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The Hybrid Vigor of Heterodox Economics: A Feminist Perspective
No full textThis case study in the evolution of heterodox economics describes the emergence of feminist perspectives on care provision and their implications for a larger theory of bargaining over the distribution of gains from cooperation. It testifies to the hybrid vigor of diverse and ongoing efforts to challenge the narrow focus of the neoclassical paradigm
'We need to offer something better to the scholars of the future.' Which way forward for heterodox economics?
No full textAfter the global financial crisis, hopes were high that there would be a pluralisation of the economics discipline and a boost for heterodox economics that challenged dominant economic models. However, mainstream economics once again proved its enormous resilience and the future of alternatives to this mainstream is anything but certain. Geoffrey Hodgson's new book on this issue has sparked fresh discussions about the stunted development of heterodox economics and proposals for possible ways forward. This article will argue that the crucial factor for the future of heterodox economics is not converging on a single unified paradigm or raising the quality of research, but rather gaining access to different kinds of capital, first and foremost professorial positions at universities. Such access is severely restricted under present conditions as a result of epistemological and ontological discrimination. Heterodox economics can only flourish if the epistemic community of economists embraces paradigmatic pluralism as part of their academic culture, or if regulations are put in place to secure access to such capital and so to academic freedom
Solving viscoelastic problems with a Laplace transform approach supplanted by ARX models, suggesting a way to upgrade Finite Element or spectral codes
No full textFinite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent concerns about the use of non-integer differential equations to describe viscoelasticity or well-founded ideas based upon the use of a behavior's law directly derived from Dynamic Mechanical Analysis (DMA) experiments in frequency domain, could make the Laplace domain approach particularly attractive if embedded in a time discretized scheme. Based upon the inversion of Laplace transforms, this paper shows that this aim is not only possible but also gives rise to a simple algorithm having good performances in terms of computation times and precision. Such an approach, which fully relies on the Laplace-defined Behavioral Transfer Function (LTBF) can be promoted if it uses AutoRegressive with eXogeneous input parametric models perfectly substitutable to the real LTBF. They avoid the hitherto prohibitive pitfall of having to store all past data in the computer's memory while maintaining an equal computation precision
Some generalizations of the variety of transposed Poisson algebras
No full textIt is shown that the variety of transposed Poisson algebras coincides withthe variety of Gelfand-Dorfman algebras in which the Novikov multiplication iscommutative. The Gr\"obner-Shirshov basis for the transposed Poisson operad iscalculated up to degree 4. Furthermore, we demonstrate that every transposedPoisson algebra is F-manifold. We verify that the special identities ofGD-algebras hold in transposed Poisson algebras. Finally, we propose aconjecture stating that every transposed Poisson algebra is special, i.e., canbe embedded into a differential Poisson algebra.Comment: 8 p, numbers of pages is change
Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming
No full textThe concept of updating a probability distribution in the light of newevidence lies at the heart of statistics and machine learning. Pearl's andJeffrey's rule are two natural update mechanisms which lead to differentoutcomes, yet the similarities and differences remain mysterious. This paperclarifies their relationship in several ways: via separate descriptions of thetwo update mechanisms in terms of probabilistic programs and samplingsemantics, and via different notions of likelihood (for Pearl and for Jeffrey).Moreover, it is shown that Jeffrey's update rule arises via variationalinference. In terms of categorical probability theory, this amounts to ananalysis of the situation in terms of the behaviour of the multiset functor,extended to the Kleisli category of the distribution monad
Joint Distributions in Probabilistic Semantics
No full textVarious categories have been proposed as targets for the denotationalsemantics of higher-order probabilistic programming languages. One suchproposal involves joint probability distributions (couplings) used in Bayesianstatistical models with conditioning. In previous treatments, composition ofjoint measures was performed by disintegrating to obtain Markov kernels,composing the kernels, then reintegrating to obtain a joint measure.Disintegrations exist only under certain restrictions on the underlying spaces.In this paper we propose a category whose morphisms are joint finite measuresin which composition is defined without reference to disintegration, allowingits application to a broader class of spaces. The category is symmetricmonoidal with a pleasing symmetry in which the dagger structure is a simpletranspose.Comment: 14 pages, MFPS 202
K-stability for varieties with a big anticanonical class
No full textWe extend the algebraic K-stability theory to projective klt pairs with a biganticanonical class. While in general such a pair could behave pathologically,it is observed in this note that K-semistability condition will force them tohave a klt anticanonical model, whose stability property is the same as theoriginal pair.Comment: 9 pages, Final versio
Crack branching at low tip speeds: spilling the T
No full textUsing the criterion that a crack will extend along the direction of maximum circumferential stress, this paper demonstrates the influence of the coupling between the crack-parallel T-stress and the tip speed on the directional (in)stability of dynamics cracks in brittle materials, i.e., branching, turning, and limiting velocities. The proposed (in)stability criterion evolves within the theory of dynamic fracture: we build on the work of Ramulu and Kobayashi (1983) by introducing a reference distance ahead of the crack-tip to incorporate the contribution of the higher-order terms in the asymptotic solution of the elastic crack-tip fields. The theoretical aspect is first explored, a methodology to numerically (and experimentally) advocate the instability—as a co-action of T-stress and a fast-running crack—is then proposed and validated on Borden et al. (2012)’s branching benchmark. An experimental setup combining Ultra-High-Speed High-Resolution imaging with advanced Digital Image Correlation algorithms and a novel crack-branching inertial impact test enables for never-seen-before quantification of the rich dynamical behaviour of the fracture. This permits the experimental validation of the developed crack (in)stability criterion
A topological counterpart of well-founded trees in dependent type theory
No full textWithin dependent type theory, we provide a topological counterpart ofwell-founded trees (for short, W-types) by using a proof-relevant version ofthe notion of inductively generated suplattices introduced in the context offormal topology under the name of inductively generated basic covers. In moredetail, we show, firstly, that in Homotopy Type Theory, W-types and proofrelevant inductively generated basic covers are propositionally mutuallyencodable. Secondly, we prove they are definitionally mutually encodable in theAgda implementation of intensional Martin-Loef's type theory. Finally, wereframe the equivalence in the Minimalist Foundation framework by introducingwell-founded predicates as the logical counterpart for predicates of dependentW-types. All the results have been checked in the Agda proof-assistant.Comment: To be published in the post-proceedings of the 39th Conference on Mathematical Foundations of Programming Semantic
A first-order logic characterization of safety and co-safety languages
No full textLinear Temporal Logic (LTL) is one of the most popular temporal logics, thatcomes into play in a variety of branches of computer science. Among the variousreasons of its widespread use there are its strong foundational properties: LTLis equivalent to counter-free omega-automata, to star-free omega-regularexpressions, and (by Kamp's theorem) to the First-Order Theory of Linear Orders(FO-TLO). Safety and co-safety languages, where a finite prefix suffices toestablish whether a word does not belong or belongs to the language,respectively, play a crucial role in lowering the complexity of problems likemodel checking and reactive synthesis for LTL. SafetyLTL (resp., coSafetyLTL)is a fragment of LTL where only universal (resp., existential) temporalmodalities are allowed, that recognises safety (resp., co-safety) languagesonly. The main contribution of this paper is the introduction of a fragment ofFO-TLO, called SafetyFO, and of its dual coSafetyFO, which are expressivelycomplete with respect to the LTL-definable safety and co-safety languages. Weprove that they exactly characterize SafetyLTL and coSafetyLTL, respectively, aresult that joins Kamp's theorem, and provides a clearer view of thecharacterization of (fragments of) LTL in terms of first-order languages. Inaddition, it gives a direct, compact, and self-contained proof that any safetylanguage definable in LTL is definable in SafetyLTL as well. As a by-product,we obtain some interesting results on the expressive power of the weak tomorrowoperator of SafetyLTL, interpreted over finite and infinite words. Moreover, weprove that, when interpreted over finite words, SafetyLTL (resp. coSafetyLTL)devoid of the tomorrow (resp., weak tomorrow) operator captures the safety(resp., co-safety) fragment of LTL over finite words