We present a set of algorithms for automated simplification of symbolic constants of the form ∑iαixi with αi rational and xi complex. The included algorithms, called SimplifySum2 and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, including (...) one, for instance, where the tool reduced a symbolic expression of approximately 100 000 characters in size enough to enable manual manipulation to one with just four simple terms.2Available from https://github.com/alexkaiser/SimplifySum. (shrink)

Cyclin-dependent kinase 5 has been implicated in Alzheimer's disease pathogenesis. Here, we demonstrate that overexpression of p25, an activator of cdk5, led to increased levels of BACE1 mRNA and protein in vitro and in vivo. A p25/cdk5 responsive region containing multiple sites for signal transducer and activator of transcription was identified in the BACE1 promoter. STAT3 interacts with the BACE1 promoter, and p25-overexpressing mice had elevated levels of pSTAT3 and BACE1, whereas cdk5-deficient mice had reduced levels. Furthermore, mice with a (...) targeted mutation in the STAT3 cdk5 responsive site had lower levels of BACE1. Increased BACE levels in p25 overexpressing mice correlated with enhanced amyloidogenic processing that could be reversed by a cdk5 inhibitor. These data demonstrate a pathway by which p25/cdk5 increases the amyloidogenic processing of APP through STAT3-mediated transcriptional control of BACE1 that could have implications for AD pathogenesis. (shrink)

We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < z < 0.7. We also compare these results with those from the publicly released (...) DR9 and DR10 samples. Assuming a concordance Λ cold dark matter cosmological model, the DR11 sample covers a volume of 13 Gpc3 and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, rd, which has a value of rd,fid = 149.28 Mpc in our fiducial cosmology. We find DV = at z = 0.32 and DV = at z = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at z = 0.57 of DA = and H =. Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant. © 2014 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society. (shrink)

Seneca ‘Rhetor’ was last critically edited by H. J. Müller in 1887; the editions of H. Bornecque and W. A. Edward lack an apparatus criticus, though the latter's notes give some attention to textual points. Whoever next addresses himself to the task can take heart from Eduard Norden : ‘der Text ist schwer korrupt, für Konjekturalkritik noch viel zu tun.’ It may be added that he will do a service by jettisoning a large proportion of what Konjekturalkritik has already produced-too (...) much of this nature in Müller's text and apparatus, to say nothing of later contributions, is merely depressing. (shrink)

According to history texts, philosophers searched for a unifying natural law whereby natural phenomena and numbers are related. More than 2300 years ago, Aristotle postulated that nature requires minimum energy. More than 220 years ago, Euler applied the minimum energy postulate. More than 200 years ago, Lagrange provided a mathematical “proof” of the postulate for conservative systems. The resulting Principle of Least Action served only to derive the differential equations of motion of a conservative system. Then, 170 years ago, Hamilton (...) presented what he claimed to be a “general method in dynamics.” Hamilton's resulting “Law of Varying Action” was supposed to apply to both conservative and non-conservative systems and was supposed to yield either the differential equations of motion or the integrals of those differential equations. However, no direct evaluation of the integrals of motion ever resulted from Hamilton's law of varying action. In 1975, a scant 29 years ago, following five years of controversy with engineer mechanicians, Dr. Wolfgang Yourgrau, Editor, Foundations of Physics, published my first paper based on Aristotle's postulate, without mathematical proof. That and subsequent papers present, through applications, a true “general method in dynamics.” In this essay, I present the mathematical proof that is missing from my 1975 and subsequent papers. Six fundamental integrals of analytical mechanics are derived from Aristotle's postulate. First, however, Hamilton must be revisited to show why his H function and his “force function” prevents the law of varying action from being the general method in dynamics that he claimed it to be. I have found that Hamilton’s Law of Varying Action (HLVA), as Hamilton presented it, cannot be applied to systems for which the force function is non-integrable. In 1972, Dr. B.E. Gatewood and Dr. D.P. Beres (then a graduate student) discovered that the end-point term associated with the principle of least action does not vanish. I named the new equation, “the general energy equation.” In 1973, because I was doing with it what Hamilton claimed could be done with HLVA, I simply assumed that this new equation was HLVA. I gave the new equation the misnomer HLVA. In 2001, I learned that I had made a grave mistake. I found that HLVA is at most a special case of the general energy equation. My interpretation of Aristotle's postulate permits one to by-pass the differential equations of motion completely for both conservative and non-conservative systems (no calculus of variations). (shrink)

This article is the text of an interview with D. H. Mellor conducted by Andrew Pyle and first published in the Spring 1993 issue of the philosophical journal Cogito.

D. H. Mellor; VI*—Conscious Belief, Proceedings of the Aristotelian Society, Volume 78, Issue 1, 1 June 1978, Pages 87–102, https://doi.org/10.1093/aristotelian.

[D. H. Mellor] Kant's claim that our knowledge of time is transcendental in his sense, while false of time itself, is true of tenses, i.e. of the locations of events and other temporal entities in McTaggart's A series. This fact can easily, and I think only, be explained by taking time itself to be real but tenseless. /// [J. R. Lucas] Mellor's argument from Kant fails. The difficulties in his first Antinomy are due to topological confusions, not the tensed nature (...) of time. Nor are McTaggart' s difficulties due to the tensed nature of time. The ego-centricity of tensed discourse is an essential feature of communication between selves, each of whom refers himself as 'I', and is required for talking about time as well as experience and agency. Arguments based on the Special Theory are misconceived. Some rest on a confused notion of 'topological simultaneity'. In the General Theory a cosmic time is defined, as also in quantum mechanics, where a natural present is defined by a unique hyperplane of collapse into eigen-ness. (shrink)

This selection of D. H. Mellor's work demonstrates the wide ranging originality of his work. It gathers together sixteen major papers on related topics. Together they form a complete modern metaphysics. The first five papers are on aspects of the mind: on our 'selves', their supposed subjectivity and how we refer to them, on the nature of conscious belief and on computational and physicalist theories of the mind. The next five papers deal with dispositions, natural kinds, laws of nature and (...) how they involve natural necessity, universals and objective chances, and the relation between properties and predicates. Then follow three papers about the relations between time, change and causation, the nature of individual causes and effects and of the causal relation between them, and how causation depends on chance. The last three papers discuss the relation between chance and degrees of belief, give a solution to the problem of induction, and argue for an objective interpretation of decision theory. (shrink)

_Probability: A Philosophical Introduction_ introduces and explains the principal concepts and applications of probability. It is intended for philosophers and others who want to understand probability as we all apply it in our working and everyday lives. The book is not a course in mathematical probability, of which it uses only the simplest results, and avoids all needless technicality. The role of probability in modern theories of knowledge, inference, induction, causation, laws of nature, action and decision-making makes an understanding of (...) it especially important to philosophers and students of philosophy, to whom this book will be invaluable both as a textbook and a work of reference. In this book D. H. Mellor discusses the three basic kinds of probability – physical, epistemic, and subjective – and introduces and assesses the main theories and interpretations of them. The topics and concepts covered include: * chance * frequency * possibility * propensity * credence * confirmation * Bayesianism. _Probability: A Philosophical Introduction_ is essential reading for all philosophy students and others who encounter or need to apply ideas of probability. (shrink)

This book deals not so much with statistical methods as with the central concept of chance, or statistical probability, which statistical theories apply to nature.

I show that the connotations of causation - temporal, explanatory, predictive and means-end - are preserved in indeterministic causation only to the extent that effects have a greater chance of occurring in the circumstances if their causes do than if they don’t.

The paper looks at the semantics and ontology of dispositions in the light of recent work on the subject. Objections to the simple conditionals apparently entailed by disposition statements are met by replacing them with so-called 'reduction sentences' and some implications of this are explored. The usual distinction between categorical and dispositional properties is criticised and the relation between dispositions and their bases examined. Applying this discussion to two typical cases leads to the conclusion that fragility is not a real (...) property and that, while both temperature and its bases are, this does not generate any problem of overdetermination. (shrink)

This paper attacks two contrary views. One denies that nature has joints, taking the properties we call natural to be merely artefacts of our theories. The other accepts real natural properties but takes their naturalness to come by degrees. I argue that both are wrong: natural properties are real, and their naturalness no more comes by degrees than does the naturalness of the things that have them.1.