General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on how counterfactuals should be interpreted and understood. Given the role of counterfactuals in the characterization of, inter alia, many accounts of scientific laws, theory confirmation and causation, general relativity once again presents us with idiosyncratic puzzles any attempt to analyze and understand the nature of (...) scientific knowledge must face. (shrink)

The definition of a pseudofinite structure can be translated verbatim into continuous logic, but it also gives rise to a stronger notion and to two parallel concepts of pseudocompactness. Our purpose is to investigate the relationship between these four concepts and establish or refute each of them for several basic theories in continuous logic. Pseudofiniteness and pseudocompactness turn out to be equivalent for relational languages with constant symbols, and the four notions coincide with the standard pseudofiniteness in the case of (...) classical structures, but the details appear to be slightly more important here than in the usual translation of definitions from classical logic. We also prove that injective “formula-definable” endofunctions are surjective, and conversely, in strongly pseudofinite omega-saturated structures. (shrink)

We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory. We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results (...) about infinitary logic on classical structures to the setting of infinitary continuous logic on continuous structures. Our encoding will also allow us to talk about not only the relations between complete metric structures, but also the potential relations between complete metric structures, i.e. those which are satisfied in some larger model of set theory. For example we will show that given any two complete metric structures we can determine if they are potentially isomorphic by looking at any admissible set which contains them both. (shrink)

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of (...) two‐sorted structures that witness approximate isomorphism. As an application, we show that the theory of any ‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. (shrink)

In tone languages, some case studies showed that the word-level tonal representation was closely related to the underlying metrical pattern. Based on different tonal patterns in prosodic units, the metrical structures could generally be divided into the left- and right-dominant types in Chinese dialects. Yet the cross-dialectal phonetic realizations (e.g., duration and pitch) between or within these two metrical structures were still unrevealed. The current study investigated the duration and pitch realizations of disyllabic prosodic words in Changsha and (...) Chengdu dialects (the left-dominant structure), and in Fuzhou and Xiamen dialects (the right-dominant structure). Results showed that not all the duration patterns across four Chinese dialects were sensitive to different metrical structures, indicating that the duration might not be the universal cue for metrical prominence in Chinese dialects. In terms of pitch realization across all the four Chinese dialects, level tones (sometimes falling tones) generally appeared in the metrically weak unit, while underlying pitch forms appeared in the metrically strong unit. Compared with duration, pitch might be more robust for prosodic realizations of metrical structures in Chinese dialects. Furthermore, there was an interaction between duration and pitch patterns in Chinese dialects, which could shed new light on the phenomenon of “metrical tone sandhi”. Meanwhile, this study also provides some references for the judgment of the metrical stress and prosodic realizations in other Chinese dialects. (shrink)

Rhythmic structure in speech is characterized by sequences of stressed and unstressed syllables. A large body of literature suggests that speakers of English attempt to achieve rhythmic harmony by evenly distributing stressed syllables throughout prosodic phrases. The question remains as to how speakers plan metrical structure during speech production and whether it is planned independently of phonemes. To examine this, we designed a tongue twister task consisting of disyllabic word pairs with overlapping phonological segments and either matching or non‐matching metrical (...) structure. Results showed that speakers had more difficulty producing metrically regular word pairs, compared to irregular pairs; that is, word pairs with irregular meter had faster productions and fewer speech errors in this production task. This finding of metrical regularity inhibiting production is inconsistent with an abstract metrical structure that is planned independently of phonemes at the point of phonological encoding. (shrink)

The general theory developed by Ben Yaacov for metric structures provides Fraïssé limits which are approximately ultrahomogeneous. We show here that this result can be strengthened in the case of relational metric structures. We give an extra condition that guarantees exact ultrahomogenous limits. The condition is quite general. We apply it to stochastic processes, the class of diversities, and its subclass of $L_1$ diversities.

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism), which implies, in particular, that isometry of locally compact Polish metric spaces is Borel reducible to graph isomorphism. We show that potentially $\boldsymbol {\Pi }^{0}_{\alpha + 1}$ isomorphism relations are Borel reducible to equality on hereditarily countable sets of rank $\alpha $, $\alpha \geq (...) 2$. We also study approximations of the Hjorth-isomorphism game, and formulate a condition ruling out classifiability by countable structures. (shrink)

We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a proof of concept we show that the result of Boney and Zambrano (Around the set-theoretical consistency of d-tameness of metric abstract elementary classes, arXiv:1508.05529, 2015) on (metric) tameness under a large cardinal assumption holds in this more general context. We briefly consider a further generalization to partial metric (...) spaces, and hint at connections to classes of fuzzy structures, and structures on sheaves. (shrink)

Is there anything more to temperature than the ordering of things from colder to hotter? Are there also facts, for example, about how much hotter (twice as hot, three times as hot...) one thing is than another? There certainly are---but the only strong justification for this claim comes from statistical mechanics. What we knew about temperature before the advent of statistical mechanics (what we knew about it from thermodynamics) provided only weak reasons to believe it.

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete...

We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with (...) results from cite{BenYaacov:Perturbations} regarding perturbations of bounded metric structures, we prove a Ryll-Nardzewski style characterisation of theories of Banach spaces which are separably categorical up to small perturbation of the norm. This last result is motivated by an unpublished result of Henson. (shrink)

For a locally compact group G, we show that it is possible to present the class of continuous unitary representations of G as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how nondegenerate ∗-representations of a general ∗-algebra A (with some mild assumptions) can be viewed as an elementary class, in a many-sorted language, and use the correspondence between continuous unitary representations of G and nondegenerate ∗-representations of L1(G). We relate (...) the notion of ultraproduct of logical structures, under this presentation, with other notions of ultraproduct of representations appearing in the literature, and we characterize property (T) for G in terms of the definability of the sets of fixed points of L1 functions on G. (shrink)

We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math (...) Soc, in press), as well as of global ${\aleph_0}$ -stability. We conclude with a study of perturbation systems (see Ben Yaacov I, On perturbations of continuous structures, submitted) in the formalism of topometric spaces. In particular, we show how the abstract development applies to ${\aleph_0}$ -stability up to perturbation. (shrink)

We prove that in a continuous ℵ₀-stable theory every type-definable group is definable. The two main ingredients in the proof are: 1. Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and 2. Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.

We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in [0, 1], we introduce two kinds of diagrams at each level: the closed diagram, which encapsulates weak inequalities of the form $$\phi ^\mathcal {M}\le r$$, and the open diagram, which encapsulates strict inequalities of the form $$\phi ^\mathcal {M}< r$$. We (...) show that the closed and open $$\Sigma _N$$ diagrams are $$\Pi ^0_{N+1}$$ and $$\Sigma ^0_N$$ respectively, and that the closed and open $$\Pi _N$$ diagrams are $$\Pi ^0_N$$ and $$\Sigma ^0_{N + 1}$$ respectively. We then introduce effective infinitary formulas of continuous logic and extend our results to the hyperarithmetical hierarchy. Finally, we demonstrate that our results are optimal. (shrink)

This paper concerns product constructions within the continuous-logic framework of Ben Yaacov, Berenstein, Henson, and Usvyatsov. Continuous-logic analogues are presented for the direct product, direct sum, and almost everywhere direct product analyzed in the work of Feferman and Vaught. These constructions are shown to possess a number of preservation properties analogous to those enjoyed by their classical counterparts in ordinary first-order logic: for example, each product preserves elementary equivalence in an appropriate sense; and if for \(i\in \mathbb {N}\) \(\mathcal {M}_i\) (...) is a metric structure and the sentence \(\theta \) is true in \(\prod _{i=0}^k\mathcal {M}_i\) for every \(k\in \mathbb {N}\), then \(\theta \) is true in \(\prod _{i\in \mathbb {N}}\mathcal {M}_i\). (shrink)

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand's theorem can be used to characterize definable functions in absolutely ubiquitous structures from classical logic.

The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept (...) of logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems. (shrink)

We prove that each ∀1 free amalgamation class K over a finite relational language L admits a countable generic structure M isometrically embedding all countable structuresin K relative to a fixed metric. We expand L by infinitely many binary predicates expressingdistance, and prove that the resulting expansion of K has a model companion axiomatizedby the first-order theory of M. The model companion is non-finitely axiomatizable, evenover a strong form of the axiom scheme of infinity.

Fix an integer $r \ge 3$. We consider metric spaces on n points such that the distance between any two points lies in $\left\{ {1, \ldots,r} \right\}$. Our main result describes their approximate structure for large n. As a consequence, we show that the number of these metric spaces is $\left\lceil {{{r + 1} \over 2}} \right\rceil ^{\left + o\left}.$Related results in the continuous setting have recently been proved by Kozma, Meyerovitch, Peled, and Samotij [34]. When r is (...) even, our structural characterization is more precise and implies that almost all such metric spaces have all distances at least $r/2$. As an easy consequence, when r is even, we improve the error term above from $o\left$ to $o\left$, and also show a labeled first-order 0-1 law in the language ${\cal L}_r $, consisting of r binary relations, one for each element of $[r]$. In particular, we show the almost sure theory T is the theory of the Fraïssé limit of the class of all finite simple complete edge-colored graphs with edge colors in $\left\{ {r/2, \ldots,r} \right\}$.Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws. (shrink)

In this paper we study the metric spaces that are definable in a polynomially bounded o-minimal structure. We prove that the family of metric spaces definable in a given polynomially bounded o-minimal structure is characterized by the valuation field Λ of the structure. In the last section we prove that the cardinality of this family is that of Λ. In particular these two results answer a conjecture given in [SS] about the countability of the metric types of (...) analytic germs. The proof is a mixture of geometry and model theory. (shrink)

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg λκ (x)=gλκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT κ λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT κ λμ (i.e.,T κ λμ (...) =δ κ λ σμ−δ κ μ σλ(σμ=∂σ/∂x μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT κ λμ. (shrink)

This book offers a solution for the problem of structure and agency in sociological theory by developing a new pair of fundamental concepts: metric and nonmetric. Nonmetric forms, arising in a crowd made out of innumerable individuals, correspond to social groups that divide the many individuals in the crowd into insiders and outsiders. Metric forms correspond to congested zones like traffic jams on a highway: individuals are constantly entering and leaving these zones so that they continue to exist, (...) even though the individuals passing through them change. Building from these concepts, we can understand “agency” as a requirement for group identity and group membership, thus associating it with nonmetric forms, and “structure” as a building-up effect following the accumulation of metric forms. This reveals the contradiction between structure and agency to be a case of forced perspective, leaving us victim to an optical illusion. (shrink)

Since summer 2019 there is a new document that defines what in science should be regarded as being one second, one meter, and one kilogram, respectively. It is the ninth edition of the SI Brochure. Compared with older editions, a new definitional approach has been used. The seven base units are now defined by being directly related to a so-called defining constant. The paper discusses the second, the meter, and the kilogram. One odd salient, but nonetheless not discussed, feature of (...) the formulations of the definitions is that, from a purely linguistic point of view, they are circular. That is, symbols for what is to be defined appear also in the defining expressions. However, underneath the circularities there are, appearances notwithstanding, substantially non-circular definitions. The aim of the paper is to uncover these never before presented definitional structures. It is made by means of the two notions absolutely discrete quantities and metrical coordinative definitions. When the true definitional structures become visible, two important substantial metrological facts can be seen. First, the new definition of the kilogram is very much in need of further discussion. Second, contrary to what the Brochure hints at, there is no need to try to exchange the atomic parameter used in the definition of the second. (shrink)

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many‐sorted metric partial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computable partial function from an effectively separable computable metric partial Σ‐algebraAto a computable metric partial Σ‐algebraBmust be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the computability of a (...) computably enumerable dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour‐El and Richards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many-sorted metric partial algebra, thus extending the axiomatisation given by Pour-El and Richards in [9] for Banach spaces. We show that every Banach-Mazur computable partial function from an effectively separable computable metric partial Σ-algebra A to a computable metric partial Σ-algebra B must be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves (...) the computability of a computably enumerable dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour-El and Richards. (shrink)

We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence of arbitrarily large models, joint embedding, amalgamation, homogeneity and a property which we call the perturbation property. We also assume that the Löwenheim-Skolem number, which in this setting refers to the (...) density character of the set instead of the cardinality, is ${\aleph_0}$ . In these settings we prove an analogue of Morley’s categoricity transfer theorem. We also give concrete examples of homogeneous MAECs. (shrink)

Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincaré as his witness Carnap asserted in his dissertation Der Raum (Carnap 1922) that the metrical structure of space is conventional while the underlying topological structure describes "objective" facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. By this means his metrical conventionalism turns out to be indefensible (...) for mathematical reasons. This implies that the relation between to-pology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as logical empiricists used to say. (shrink)

Geometry was a main source of inspiration for Carnap's conventionalism. Taking Poincaré as his witness, Carnap asserted in his dissertation Der Raum that the metrical structure of space is conventional while the underlying topological structure describes ‘objective’ facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. It is shown that his metrical conventionalism is indefensible for mathematical reasons. This (...) implies that the relation between topology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as the logical empiricists used to say. (shrink)

Using the Weyl-type canonical coordinates, an integration of Einstein's field equations in the cylindrosymmetric case considered by Kurşunoğlu is reexamined. It is made clear that the resulting metric is not describing the spacetime in a rotating frame, but in astatic cylindrical elastic medium. The conclusion of Kurşunoğlu that “for an observer on a rotating disk there is no way of escape from a curved spacetime” is therefore not valid. The metric in an empty rotating frame is found as (...) a solution of Einstein's field equations, and is not orthogonal. It is shown that the corresponding orthogonal solution represents spacetime in an inertial frame expressed in cylindrical coordinates. Introducing a noncoordinate basis, the metric in a rotating frame is given the static form of Kurşunoğlu's solution. The essential role played by the nonvanishing structure coefficients in this case is made clear. (shrink)

Computability theoretic aspects of Polish metric spaces are studied by adapting notions and methods of computable structure theory. In this dissertation, we mainly investigate index sets and classification problems for computably presentable Polish metric spaces. We find the complexity of a number of index sets, isomorphism problems, and embedding problems for computably presentable metric spaces. We also provide several computable structure theory results related to some classical Polish metric spaces such as the Urysohn space $\mathbb {U}$, (...) the Cantor space $2^{\mathbb {N}}$, the Baire space $\mathbb {N}^{\mathbb {N}}$, and spaces of continuous functions.Abstract prepared by Teerawat Thewmorakot.E-mail: [email protected]. (shrink)

This paper discusses the relationship between internationalisation, mobility, quality and equality in the context of recent developments in research policy in the European Research Area (ERA). Although these developments are specifically concerned with the growth of research capacity at European level, the issues raised have much broader relevance to those concerned with research policy and highly skilled mobility. The paper draws on a wealth of recent research examining the relationship between mobility and career progression with particular reference to a recently (...) completed empirical study of doctoral mobility in the social sciences (Ackers et al. Doctoral Mobility in the Social Sciences. Report to the NORFACE ERA-Network, 2007). The paper is structured as follows. The first section introduces recent policy developments including the European Charter for Researchers and Code of Conduct for the Recruitment of Researchers and the European Commission’s Green Paper on the ERA. The discussion focuses on concerns around the definition of ‘mobility’ and the tendency (in both policy circles and academic research) to conflate different forms of mobility and to equate these with notions of excellence or quality. Scientific mobility is shaped as much by ‘push’ factors (limited opportunity) as it is by the ‘draw’ of excellence. Scientists are exercising a degree of ‘choice’ within a specific and individualised framework of constraints. The following sections consider some of the ‘professional’ and ‘personal’ factors shaping scientific mobility and the influence that these have on the relationship between mobility, internationalisation and excellence. The paper concludes that mobility is not an outcome in its own right and must not be treated as such (as an implicit indicator of internationalisation). To do so contributes to differential opportunity in scientific labour markets reducing both efficiency and equality. (shrink)

In this study a combination of computer tools for coupling and virtual screening is detailed, in 108 active molecules and 3620 decoys to find stabilizers for G quadruplex. To have more precise results, combinations of coupling programs with fifteen energy scoring functions were applied. The validation and evaluation of the metrics was done with the CompScore genetic algorithm. The results showed an increase in BEDROC and EF of 50% compared to other strategies, as well as reflecting early recognition of active (...) molecules. From these results it is possible to work with the molecules that showed a good early recognition and evaluate their effect as G4 stabilizers. This ensures more efficient and accurate results in the preclinical stage for the development of anticancer drugs. Keywords: Enrichment metrics; telomere; G quadruplex ; CompScore. References [1]M. Porru, P. Zizza, M. Franceschin, C. Leonetti and A. Biroccio. «EMICORON: A multi-targeting G4 ligand with a promising preclinical profile» 2017. Biochimica et Biophysica Acta - General Subjects, 1861, 1362–1370. [Online]. Available: https://doi.org/10.1007/s00294-018-0836-6. [2]K. Tomita. «How long does telomerase extend telomeres? Regulation of telomerase release and telomere length homeostasis». Current Genetics, 64, 1177–1181. 2018. [Online]. Available: https://doi.org/10.1016/j.bbagen. 2016.11.010. [3]M. Jafri, S. Ansari, M. Alqahtani and J. Shay. «Roles of telomeres and telomerase in cancer, and advances in telomerase-targeted therapies. Genome Medicine., 2016. [Online]. Available: https://doi.org/10.3390/ijms19020482. [4]J. Huppert and S. Balasubramanian. «G-quadruplexes in promoters throughout the human genome». 35, 406–413. 2007. [Online]. Available: https://doi.org/10.1016/j.bbapap.2017.06.012. [5]S. Joy, Vijayakumar, S. Choi and H. Sunhye. «Role of computer-aided drug design in modern drug discovery». Archives of Pharmacal Research. 2015. [Online]. Available: https://doi.org/10.1007/s12272-015-0640-5. [6]S. Asamitsu, S. Obata, Z. Yu, T. Bando and H. Sugiyama. «Recent Progress of Targeted G-Quadruplex-Preferred Ligands Toward Cancer Therapy». Molecules, 24, 429. 2019. [En línea]. Available: https://doi.org/10.3390/molecules24030429. [7]R. Monsen and J. Trent. «Biochimie G-quadruplex virtual drug screening : A review». Biochimie, 152, 134–148. 2018. [Online]. Available: https://doi.org/10.1039/c9cc06748e. [8]J. Beauvarlet, P. Bensadoun, E. Darbo, G. Labrunie, E. Richard, I. Draskovic and M. Djavaheri-mergny. «Modulation of the ATM / autophagy pathway by a G-quadruplex ligand tips the balance between senescence and apoptosis in cancer cells». 1–18. 2019. [Online]. Available: https://doi.org/10.1093/nar/gkz095. [9].Z. Crees, J. Girard, Z. Rios, G. Botting, K. Harrington and C. Shearrow. « Oligonucleotides and G-quadruplex stabilizers: targeting telomeres and telomerase in cancer therapy».2014. [Online]. Available: https://doi.org/10.2174/1381612820666140630100702. [10].M. Meier, A. Moya-torres, N. Krahn, M. Mcdougall, L. Orriss, E. Mcrae and T. Patel. «Structure and hydrodynamics of a DNA Gquadruplex with a cytosine bulge»., 1–13. 2018. [Online]. Available: https://doi.org/10.1093/nar/gky307. (shrink)

From Einstein's point of view, his General Relativity Theory had strengths as well as failings. For him, its shortcoming mainly was that it did not unify gravitation and electromagnetism and did not provide solutions to field equations which can be interpreted as particle models with discrete mass and charge spectra, As a consequence, General Relativity did not solve the quantum problem, either. Einstein tried to get rid of the shortcomings without losing the achievements of General Relativity Theory. Stimulated by papers (...) of Weyl 465) and Eddington 194), from 1923 onward, he believed that, to reach this goal, one has to transit to space–times which possess more comprehensive geometrical structures than the Riemann space–time. This was the beginning of a decade's lasting search for a unitary field theory. We describe this exciting part of the history of physics, discuss achievements and failures of this development, and ask how these early attempts of a unified theory strike us today. Taking into account the fact that the Equivalence Principle only speaks for a geometrization of gravitation, we consider an alternative way to give those non-Riemannian structures which were introduced by the unitary field approach a physical meaning, namely the meaning of a generalized gravitational field. This is interesting since there are arguments in favor of such a generalization of General Relativity Theory, e.g., the problems the latter theory meets with if one tries to quantize it and to unify gravitation with other interactions. (shrink)

This article motivates and develops a reductive account of the structure of certain physical quantities in terms of their mereology. That is, I argue that quantitative relations like "longer than" or "3.6-times the volume of" can be analyzed in terms of necessary constraints those quantities put on the mereological structure of their instances. The resulting account, I argue, is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they’re called upon to describe and explain.

The physical and relational structure of the biologic continuum (both internal and external to the organism) creates the information signature that is the basis for the origination of meaning in the living system. A meaning metric can be grounded in the significance of that information to the stability of the system during the process of adaptive reconciliation of divergences from the steady state condition. From this perspective, an information-theoretic formulation of the process for translating incident information into adaptive action (...) is proposed that can be practically used in defining and quantifying the meaning of that information for the living system. (shrink)