Interactive Coding Resilient to an Unknown Number of Erasures

We consider distributed computations between two parties carried out over a noisy channel that may erase messages. Following a noise model proposed by Dani et al. (2018), the noise level observed by the parties during the computation in our setting is arbitrary and a priori unknown to the parties. We develop interactive coding schemes that adapt to the actual level of noise and correctly execute any two-party computation. Namely, in case the channel erases T transmissions, the coding scheme will take N+2T transmissions using an alphabet of size 4 (alternatively, using 2N+4T transmissions over a binary channel) to correctly simulate any binary protocol that takes N transmissions assuming a noiseless channel. We can further reduce the communication to N+T by relaxing the communication model and allowing parties to remain silent rather than forcing them to communicate in every round of the coding scheme. Our coding schemes are efficient, deterministic, have linear overhead both in their communication and round complexity, and succeed (with probability 1) regardless of the number of erasures T

Probing gas-phase radical reactions and modeling the detection of aerosol precursors using computational and experimental methods

Understanding the gas-phase chemistry of secondary organic aerosol (SOA) formation is critical for accurate estimation of the effect of these aerosol on Earth's radiative balance. Additionally, the direct detection of the precursor molecules involved in these chemical reactions at atmospheric pressure without pre-treatment is valuable. In this work, computational and experimental methods are employed to 1) elucidate the thermodynamics and the mechanisms of selected key radical-radical reactions in the atmosphere and 2) investigate the efficiency of some of the chemical ionization mass spectrometry methods in detecting the atmospherically relevant acids and precursor compounds involved in the formation of SOA. The main oxygen containing radical species in our atmosphere, and also the key focus of this study, are hydroxy (OH), hydroperoxy (HO2), alkoxy (RO) and peroxy (RO2) radicals. Our computational study on the favorability of the radical recycling product channels of RO2 + HO2 and RO2 + RO2 reactions (RO + OH + O2 and RO + RO + O2, respectively) for RO2s derived from the oxidation of a set of the highest globally emitted monoterpenes showed that the two reactions were thermodynamically favorable for all the studied systems, and that for some of them, especially the O3 oxidized systems, the rate-limiting transition state energies can be low enough to render the reactions competitive in atmospheric conditions. Peroxy radical reactions with the atmospheric oxidant OH and alkoxy radicals RO were found to first form a trioxide adduct (ROOOH and ROOOR, respectively). While the former rapidly decompose to RO + HO2 and R(O)OH + O2 products for the model β-oxo and acetyl RO2 systems, respectively, the ROOOR adducts from the latter can have lifetimes in the range of 10 - 100 s (for the homo and hetero alkyl and β-oxo systems). If the reacting RO2 and RO radicals are sufficiently large and oxidized, the product adducts can directly be involved in SOA formation. The modeling of iodide-based chemical ionization mass spectrometer (iodide-CIMS) using computational methods showed that relatively low-level computational theory can produce reasonable correlation between molecule•I- cluster binding enthalpies and iodide-CIMS instrumental sensitivities. While some outliers were observed (lower than expected binding enthalpies for clusters that were detected at the maximum possible sensitivity of the instrument, for example), the method outlined in our study can be a quick indicator of the detectibility of an analyte by an iodide-CIMS. Additionally, the direct detection of the HO2 radical experimentally using an iodide-CIMS was demonstrated. The comparison of iodide- and nitrate-CIMS spectra for a cyclohexene ozonolysis experiment showed that the iodide-CIMS method was capable of detecting the less oxidized (oxygen:carbon O/C ratio of 0.5 - 0.66) molecules more efficiently than nitrate-CIMS. Higher oxidized molecules (O/C ratio 1 - 1.5) were detected equally well by both methods. Finally, the use of a new chemical ionization inlet (Multi-scheme chemical IONization inlet, MION, Karsa Ltd, Helsinki, Finland), which is capable of switching between two different reagent ions, bromide and nitrate, in 1 s timescales was demonstrated and used to detect the ozonolysis products of cyclohexene and α-pinene. The successful demonstration of the MION inlet opens up the possibility to use multiple CIMS methods concurrently and detect a widest possible range of volatile organic compound (VOC) oxidation products.Jotta voitaisiin arvioida sekundääristen orgaanisten aerosolihiukkasten (SOA) vaikutusta Maapallon säteilytaseeseen, meidän tulee ymmärtää niiden muodostukseen johtavaa kaasufaasin kemiaa. Lisäksi näiden kemiallisten reaktioiden lähtöainemolekyylien suora havaitseminen vallitsevassa ilmanpaineessa ilman esikäsittelyä on arvokasta. Tässä tutkimuksessa on käytetty laskennallisia- ja kokeellisia menetelmiä selvittämään 1) valittujen ilmakehässä merkittävien radikaali-radikaali reaktioiden termodynamiikkaa ja reaktiomekanismeja, ja 2) tiettyjen kemialliseen ionisaation perustuvien massaspektrometriamenetelmien (CIMS) tehokkuutta havaitsemaan SOA:n muodostumisessa oleellisia happoja ja lähtöaineyhdisteitä. Pääasialliset happea sisältävät ilmakehän radikaalit, jotka ovat myös tämän tutkimuksen painopisteet, ovat hydroksi- (OH), hydroperoksi- (HO2), alkoksi- (RO) ja peroksiradikaalit (RO2). Laskennallisessa tutkimuksessamme selvisi, että RO2 + HO2 ja RO2 + RO2 reaktioiden radikaaleja kierrättävät tuotekanavat (RO + O2 + OH ja RO + O2 + RO2) ovat termodynaamisesti suotuisia kaikille tutkituille peroksiradikaaleille, jotka ovat peräisin jostakin ilmakehässä eniten esiintyvien monoterpeenien hapetusreaktioista. Lisäksi useilla näistä tutkituista systeemeistä, etenkin otsonihapetuksessa muodostuvilla peroksiradikaaleilla, reaktion nopeuden määrittävä reaktiovaiheen siirtymätilan energia voi olla niin alhainen, että reaktio on tärkeä myös ilmakehän olosuhteissa. Peroksiradikaalien huomattiin reagoivan OH-radikaalin (ilmakehän tärkeimmän hapettimen) sekä myös alkoksiradikaalien kanssa, muodostaen trioksidiadduktin (ROOOH ja ROOOR). Ensiksimainittu hajoaa nopeasti RO + HO2 ja R(O)OH + O2 tuotteiksi mallinnetuilla β-okso- ja asetyyli-RO2 systeemeillä, mutta jälkimmäisessä tapauksessa muodostuvien ROOOR adduktien elinajat voivat olla jopa 10-100 sekuntia (homo- ja heteroalkyyli- ja β-oksosysteemeillä). Jodidi-ionisaatio massaspektrometrin (jodidi-CIMS) laskennallisessa mallintamisessa huomattiin, että melko alhaisellakin laskennan teoriatasolla voidaan saavuttaa järkevä korrelaatio molekyyli•I- -klusterin sidosentalpian ja jodidi-CIMS:n mittausherkkyyden välille. Muutamista poikkeavuuksista huolimatta (esimerkiksi odotettua alhaisemmat sidosentalpiat klustereille, jotka havaittiin mittalaitteen maksimiherkkyydellä) tutkimuksessamme esitettyä menetelmää voidaan käyttää nopeana kohteen havaittavuuden osoittimena jodidi-CIMS menetelmällä. Lisäksi tutkimuksessa näytettiin HO2-radikaalin suora havainnointi käyttämällä jodidi-CIMS menetelmää. Jodidi- ja nitraatti-CIMS –menetelmällä mitatut syklohekseenin otsonolyysikokeiden tulokset osoittivat, että jodidi-CIMS –menetelmällä voitiin havaita vähemmän hapettuneita molekyylejä (happi:hiili O/C suhdeluku 0.5 – 0.66) nitraatti-CIMS –menetelmää tehokkaammin. Enemmän hapettuneita molekyylejä (O/C suhdeluku 1 - 1.5) voitiin mitata kummallakin menetelmällä yhtä hyvin. Lopuksi, uuden kemiallisen ionisaation inletti (Multi-scheme chemical IONization inlet, MION, Karsa Ltd, Helsinki, Finland) käyttöönotto mahdollisti nopean vaihdon kahden eri reagenssi-ionin, bromidin ja nitraatin välillä sekunnin aikaskaalassa, mitä hyödynnettiin sykloheksaanin ja α-pineenin otsonolyysituotteiden havainnoinnissa. MION-läpiviennin hyödyllisyyden onnistunut havainnollistus avaa mahdollisuuden havaita laajimman mahdollisimman kirjon haihtuvien orgaanisten yhdisteiden (volatile organic compounds, VOC) hapettumistuotteita käyttämällä useita CIMS-menetelmiä rinnakkain

Gas refractometry using hollow core photonic bandgap fiber

Over the last two decades, much research has been carried out on sensors based on photonic crystal fibers. Their unique structure comprising of a periodic array of air holes running along their length provides optical properties that are highly suited for refractometer sensors. The thesis presents a fiber-optic interferometric gas refractometer which is capable of spectrally resolved measurements of both real and imaginary parts of the complex refractive index. The refractometer is based on an earlier fiber based Mach-Zehnder-type refractometer design that was used to determine the refractive index of air-acetylene mixture. The aim of the thesis was to improve the device design in order to ascertain the refractive index of pure acetylene. The device adopts a hollow-core photonic bandgap fiber as both a sample cell and a waveguide. This provides the best overlap between probing light and the analyte. In addition, it requires a very small volume of the analyte due to the small dimensions of the fiber, and the sample cell can be made long while keeping the device compact. The complex refractive index of approx. 96 percent pure acetylene was measured within the optical C band where the gas has a number of pronounced resonance frequencies. The measurement was repeated in approx. 500 Pa air and was used as reference for interpreting the results for acetylene. The optical absorption and refractive index change of acetylene over the resonance frequencies were analyzed and its absorption coefficient and refractive index were calculated. The demonstrated capability of this device to measure the real and imaginary parts of the refractive index of an analyte has important implications in the sensor industry

Character sums over elements of extensions of finite fields with restricted coordinates

We obtain nontrivial bounds for character sums with multiplicative and additive characters over finite fields over elements with restricted coordinate expansion. In particular, we obtain a nontrivial estimate for such a sum over a finite field analogue of the Cantor set.

Thermal transport in sodium boiling flows for concentrating solar thermal applications

Understanding heat and mass transfer phenomena in nucleate boiling of liquid metals such as sodium is an emerging field of study, in particular for the development of next generation concentrating solar thermal power plants with boiling sodium as the heat transfer fluid. The research presented in this doctoral project is focused on advancing the knowledge of sodium boiling by developing comprehensive physics-based bubble growth models. Such models can highlight the governing heat transfer and hydrodynamic phenomena dominating the bubble growth process in sodium, thus aiding the development of efficient sodium boiling systems. In the first part of this work, two numerical heat transfer models are developed with the aim of quantifying the influence of heat transfer mechanisms on the growth of a bubble in sodium pool boiling. In the first model the governing mass, momentum and energy conservation equations are solved to compute the evaporative heat flux from a region where the liquid-vapour interface of the bubble meets the wall, referred to as the contact line region. The model accounts for the influence of an electron pressure component on the evaporation of the fluid film in the contact line region in sodium. The results show that for the same wall superheat, the heat flux from sodium is six times larger compared to a high Prandtl number fluid, here FC-72, due to the high thermal conductivity of the liquid metal. The second numerical model predicts the growth rate of a sodium bubble based on the heat transferred from a microlayer (which is a thin layer of fluid formed underneath a bubble), the thermal boundary layer, and the bulk liquid surrounding the bubble. The model accounts for the variation in the wall temperature below the bubble as the liquid in the microlayer and the thermal boundary layer evaporates. Predictions from the model for a bubble growing with a constant contact angle indicate that the microlayer evaporation is the dominant heat transfer mechanism during the initial phase of bubble growth after nucleation. In addition, a parametric study conducted to study the effect of wall superheat indicated that the larger the wall superheat, the larger is the growth rate and radius of a sodium bubble. The development of a comprehensive mechanistic bubble growth model accounting for the variation in the contact angle and the shape of a bubble is pursued next. The heat transfer model that was developed based on the evaporation of the microlayer in the first part of this project is coupled to a force and a contact angle sub-model to study the complete bubble growth process from nucleation to departure in pool boiling. A novel methodology is presented to approximate the balloon-like shape of a bubble prior to departure as a truncated sphere atop a conical bottleneck. The model is extensively verified and validated against high-fidelity CFD simulations and experimental data on pool boiling of water and methanol from literature, and shows good agreement. The validated mechanistic model is then used to simulate the bubble growth process in sodium and to investigate the effects of wall superheat, contact angle rate, bulk liquid temperature and the accommodation coefficient on the bubble growth and departure characteristics. It is found that a sodium bubble is typically large with departure radius on the order of a few centimetres. In addition, it is observed that smaller the wall superheat, the greater is the tendency of the bubble to have a balloon-like shape at departure

Reaction between Peroxy and Alkoxy Radicals Can Form Stable Adducts

Peroxy (RO2) and alkoxy (RO) radicals are prototypical intermediates in any hydrocarbon oxidation. In this work, we use computational methods to (1) study the mechanism and kinetics of the RO2 + OH reaction for previously unexplored “R” structures (R = CH(O)CH2 and R = CH3C(O)) and (2) investigate a hitherto unaccounted channel of molecular growth, R′O2 + RO. On the singlet surface, these reactions rapidly form ROOOH and R′OOOR adducts, respectively. The former decomposes to RO + HO2 and R(O)OH + O2 products, while the main decomposition channel for the latter is back to the reactant radicals. Decomposition rates of R′OOOR adducts varied between 103 and 0.015 s–1 at 298 K and 1 atm. The most long-lived R′OOOR adducts likely account for some fraction of the elemental compositions detected in the atmosphere that are commonly assigned to stable covalently bound dimers.Peer reviewe

Shortest k-Disjoint Paths via Determinants

The well-known $k$-disjoint path problem ($k$-DPP) asks for pairwise vertex-disjoint paths between $k$ specified pairs of vertices $(s_i, t_i)$ in a given graph, if they exist. The decision version of the shortest $k$-DPP asks for the length of the shortest (in terms of total length) such paths. Similarly the search and counting versions ask for one such and the number of such shortest set of paths, respectively. We restrict attention to the shortest $k$-DPP instances on undirected planar graphs where all sources and sinks lie on a single face or on a pair of faces. We provide efficient sequential and parallel algorithms for the search versions of the problem answering one of the main open questions raised by Colin de Verdiere and Schrijver for the general one-face problem. We do so by providing a randomised $NC^2$ algorithm along with an $O(n^{\omega})$ time randomised sequential algorithm. We also obtain deterministic algorithms with similar resource bounds for the counting and search versions. In contrast, previously, only the sequential complexity of decision and search versions of the "well-ordered" case has been studied. For the one-face case, sequential versions of our routines have better running times for constantly many terminals. In addition, the earlier best known sequential algorithms (e.g. Borradaile et al.) were randomised while ours are also deterministic. The algorithms are based on a bijection between a shortest $k$-tuple of disjoint paths in the given graph and cycle covers in a related digraph. This allows us to non-trivially modify established techniques relating counting cycle covers to the determinant. We further need to do a controlled inclusion-exclusion to produce a polynomial sum of determinants such that all "bad" cycle covers cancel out in the sum allowing us to count "good" cycle covers.Comment: 17 pages, 6 figure

Multi-scheme chemical ionization inlet (MION) for fast switching of reagent ion chemistry in atmospheric pressure chemical ionization mass spectrometry (CIMS) applications

A novel chemical ionization inlet named the Multi-scheme chemical IONization inlet (MION), Karsa Ltd., Helsinki, Finland) capable of fast switching between multiple reagent ion schemes is presented, and its performance is demonstrated by measuring several known oxidation products from much-studied cyclohexene and alpha-pinene ozonolysis systems by applying consecutive bromide (Br-) and nitrate (NO3-) chemical ionization. Experiments were performed in flow tube reactors under atmospheric pressure and room temperature (22 degrees C) utilizing an atmospheric pressure interface time-of-flight mass spectrometer (APi-ToF-MS, Tofwerk Ltd., Thun, Switzerland) as the detector. The application of complementary ion modes in probing the same steady-state reaction mixture enabled a far more complete picture of the detailed autoxidation process; the HO2 radical and the least-oxidized reaction products were retrieved with Br- ionization, whereas the highest-oxidized reaction products were detected in the NO3- mode, directly providing information on the first steps and on the ultimate endpoint of oxidation, respectively. While chemical ionization inlets with multiple reagent ion capabilities have been reported previously, an application in which the charging of the sample occurs at atmospheric pressure with practically no sample pretreatment, and with the potential to switch the reagent ion scheme within a second timescale, has not been introduced previously. Also, the ability of bromide ionization todetect highly oxygenated organic molecules (HOM) from atmospheric autoxidation reactions has not been demonstrated prior to this investigation.Peer reviewe