability, and what we see as a confusion between normative and positive theory.

“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and for wave-particle (...) dualism. Its meaning:- mathematically: a ratio of two measures (of sets), which are not collinear; physically: the ratio of the measurements of two physical quantities, which are not simultaneously measurable. The main innovation is in the mapping between phase and Hilbert space, since both are sums. Phase space is a sum of cells, and Hilbert space is a sum of qubits. The mapping is reduced to the mapping of a cell into a qubit and vice versa. Negative probability helps quantum mechanics to be represented quasi-statistically by quasi-probabilistic distributions. Pure states of negative probability cannot exist, but they, where the conditions for their expression exists, decrease the sum probability of the integrally positive regions of the distributions. They reflect the immediate interaction (interference) of probabilities common in quantum mechanics. (shrink)

The linguistic complexity of words has largely been studied on the behavioral level and in experimental settings. Only little is known about the neural processes underlying it in uninstructed, spontaneous conversations. We built up a multimodal neurolinguistic corpus composed of synchronized audio, video, and electrocorticographic (ECoG) recordings from the fronto-temporo-parietal cortex to address this phenomenon based on uninstructed, spontaneous speech production. We performed extensive linguistic annotations of the language material and calculated word complexity using several numeric parameters. We orthogonalized the (...) parameters with the help of a linear regression model. Then, we correlated the spectral components of neural activity with the individual linguistic parameters and with the residuals of the linear regression model, and compared the results. The proportional relation between the number of consonants and vowels, which was the most informative parameter with regard to the neural representation of word complexity, showed effects in two areas: the frontal one was at the junction of the premotor cortex, the prefrontal cortex, and Brodmann area 44. The postcentral one lay directly above the lateral sulcus and comprised the ventral central sulcus, the parietal operculum and the adjacent inferior parietal cortex. Beyond the physiological findings summarized here, our methods may be useful for those interested in ways of studying neural effects related to natural language production and in surmounting the intrinsic problem of collinearity between multiple features of spontaneously spoken material. (shrink)

This study aims to alleviate the current tense employment situation and study the entrepreneurial situation of teachers and students in colleges and universities. Firstly, based on the educational concept of Science Technology Engineering Arts Mathematics, Ideological and Political Education is added to psychological capital to explore the effect of the combination of the two on entrepreneurial performance. An entrepreneurial performance impact model is constructed, and the questionnaire is set. Secondly, the influence of psychological capital combined with IPE on sports morality (...) is explored, and a sports morality questionnaire is designed. Finally, the questionnaire results are analyzed. The results showed that most of the participants in the survey are under the age of 25. The 25- to 29-year-olds are the smallest among those surveyed. The respondents who participated in the survey had the most undergraduate degrees, accounting for 43.4%. The 40 items on entrepreneurial performance this time obey a normal distribution, and the scale has good reliability and validity. The main factor analysis results obtained by principal component analysis include 6 factors. Their total explanatory power exceeds 67%, and the six factors screened out this time are well represented. The model tolerance is between 0.45 and 0.5, and the Variance Inflation Factor value is less than 10. The scale does not suffer from multi-collinearity issues. IPE significantly strengthens the effect of psychological capital on entrepreneurial performance. The influences of various sports on sportsmanship, bravery, self-confidence, and self-transcendence are significantly different, and the P value is less than 0.001. The difference in aggressiveness is less than 0.01, indicating that it is very significant. Different sports have significant differences in the cultivation of sports morality, and the P value is less than 0.05. The differences in self-discipline are also significant, and there are extremely significant differences in compliance with rules, and the P value here is less than 0.001. There are no significant differences in sporting qualities. IPE combined with psychological capital has a significant impact on entrepreneurial performance. These contents provide references for the entrepreneurship education of teachers and students in colleges and universities. The contribution lies in expanding the research on psychological capital in entrepreneurial performance and laying a foundation for the combination of psychological capital and IPE. (shrink)

The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.

We study the notion of weak canonical bases in an NSOP $_{1}$ theory T with existence. Given $p=\operatorname {tp}$ where $B=\operatorname {acl}$ in ${\mathcal M}^{\operatorname {eq}}\models T^{\operatorname {eq}}$, the weak canonical base of p is the smallest algebraically closed subset of B over which p does not Kim-fork. With this aim we firstly show that the transitive closure $\approx $ of collinearity of an indiscernible sequence is type-definable. Secondly, we prove that given a total $\mathop {\smile \hskip -0.9em ^| (...) \ }^K$ -Morley sequence I in p, the weak canonical base of $\operatorname {tp}$ is $\operatorname {acl}$, if the hyperimaginary $I/\approx $ is eliminable to e, a sequence of imaginaries. We also supply a couple of criteria for when the weak canonical base of p exists. In particular the weak canonical base of p is the intersection of the weak canonical bases of all total $\mathop {\smile \hskip -0.9em ^| \ }^K$ -Morley sequences in p over B. However, while we investigate some examples, we point out that given two weak canonical bases of total $\mathop {\smile \hskip -0.9em ^| \ }^K$ -Morley sequences in p need not be interalgebraic, contrary to the case of simple theories. Lastly we suggest an independence relation relying on weak canonical bases, when T has those. The relation, satisfying transitivity and base monotonicity, might be useful in further studies on NSOP $_1$ theories. (shrink)

An important factor in judging whether two retinal images arise from the same object viewed from different positions may be the presence of certain properties or cues that are 'qualitative invariants' with respect to the natural transformations, particularly affine transformations, associated with changes in viewpoint. To test whether observers use certain affine qualitative cues such as concavity, convexity, collinearity, and parallelism of the image elements, a 'same-different' discrimination experiment was carried out with planar patterns that were defined by four (...) points either connected by straight line segments (line patterns) or marked by dots (dot patterns). The first three points of each pattern were generated randomly; the fourth point fell on their diagonal bisector. According to the position of that point, the patterns were concave, triangular (three points being collinear), convex, or parallel sided. In a 'same' trial, an affine transformation was applied to one of two identical patterns; in a 'different' trial, the affine transformation was applied after the point lying on the diagonal bisector was perturbed a short, fixed distance along the bisector, inwards for one pattern and outwards for the other. Observers' ability to discriminate 'same' from 'different' pairs of patterns depended strongly on the position of the fourth, displaced, point: performance varied rapidly when the position of the displaced point was such that the patterns were nearly triangular or nearly parallel sided, consistent with observers using the hypothesised qualitative cues. The experimental data were fitted with a simple probabilistic model of discrimination performance that used a combination of these qualitative cues and a single quantitative cue. (shrink)

Several studies showed evidence supporting the possibility of hand trajectory decoding from low-frequency electroencephalography. However, the decoding in the source space via source localization is scarcely investigated. In this study, we tried to tackle the problem of collinearity due to the higher number of signals in the source space by two folds: first, we selected signals in predefined regions of interest ; second, we applied dimensionality reduction techniques to each ROI. The dimensionality reduction techniques were computing the mean, principal (...) component analysis, and locality preserving projections. We also investigated the effect of decoding between utilizing a template head model and a subject-specific head model during the source localization. The results indicated that applying source-space decoding with PCA yielded slightly higher correlations and signal-to-noise ratios than the sensor-space approach. We also observed slightly higher correlations and SNRs when applying the subject-specific head model than the template head model. However, the statistical tests revealed no significant differences between the source-space and sensor-space approaches and no significant differences between subject-specific and template head models. The decoder with Mean and PCA utilizes information mainly from precuneus and cuneus to decode the velocity kinematics similarly in the subject-specific and template head models. (shrink)

The segregation of image parts into foreground and background is an important aspect of the neural computation of 3D scene perception. To achieve such segregation, the brain needs information about border ownership; that is, the belongingness of a contour to a specific surface represented in the image. This article presents psychophysical data derived from 3D percepts of figure and ground that were generated by presenting 2D images composed of spatially disjoint shapes that pointed inward or outward relative to the continuous (...) boundaries that they induced along their collinear edges. The shapes in some images had the same contrast (black or white) with respect to the background gray. Other images included opposite contrasts along each induced continuous boundary. Psychophysical results demonstrate conditions under which figure-ground judgment probabilities in response to these ambiguous displays are determined by the orientation of contrasts only, not by their relative contrasts, despite the fact that many border ownership cells in cortical area V2 respond to a preferred relative contrast. Studies are also reviewed in which both polarity-specific and polarity-invariant properties obtain perceptual figure-ground grouping results. The FACADE and 3D LAMINART models are used to explain these data. Keywords: figure-ground separation, border ownership, perceptual grouping, surface filling-in, V2, V4, FACADE Theory. (shrink)

© 2018, Springer International Publishing AG, part of Springer Nature. Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design (...) principles such as congruence/isomorphism and apprehension. The cognitive effectiveness of the different visualizations is compared for the representation of implication versus opposition relations, and for subdiagram embeddings. (shrink)

The thresholds of human observers detecting line targets improve significantly when the targets are presented in a spatial context of collinear inducing stimuli. This phenomenon is referred to as spatial facilitation, and may reflect the output of long-range interactions between cortical feature detectors. Spatial facilitation has thus far been observed with luminance-defined, achromatic stimuli on achromatic backgrounds. This study compares spatial facilitation with line targets and collinear, edge-like inducers defined by luminance contrast to spatial facilitation with targets and inducers defined (...) by color contrast. The results of a first experiment show that achromatic inducers facilitate the detection of achromatic targets on gray and colored backgrounds, but tend to suppress the detection of chromatic targets. Chromatic inducers facilitate the detection of chromatic targets on gray and colored backgrounds, but tend to suppress the detection of achromatic targets. Chromatic spatial facilitation appears to be strongest when inducers and background are isoluminant. The results of a second experiment show that spatial facilitation with chromatic targets and inducers requires a longer exposure duration of the inducers than spatial facilitation with achromatic targets and inducers, which is already fully effective at an inducer exposure of 30 ms only. The findings point towards two separate mechanisms for spatial facilitation with collinear form stimuli: one that operates in the domain of luminance, and one that operates in the domain of color contrast. These results are consistent with neural models of boundary and surface formation which suggest that achromatic and chromatic visual cues are represented on different cortical surface representations that are capable of selectively attracting attention. Multiple copies of these achromatic and chromatic surface representations exist corresponding to different ranges of perceived depth from an observer, and each can attract attention to itself. Color and contrast differences between inducing and test stimuli, and transient responses to inducing stimuli, can cause attention to shift across these surface representations in ways that sometimes enhance and sometimes interfere with target detection. (shrink)

This article introduces an experimental paradigm to selectively probe the multiple levels of visual processing that influence the formation of object contours, perceptual boundaries, and illusory contours. The experiments test the assumption that, to integrate contour information across space and contrast sign, a spatially short-range filtering process that is sensitive to contrast polarity inputs to a spatially long-range grouping process that pools signals from opposite contrast polarities. The stimuli consisted of thin subthreshold lines, flashed upon gaps between collinear inducers which (...) potentially enable the formation of illusory contours. The subthreshold lines were composed of one or more segments with opposite contrast polarities. The polarity nearest to the inducers was varied to differentially excite the short-range filtering process. The experimental results are consistent with neurophysiological evidence for cortical mechanisms of contour processing and with the Boundary Contour System model, which identifies the short-range filtering process with cortical simple cells, and the long-range grouping process with cortical bipole cells. (shrink)

Most of the descriptions of interval time structures in the first order predicate calculus are based on linear time. However, in the case of intervals, abandoning the condition oflinearity (e.g.LIN in van Benthem's systems) is not sufficient. In this paper, some properties of non-linear time structures are discussed. The most important one is the characterization of location of intervals in a fork of branches. This is connected with the fact that an interval can contain non-collinear subintervals. As a result of (...) non-linearity, some basic properties of interval structures must be formulated in a weaker form. Moreover, time must be filled by intervals to indicate that time cannot pass without events occurring in it. Finally, it is shown that when intervals cannot contain non-collinear subintervals, most of the conditions described in the paper are satisfied. (shrink)

PurposeThis study investigated the impact of age and myopia on visual form perception among Chinese school-age children.MethodsThis cross-sectional study included 1,074 students with a mean age of 12.1 ± 4.7 years. The mean spherical equivalence refraction of the participants was −1.45 ± 2.07 D. All participants underwent distance visual acuity, refraction measurement and local and global visual form perception test including orientation, parallelism, collinearity, holes and color discrimination tasks.ResultsThe reaction times of emmetropes were slower than those of myopic and (...) high myopic groups on both local and global discrimination tasks. A reduction in reaction times was found with increasing age on both local and global discrimination tasks. Age was significantly associated with both local and global visual perception performance after adjusting for gender, visual acuity and SER.ConclusionsThis study revealed that both local and global visual perception improve with age among Chinese children and that myopes seem to have better visual perception than emmetropes. (shrink)

In 1803 Louis Poinsot published a textbook on statics, in which he made clear that the subject dealt not only with forces but also with 'couples' (his word), pairs of coplanar non-collinear forces equal in magnitude and direction but opposite in sense. His innovation was not understood or even welcomed by some contemporary mathematicians. Later he adapted his theory to put forward a new relationship between rectilinear and rotational motion in dynamics; its reception was more positive, although not always appreciative (...) of the generality. After summarising the creation of these two theories and noting their respective receptions, this paper considers his advocacy of spatial and geometrical thinking in mechanics and the fact that, despite its importance, historians of statics who cover his period usually ignore his theory of couples. (shrink)

The famous Allen's interval relations constraint propagation algorithm was intended for linear time. Its 13 primitive relations define all the possible mutual locations of two intervals on the time-axis. In this paper an application of the algorithm for non-linear time is suggested. First, a new primitive relation is added. It is called excludes since an occurrence of one event in a certain course of events excludes an occurrence of the other event in this course. Next, new composition rules for relations (...) between intervals are presented: some of the old rules are extended by the relation excludes, and entirely new ones are formulated for composing the relation excludes with the other relations. Four different composition tables are considered. The choice of a composition table depends on whether time is branching or not, and whether intervals can contain non-collinear subintervals or not. (shrink)

This thesis concerns alternative concatenating operations in extensive measurements and the degree to which concatenating operations are matter of convention. My arguments are directed against Ellis' claim that what prevents us from choosing alternative ways of combining extensive quantities is only convenience and simplicity and that the choice is not based on empirical reasons. ;My first argument is that, given certain relational theories of measurement, there can be no more than one concatenating operation per quantity; because combining operations are the (...) only conclusive distinguishing characteristic among distinct extensive measurements and thus the only thing that can serve as an indicator for the identity of a quantity. Rectangular and collinear concatenation, for example, cannot both be used as a way of combining lengths. However, rectangular concatenation could be used to measure some other extensive quantity since it fulfills the necessary conditions for adequate numerical assignment. ;For those that adopt theories of measurement which can support the claim that dinches measure length, I demonstrate, in the second argument, that rectangular concatenation would be a bad alternative and thus no alternative at all. Implementation of rectangular concatenation requires a new science; a science compatible with dinches violates present invariance principles and a new set must be provided, if possible. It is not clear that there is a set of invariance principles compatible with dinches which also gives basis for a science that explains the phenomena as well as the old one. Moreover, new invariance principles would be unintuitive and would require that certain fundamental concepts change their meaning. For these reasons the choice between them is guided by a number of empirical reasons and is not only a matter of convention. (shrink)

A complete treatment of the Thomas rotation involves algebraic manipulations of overwhelming complexity. In this paper, we show that a choice of convenient vectorial forms for the relativistic addition law of velocities and the successive Lorentz transformations allows us to obtain straightforwardly the Thomas rotation angle by three new methods: (a) direct computation as the angle between the composite vectors of the non-collinear velocities, (b) vectorial approach, and (c) matrix approach. The new expression of the Thomas rotation angle permits us (...) to simply obtain the Thomas precession. Original diagrams are given for the first time. (shrink)

We revisit the introduction of the Superluminal Lorentz transformations which carry from “bradyonic” inertial frames to “tachyonic” inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we show the (...) connection between that procedure and the former one. In other words, in order to clarify the physical meaning of the imaginary units entering the classical theory of tachyons, we have temporarily to call into play anauxiliary six-dimensional space-time M(3, 3); however, we are eventually able to go back to the four-dimensional Minkowski space-time. We revisit the introduction of the Superluminal Lorentz transformations also under another aspect. In fact, the generalized Lorentz transformations had been previously written down in a form suited only for the simple case of collinear boosts (e.g., they formed a group just for collinear boosts). We express now the Superluminal Lorentz transformations in a more general form, so that they constitute a group together with the ordinary—orthochronousand antichronous—Lorentz transformations, and reduce to the previous form in the case of collinear boosts. Our approach introduces either real or imaginary quantities, with exclusion of (generic) complex quantities. In the present context, a procedure—in two steps—for interpreting the imaginary quantities is put forth and discussed. In the case of a chain of generalized Lorentz transformations, such a procedure (when necessary) is to be applied only at the end of the chain. Finally, we justify why we call “transformations” also the Superluminal ones. (shrink)

A molecular dynamics (MD) approach which determines automatically the complex magnetic structures in itinerant electron systems is applied to Fe-Cr alloys with use of 250 atoms in a MD unit cell (5×5×5 bcc lattice). It is demonstrated that the Fe-Cr alloys show various complex magnetic structures due to competing interactions: the collinear ferromagnetism (F) of matrix Fe with antiparallel Cr moments beyond 80 at.% Fe, the coexistence of non-collinear structure of Cr and collinear F of Fe between 50 and 75 (...) at.% Fe, the coexistence of broken antiferromagnetism (AF) of Cr and the F of Fe between 25 and 45 at.% Fe, the coexistence of F of Fe and antiferromagnetic long-range order of Cr around 20 at.% Fe, the AF of Cr matrix with non-collinear Fe moments (spin-glass like structure) between 5 and 15 at.% Fe, and the AF below 5 at.% Fe. In the concentration region between 5 and 20 at.% Fe, ferromagnetic Fe pairs which are stabilized with different amplitudes of local moments are found. The magnetic phase diagram and calculated magnetic moments are shown to be consistent with the neutron, Mössbauer, and photoemission experiments. (shrink)