In search of dark horses: Affinity maturation of phage-displayed ligands

Summary Most combinatorial libraries are sparse in that only a tiny fraction of the relevant class of compounds is represented. This sparseness can be compensated in some measure by alternating rounds of selection with rounds of mutagenesis. Thus, clones are selected from the initial library by some criterion of fitness, such as affinity for a particular receptor. The selected clones are then mutagenized to generate a mutant library, which serves as input to the next round of selection, and so on. If the first round of selection is too stringent, rejecting all but the very fittest clone in the initial library (the initial champion), we might miss dark horses; clones in the initial library that are inferior to the initial champion, yet can be mutated to even higher fitness than can that champion. A more thoughtful strategy is to alternate nonstringent selection with simultaneous mutagenesis of many selected clones en masse.     

Analysis of signal-to-noise ratio of the laser Doppler velocimeter

The signal-to-shot-noise ratio of the photocurrent of a laser Doppler anemometer is calculated as a function of the parameters which describe the system. It is found that the S/N is generally a growing function of receiver area, that few large particles are better than many small ones, and that generally the fringe or differential mode configuration is equal to, or better than, the reference beam mode.     

The many faces of a character

We prove an identity between three infinite families of polynomials which are defined in terms of bosonic, fermionic, and one-dimensional configuration sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-ansatz solution of the Heisenberg spin chain.     

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On quantum holonomy for mixed states

There is a natural connection and parallel transport on the Hilbert tensor product (or, equivalently, the space of Hilbert-Schmidt operators), the elements of which represent density matrices in up to unitary operators. We postulate a time evolution equation, which leads to this connection after extracting a proper dynamical unitary phase. As an example, we compute the holonomy of a loop of temperature states for the spin in a rotating magnetic field.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P5588.     

Asymptotic Completeness for Compton Scattering

Scattering in a model of a massive quantum-mechanical particle, an electron, interacting with massless, relativistic bosons, photons, is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of photons by the electron; but electron-positron pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed electron is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one–electron states with propagation estimates for the electron and the photons.Dedicated to Freeman Dyson on the occasion of his 80th birthdayWork partially supported by U.S. National Science Foundation grant DMS 01-00160.Acknowledgement. We thank V. Bach for his hospitality at the University of Mainz, where part of this work was done, and we are indebted to Gian Michele Graf for pointing out a serious gap in an earlier version of this paper. We also thank one of the referees for pointing out many typos and some small errors.     

‘In’ and ‘out’ vertex operators in a class of UV-finite nonlinear σ-models

In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions.     

Perturbed periodic Hamiltonians: Essential Spectrum and exponential decay of eigenfunctions

Spectral properties of – +V(x), whereV(x) lies in a neighbourhood of the periodic case and describes various models of disorder, are studied. We prove the exponential decay of generalized eigenfunctions corresponding to energies in the resolvent set of the unperturbed periodic Hamiltonian, as well as the stability of the essential spectrum for the dislocation disorder in two dimensions.     

On the relation between weak and strong invariance of differential equations

Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie groupG. In particular, it is shown that if a strongly invariant equation exists, then all weakly invariant equations differ from it only by an arbitrary multiplicative factor. If no strongly invariant equation exists, then cohomology theory can be used to simplify the search for weakly invariant equations.     

Synthesis and characterization of cyclic pseudopeptide libraries containing thiomethylene and thiomethylene-sulfoxide amide bond surrogates

We describe the first examples of a series of cyclic pseudopeptide libraries that have been prepared in a systematic approach in order to facilitate both synthesis and subsequent deconvolution attempts. Our synthetic strategy involved the attachment of a trifunctional amino acid (Asp, Asn or Glu) to a polystyrene resin via its side chain, and stepwise chain elongation using either protected amino acids or a pseudodipeptide building block. Head to tail cyclic peptides were formed by removal of the temporary N- and C-terminal protecting groups followed by ring closure by amide formation. Cyclization of the hexa, hepta, and octapseudopeptides on the resin avoided dimer formation, as monitored by mass spectrometry. We utilized a psi-scan approach in which a second fixed position was serially addressed by stepping a dipeptide surrogate, Pro[CH₂S]Gly around the rings to generate a group of cyclic pseudopeptide sub-libraries. Oxidation of [CH₂S] to [CH₂SO] helped validate the synthesis and also provides a strategy for forming a new set of pseudopeptide libraries (previously described as libraries from libraries). Our results suggest that libraries of cyclic pseudopeptides are an efficient method of preparing and assaying these synthetically more challenging entities as potential drug leads.     

Maximal structures of determinate propositions in quantum mechanics

I formulate and answer some questions concerning maximal structures of determinate quantum propositions, i.e., maximal structures of propositions that can be taken as having definite (but perhaps unknown) truth values for a given quantum state. The basic constraint on such structures is the Kochen and Specker no-go hidden-variables theorem, which demonstrates that no value assignment to certain finite sets of observables can preserve the functional relations between commuting observables. The problem I want to consider is how large we can take the set of determinate observables without violating the functional relationship constraint. I show how to construct maximal determinate sublattices of quantum propositions that are unique, subject to certain constraints, and I comment on the relevance of this go theorem for the interpretation of quantum mechanics.     

Quantum fog and the degradation of information by the gravitational field

In this paper we discuss how information transferred optically through a gravitational field is degraded as the quanta interact with the madium (vacuum state). We quantify information by means of Shannon's entropy, and consider information carriers that are quanta of some field. Next, we obtain the quantum noise (quantum fog) produced by the gravitational field and derive the appropriate channel capacity formula, which quantifies the maximum amount of information that can be transmitted per pulse, in the face of this noise. We show that the channel capacity formula vanishes if the source of information is a space-time singularity because a very intense noise is produced in the vicinity of the singularity. In other words, space-time singularities are hidden behind a very intense quantum fog and cannot be optically observed. A second consequence is that information is degraded as anisotropies (lumpiness) develop in the universe.     

The ground state of the Bose gas

The mathematical formalism describing the Bose gas at zero temperature is analysed with the aid of methods that have recently been successful in relativistic quantum field theory. First the spectrum conditions for an infinitely extended system are given and the algebra of observables and the algebra of field operators are defined. General properties of states over these algebras are discussed and theorems are given which connect the linked cluster property, translation invariance and the purity of the states. It is proved that pure states over the algebra of observables have the property of factorisable off-diagonal long range order. The class of quasi free states is defined and of these states those which are translation invariant and possess the linked cluster property are analysed. It is shown that this class of states contains a subclass of pure states of the Bogoliubov type and a subclass of states which are mixtures of non-translationally invariant pure states. The applications of these quasi free states to the interacting Bose gas are summarized.     

Gauge-invariant variations in the redshift and cosmic background radiation anisotropies

The gauge-invariance of the calculations determining anisotropics in the cosmic microwave background radiation (the Sachs-Wolfe effect) is re-examined. It is shown that the results obtained are gauge-invariant only if a physically-based definition of the surface of last scattering is implemented, in a context where perturbations of the surface of last scattering as well as of the space-time are taken into account. Any physical interpretation of the results based on their splitting into scalar, vector, and tensor parts, is unique only if non-local (unverifiable) conditions are imposed; locally, any such interpretation is non-unique. The physical meaning of the Sachs-Wolfe potentialB and associated redshift formula depends on implementing a very specific gauge, without a clear physical or geometric meaning; its implications do not extend to other, more usual, gauges.     

Eigenresonance states in the Kronig-Penney model

We investigate a sandwich of three layer systems with Dirac -functions in the Kronig-Penney model. The inner system ofN=5 atomic layers is enclosed by the two outer systems with different potential strength. The numberM of the atomic layers in the outer system is varied betweenM=9 and infinity, whereas the numberN of the inner layers is held fixed. We obtain the transmission coefficient for the finite system in the region of scattering energies (E>0). An alternating set of transmission gaps, transmission bands and bands of eigenresonance states is obtained. The normalizable eigenresonances occur (forM going to infinity), if a transmission band of the inner system overlaps a transmission gap of the outer systems. The reason for obtaining solutions of standing waves in the band of eigenresonances is the rapid change of the wave phase of a traveling wave, which occurs in a transmission band of the inner system.     

Electron-capture decays of 100Tc and 116In and nuclear structure relevant for 2β decays

Both ^l00Mo and ¹¹⁶Cd are double--decay candidates, whose intermediate (virtual) state is a nucleus with J = 1⁺ in the ground state. Consequently, in these cases one can measure the single--decay matrix elements in addition to the 2-decay rate and test models in a more stringent way. We have measured the electron-capture decays of ¹⁰⁰Tc and ¹¹⁶In which show that: a) the ground state dominance hypothesis works very well; b) deformation plays a role which cannot be neglected in QRPA calculations. QRPA predictions work better in the spherical A = 116 system than in the transition A = 100 system.     

3-dimensional photonic band structure

Three-dimensionally periodic dielectric structures, (photonic crystals), possessing a forbidden gap for electromagnetic wave propagation, (a photonic bandgap), are now known. If the perfect 3-dimensional periodicity is broken by a local defect, then local electromagnetic modes can occur within the forbidden bandgap. The addition of extra dielectric material locally, inside the photonic crystal, produces donor modes. Conversely, the local removal of dielectric material from the photonic crystal produces acceptor modes. It will now be possible to make high-Q electromagnetic cavities of volume 1 cubic wavelength, for short wavelengths at which metallic cavities are useless. These new dielectric cavities can cover the range all the way from millimeter waves, down to ultraviolet wavelengths.     

УпРУгОЕ РАссЕьНИЕ НУклОНОВ НА МИшЕНИ сО спИНОМ 1

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Elastic scattering of nucleons on a target with spin 1

A method, by means of which it is possible to reconstruct a potential on the basis of data on elastic scattering, is investigated for the case of scattering of nucleons on targets with spin 1. Formulas are given which express the relations between a phenomenological potential and the elements of the scattering matrix.

     

Die magnetische Suszeptibilität der ternären Systeme halbleitender Verbindungen

Zusammenfassung Im vorliegenden Artikel wird der Versuch unternommen, die für die Suszeptibilität der binären Systeme zutreffenden empirischen Beziehungen auf die ternären halbleitenden Systeme auszudehnen. Die Richtigkeit der Erwägungen wird an den Systemen Zn-Cd-Sb, In-Ga-Te und an einigen festen Lösungen anderer halbleitender Verbindungen überprüft. Im Artikel wird weiter gezeigt, daß sich im Falle, wenn sich die Suszeptibilitäten der Komponenten des ternären Systems additiv verhalten, zur Berechnung der molaren Suszeptibilität einer festen Lösung die Mischungsregel verwenden läßt, was im Gegenteil in diesem Falle als Kriterium dienen kann, ob zwei den Erfordernissen der Additivität der Suszeptibilitäten der Bestandteile Genüge leistende Stoffe eine feste Lösung oder ein mehrphasiges System bilden.

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, , . Zn-Cd-Sb, In-Ga-Te . , , , , , , , , , .

     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.