Geometry of Banach spaces with an octahedral norm

We discuss the geometry of Banach spaces whose norm is octahedral or, more generally, locally or weakly octahedral. Our main results characterize these spaces in terms of covering of the unit ball

Majorana qubit decoherence by quasiparticle poisoning

We consider the problem of quasiparticle poisoning in a nanowire-based realization of a Majorana qubit, where a spin-orbit-coupled semiconducting wire is placed on top of a (bulk) superconductor. By making use of recent experimental data exhibiting evidence of a low-temperature residual non-equilibrium quasiparticle population in superconductors, we show by means of analytical and numerical calculations that the dephasing time due to the tunneling of quasiparticles into the nanowire may be problematically short to allow for qubit manipulation.Comment: 10 pages, 7 figure

Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm

We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under 1-sums, i.e., the direct sum of two spaces with the diametral strong diameter 2 property equipped with the 1-norm has again this property.Comment: 4 page

Uurimus signaalide töötlemisest S. cerevisiae tsükliinsõltuva kinaasi inhibiitori Sic1 mitmikfosforüülitavatel radedel

Väitekirja elektrooniline versioon ei sisalda publikatsiooneRakkude jagunemine käivitatakse DNA-sünteesi algatamisega. See toimub aga alles siis, kui rakud on valmis kogu järgneva raku jagunemise tsükli peatumata läbi tegema. Rakkude jagunemise käivitavad ja kogu edasist protsessi juhivad tsükliinsõltuvad kinaasid (Tsk). Need on valgud, mis kontrollivad teiste valkude asukohta, eluiga või aktiivsust neile foforhappejääke lisades. Rakutsükli etapid käivitatakse erinevate kindla spetsiifikaga Tsk komplekside poolt. Rakkude jagunemist kontrolliva mehhanismi uurimiseks kasutatakse laialdaselt mudelorganismina pagaripärmi S. cerevisiae, mille jagunemise tsükli üldine ülesehitus meenutab lihtsustatult inimese rakkudes toimuvat. Pärmirakkude kasvufaasi (G1) käigus rakud akumuleerivad mitmeid Tsk´se. Osad TSK´d on koheselt aktiivsed ning asuvad oma sihtmärke fosforüülima, valmistades rakku S-faasiks ette. Osad Tsk´d, mille aktiivust läheb tarvis alles S-faasi käivitamiseks ja läbiviimiseks, toodetakse inhibeeritud olekus. Nende aktiivsus on blokeeritud valgu Sic1 poolt. Kogu S-faasi käivitamiseks vajalik Tsk toodetakse kasvufaasis tihedalt kompleksis Sic1 valguga, et vältida juhuslikku S-faasi käivitava aktiivsuse lekkimist enne õiget aega. S-faasi käivitamiseks tuleb Sic1 lagundada, mis vabastab S-faasi spetsiifilise Tsk aktiivsuse. Sic1 ise on Tsk´de sihtmärk ja sisaldab palju fosforüülimiseks sobivaid aminohappeid. Nende fosforüülimine suunab Sic1 lagundamisele, mis määrab S-faasi käivitamise ajastuse ja dünaamika ning on üheks keskseks osaks rakutsükli reguleerimise mehhanismis. Varasemalt ei olnud teada, millised kinaasid millise dünaamikaga Sic1 fosforüülivad ning seetõttu puudus detailne mudel, kuidas seeläbi saavutatakse kontroll raku jagunemise käivitamise üle. Käesoleva uurimistöö käigus selgitati välja, mis kinaasid ja millise dünaamikaga Sic1 valku fosforüülivad. Sellega avastastasid uurimistöö autorid kvantitatiivse S-faasi käivitamise kontrollmehhanismi, mis reguleerib minutilise täpsusega rakkude jagunemise algust ja tagab selle käivitamiseks piisava koguse Tsk aktiivsust. Selle mehhanismi keskne osa – mitmiksfosforüülitav valk Sic1 – toimib mikrokiibina, mis salvestab kasvufaasis olevas rakus jagunemist toetavad ja takistavad signaalid. Neid signaale tõlgendatakse S-faasi käivitamise ajaks ja dünaamikaks S-faasi käivitava Tsk poolt Sic1 sidumise käigus.The cell division cycle is initiated with the onset of S-phase where cells replicate their DNA. The DNA-replication is triggered only when cells are sufficiently prepared to conduct following events of cellular division without stopping. The cell division is triggered and following events conducted by cyclin-dependent kinase holoenzymes (Cdk). These multi-component proteins that phosphorylate others to control the localization, lifespan or activity of target proteins. For proper initiation of each cell cycle phase specific Cdk holoenzyme complex is activated. To study the control mechanism of the cell cycle the S. cerevisiae is widely used as a model due to its simplicity and similarity to human cells. During the growth phase (G1) of yeast cells they accumulate different Cdk´s. Some of them are instantly active and begin to phosphorylate their targets preparing cell for the S-phase. Others Cdks necessary to trigger and conduct upcoming S-phase are accumulated in inhibited form. The activity is inhibited by Sic1 protein. All the Cdk necessary for S-phase initiation is accumulated in tight complex with Sic1 protein to avoid early leakage of S-phase kinase activity. To initiate S-phase the Sic1 protein must be degraded that in turn release S-phase specific Cdk activity. Sic1 itself is a Cdk target and contains multiple phosphorylation sites. For Sic1 destruction its phosphorylation from multiple sites is necessary. The phosphorylation of Sic1 determines the timing and dynamics of S-phase onset and has therefore central importance in cell cycle regulating mechanism. Limited knowledge about phosphorylation dynamics of Sic1 shielded quantitative regulatory mechanism of S-phase initiation and left the question of how is the onset of S-phase controlled unsolved. This study unveiled missing details of Sic1 phosphorylation inputs and their quantitative dynamics. Authors discovered a regulatory mechanism, how yeast cells regulate the timing and dynamics of S-phase onset. The central part of this discovery is that Sic1 works as a microprocessor that records growth phase signals and enables these to be transformed to S-phase initiation parameters via S-phase Cdks

Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums

We prove that, if Banach spaces $X$ and $Y$ are $\delta$-average rough, then their direct sum with respect to an absolute norm $N$ is $\delta/N(1,1)$-average rough. In particular, for octahedral $X$ and $Y$ and for $p$ in $(1,\infty)$ the space $X\oplus_p Y$ is $2^{1-1/p}$-average rough, which is in general optimal. Another consequence is that for any $\delta$ in $(1,2]$ there is a Banach space which is exactly $\delta$-average rough. We give a complete characterization when an absolute sum of two Banach spaces is octahedral or has the strong diameter 2 property. However, among all of the absolute sums, the diametral strong diameter 2 property is stable only for 1- and $\infty$-sums.Comment: 19 pages, 2 figure

Decoherence of Majorana qubits by noisy gates

We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled by non-interacting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate temperature. Based on this result, we provide simple rules for gate geometries and materials optimized for reducing the negative effect of thermal charge fluctuations on the gate

Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions

Motivated by recent experiments searching for Majorana fermions (MFs) in hybrid semiconducting-superconducting nanostructures, we consider a realistic tight-binding model and analyze its transport behavior numerically. In particular, we take into account the presence of a superconducting contact, used in real experiments to extract the current, which is usually not included in theoretical calculations. We show that important features emerge that are absent in simpler models, such as the shift in energy of the proximity gap signal, and the enhanced visibility of the topological gap for increased spin-orbit interaction. We find oscillations of the zero bias peak as a function of the magnetic field and study them analytically. We argue that many of the experimentally observed features hint at an actual spin-orbit interaction larger than the one typically assumed. However, even taking into account all the known ingredients of the experiments and exploring many parameter regimes for MFs, we are not able to reach full agreement with the reported data. Thus, a different physical origin for the observed zero-bias peak cannot be excluded.Comment: 7 pages, 7 figures; Published versio