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1. Effects of germicidal far-UVC on ozone and particulate matter in a conference room

   https://doi.org/10.1371/journal.pone.0328224  

   Narouei, Farideh Hosseini; Tang, Zifeng; Wang, Shiqi Ian; Hashmi, Raabia H; Welch, David; Sethuraman, Sandhya; Brenner, David J; McNeill, V Faye (August 2025, PLOS One)

   Hemati, Sara (Ed.)

   The application of 222 nm light from KrCl excimer lamps (GUV222 or far-UVC) is a promising approach to reduce the indoor transmission of airborne pathogens, including the SARS-CoV-2 virus. GUV222 inactivates airborne pathogens and is believed to be relatively safe for human skin and eye exposure. However, UV light initiates photochemical reactions which may negatively impact indoor air quality. We conducted a series of experiments to assess the formation of ozone ( ${\text{O}}_3$), and resulting formation of secondary organic aerosols (SOA), induced by commercial far-UVC devices in an office environment (small conference room) with an air exchange rate of $1.3{\text{h}}^{-1}$. We studied scenarios with a single far-UVC lamp, corresponding to the manufacturer’s recommendations for disinfection of a space that size, and with four far-UVC lamps, to test conditions of greater far-UVC fluence. The single lamp did not significantly impact ${\text{O}}_3$or fine particulate matter levels in the room. Consistent with previous studies in the literature, the higher far-UVC fluences lead to increases in ${\text{O}}_3$of 5 to 10 ppb above background, and minor increases in particulate matter (16% ± 10 % increase in particle number count). The use of far-UVC at minimum intensities required for disinfection, and in conjunction with adequate ventilation rates (e.g. ANSI/ASHRAE recommendations), may allow the reduction of airborne pathogen levels while minimizing the formation of air pollutants in furnished indoor environments. 

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2. Identifying topologically associating domains using differential kernels

   https://doi.org/10.1371/journal.pcbi.1012221  

   Maisuradze, Luka; King, Megan C; Surovtsev, Ivan V; Mochrie, Simon_G J; Shattuck, Mark D; O’Hern, Corey S (July 2024, PLOS Computational Biology)

   Dunbrack, Roland L (Ed.)

   Chromatin is a polymer complex of DNA and proteins that regulates gene expression. The three-dimensional (3D) structure and organization of chromatin controls DNA transcription and replication. High-throughput chromatin conformation capture techniques generate Hi-C maps that can provide insight into the 3D structure of chromatin. Hi-C maps can be represented as a symmetric matrix ${\mathcal{A}}_{ij}$, where each element represents the average contact probability or number of contacts between chromatin lociiandj. Previous studies have detected topologically associating domains (TADs), or self-interacting regions in ${\mathcal{A}}_{ij}$within which the contact probability is greater than that outside the region. Many algorithms have been developed to identify TADs within Hi-C maps. However, most TAD identification algorithms are unable to identify nested or overlapping TADs and for a given Hi-C map there is significant variation in the location and number of TADs identified by different methods. We develop a novel method to identify TADs, KerTAD, using a kernel-based technique from computer vision and image processing that is able to accurately identify nested and overlapping TADs. We benchmark this method against state-of-the-art TAD identification methods on both synthetic and experimental data sets. We find that the new method consistently has higher true positive rates (TPR) and lower false discovery rates (FDR) than all tested methods for both synthetic and manually annotated experimental Hi-C maps. The TPR for KerTAD is also largely insensitive to increasing noise and sparsity, in contrast to the other methods. We also find that KerTAD is consistent in the number and size of TADs identified across replicate experimental Hi-C maps for several organisms. Thus, KerTAD will improve automated TAD identification and enable researchers to better correlate changes in TADs to biological phenomena, such as enhancer-promoter interactions and disease states. 

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3. Calderón–Zygmund theory for strongly coupled linear system of nonlocal equations with Hölder-regular coefficient

   https://doi.org/10.1515/acv-2024-0005  

   Mengesha, Tadele; Schikorra, Armin; Seesanea, Adisak; Yeepo, Sasikarn (November 2024, Advances in Calculus of Variations)

   Abstract We extend the Calderón–Zygmund theory for nonlocal equations tostrongly coupled system of linear nonlocal equations ${\mathcal{ℒ}}_A^{s}u=f${\mathcal{L}^{s}_{A}u=f}, where the operator ${\mathcal{ℒ}}_A^s${\mathcal{L}^{s}_{A}}is formally given by ${\mathcal{ℒ}}_A^{s}u={\int }_{{ℝ}^n}\frac{A(x,y)}{{\left|x-y\right|}^{n+2s}}\frac{\left(x-y\right)\otimes \left(x-y\right)}{{\left|x-y\right|}^2}\left(u\left(x\right)-u\left(y\right)\right)𝑑y.$\mathcal{L}^{s}_{A}u=\int_{\mathbb{R}^{n}}\frac{A(x,y)}{|x-y|^{n+2s}}\frac{(x-%y)\otimes(x-y)}{|x-y|^{2}}(u(x)-u(y))\,dy. For $0<s<1${0<1}and $A:{ℝ}^n\times {ℝ}^n\to ℝ${A:\mathbb{R}^{n}\times\mathbb{R}^{n}\to\mathbb{R}}taken to be symmetric and serving asa variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier–Lamé linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if $A(\cdot ,y)${A(\,\cdot\,,y)}is uniformly Holder continuous and ${inf}_{x\in {ℝ}^n}A(x,x)>0${\inf_{x\in\mathbb{R}^{n}}A(x,x)>0}, then for $f\in L_{\mathrm{loc}}^p${f\in L^{p}_{\rm loc}}, for $p\ge 2${p\geq 2}, the solution vector $u\in H_{\mathrm{loc}}^{2s-\delta ,p}${u\in H^{2s-\delta,p}_{\rm loc}}for some $\delta \in (0,s)${\delta\in(0,s)}. 

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4. Multipliers on bi-parameter Haar system Hardy spaces

   https://doi.org/10.1007/s00208-024-02887-9  

   Lechner, R.; Motakis, P.; Müller, P_F_X; Schlumprecht, Th (May 2024, Mathematische Annalen)

   Abstract Let$$(h_I)$$ $\left(h_I\right)$denote the standard Haar system on [0, 1], indexed by$$I\in \mathcal {D}$$ $I\in D$, the set of dyadic intervals and$$h_I\otimes h_J$$ $h_I\otimes h_J$denote the tensor product$$(s,t)\mapsto h_I(s) h_J(t)$$ $(s,t)\mapsto h_I\left(s\right)h_J\left(t\right)$,$$I,J\in \mathcal {D}$$ $I,J\in D$. We consider a class of two-parameter function spaces which are completions of the linear span$$\mathcal {V}(\delta ^2)$$ $V\left({\delta }^2\right)$of$$h_I\otimes h_J$$ $h_I\otimes h_J$,$$I,J\in \mathcal {D}$$ $I,J\in D$. This class contains all the spaces of the formX(Y), whereXandYare either the Lebesgue spaces$$L^p[0,1]$$ $L^p[0,1]$or the Hardy spaces$$H^p[0,1]$$ $H^p[0,1]$,$$1\le p < \infty $$ $1\le p<\infty$. We say that$$D:X(Y)\rightarrow X(Y)$$ $D:X\left(Y\right)\to X\left(Y\right)$is a Haar multiplier if$$D(h_I\otimes h_J) = d_{I,J} h_I\otimes h_J$$ $D(h_I\otimes h_J)=d_{I,J}{h}_I\otimes h_J$, where$$d_{I,J}\in \mathbb {R}$$ $d_{I,J}\in R$, and ask which more elementary operators factor throughD. A decisive role is played by theCapon projection$$\mathcal {C}:\mathcal {V}(\delta ^2)\rightarrow \mathcal {V}(\delta ^2)$$ $C:V\left({\delta }^2\right)\to V\left({\delta }^2\right)$given by$$\mathcal {C} h_I\otimes h_J = h_I\otimes h_J$$ $C{h}_I\otimes h_J=h_I\otimes h_J$if$$|I|\le |J|$$ $\left|I\right|\le \left|J\right|$, and$$\mathcal {C} h_I\otimes h_J = 0$$ $C{h}_I\otimes h_J=0$if$$|I| > |J|$$ $\left|I\right|>\left|J\right|$, as our main result highlights: Given any bounded Haar multiplier$$D:X(Y)\rightarrow X(Y)$$ $D:X\left(Y\right)\to X\left(Y\right)$, there exist$$\lambda ,\mu \in \mathbb {R}$$ $\lambda ,\mu \in R$such that$$\begin{aligned} \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C})\text { approximately 1-projectionally factors through }D, \end{aligned}$$ $\begin{array}{c}\lambda C+\mu (\text{Id}-C)\text{approximately 1-projectionally factors through}D,\end{array}$i.e., for all$$\eta > 0$$ $\eta >0$, there exist bounded operatorsA, Bso thatABis the identity operator$${{\,\textrm{Id}\,}}$$ $\text{Id}$,$$\Vert A\Vert \cdot \Vert B\Vert = 1$$ $\Vert A\Vert ·\Vert B\Vert =1$and$$\Vert \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C}) - ADB\Vert < \eta $$ $\Vert \lambda C+\mu (\text{Id}-C)-ADB\Vert <\eta$. Additionally, if$$\mathcal {C}$$ $C$is unbounded onX(Y), then$$\lambda = \mu $$ $\lambda =\mu$and then$${{\,\textrm{Id}\,}}$$ $\text{Id}$either factors throughDor$${{\,\textrm{Id}\,}}-D$$ $\text{Id}-D$. 

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5. Diffeomorphism groups of prime 3-manifolds

   https://doi.org/10.1515/crelle-2023-0069  

   Bamler, Richard H; Kleiner, Bruce (October 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract LetXbe acompact orientable non-Haken 3-manifold modeled on the Thurston geometry $\mathrm{Nil}${\operatorname{Nil}}. We show that the diffeomorphism group $\mathrm{Diff}\left(X\right)${\operatorname{Diff}(X)}deformation retracts to the isometry group $\mathrm{Isom}\left(X\right)${\operatorname{Isom}(X)}. Combining this with earlier work by many authors, this completes the determination the homotopy type of $\mathrm{Diff}\left(X\right)${\operatorname{Diff}(X)}for any compact, orientable, prime 3-manifoldX. 

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