Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

Ultraviolet Complete Quantum Gravity

An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity.Comment: 11 pages, no figures. Changes to text. Results remain the same. References added. To be published in European Physics Journal Plu

Continuous non-perturbative regularization of QED

We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the gauge group, this regularization scheme is intrinsically non-perturbative. Despite the fact that the non-local action converges formally to the local one as the cutoff goes to infinity, the regularized theory keeps trace of the non-locality through the appearance of a quadratic divergence in the transverse part of the polarization operator. This term which is uniquely defined by the choice of the cutoff functions can be removed by a redefinition of the regularized action. We notice that as for chiral fermions on the lattice, there is an obstruction to construct a continuous and non ambiguous regularization in four dimensions. With the help of the regularized equations of motion, we calculate the one particle irreducible functions which are known to be divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and revised version, to appear in Phys. Rev.

Next-generation muscle-directed gene therapy by in silico vector design

There is an urgent need to develop the next-generation vectors for gene therapy of muscle disorders, given the relatively modest advances in clinical trials. These vectors should express substantially higher levels of the therapeutic transgene, enabling the use of lower and safer vector doses. In the current study, we identify potent muscle-specific transcriptional cisregulatory modules (CRMs), containing clusters of transcription factor binding sites, using a genome-wide data-mining strategy. These novel muscle-specific CRMs result in a substantial increase in muscle-specific gene transcription (up to 400-fold) when delivered using adeno-associated viral vectors in mice. Significantly higher and sustained human micro-dystrophin and follistatin expression levels are attained than when conventional promoters are used. This results in robust phenotypic correction in dystrophic mice, without triggering apoptosis or evoking an immune response. This multidisciplinary approach has potentially broad implications for augmenting the efficacy and safety of muscle-directed gene therapy

Multiplicative slices, relativistic Toda and shifted quantum affine algebras

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces. In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.Comment: 125 pages. v2: references updated; in section 11 the third local Lax matrix is introduced. v3: references updated. v4=v5: 131 pages, minor corrections, table of contents added, Conjecture 10.25 is now replaced by Theorem 10.25 (whose proof is based on the shuffle approach and is presented in a new Appendix). v6: Final version as published, references updated, footnote 4 adde

‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal

Analyzing collaborative learning processes automatically

In this article we describe the emerging area of text classification research focused on the problem of collaborative learning process analysis both from a broad perspective and more specifically in terms of a publicly available tool set called TagHelper tools. Analyzing the variety of pedagogically valuable facets of learners’ interactions is a time consuming and effortful process. Improving automated analyses of such highly valued processes of collaborative learning by adapting and applying recent text classification technologies would make it a less arduous task to obtain insights from corpus data. This endeavor also holds the potential for enabling substantially improved on-line instruction both by providing teachers and facilitators with reports about the groups they are moderating and by triggering context sensitive collaborative learning support on an as-needed basis. In this article, we report on an interdisciplinary research project, which has been investigating the effectiveness of applying text classification technology to a large CSCL corpus that has been analyzed by human coders using a theory-based multidimensional coding scheme. We report promising results and include an in-depth discussion of important issues such as reliability, validity, and efficiency that should be considered when deciding on the appropriateness of adopting a new technology such as TagHelper tools. One major technical contribution of this work is a demonstration that an important piece of the work towards making text classification technology effective for this purpose is designing and building linguistic pattern detectors, otherwise known as features, that can be extracted reliably from texts and that have high predictive power for the categories of discourse actions that the CSCL community is interested in

Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2 and

Dissolving the Dichotomies Between Online and Campus-Based Teaching: a Collective Response to The Manifesto for Teaching Online (Bayne et al. 2020)

This article is a collective response to the 2020 iteration of The Manifesto for Teaching Online. Originally published in 2011 as 20 simple but provocative statements, the aim was, and continues to be, to critically challenge the normalization of education as techno-corporate enterprise and the failure to properly account for digital methods in teaching in Higher Education. The 2020 Manifesto continues in the same critically provocative fashion, and, as the response collected here demonstrates, its publication could not be timelier. Though the Manifesto was written before the Covid-19 pandemic, many of the responses gathered here inevitably reflect on the experiences of moving to digital, distant, online teaching under unprecedented conditions. As these contributions reveal, the challenges were many and varied, ranging from the positive, breakthrough opportunities that digital learning offered to many students, including the disabled, to the problematic, such as poor digital networks and access, and simple digital poverty. Regardless of the nature of each response, taken together, what they show is that The Manifesto for Teaching Online offers welcome insights into and practical advice on how to teach online, and creatively confront the supremacy of face-to-face teaching