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1. On asymptotic stability of connective groups

   https://doi.org/doi:10.2969/aspm/08010000  

   Dadarlat, Marius ( April 2019 , Operator algebras and mathematical physics)

   In their study of almost group representations, Manuilov and Mishchenko introduced and investigated the notion of asymptotic stability of a finitely presented discrete group. In this paper we establish connections between connectivity of amenable groups and asymptotic stability and exhibit new classes of asymptotically stable groups. In particular, we show that if G is an amenable and connective discrete group whose classifying space BG is homotopic to a finite simplicial complex, then G is asymptotically stable. 

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2. The role of elastin on the mechanical properties of the anterior leaflet in porcine tricuspid valves

   https://doi.org/10.1371/journal.pone.0267131  

   Salinas, Samuel D. ; Farra, Yasmeen M. ; Amini Khoiy, Keyvan ; Houston, James ; Lee, Chung-Hao ; Bellini, Chiara ; Amini, Rouzbeh ( May 2022 , PLOS ONE)

   Jiang, Yi (Ed.)

   Elastin is present in the extracellular matrix (ECM) of connective tissues, and its mechanical properties are well documented. In Marfan syndrome, however, the inability to properly code for the protein fibrillin-1 prematurely leads to the degradation and loss of elastin fiber integrity in the ECM. In this study, the role of elastin in the ECM of the anterior leaflet of the tricuspid valve was investigated by examining the biomechanical behavior of porcine leaflets before and after the application of the enzyme elastase. Five loading protocols were applied to the leaflet specimens in two groups (elastase-treated and control samples). The mechanical response following elastase application yielded a significantly stiffer material in both the radial and circumferential directions. At a physiological level of stress (85 kPa), the elastase group had an average strain of 26.21% and 6.32% in the radial and circumferential directions, respectively, at baseline prior to elastase application. Following elastase treatment, the average strain was 5.28% and 0.97% in the radial and circumferential directions, respectively. No statistically significant change was found in the control group following sham treatment with phosphate-buffered saline (PBS). Two-photon microscopy images confirmed that after the removal of elastin, the collagen fibers displayed a loss of undulation. With a significant reduction in radial compliance, the ability to withstand physiological loads may be compromised. As such, an extracellular matrix that is structurally deficient in elastin may hinder normal tricuspid valve function. 

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3. Frozen pipes: lattice models for Grothendieck polynomials

   Brubaker, Ben ; Frechette, Claire ; Hardt, Andrew ; Tibor, Emily ; Weber, Katherine ( June 2023 , Algebraic combinatorics)

   We introduce families of two-parameter multivariate polynomials indexed by pairs of partitions $v,w$ -- {\it biaxial double} $(\beta,q)$-{\it Grothendieck polynomials} -- which specialize at $q=0$ and $v=1$ to double $\beta$-Grothendieck polynomials from torus-equivariant connective K-theory. Initially defined recursively via divided difference operators, our main result is that these new polynomials arise as partition functions of solvable lattice models. Moreover, the associated quantum group of the solvable model for polynomials in $n$ pairs of variables is a Drinfeld twist of the $U_q(\widehat{\mathfrak{sl}}_{n+1})$ $R$-matrix. By leveraging the resulting Yang-Baxter equations of the lattice model, we show that these polynomials simultaneously generalize double $\beta$-Grothendieck polynomials and dual double $\beta$-Grothendieck polynomials for arbitrary permutations. We then use properties of the model and Yang-Baxter equations to reprove Fomin-Kirillov's Cauchy identity for $\beta$-Grothendieck polynomials, generalize it to a new Cauchy identity for biaxial double $\beta$-Grothendieck polynomials, and prove a new branching rule for double $\beta$-Grothendieck polynomials. 

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4. Emotions and the Systematization of Connective Labor

   https://doi.org/10.1177/02632764211049475  

   Pugh, Allison J. ( October 2021 , Theory, Culture & Society)

   A profusion of jobs has arisen in contemporary capitalism involving ‘connective labor’, or the work of emotional recognition. Yet the expansion of this interpersonal work occurs at the same time as its systematization, as pressures of efficiency, measurement and automation reshape the work, generating a ‘colliding intensification’. Existing scholarship offers three different ways of understanding the role of emotions in connective labor – as tool, commodity or vulnerability – depending on their view of systematization as useful, inseparable or dehumanizing. Based on 106 in-depth interviews and 300+ hours of observations, I found that vestiges of all three models lurked in the experience of providing connective labor, yet none fully captured the profound meaning practitioners reported finding in their work. Systems varied on three dimensions, reflecting the relative worth of worker, recipient or the work, extracting value from the forged connections, while the meanings workers derived shaped their perspective on its systematization. 

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5. The Complexity of Approximating the Matching Polynomial in the Complex Plane

   https://doi.org/10.1145/3448645  

   Bezáková, Ivona ; Galanis, Andreas ; Goldberg, Leslie Ann ; Štefankovič, Daniel ( June 2021 , ACM Transactions on Computation Theory)

   We study the problem of approximating the value of the matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in the complex plane. When γ is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs. For general complex values of γ, Patel and Regts, building on methods developed by Barvinok, showed that the problem admits an FPTAS on graphs of maximum degree Δ as long as γ is not a negative real number less than or equal to −1/(4(Δ −1)). Our first main result completes the picture for the approximability of the matching polynomial on bounded degree graphs. We show that for all Δ ≥ 3 and all real γ less than −1/(4(Δ −1)), the problem of approximating the value of the matching polynomial on graphs of maximum degree Δ with edge parameter γ is #P-hard. We then explore whether the maximum degree parameter can be replaced by the connective constant. Sinclair et al. showed that for positive real γ, it is possible to approximate the value of the matching polynomial using a correlation decay algorithm on graphs with bounded connective constant (and potentially unbounded maximum degree). We first show that this result does not extend in general in the complex plane; in particular, the problem is #P-hard on graphs with bounded connective constant for a dense set of γ values on the negative real axis. Nevertheless, we show that the result does extend for any complex value γ that does not lie on the negative real axis. Our analysis accounts for complex values of γ using geodesic distances in the complex plane in the metric defined by an appropriate density function. 

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