Groups with infinite FC-center have the Schmidt property

We show that every countable group with infinite finite conjugacy (FC)-center has the Schmidt property, that is, admits a free, ergodic, measure-preserving action on a standard probability space such that the full group of the associated orbit equivalence relation contains a non-trivial central sequence. As a consequence, every countable, inner amenable group with property (T) has the Schmidt property.

Philosophische Superlative und die Maschine als Symbol

Philosophical Superlatives: Machines as Symbols. – In this paper, my chief aim is to present a close reading of parts of a central sequence of remarks from Wittgenstein’s Philosophical Investigations (191 – 197, cf. Remarks on the Foundations of Mathematics, I, 121 – 130). The apparent theme of this sequence is the idea of a ‘machine as a symbol of its mode of operation’. Obviously, this idea requires a good deal of clarification, and the present paper attempts to elucidate relevant passages which, in their turn, are discussed in the hope of succeeding in spelling out some of the points Wittgenstein has in mind in appealing to the picture of a machine as a symbol of its mode of operation. What will serve as a kind of framework of these elucidations is the notion of a philosophical superlative appealed to by Wittgenstein in a number of remarks that can be seen as particularly characteristic of his later thought. In the course of developing the idea of a philosophical superlative six aspects, or types, of superlatives are distinguished, and the last of these is found to shade into the image of a machine as symbol in a way that allows us to draw on various superlatives in striving to clarify the train of thought underpinning the sequence PI 191 – 197 and related passages.

CENTRAL SEQUENCES IN SUBHOMOGENEOUS UNITAL C*-ALGEBRAS

Suppose that $\mathcal {A}$ is a unital subhomogeneous C*-algebra. We show that every central sequence in $\mathcal {A}$ is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every central sequence in $\mathcal {A}$ is trivial if and only if every pointwise limit of irreducible representations is irreducible. Finally, we give a nice representation of the latter algebras.

Dynamical Modeling, Analysis, and Control of Information Diffusion over Social Networks: A Deep Learning-Based Recommendation Algorithm in Social Network

The recommendation algorithm can break the restriction of the topological structure of social networks, enhance the communication power of information (positive or negative) on social networks, and guide the information transmission way of the news in social networks to a certain extent. In order to solve the problem of data sparsity in news recommendation for social networks, this paper proposes a deep learning-based recommendation algorithm in social network (DLRASN). First, the algorithm is used to process behavioral data in a serializable way when users in the same social network browse information. Then, global variables are introduced to optimize the encoding way of the central sequence of Skip-gram, in which way online users’ browsing behavior habits can be learned. Finally, the information that the target users’ have interests in can be calculated by the similarity formula and the information is recommended in social networks. Experimental results show that the proposed algorithm can improve the recommendation accuracy.

INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES

We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Among other things, we show that every free ergodic p.m.p. compact action of an inner amenable group gives rise to an inner amenable orbit equivalence relation. We also obtain an analogous result for compact extensions of equivalence relations that either are stable or have a nontrivial central sequence in their full group.

II1 FACTORS WITH EXOTIC CENTRAL SEQUENCE ALGEBRAS

We provide a class of separable II1 factors $M$ whose central sequence algebra is not the ‘tail’ algebra associated with any decreasing sequence of von Neumann subalgebras of $M$ . This settles a question of McDuff [On residual sequences in a II1 factor, J. Lond. Math. Soc. (2) (1971), 273–280].

Rheology of Dispersions of High-Aspect-Ratio Nanofibers Assembled from Elastin-Like Double-Hydrophobic Polypeptides

Elastin-like polypeptides (ELPs) are promising candidates for fabricating tissue-engineering scaffolds that mimic the extracellular environment of elastic tissues. We have developed a “double-hydrophobic” block ELP, GPG, inspired by non-uniform distribution of two different hydrophobic domains in natural elastin. GPG has a block sequence of (VGGVG)5-(VPGXG)25-(VGGVG)5 that self-assembles to form nanofibers in water. Functional derivatives of GPG with appended amino acid motifs can also form nanofibers, a display of the block sequence’s robust self-assembling properties. However, how the block length affects fiber formation has never been clarified. This study focuses on the synthesis and characterization of a novel ELP, GPPG, in which the central sequence (VPGVG)25 is repeated twice by a short linker sequence. The self-assembly behavior and the resultant nanostructures of GPG and GPPG were when compared through circular dichroism spectroscopy, atomic force microscopy, and transmission electron microscopy. Dynamic rheology measurements revealed that the nanofiber dispersions of both GPG and GPPG at an extremely low concentration (0.034 wt%) exhibited solid-like behavior with storage modulus G′ > loss modulus G” over wide range of angular frequencies, which was most probably due to the high aspect ratio of the nanofibers that leads to the flocculation of nanofibers in the dispersion.

Embodied Seeing-In, Empathy, and Expansionism

I will argue that the ambition to provide a naturalized aesthetics of film in Murray Smith’s Film, Art, and the Third Culture is not fully matched by the actual explanatory work done. This is because it converges too much on the emotional engagement with character at the expense of other features of film. I will make three related points to back up my claim. I will argue (1) that Smith does not adequately capture in what ways the phenomenon of seeing-in, introduced early in the book, could explain our complex engagement with moving images; (2) that because of this oversight he also misconstrues the role of the mirror neuron system in our engagement with filmic scenes; and (3) that an account of embodied seeing-in could be a remedy for the above. In order to demonstrate the latter point, I will show how such an account could contribute to the analysis of a central sequence in Alfred Hitchcock’s Strangers on a Train (1951) that Smith also discusses.

Appendix to ``Regularity of Villadsen algebras'': The failure of the Corona Factorization Property for the Villadsen algebra $\mathcal{V}_\infty$

In this appendix to M. S. Christensen, “Regularity of Villadsen algebras and characters on their central sequence algebras”, Math. Scand. ?? (????), ???--???, we prove that the Villadsen algebra $\mathcal{V} _\infty $ does not satisfy the Corona Factorization Property (CFP).

Regularity of Villadsen algebras and characters on their central sequence algebras

We show that if $A$ is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then $A$ absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of $A$ does not admit characters.Additionally, in a joint appendix with Joan Bosa (see the following paper), we show that the Villadsen algebra of the second type with infinite stable rank fails the Corona Factorization Property, thus providing the first example of a unital, simple, separable and nuclear $C^\ast $-algebra with a unique tracial state which fails to have this property.