Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

ISL1 expression is not restricted to pancreatic well-differentiated neuroendocrine neoplasms, but is also commonly found in well and poorly differentiated neuroendocrine neoplasms of extrapancreatic origin

The human insulin gene enhancer-binding protein islet-1 (ISL1) is a transcription factor involved in the differentiation of the neuroendocrine pancreatic cells. Recent studies identified ISL1 as a marker for pancreatic well-differentiated neuroendocrine neoplasms. However, little is known about ISL1 expression in pancreatic poorly differentiated and in extrapancreatic well and poorly differentiated neuroendocrine neoplasms. We studied the immunohistochemical expression of ISL1 in 124 neuroendocrine neoplasms. Among pancreatic neuroendocrine neoplasms, 12/13 with poor differentiation were negative, whereas 5/7 with good differentiation but a Ki67 >20% were positive. In extrapancreatic neuroendocrine neoplasms, strong positivity was found in Merkel cell carcinomas (25/25), pulmonary small cell neuroendocrine carcinomas (21/23), medullary thyroid carcinomas (9/9), paragangliomas/pheochromocytomas (6/6), adrenal neuroblastomas (8/8) and head and neck neuroendocrine carcinomas (4/5), whereas no or only weak staining was recorded in pulmonary carcinoids (3/15), olfactory neuroblastomas (1/4) and basaloid head and neck squamous cell carcinomas (0/15). ISL1 stained the neuroendocrine carcinoma component of 5/8 composite carcinomas and also normal neuroendocrine cells in the thyroid, adrenal medulla, stomach and colorectum. Poorly differentiated neuroendocrine neoplasms, regardless of their ISL1 expression, were usually TP53 positive. Our results show the almost ubiquitous expression of ISL1 in extrapancreatic poorly differentiated neuroendocrine neoplasms and neuroblastic malignancies and its common loss in pancreatic poorly differentiated neuroendocrine neoplasms. These findings modify the role of ISL1 as a marker for pancreatic neuroendocrine neoplasms and suggest that ISL1 has a broader involvement in differentiation and growth of neuroendocrine neoplasms than has so far been assumed.

The developmental and evolutionary origins of psychological essentialism lie in sortal object individuation

Cimpian & Salomon (C&S) present promising steps towards understanding the cognitive underpinnings of adult essentialism. However, their approach is less convincing regarding ontogenetic and evolutionary aspects. In contrast to C&S's claim, the so-called inherence heuristic, though perhaps vital in adult reasoning, seems an implausible candidate for the developmental and evolutionary foundations of psychological essentialism. A more plausible candidate is kind-based object individuation that already embodies essentialist modes of thinking and that is present in infants and nonhuman primates.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

Nucleic-Acid Analogs with Restricted Conformational Flexibility in the Sugar-Phosphate Backbone (‘Bicyclo-DNA’). Part 5. Synthesis, Characterization, and Pairing Properties of Oligo-αlpha-D-(bicyclodeoxynucleotides) of the Bases Adenine and Thymine (αlpha-Bicyclo-DNA)

10.1002/hlca.19950780816.abs A conformational analysis of the (3′S,5′R)-2′-deoxy-3′,5′-ethano-α-D-ribonucleosides (a-D-bicyclodeoxynucleosides) based on the X-ray analysis of N4-benzoyl-α-D-(bicyclodeoxycytidine) 6 and on 1H-NMR analysis of the α-D-bicyclodeoxynucleoside derivatives 1-7 reveals a rigid sugar structure with the furanose units in the l′-exo/2′-endo conformation and the secondary OH groups on the carbocyclic ring in the pseudoequatorial orientation. Oligonucleotides consisting of α-D-bicyclothymidine and α-D-bicyclodeoxyadenosine were successfully synthesized from the corresponding nucleosides by phosphoramidite methodology on a DNA synthesizer. An evaluation of their pairing properties with complementary natural RNA and DNA by means of UV/melting curves and CD spectroscopy show the following characteristics: i) α-bcd(A10) and α-bcd(T10) (α = short form of α-D)efficiently form complexes with complementary natural DNA and RNA. The stability of these hybrids is comparable or slightly lower as those with natural β-d(A10) or β-d(T10)( β = short form ofβ-D). ii) The strand orientation in α-bicyclo-DNA/β-DNA duplexes is parallel as was deduced from UV/melting curves of decamers with nonsymmetric base sequences. iii) CD Spectroscopy shows significant structural differences between α-bicyclo-DNA/β-DNA duplexes compared to α-DNA/β-DNA duplexes. Furthermore, α-bicyclo-DNA is ca. 100-fold more resistant to the enzyme snake-venom phosphodiesterase with respect to β-DNA and about equally resistant as α-DNA.