Vienna Circle and Logical Analysis of Relativity Theory

In this paper we present some of our school's results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a case-study showing that the Vienna Circle's (VC) approach to doing science is workable and fruitful when performed with using the insights and tools of mathematical logic acquired since its formation years at the very time of the VC activity. We think that logical positivism was based on the insight and anticipation of what mathematical logic is capable when elaborated to some depth. Logical positivism, in great part represented by VC, influenced and took part in the birth of modern mathematical logic. The members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure

PIG-1 MELK-dependent phosphorylation of nonmuscle myosin II promotes apoptosis through CES-1 Snail partitioning

The mechanism(s) through which mammalian kinase MELK promotes tumorigenesis is not understood. We find that the C. elegans orthologue of MELK, PIG-1, promotes apoptosis by partitioning an anti-apoptotic factor. The C. elegans NSM neuroblast divides to produce a larger cell that differentiates into a neuron and a smaller cell that dies. We find that in this context, PIG-1 is required for partitioning of CES-1 Snail, a transcriptional repressor of the pro-apoptotic gene egl-1 BH3-only. pig-1 MELK is controlled by both a ces-1 Snail- and par-4 LKB1-dependent pathway, and may act through phosphorylation and cortical enrichment of nonmuscle myosin II prior to neuroblast division. We propose that pig-1 MELK-induced local contractility of the actomyosin network plays a conserved role in the acquisition of the apoptotic fate. Our work also uncovers an auto-regulatory loop through which ces-1 Snail controls its own activity through the formation of a gradient of CES-1 Snail protein

A Geometrical Characterization of the Twin Paradox and its Variants

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.Comment: 22 pages, 3 figure

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Robust gap repair in the contractile ring ensures timely completion of cytokinesis.

Cytokinesis in animal cells requires the constriction of an actomyosin contractile ring, whose architecture and mechanism remain poorly understood. We use laser microsurgery to explore the biophysical properties of constricting rings in Caenorhabditis elegans embryos. Laser cutting causes rings to snap open. However, instead of disintegrating, ring topology recovers and constriction proceeds. In response to severing, a finite gap forms and is repaired by recruitment of new material in an actin polymerization-dependent manner. An open ring is able to constrict, and rings repair from successive cuts. After gap repair, an increase in constriction velocity allows cytokinesis to complete at the same time as controls. Our analysis demonstrates that tension in the ring increases while net cortical tension at the site of ingression decreases throughout constriction and suggests that cytokinesis is accomplished by contractile modules that assemble and contract autonomously, enabling local repair of the actomyosin network. Consequently, cytokinesis is a highly robust process impervious to discontinuities in contractile ring structure.This project has received funding from the European Research Council (grants 640553, 260892, and 338410), Fundo Europeu de Desenvolvimento Regional (FED ER) funds through the Operational Competitiveness Program (COM PETE), national funds through Fundação para a Ciência e a Tecnologia (FCT) under the project FCO MP-01-0124-FED ER-028255 (PTDC/BEX-BCM/0654/2012), Fundação Luso-Americana para o Desenvolvimento Life Science 2020, and the Louis-Jeantet Young Investigator Award to H. Maiato. A.X. Carvalho, R. Gassmann, and I.A. Telley have FCT Investigator positions funded by FCT and cofunded by the European Social Fund through Programa Operacional Temático Potencial Type 4.2 promotion of scientific employment. A.M. Silva holds an FCT fellowship (SFRH/BPD/95707/2013). D.S. Osório was cofunded by the Programa Operacional Regional do Norte under the Quadro de Downloaded from jcb.rupress.org on February 27, 2018 Laser microsurgery in the contractile ring • Silva et al. 799 Referência Estratégico Nacional through FED ER and by FCT grant NOR TE-07-0124-FED ER-000003 (Cell Homeostasis Tissue Organization and Organism Biology)

Experimental and numerical study on soot formation in laminar diffusion flames of biodiesels and methyl esters

Biodiesel and blends with petroleum diesel are promising renewable alternative fuels for engines. In the present study, the soot concentration generated from four biodiesels, two pure methyl esters, and their blends with petroleum diesel are measured in a series of fully pre-vapourised co-flow diffusion flames. The experimental measurements are conducted using planar laser induced-incandescence (LII) and laser extinction optical methods. The results show that the maximum local soot volume fractions of neat biodiesels are 24.4% - 41.2% of pure diesel, whereas the mean soot volume fraction of neat biodiesel cases was measured as 11.3% - 21.3% of pure diesel. The addition of biodiesel to diesel not only reduces the number of inception particles, but also inhibits their surface growth. The discretised population balance modelling of a complete set of soot processes is employed to compute the 2D soot volume fraction and size distribution across the tested flames. The results show that the model also demonstrates a reduction of both soot volume fraction and primary particle size by adding biodiesel fuels. However, it is not possible to clearly determine which factors are responsible for the reduction from the comparison alone. Moreover, analysis of the discrepancies between numerical and experimental results for diesel and low-blending cases offers an insight for the refinement of soot formation modelling of combustion with large-molecule fuels.Bo Tian is supported by the fellowship provided by ZEPI. C. T. Chong is supported by the Newton Advanced Fellowship of the Royal Society (NA160115). Anxiong Liu gratefully acknowledges the financial support of the Chinese Scholarship Council (CSC) and the EPSRC grant No. EP/S012559/1

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure

Axiomatizing relativistic dynamics without conservation postulates

A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous $E=mc^2$. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.Comment: 21 pages, 7 figure

Trapped lipopolysaccharide and LptD intermediates reveal lipopolysaccharide translocation steps across the Escherichia coli outer membrane

Lipopolysaccharide (LPS) is a main component of the outer membrane of Gram-negative bacteria, which is essential for the vitality of most Gram-negative bacteria and plays a critical role for drug resistance. LptD/E complex forms a N-terminal LPS transport slide, a hydrophobic intramembrane hole and the hydrophilic channel of the barrel, for LPS transport, lipid A insertion and core oligosaccharide and O-antigen polysaccharide translocation, respectively. However, there is no direct evidence to confirm that LptD/E transports LPS from the periplasm to the external leaflet of the outer membrane. By replacing LptD residues with an unnatural amino acid p-benzoyl-L-phenyalanine (pBPA) and UV-photo-cross-linking in E.coli, the translocon and LPS intermediates were obtained at the N-terminal domain, the intramembrane hole, the lumenal gate, the lumen of LptD channel, and the extracellular loop 1 and 4, providing the first direct evidence and “snapshots” to reveal LPS translocation steps across the outer membrane