Excerpt from Vector Analysis and the Theory of Relativity One of the most striking effects of the publication of Einstein's papers on generalized relativity and of the discussions which arose in connection with the subsequent astronomical observations was to make students of physics renew their study of mathematics. At first they attempted to learn simply the technique, but soon there was a demand to understand more; real mathematical insight was sought. Unfortunately there were no books available, not even papers. Dr. (...) Murnaghan's little book is a most successful attempt to supply what is a definite need. Every physicist can read it with profit. He will learn the meaning of a vector for the first time. He will learn methods which are available for every field of mathematical physics. He will see which of the processes used by Einstein and others are strictly mathematical and which are physical. Every chapter is illuminating, and the treatment of the subject is that of a student of mathematics and is not developed ad hoc. The extension of surface and line integrals is most interesting for physicists and the discussion of the space relations in a four-dimensional geometry is one most needed. This is specially true concerning the case of point-symmetry which forms the basis of Einstein's formulae for gravitation as applied to the solar system. I feel personally that I owe to this book a great debt. I have read it with care and shall read it again. It has given me a definiteness of understanding which I never had before, and a vision of a field of knowledge which before was remote. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Vectorization of a class of structures is a natural notion in finite model theory. Roughly speaking, vectorizations allow tuples to be treated similarly to elements of structures. The importance of vectorizations is highlighted by the fact that if the complexity class PTIME corresponds to a logic with reasonable syntax, then it corresponds to a logic generated via vectorizations by a single generalized quantifier (Dawar in J Log Comput 5(2):213–226, 1995). It is somewhat surprising, then, that there have been few systematic (...) studies of the expressive power of vectorizations of various quantifiers. In the present paper, we consider the simplest case: the cardinality quantifiers C S. We show that, in general, the expressive power of the vectorized quantifier logic $${{\rm FO}(\{{\mathsf C}_S^{(n)}\, | \, n \in \mathbb{Z}_+\})}$$ is much greater than the expressive power of the non-vectorized logic FO(C S ). (shrink)

Why do forces compose according to the parallelogram of forces? This question has been controversial; it is one episode in a longstanding, fundamental dispute regarding which facts are not to be explained dynamically. If the parallelogram law is explained statically, then the laws of statics are separate from and “transcend” the laws of dynamics. Alternatively, if the parallelogram law is explained dynamically, then statical laws become mere corollaries to the dynamical laws. I shall attempt to trace the history of this (...) controversy in order to identify what it would be for one or the other of these rival views to be correct. I shall argue that various familiar accounts of natural law not only make it difficult to see what the point of this dispute could have been, but also improperly foreclose some serious scientific options. I will sketch an alternative account of laws that helps us to understand what this dispute was all about. (shrink)

Support vector machines are being used increasingly in affective science as a data-driven classification method and feature reduction technique. Whereas traditional statistical methods typically compare group averages on selected variables, SVMs use a predictive algorithm to learn multivariate patterns that optimally discriminate between groups. In this review, we provide a framework for understanding the methods of SVM-based analyses and summarize the findings of seminal studies that use SVMs for classification or data reduction in the behavioral and neural study of emotion (...) and affective disorders. We conclude by discussing promising directions and potential applications of SVMs in future research in affective science. (shrink)

Vector autoregression (VAR) modeling allows probing bidirectional relationships in gender/sex development and may support hypothesis testing following multi-modal data collection. We show VAR in three lights: supporting a hypothesis, rejecting a hypothesis, and opening up new questions. To illustrate these capacities of VAR, we reanalyzed longitudinal data that recorded dyadic mother-infant interactions for 15 boys and 15 girls aged 3 to 11 months of age. We examined monthly counts of 15 infant behaviors and 13 maternal behaviors (Seifert et al., 1994). (...) VAR models demonstrated that infant crawling predicted a subsequently close feedback loop from mothers of boys but a subsequently open ended, branched response from mothers of girls. A different finding showed that boys’ standing independently later predicted significant later increases of four maternal behaviors: rocking/jiggling, lifting, affectionate touching, and stimulation of infant gross-motor activity. In contrast, crawling by girls led mothers to later decrease the same maternal behaviors. Thus, VAR might allow us to identify how mothers respond differently during daily interactions depending on infant gender/sex. The present work intends mainly to showcase the VAR method in the specific context of the empirical study of gender/sex development. (shrink)

Vectors, we will argue, are not just mathematical abstractions. They are also physical properties--universals. What make them distinctive are the rich and varied essences of these universals, and the complex pattern of internal relations which hold amongst them.

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the ‘usual’ first order (...) formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)

Retroviral vectors utilize the biochemical processes unique to retroviruses, to transfer genes with high efficiency into a wide variety of cell types in tissue culture and in living animals. With such vectors, the effect of newly introduced genes and the mechanism of gene expression can be studied in cell types so far refractory to other methods of transfer.

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in “six-vector” form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's four equations expressed (...) as one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated. (shrink)

Critics of reliability theories of epistemic justificationoften claim that the `generality problem' is an insurmountabledifficulty for such theories. The generality problem is theproblem of specifying the level of generality at which abelief-forming process is to be described for the purposeof assessing its reliability. This problem is not asintractable as it seems. There are illuminating solutionsto analogous problems in the ethics literature. Reliabilistsought to attend to utilitarian approaches to choices betweeninfinite utility streams; they also ought to attend towelfarist approaches to social (...) choice situations that donot demand full aggregation of individual welfares.These analogies suggest that the traditional `single number'approach to reliability is misguided. I argue that a newapproach – the `vector reliability' approach – is preferable.Vector reliability theories associate target beliefs withreliability vectors – that is, structured collections ofreliability numbers – and construct criteria of epistemicjustification that appeal to these vectors. The bulk of thetheoretical labor involved in a reliability account of epistemicjustification is thus transferred from picking a uniquereliability number to constructing a plausible criterionof epistemic justification. (shrink)

We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms.

Critics of reliability theories of epistemic justificationoften claim that the `generality problem' is an insurmountabledifficulty for such theories. The generality problem is theproblem of specifying the level of generality at which abelief-forming process is to be described for the purposeof assessing its reliability. This problem is not asintractable as it seems. There are illuminating solutionsto analogous problems in the ethics literature. Reliabilistsought to attend to utilitarian approaches to choices betweeninfinite utility streams; they also ought to attend towelfarist approaches to social (...) choice situations that donot demand full aggregation of individual welfares.These analogies suggest that the traditional `single number'approach to reliability is misguided. I argue that a newapproach – the `vector reliability' approach – is preferable.Vector reliability theories associate target beliefs withreliability vectors – that is, structured collections ofreliability numbers – and construct criteria of epistemicjustification that appeal to these vectors. The bulk of thetheoretical labor involved in a reliability account of epistemicjustification is thus transferred from picking a uniquereliability number to constructing a plausible criterionof epistemic justification. (shrink)

In this paper I provide an ontology for the co‐variant vectors, contra‐variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is that if vector quantities are universals then there should be a way of identifying the same vector quantity at two different places, but there is no absolute identification of vector quantities, merely a (...) path‐relative one.My solution to the problem is to use the mathematical characterization of vectors as differential operators on scalar fields. On the proposed hypothesis a scalar field is a conjunctive state of affairs, and vector and tensor fields are relations instantiated by scalar fields. (shrink)

Programming artificial intelligence to make fairness assessments of texts through top-down rules, bottom-up training, or hybrid approaches, has presented the challenge of defining cross-cultural fairness. In this paper a simple method is presented which uses vectors to discover if a verb is unfair or fair. It uses already existing relational social ontologies inherent in Word Embeddings and thus requires no training. The plausibility of the approach rests on two premises. That individuals consider fair acts those that they would be (...) willing to accept if done to themselves. Secondly, that such a construal is ontologically reflected in Word Embeddings, by virtue of their ability to reflect the dimensions of such a perception. These dimensions being: responsibility vs. irresponsibility, gain vs. loss, reward vs. sanction, joy vs. pain, all as a single vector. The paper finds it possible to quantify and qualify a verb as fair or unfair by calculating the cosine similarity of the said verb’s embedding vector against FairVec—which represents the above dimensions. We apply this to Glove and Word2Vec embeddings. Testing on a list of verbs produces an F1 score of 95.7, which is improved to 97.0. Lastly, a demonstration of the method’s applicability to sentence measurement is carried out. (shrink)

The paper contains a discussion on two kinds of coincidence experiments. First, a standard two-photon coincidence experiment is considered and it is shown that its outcomes are incompatible with any classical radiation theory because of the role of the state vector reduction phenomenon in such an experiment. In the second part of the paper a proposed new kind of photon coincidence experiment is discussed. The classical and quantum predictions for the outcomes of this experiment differ dramatically and therefore the experiment (...) should constitute a new limitation to the classical radiation theories. The proposed experiment should also yield information about the kinematics of the reduction of the state vector process. (shrink)

Epistemologists have addressed a variety of modal epistemic standings, such as sensitivity, safety, risk, and epistemic virtue. These concepts mark out the ways that beliefs can fail to track the truth, articulate the conditions needed for knowledge, and indicate ways to become a better epistemic agent. However, it is our contention that current ways of carving up epistemic modality ignore the complexities that emerge when individuals are embedded within a community and listening to a variety of sources, some of whom (...) are intentionally engaged in deception or bullshit. In this context we want our beliefs to be secure. In this paper we translate the epistemic modal standing of safety into a framework appropriate for social epistemology and argue for the importance of epistemic network-security and belief-security to be added to this framework. We discuss the virtues that are salient for promoting network-security and the vices that undermine it. In particular, we highlight monitoring, adjusting, and restructuring virtues and vices. Importantly, each of these vices can be other-regarding or self-regarding. For example, one tempting way of dealing with insecurity within a network is to completely cut oneself off from biased sources. However, we argue that this is a self-regarding restructuring vice because it closes oneself off from opportunities for epistemic growth. By contrast, an other-regarding restructuring vice would be to cut off others from hearing from sources of information that would make their network more secure. (shrink)

Programming artificial intelligence to make fairness assessments of texts through top-down rules, bottom-up training, or hybrid approaches, has presented the challenge of defining cross-cultural fairness. In this paper a simple method is presented which uses vectors to discover if a verb is unfair or fair. It uses already existing relational social ontologies inherent in Word Embeddings and thus requires no training. The plausibility of the approach rests on two premises. That individuals consider fair acts those that they would be (...) willing to accept if done to themselves. Secondly, that such a construal is ontologically reflected in Word Embeddings, by virtue of their ability to reflect the dimensions of such a perception. These dimensions being: responsibility vs. irresponsibility, gain vs. loss, reward vs. sanction, joy vs. pain, all as a single vector. The paper finds it possible to quantify and qualify a verb as fair or unfair by calculating the cosine similarity of the said verb’s embedding vector against FairVec—which represents the above dimensions. We apply this to Glove and Word2Vec embeddings. Testing on a list of verbs produces an F1 score of 95.7, which is improved to 97.0. Lastly, a demonstration of the method’s applicability to sentence measurement is carried out. (shrink)

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the vector models, (...) the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

From a metaphysical point of view, it is important clearly to see the ontological difference between what is studied in mathematics and mathematical physics, respectively. In this respect, the paper is concerned with the vectors of classical physics. Vectors have both a scalar magnitude and a direction, and it is argued that neither conventionalism nor wholesale anti‐conventionalism holds true of either of these components of classical physical vectors. A quantification of a physical dimension requires the discovery of (...) ontological order relations among all the determinate properties of this dimension, as well as a conventional definition that connects the number one and mathematical unit vectors to determinate spatiotemporal physical entities. One might say that mathematics deals with numbers and vectors, but mathematical physics with scalar quantities and vector quantities, respectively. The International System of Units distinguishes between basic and derived scalar quantities; if a similar distinction should be introduced for the vector quantities of classical physics, then duration in directed time ought to be chosen as the basic vector quantity. The metaphysics of physical vectors is intimately connected with the metaphysics of time. From a philosophical‐historical point of view, the paper revives W. E. Johnson's distinction ‘determinates‐determinables’ and Hans Reichenbach's notion of ‘coordinative definition’. (shrink)

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

This paper resists the virality of contemporary paranoia by turning to “French epistemology”, a philosophical ethos that embraces uncertainty and complexity by registering the transformative impact of scientific knowledge on thought. Despite its popular uses describing phenomena of communication today, the idea of virality comes from biomedicine. This paper, therefore, investigates the extent to which an epidemiological concept of viral transmission—the disease vector—can comprehend and encourage new possibilities of thought beyond paranoia. Briefly, I attempt to analyze thought as a vector. (...) I pursue this by examining Delaporte’s important, but neglected, study of the 1832 Parisian cholera epidemic. First elucidating his reconstruction of the ways tentative epistemological progress intertwined with and supported projects of working-class and colonial control. My vectorial analysis then considers how his argument infects contemporary readers with doubts that undo the bases of paranoia. I pursue this analysis further via a methodological examination of Delaporte’s study as both carrier of predecessors’ methods and host in which they alter, becoming newly infectious. I conclude by reflecting on this formulation of thought as disease vector and what Delaporte’s singular treatment of the problem of error reveals about an ethos committed to registering the impact of knowledge on thought. (shrink)

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to my Linear and Geometric Algebra. That text is a prerequisite for this one. -/- Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways.

Mass vaccination has been a successful public health strategy for many contagious diseases. The immunity of the vaccinated also protects others who cannot be safely or effectively vaccinated—including infants and the immunosuppressed. When vaccination rates fall, diseases like measles can rapidly resurge in a population. Those who cannot be vaccinated for medical reasons are at the highest risk of severe disease and death. They thus may bear the burden of others' freedom to opt out of vaccination. It is often asked (...) whether it is legitimate for states to adopt and enforce mandatory universal vaccination. Yet this neglects a related question: are those who opt out, where it is permitted, morally responsible when others are harmed or die as a result of their decision? In this article, we argue that individuals who opt out of vaccination are morally responsible for resultant harms to others. Using measles as our main example, we demonstrate the ways in which opting out of vaccination can result in a significant risk of harm and death to others, especially infants and the immunosuppressed. We argue that imposing these risks without good justification is blameworthy and examine ways of reaching a coherent understanding of individual moral responsibility for harms in the context of the collective action required for disease transmission. Finally, we consider several objections to this view, provide counterarguments and suggest morally permissible alternatives to mandatory universal vaccination including controlled infection, self-imposed social isolation and financial penalties for refusal to vaccinate. (shrink)

In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two opposite truth (...) values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT. (shrink)

The Anthropocene, a concept to describe the planetary consequences of human culture, demands that we imagine the earth itself as an image-recording medium. It is a concept that confronts the entangled histories of industrialization and abstraction, revealing the thoroughly mediated circumstances from which perceptions of ‘nature’ emerge. This article considers an accelerated form of abstraction induced by technological capitalism, a form with thoroughly material consequences described by McKenzie Wark as ‘vectoral’. If the age of the human is recorded on the (...) earth, the vector is the tool of its stratigraphic inscription. Taking Tom McCarthy’s novel Satin Island as an example, this article speculates on a photographic practice immanent to the vector. In Satin Island, photographic images do not reinforce a human world but instead provoke a growing awareness of otherworldliness. These images confront the more radical and paradoxical consequences of the Anthropocene, an era that in fact names the end of the very category of human. (shrink)

The Anthropocene, a concept to describe the planetary consequences of human culture, demands that we imagine the earth itself as an image-recording medium. It is a concept that confronts the entangled histories of industrialization and abstraction, revealing the thoroughly mediated circumstances from which perceptions of ‘nature’ emerge. This article considers an accelerated form of abstraction induced by technological capitalism, a form with thoroughly material consequences described by McKenzie Wark as ‘vectoral’. If the age of the human is recorded on the (...) earth, the vector is the tool of its stratigraphic inscription. Taking Tom McCarthy’s novel Satin Island (2015) as an example, this article speculates on a photographic practice immanent to the vector. In Satin Island (2015), photographic images do not reinforce a human world but instead provoke a growing awareness of otherworldliness. These images confront the more radical and paradoxical consequences of the Anthropocene, an era that in fact names the end of the very category of human. (shrink)

Edelman suggests that any shape is encoded by an excitation vector with components corresponding to excitations of corresponding neuronal modules. This results in discrimination of stimuli in a shape space of low dimensionality. Similar vector encoding is present in color vision. Red-green, blue-yellow, bright and dark neurons are modules that represent a number of different color stimuli in color space of low dimensionality. Vector encoding allows effective computation of color differences and color similarities. Such a neuronal vector-encoding approach has also (...) been applied to the perception of visual movement, line orientation, and stereopsis. (shrink)

We define rational Hermite interpolants to vector-valued functions and show that, in the context of Clifford algebras, the numerator and denominator polynomials belong to a complex extension of the Lipschitz group. We also discuss the problem of constructing an algebraic representation for the generalized inverse of a vector, which is at the heart of the usual development of vector rational approximation.

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with Nv vector dimensions and Ns spinor dimensions, where Nv=2k and Ns=2 k, k⩾3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with Nv−4 vector and Ns−4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, (...) Yang-Mills gauge fields, and wave functions of bosons and fermions. (shrink)

This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.

Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and (...) Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. (shrink)

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown (...) that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

En este artículo se estudia la conexión entre tecnología social e innovación oculta a partir de un conjunto de vectores éticos. Estos vectores éticos permiten que aflore y se difunda la innovación oculta que se produce a través de la tecnología social en entornos colaborativos. Entender la dimensión ética de la tecnología social permite identificar el papel que juega un conjunto de leyes (ley de Metcalfe, ley de rendimientos crecientes de adopción y ley de externalidades positivas) en el desarrollo de (...) prácticas de empoderamiento social en dichos entornos, definidos como "comunidades de conocimiento". Se analizan estos vectores éticos presentes en la tecnología social a partir de las siguientes categorías: conocimiento e innovación comunitarios, participación ciudadana y democracia, diálogo entre saberes populares y saberes científicos, y proceso pedagógico holístico. (shrink)

A “mental” multiplication scheme is given for the super hypercomplex numbers, which extend the 16-element Dirac algebra to 32 elements by appending the complex octonions. This extends the 5-vectors of relativity to 9-vectors. The problems with nonassociativity, for the group structures and wave equation covariance, are explored.

Einstein's linear Lagrangian is replaced by a Lagrangian which is quadratic in the curvature quantities (gauge invariance). The hypothesis is made that the basic metrical field is highly agitated (due to periodic boundary conditions) thus establishing a submicroscopic basic lattice structure of the space-time world which, however, is macroscopically isotropic. All consequences follow from these assumptions. The “free vector” of Einstein's theory (void of physical significance and used for the normalization of the reference system) is no longer free but of (...) physical significance. It becomes subject to the wave equation and the Lorentz condition. It can thus be identified with the electromagnetic vector potential. Although the present investigation does not go beyond the linear approximation, the contours of auniverse of maxium rationality emerge. (shrink)

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace zero. (...) In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality. (shrink)

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian. The structure of our observed world, including space and fields living within it, should arise as a higher-level emergent description. I sketch how this might come about, although much work remains to be done.

Apoptosis proteins have a central role in the development and homeostasis of an organism. These proteins are very important for understanding the mechanism of programmed cell death, and their function is related to their types. According to the classification scheme by Zhou and Doctor (2003), the apoptosis proteins are categorized into the following four types: (1) cytoplasmic protein; (2) plasma membrane-bound protein; (3) mitochondrial inner and outer proteins; (4) other proteins. A powerful learning machine, the Support Vector Machine, is applied (...) for predicting the type of a given apoptosis protein by incorporating the sqrt-amino acid composition effect. High success rates were obtained by the re-substitute test (98/98 = 100 %) and the jackknife test (89/98 = 90.8%). (shrink)