1,25-Dihydroxvitamin D3 [1,25(OH)2D3] is the hormonally active form of vitamin D. The genomic mechanism of 1,25(OH)2D3 action involves the direct binding of the 1,25(OH)2D3 activated vitamin D receptor/retinoic X receptor (VDR/RXR) heterodimeric complex to specific DNA sequences. Numerous VDR co-regulatory proteins have been identified, and genome-wide studies have shown that the actions of 1,25(OH)2D3 involve regulation of gene activity at a range of locations many kilobases from the transcription start site. The structure of the liganded VDR/RXR complex was recently characterized using cryoelectron microscopy, X-ray scattering, and hydrogen deuterium exchange. These recent technological advances will result in a more complete understanding of VDR coactivator interactions, thus facilitating cell and gene specific clinical applications. Although the identification of mechanisms mediating VDR-regulated transcription has been one focus of recent research in the field, other topics of fundamental importance include the identification and functional significance of proteins involved in the metabolism of vitamin D. CYP2R1 has been identified as the most important 25-hydroxylase, and a critical role for CYP24A1 in humans was noted in studies showing that inactivating mutations in CYP24A1 are a probable cause of idiopathic infantile hypercalcemia. In addition, studies using knockout and transgenic mice have provided new insight on the physiological role of vitamin D in classical target tissues as well as evidence of extraskeletal effects of 1,25(OH)2D3 including inhibition of cancer progression, effects on the cardiovascular system, and immunomodulatory effects in certain autoimmune diseases. Some of the mechanistic findings in mouse models have also been observed in humans. The identification of similar pathways in humans could lead to the development of new therapies to prevent and treat disease.

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Vitamin D: Metabolism, Molecular Mechanism of Action, and Pleiotropic Effects.

Studies of teachers’ use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a single curriculum to regulate mathematics teaching. A review of the research on mathematics curriculum use over the last 25 years reveals significant variation in findings and in theoretical foundations. The aim of this review is to examine the ways that central constructs of this body of research—such as curriculum use, teaching, and curriculum materials—are conceptualized and to consider the impact of various conceptualizations on knowledge in the field. Drawing on the literature, the author offers a framework for characterizing and studying teachers’ interactions with curriculum materials.

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Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula

This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

http://types10.mimuw.edu.pl/content/slides/day1/HenkBarendregt.pdf

Lambda Calculus with Types

Handbook of logic in computer science.

Structure and interpretation of computer programs

To study the operational behaviour of λ-terms, we will use the denotational (mathematical) approach. A denotational semantics for a language is based on the choice of a space of semantics values, or denotations, where terms are to be interpreted. Choosing a space with nice mathematical properties can help in proving the semantic properties of terms, since to this aim standard mathematical techniques can be used.

λ Δ -Models

Operational, denotational and logical descriptions: a case study

We propose a characterization of PSPACE by means of atype assignment for an extension of lambda calculus with a conditional construction. The type assignment STAB is an extension of STA, a type assignment for lambda-calculus inspired by Lafont's Soft Linear Logic.We extend STA by means of a ground type and terms for booleans. The key point is that the elimination rule for booleans is managed in an additive way. Thus, we are able to program polynomial time Alternating Turing Machines. Conversely, we introduce a call-by-name evaluation machine in order tocompute programs in polynomial space. As far as we know, this is the first characterization of PSPACE which is based on lambda calculusand light logics.

https://hal.archives-ouvertes.fr/hal-00342323/document

A logical account of pspace

The notion of solvability in the call-by-value λ -calculus is defined and completely characterized, both from an operational and a logical point of view. The operational characterization is given through a reduction machine, performing the classical β -reduction, according to an innermost strategy. In fact, it turns out that the call-by-value reduction rule is too weak for capturing the solvability property of terms. The logical characterization is given through an intersection type assignment system, assigning types of a given shape to all and only the call-by-value solvable terms.

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Call-by-value Solvability

The resource calculus is an extension of the λ-calculus allowing to model resource consumption. Namely, the argument of a function comes as a finite multiset of resources, which in turn can be either linear or reusable, giving rise to non-deterministic choices, expressed by a formal sum. Using the λ-calculus terminology, we call solvable a term that can interact with the environment: solvable terms represent meaningful programs. Because of the non-determinism, different definitions of solvability are possible in the resource calculus. Here we study the optimistic (angelical, or may) notion, and so we define a term solvable whenever there is a simple head context reducing the term into a sum where at least one addend is the identity. We give a syntactical, operational and logical characterization of this kind of solvability.

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Simona Ronchi Della Rocca

Papers

λ Δ -Models

Operational, denotational and logical descriptions: a case study

A logical account of pspace

Call-by-value Solvability

Solvability in resource lambda-calculus