Functions of real variables. Functions of a complex variable.

Mode of access: Internet.

Tables of Bessel-Clifford functions of orders zero and one.

Mode of access: Internet.

Elements of the theory of functions of a complex variable with especial reference to the methods of Riemann,

Translation of Elemente der Theorie der Funktionen einer complexen veränderlichen Grösse.

Theory of functions of a complex variable,

Available on demand as hard copy or computer file from Cornell University Library.

Theory of functions of a complex variable /

Mode of access: Internet.

Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks

Secret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution this is achieved without relying on the hardness of mathematical problems, which might be compromised by improved algorithms or by future quantum computers. State-of-the-art quantum key distribution requires composable security against coherent attacks for a finite number of distributed quantum states as well as robustness against implementation side channels. Here we present an implementation of continuous-variable quantum key distribution satisfying these requirements. Our implementation is based on the distribution of continuous-variable Einstein–Podolsky–Rosen entangled light. It is one-sided device independent, which means the security of the generated key is independent of any memoryfree attacks on the remote detector. Since continuous-variable encoding is compatible with conventional optical communication technology, our work is a step towards practical implementations of quantum key distribution with state-of-the-art security based solely on telecom components.

Novel insights on functions of myotilin/palladin family members

Poikkijuovaisen luuranko- ja sydänlihaksen supistumisyksikkö, sarkomeeri, koostuu tarkoin järjestyneistä aktiini- ja myosiinisäikeistä. Rakenne eroaa muista solutyypeistä, joissa aktiinisäikeistö muovautuu jatkuvasti ja sen järjestyminen säätelee solun muotoa, solujakautumista, soluliikettä ja solunsisäisten organellien kuljetusta. Myotilin, palladin ja myopalladin kuuluvat proteiiniperheeseen, jonka yhteispiirteenä ovat immunoglobuliinin kaltaiset (Igl) domeenit. Proteiinit liittyvät aktiinitukirankaan ja niiden arvellaan toimivan solutukirangan rakenne-elementteinä ja säätelijöinä. Myotilinia ja myopalladinia ilmennetään poikkijuovaisessa lihaksessa. Sen sijaan palladinin eri silmukointimuotoja tavataan monissa kudostyypeissä kuten hermostossa, ja eri muodoilla saattaa olla solutyypistä riippuvia tehtäviä. Poikkijuovaisessa lihaksessa kaikki perheen jäsenet sijaitsevat aktiinisäikeitä yhdistävässä Z-levyssä ja ne sitovat Z-levyn rakenneproteiinia, -aktiniinia. Myotilingeenin pistemutaatiot johtavat periytyviin lihastauteihin, kun taas palladinin mutaatioiden on kuvattu liittyvän periytyvään haimasyöpään ja lisääntyneeseen sydäninfarktin riskiin. Tässä tutkimuksessa selvitettin myotilinin ja pallainin toimintaa. Kokeissa löydettiin uusia palladinin 90-92kDa alatyyppiin sitoutuvia proteiineja. Yksi niistä on aktiinidynamiikkaa säätelevä profilin. Profilinilla on kahdenlaisia tehtäviä; se edesauttaa aktiinisäikeiden muodostumista, mutta se voi myös eristää yksittäisiä aktiinimolekyylejä ja edistää säikeiden hajoamista. Solutasolla palladinin ja profilinin sijainti on yhtenevä runsaasti aktiinia sisältävillä solujen reuna-alueilla. Palladinin ja profilinin sidos on heikko ja hyvin dynaaminen, joka sopii palladinin tehtävään aktiinisäideiden muodostumisen koordinoijana. Toinen palladinin sitoutumiskumppani on aktiinisäikeitä yhteensitova -aktiniini. -Aktiniini liittää solutukirangan solukalvon proteiineihin ja ankkuroi solunsisäisiä viestintämolekyylejä. Sitoutumista välittävä alue on hyvin samankaltainen palladinissa ja myotilinissa. Luurankolihaksen liiallinen toistuva venytys muuttaa Z-levyjen rakennetta ja muotoa. Prosessin aikana syntyy uusia aktiinifilamenttejä sisältäviä tiivistymiä ja lopulta uusia sarkomeereja. Löydöstemme perusteella myotilinin uudelleenjärjestyminen noudattaa aktiinin muutoksia. Tämä viittaa siihen, että myotilin liittää yhteen uudismuodostuvia aktiinisäikeitä ja vakauttaa niitä. Myotilin saattaa myös ankkuroida viesti- tai rakennemolekyylejä, joiden tehtävänä on edesauttaa Z-levyjen uudismuodostusta. Tulostemme perusteella arvelemme, että myotilin toimii Z-levyjen rakenteen vakaajana ja aktiinisäikeiden säätelijänä. Palladinin puute johtaa sikiöaikaiseen kuolemaan hiirillä, mutta myotilinin puutoksella ei ole samanlaisia vaikutuksia. Tuotettujen myotilin poistogeenisten hiirten todetiin syntyvän ja kehittyvän normaalisti eikä niillä esiintynyt rakenteellisia tai toiminnallisia häiriöitä. Toisaalta aiemmissa kokeissa, joissa hiirille on siirretty ihmisen lihastautia aikaansaava myotilingeeni, nähdään samankaltaisia kuin sairailla ihmisillä. Näin ollen muuntunut myotilin näyttä olevan lihaksen toiminnalle haitallisempi kuin myotilinin puute. Myotilinin ja palladinin yhteisvaikutusta selvittääksemme risteytimme myotilin poistegeenisen hiiren ja hiirilinjan, joka ilmentää puutteellisesti palladinin 200 kDa muotoa. Puutteellisesti 200 kDa palladinia ilmentävien hiirten sydänlihaksessa todettiin vähäisiä hienorakenteen muutoksia, mutta risteytetyillä hiirillä tavattiin rakenteellisia ja toiminnallisia muutoksia myös luurankolihaksessa. Tulosten perusteella voidaan todeta, että palladinin 200 kDa muoto säätelee sydänlihassolujen rakennetta. Luurankolihaksessa sen sijaan myotilinilla ja palladinilla näyttäisi olevan päällekkäisiä tehtäviä.

Structural characteristics affecting functions of two actin regulating proteins

Structural biology is a branch of science that concentrates on the relationship between the structure and function of biological macromolecules. The prevalence of a large number of three dimensional structures offers effective tools for bio-scientists to understand the living world. Actin is the most abundant cellular protein and one of its main functions is to produce movement in living cells. Actin forms filaments that are dynamic and which are regulated by a number of different proteins. A class of these regulatory proteins contains actin depolymerizing factor homology (ADF-H) domains. These directly interact with actin through their ADF-H domains. Although ADF-H domains possess very similar three dimensional structures to one another, they vary in their functional properties. One example of this is the ability to bind to actin monomers or filaments. During the work for this thesis two structures of ADF-H domains were solved by nuclear magnetic resonance spectroscopy (NMR). The elucidated structures help us understand the binding specificities of the ADF-H family members.

The Structure and Functions of Hantavirus Nucleocapsid Protein

Hantaviruses, members of the genus Hantavirus in the Bunyaviridae family, are enveloped single-stranded RNA viruses with tri-segmented genome of negative polarity. In humans, hantaviruses cause two diseases, hemorrhagic fever with renal syndrome (HFRS) and hantavirus pulmonary syndrome (HPS), which vary in severity depending on the causative agent. Each hantavirus is carried by a specific rodent host and is transmitted to humans through excreta of infected rodents. The genome of hantaviruses encodes four structural proteins: the nucleocapsid protein (N), the glycoproteins (Gn and Gc), and the polymerase (L) and also the nonstructural protein (NSs). This thesis deals with the functional characterization of hantavirus N protein with regard to its structure. Structural studies of the N protein have progressed slowly and the crystal structure of the whole protein is still not available, therefore biochemical assays coupled with bioinformatical modeling proved essential for studying N protein structure and functions. Presumably, during RNA encapsidation, the N protein first forms intermediate trimers and then oligomers. First, we investigated the role of N-terminal domain in the N protein oligomerization. The results suggested that the N-terminal region of the N protein forms a coiled-coil, in which two antiparallel alpha helices interact via their hydrophobic seams. Hydrophobic residues L4, I11, L18, L25 and V32 in the first helix and L44, V51, L58 and L65 in the second helix were crucial for stabilizing the structure. The results were consistent with the head-to-head, tail-to-tail model for hantavirus N protein trimerization. We demonstrated that an intact coiled-coil structure of the N terminus is crucial for the oligomerization capacity of the N protein. We also added new details to the head-to-head, tail-to-tail model of trimerization by suggesting that the initial step is based on interaction(s) between intact intra-molecular coiled-coils of the monomers. We further analyzed the importance of charged aa residues located within the coiled-coil for the N protein oligomerization. To predict the interacting surfaces of the monomers we used an upgraded in silico model of the coiled-coil domain that was docked into a trimer. Next the predicted target residues were mutated. The results obtained using the mammalian two-hybrid assay suggested that conserved charged aa residues within the coiled-coil make a substantial contribution to the N protein oligomerization. This contribution probably involves the formation of interacting surfaces of the N monomers and also stabilization of the coiled-coil via intramolecular ionic bridging. We proposed that the tips of the coiled-coils are the first to come into direct contact and thus initiate tight packing of the three monomers into a compact structure. This was in agreement with the previous results showing that an increase in ionic strength abolished the interaction between N protein molecules. We also showed that residues having the strongest effect on the N protein oligomerization are not scattered randomly throughout the coiled-coil 3D model structure, but form clusters. Next we found evidence for the hantaviral N protein interaction with the cytoplasmic tail of the glycoprotein Gn. In order to study this interaction we used the GST pull-down assay in combination with mutagenesis technique. The results demonstrated that intact, properly folded zinc fingers of the Gn protein cytoplasmic tail as well as the middle domain of the N protein (that includes aa residues 80 248 and supposedly carries the RNA-binding domain) are essential for the interaction. Since hantaviruses do not have a matrix protein that mediates the packaging of the viral RNA in other negatve stranded viruses (NSRV), hantaviral RNPs should be involved in a direct interaction with the intraviral domains of the envelope-embedded glycoproteins. By showing the N-Gn interaction we provided the evidence for one of the crucial steps in the virus replication at which RNPs are directed to the site of the virus assembly. Finally we started analysis of the N protein RNA-binding region, which is supposedly located in the middle domain of the N protein molecule. We developed a model for the initial step of RNA-binding by the hantaviral N protein. We hypothesized that the hantaviral N protein possesses two secondary structure elements that initiate the RNA encapsidation. The results suggest that amino acid residues (172-176) presumably act as a hook to catch vRNA and that the positively charged interaction surface (aa residues 144-160) enhances the initial N-RNA interacation. In conclusion, we elucidated new functions of hantavirus N protein. Using in silico modeling we predicted the domain structure of the protein and using experimental techniques showed that each domain is responsible for executing certain function(s). We showed that intact N terminal coiled-coil domain is crucial for oligomerization and charged residues located on its surface form a interaction surface for the N monomers. The middle domain is essential for interaction with the cytoplasmic tail of the Gn protein and RNA binding.

Transmembrane domains participate in functions of integral membrane proteins

Integral membrane proteins have one or more transmembrane a-helical domains and carry out a variety of functions such as enzyme catalysis, transport across membranes, transducing signals as receptors of hormones and growth factors, and energy transfer in ATP synthesis. These transmembrane domains are not mere structural units anchoring the protein to the lipid bilayer but seem to-contribute in the overall activity. Recent findings in support of this are described using some typical examples-LDL receptor, growth factor receptor tyrosine kinase, HMG-CoA reductase, F-0-ATPase and adrenergic receptors. The trends in research indicate that these transmembrane domains participate in a variety of ways such as a linker, a transducer or an exchanger in the overall functions of these proteins in transfer of materials, energy and signals.

Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors. The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts. In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin < S-A(2)> of odd or even-numbered sites is discontinuous. There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous < S-A(2)>. Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors. The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts. In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin < S-A(2)> of odd or even-numbered sites is discontinuous. There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous < S-A(2)>. Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Nonequilibrium statistical mechanics of one-dimensional turbulence

The method of statistical mechanics is applied to the study of the one-dimensional model of turbulence proposed in an earlier paper. The closure problem is solved by the variational approach which has been developed for the three-dimensional case, yielding two integral equations for two unknown functions. By solving the two integral equations, the Kolmogorov k−5/3 law is derived and the (one-dimensional) Kolmogorov constant Ko is evaluated, obtaining Ko=0.55, which is in good agreement with the result of numerical experiments on one-dimensional turbulence.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Singing Behavior and Singing Functions of Black-Crested Gibbons (Nomascus concolor jingdongensis) at Mt. Wuliang, Central Yunnan, China

We used data on loud duetted and solo songs collected from one habituated polygynous group of black-crested gibbons (Nomascus concolor jingdongensis) on Mt. Wuliang, Yunnan, to test several hypotheses about the functions of these songs. The major function