Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\infty})-functional calculus on these spaces. This provides a new way of proving functional calculus of (A) on the Bochner spaces (L^p(\R^n;X)) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when (X=\C), our approach gives refined (p)-dependent versions of known results.Comment: 28 pages; submitted for publicatio

Pointwise convergence of vector-valued Fourier series

We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f converge to f pointwise almost everywhere. Apparently, all known examples of UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer affirmatively a question of Rubio de Francia on the pointwise convergence of Fourier series of Schatten class valued functions.Comment: 26 page

Tilakohtaiset ilmanvaihto- ja ilmanpuhdistusmenetelmät

Tiivistelmä. Ilmanvaihdon tehtävä on ylläpitää hyvää sisäilman laatua ja tuoda tilaan puhdasta ilmaa. Riittävä ilmanvaihto on edellytys hyvälle sisäilmalle, jolla puolestaan on suuri vaikutus rakennuksen käyttäjien terveyteen, viihtyvyyteen ja suorituskykyyn. Ilmanvaihdon merkitys korostuu erityisesti sellaisissa tiloissa, joissa on useita käyttäjiä päivittäin. Esimerkki tällaisesta tilasta on opetusrakennus. Tutkimukset osoittavat, että riittämätön ilmanvaihto on myös yhteydessä esimerkiksi väsymykseen ja oppimisvaikeuksiin, minkä vuoksi riittävän ilmanvaihdon takaaminen olisi tärkeää opetusrakennuksissa. Tavallisimmat ilmanvaihtomenetelmät ovat painovoimainen ilmanvaihto, koneellinen poisto- sekä koneellinen tulo- ja poistoilmanvaihto. Ilmanvaihtomenetelmät voidaan jakaa tilakohtaisiin ja keskitettyihin menetelmiin. Tilakohtainen ilmanvaihtomenetelmä on ratkaisu, jossa tilan ilmanvaihtokoneen vaikutusalue on juuri kyseinen tila, kun taas keskusilmanvaihdon vaikutusalue on koko rakennus. Ilmanvaihtomenetelmien lisäksi on olemassa ilman puhdistamiseen kehitettyjä menetelmiä. Tutkimuksen tarkoitus on selvittää, millaisia tilakohtaisia ilmanvaihto- ja ilmanpuhdistusmenetelmiä on olemassa, ja arvioida niiden soveltuvuutta opetusrakennuksiin. Tutkimus on toteutettu kirjallisuusselvityksenä, ja siinä on esitelty tavallisimpia ilmanvaihtomenetelmiä ja niiden tehostamistapoja, joitakin tilakohtaisia menetelmiä sekä ilmanpuhdistustekniikoita.Room-based ventilation and air purification techniques. Abstract. The purpose of ventilation is to maintain good indoor air quality and supply fresh air to the indoor space. Adequate ventilation is the requirement for good indoor air which has a great effect on the health, comfort and efficiency of the occupants in the building. Ventilation is more important in buildings with many daily occupants. An example of this is an educational building. According to studies, insufficient ventilation is linked to tiredness and learning difficulties. On that basis, guaranteeing sufficient ventilation in educational buildings is important. The most conventional ventilation techniques are natural ventilation, mechanical exhaust and mechanical supply and exhaust ventilation. Ventilation techniques can be divided into decentralized and centralized methods. Decentralized ventilation system has a coverage area of only the exact room whereas centralized ventilation system affects around the whole building. In addition to ventilation techniques, there are methods developed for air purification. The aim of this thesis is to investigate decentralized ventilation and air purification techniques existing and assess their applicability in educational buildings. This thesis is carried out as a literature survey and it introduces the most conventional ventilation techniques and how to enhance them, some decentralized ventilation techniques, and air purification methods

webGQT: A Shiny Server for Genotype Query Tools for Model-Based Variant Filtering

Genotype Query Tools (GQT) were developed to discover disease-causing variations from billions of genotypes and millions of genomes, processes data at substantially higher speed over other existing methods. While GQT has been available to a wide audience as command-line software, the difficulty of constructing queries among non-IT or non-bioinformatics researchers has limited its applicability. To overcome this limitation, we developed webGQT, an easy-to-use tool with a graphical user interface. With pre-built queries across three modules, webGQT allows for pedigree analysis, case-control studies, and population frequency studies. As a package, webGQT allows researchers with less or no applied bioinformatics/IT experience to mine potential disease-causing variants from billions. Results webGQT offers a flexible and easy-to-use interface for model-based candidate variant filtering for Mendelian diseases from thousands to millions of genomes at a reduced computation time. Additionally, webGQT provides adjustable parameters to reduce false positives and rescue missing genotypes across all modules. Using a case study, we demonstrate the applicability of webGQT to query non-human genomes. In addition, we demonstrate the scalability of webGQT on large data sets by implementing complex population-specific queries on the 1000 Genomes Project Phase 3 data set, which includes 8.4 billion variants from 2504 individuals across 26 different populations. Furthermore, webGQT supports filtering single-nucleotide variants, short insertions/deletions, copy number or any other variant genotypes supported by the VCF specification. Our results show that webGQT can be used as an online web service, or deployed on personal computers or local servers within research groups. Availability webGQT is made available to the users in three forms: 1) as a webserver available at https://vm1138.kaj.pouta.csc.fi/webgqt/, 2) as an R package to install on personal computers, and 3) as part of the same R package to configure on the user's own servers. The application is available for installation at https://github.com/arumds/webgqt.Peer reviewe

Maximal regularity for non-autonomous equations with measurable dependence on time

In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the $L^p$-boundedness of a class of vector-valued singular integrals which does not rely on H\"ormander conditions in the time variable. This is then used to develop an abstract operator-theoretic approach to maximal regularity. The results are applied to the case of $m$-th order elliptic operators $A$ with time and space-dependent coefficients. Here the highest order coefficients are assumed to be measurable in time and continuous in the space variables. This results in an $L^p(L^q)$-theory for such equations for $p,q\in (1, \infty)$. In the final section we extend a well-posedness result for quasilinear equations to the time-dependent setting. Here we give an example of a nonlinear parabolic PDE to which the result can be applied.Comment: Application to a quasilinear equation added. Accepted for publication in Potential Analysi

Construction of Chimeric Dual-Chain Avidin by Tandem Fusion of the Related Avidins

BACKGROUND: Avidin is a chicken egg-white protein with high affinity to vitamin H, also known as D-biotin. Many applications in life science research are based on this strong interaction. Avidin is a homotetrameric protein, which promotes its modification to symmetrical entities. Dual-chain avidin, a genetically engineered avidin form, has two circularly permuted chicken avidin monomers that are tandem-fused into one polypeptide chain. This form of avidin enables independent modification of the two domains, including the two biotin-binding pockets; however, decreased yields in protein production, compared to wt avidin, and complicated genetic manipulation of two highly similar DNA sequences in the tandem gene have limited the use of dual-chain avidin in biotechnological applications. PRINCIPAL FINDINGS: To overcome challenges associated with the original dual-chain avidin, we developed chimeric dual-chain avidin, which is a tandem fusion of avidin and avidin-related protein 4 (AVR4), another member of the chicken avidin gene family. We observed an increase in protein production and better thermal stability, compared with the original dual-chain avidin. Additionally, PCR amplification of the hybrid gene was more efficient, thus enabling more convenient and straightforward modification of the dual-chain avidin. When studied closer, the generated chimeric dual-chain avidin showed biphasic biotin dissociation. SIGNIFICANCE: The improved dual-chain avidin introduced here increases its potential for future applications. This molecule offers a valuable base for developing bi-functional avidin tools for bioseparation, carrier proteins, and nanoscale adapters. Additionally, this strategy could be helpful when generating hetero-oligomers from other oligomeric proteins with high structural similarity

The ℓs\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665

Bifunctional Avidin with Covalently Modifiable Ligand Binding Site

The extensive use of avidin and streptavidin in life sciences originates from the extraordinary tight biotin-binding affinity of these tetrameric proteins. Numerous studies have been performed to modify the biotin-binding affinity of (strept)avidin to improve the existing applications. Even so, (strept)avidin greatly favours its natural ligand, biotin. Here we engineered the biotin-binding pocket of avidin with a single point mutation S16C and thus introduced a chemically active thiol group, which could be covalently coupled with thiol-reactive molecules. This approach was applied to the previously reported bivalent dual chain avidin by modifying one binding site while preserving the other one intact. Maleimide was then coupled to the modified binding site resulting in a decrease in biotin affinity. Furthermore, we showed that this thiol could be covalently coupled to other maleimide derivatives, for instance fluorescent labels, allowing intratetrameric FRET. The bifunctional avidins described here provide improved and novel tools for applications such as the biofunctionalization of surfaces