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1. Hyperbolic families and coloring graphs on surfaces

   https://doi.org/https://doi.org/10.1090/btran/26  

   Postle, Luke; Thomas, Robin (December 2018, Transactions of the American Mathematical Society. Series B)

   We develop a theory of linear isoperimetric inequalities for graphs on surfaces and apply it to coloring problems, as follows. Let $ G$ be a graph embedded in a fixed surface $$ \Sigma $$ of genus $ g$ and let $$ L=(L(v):v\in V(G))$$ be a collection of lists such that either each list has size at least five, or each list has size at least four and $ G$ is triangle-free, or each list has size at least three and $ G$ has no cycle of length four or less. An $ L$-coloring of $ G$ is a mapping $$ \phi $$ with domain $ V(G)$ such that $$ \phi (v)\in L(v)$$ for every $$ v\in V(G)$$ and $$ \phi (v)\ne \phi (u)$$ for every pair of adjacent vertices $$ u,v\in V(G)$$. We prove if every non-null-homotopic cycle in $ G$ has length $$ \Omega (\log g)$$, then $ G$ has an $ L$-coloring, if $ G$ does not have an $ L$-coloring, but every proper subgraph does (``$ L$-critical graph''), then $$ \vert V(G)\vert=O(g)$$, if every non-null-homotopic cycle in $ G$ has length $$ \Omega (g)$$, and a set $$ X\subseteq V(G)$$ of vertices that are pairwise at distance $$ \Omega (1)$$ is precolored from the corresponding lists, then the precoloring extends to an $ L$-coloring of $ G$, if every non-null-homotopic cycle in $ G$ has length $$ \Omega (g)$$, and the graph $ G$ is allowed to have crossings, but every two crossings are at distance $$ \Omega (1)$$, then $ G$ has an $ L$-coloring, if $ G$ has at least one $ L$-coloring, then it has at least $$ 2^{\Omega (\vert V(G)\vert)}$$ distinct $ L$-colorings. We show that the above assertions are consequences of certain isoperimetric inequalities satisfied by $ L$-critical graphs, and we study the structure of families of embedded graphs that satisfy those inequalities. It follows that the above assertions hold for other coloring problems, as long as the corresponding critical graphs satisfy the same inequalities. 

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2. Search for the double-beta decay of $$^{82}$$Se to the excited states of $$^{82}$$Kr with NEMO-3

   https://doi.org/doi:10.1016/j.nuclphysa.2020.121701  

   R.Arnolda, C.Augierb (December 2021, Nuclear physics)

   The double-beta decay of 82Se to the 0+1excited state of 82Kr has been studied with the NEMO-3 detector using 0.93kg of enriched 82Se measured for 4.75y, corresponding to an exposure of 4.42kg·y. Adedicated analysis to reconstruct the γ-rays has been performed to search for events in the 2e2γchannel. No evidence of a 2νββdecay to the 0+1state has been observed and a limit of T2ν1/2(82Se, 0+gs→0+1) >1.3 ×1021yat 90%CL has been set. Concerning the 0νββdecay to the 0+1state, alimit for this decay has been obtained with T0ν1/2(82Se, 0+gs→0+1) >2.3 ×1022yat 90%CL, independently from the 2νββdecay process. These results are obtained for the first time with a tracko-calo detector, reconstructing every particle in the final state. 

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3. MOST(?) THEORIES HAVE BOREL COMPLETE REDUCTS

   https://doi.org/10.1017/jsl.2021.78  

   LASKOWSKI, MICHAEL C.; ULRICH, DOUGLAS S. (March 2023, The Journal of Symbolic Logic)

   Abstract We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete one-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $$M^{eq}$$ has a Borel complete reduct, and if a theory T is not $$\omega $$ -stable, then the elementary diagram of some countable model of T has a Borel complete reduct. 

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4. Sequencing and Analysis of the Entire Genome of the Mycoparasitic Bioeffector Fungus Trichoderma asperelloides Strain T 203 (Hypocreales)

   https://doi.org/10.1128/mra.00995-21  

   Gortikov, Maggie; Wang, Zheng; Steindorff, Andrei S.; Grigoriev, Igor V.; Druzhinina, Irina S.; Townsend, Jeffrey P.; Yarden, Oded (February 2022, Microbiology Resource Announcements)

   Stajich, Jason E. (Ed.)

   ABSTRACT The filamentous mycoparasitic fungus Trichoderma asperelloides (Hypocreales, Ascomycota, Dikarya) strain T 203 was isolated from soil in Israel by the Ilan Chet group in the 1980s. As it has been the subject of laboratory, greenhouse, and field experiments and has been incorporated into commercial agricultural preparations, its genome has been sequenced and analyzed. 

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5. Invited: IoB: The Vision of the Internet of Bodies

   https://doi.org/10.1109/MWSCAS57524.2023.10405903  

   Datta, Arunashish; Sen, Shreyas (August 2023, IEEE)

   Over six decades of semiconductor technology scaling (Moore's Law) and subsequently system size scaling (Bell's Law) has reduced the size of unit computing to virtually zero. This has led to computing becoming ubiquitous in everything around us, making everyday things smart. Similarly, tremendous progress in communication capacity (Shannon's theorem) has made these smart things connected to the internet and forming the Internet of Things (IoT). Many of these smart, connected devices are present in, on, or around the human body. This subset of IoT around the human body has a distinguishing feature, that it has a common medium, i.e. the body itself. This subset is increasingly becoming popular as the Internet of Bodies (IoB). In this paper, we look into the need and growth of IoB devices, including the technological landscape, current challenges and the future that IoB will enable for empowering humans. 

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