String Operations Research Articles

Interactive exhibits illustrating wind instrument acoustics

The authors were recently involved in developing demonstration equipment for musical instrument museums. The aim of this project, funded by the European Union, was to provide hands-on exhibits which would allow the user to explore some of the basic science underlying the operation of string, wind, and percussion instruments. While it is fairly straightforward to devise exhibits in which the user can pluck a guitar string, strike a tubular bell, or bow a violin, considerations of hygiene and the requirement for skilled embouchure techniques make it impossible to expect members of the public to blow demonstration wind instruments. To overcome this limitation, exhibits have been constructed in which a clarinet and a trumpet are played using artificial mouths. The user can adjust a valve controlling the flow of air from a blower to the artificial mouth; a digital manometer monitors the mouth pressure. The note played can be changed by operating a piston on the trumpet, or a key on the clarinet. The signal from a microphone registering the sound output is fed to the sound card of a PC, and specially written software allows the user to examine the waveform and the frequency spectrum of the sound.

DVCS amplitude with kinematical twist-3 terms

We compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude we include the operators of twist-3 which appear as total derivatives of twist-2 operators. Our results are equivalent to a Wandzura–Wilczek approximation for twist-3 skewed parton distributions. We find that, for the tensor amplitude T μν , this approximation gives a finite result for the longitudinal polarization of the virtual photon and a divergent result in case of transverse polarization. However, the divergent part has zero projection onto the polarization vector of the final real photon.

Evolutionary systems: a language generating device inspired by evolving communities of cells

We introduce a language generating device based on string operations suggested by the evolution of cell populations, called evolutionary system. Cells are represented by strings which describe their DNA sequences. The cell community evolves according to gene mutations and cell divison defined by operations on strings. The paper deals with the generative power of these mechanisms (a characterization of the class of recursively enumerable languages is presented) and the dynamics of the string population. A connection between the growth function of D0L systems and the population growth relation of evolutionary systems is also given.

Adjoint string breaking in 4d SU(2) Yang–Mills theory

We compute the static potential of adjoint sources in SU(2) Yang–Mills theory in four dimensions by numerical Monte Carlo simulations. Following a recent calculation in 2+1 dimensions, we employ a variational approach involving string and gluelump operators and obtain clear evidence for string breaking and the saturation of the potential at large distances. For the string breaking scale we find r b≈1.25 fm , 2.3 r 0, or in units of the lightest glueball, r b m 0++≈9.7. We furthermore resolve the first excitation of the flux-tube and observe its breaking as well. The result for r b is in remarkable quantitative agreement with the three-dimensional one.

Conformal string operators and skewed parton distributions

We discuss skewed parton distributions in the coordinate space. Solution of the corresponding LO evolution equation is constructed in terms of eigenfunctions of the evolution kernel and its relation to the conformal symmetry is explained.

Conformal string operators and evolution of skewed parton distributions

We have investigated skewed parton distributions in coordinate space. We found that their evolution can be described in a simple manner in terms of non-local, conformal operators introduced by Balitsky and Braun. The resulting formula is given by a Neumann series expansion. Its structure resembles, for all values of the asymmetry parameter, the well-known solution of the ERBL equation in momentum space. Performing aFourier transformation we have reproduced known results for the evolution of momentum-space distributions.

Scale dependence of QCD string operators

We have obtained a general solution of evolution equations for QCD twist-2 string operators in form of expansion over complete set of orthogonal eigenfunctions of evolution kernels in coordinate-space representation. In the leading logarithmic approximation the eigenfunctions can be determined using constraints imposed by conformal symmetry. Explicit formulae for the LO scale-dependence of quark and gluon twist-2 string operators are given.

String breaking in SU(2) Yang Mills theory with adjoint sources

We compute the static potential in three-dimensional SU(2) Yang Mills Theory with adjoint sources using numerical simulations. By employing a variational approach involving string and gluelump operators, we obtain clear evidence for string breaking in the adjoint potential. The breaking scale r b is computed and extrapolated to the continuum limit. The result in units of the scalar glueball mass is r b m G=10.3±1.5 . We also resolve the structure of higher excitations of the flux-tube and gluelumps. Furthermore we discuss the implications of our findings for the case of the four-dimensional theory.

Hard exclusive meson production and nonforward parton distributions

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive π0, η), and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections.

Hard exclusive meson production and nonforward parton distributions

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive pi^0, eta, and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections.

Scale dependence of the chiral-odd twist-3 distributions hL( x) and e( x)

We evaluate the complete leading-order evolution kernels for the chiral-odd twist-3 distributions e( x) and h ̃ L(x) of the nucleon. We establish the connection between the evolution equations in light-cone position and light-cone fraction representations, which makes a correspondence between the non-local string operator product expansion and the QCD-inspired parton model. The compact expression obtained for the local anomalous dimension matrix coincides with previous calculations. In the multicolour QCD as well as in the large- x limit the twist-3 distributions obey simple DGLAP equations. Combining these two limits, we propose improved DGLAP equations and compare them numerically with the solutions of the exact evolution equations.

Ioffe-time distribution of quarks in the photon

We have analysed the Ioffe-time distribution of quarks in virtual photons using Operator Product Expansion of the correlation function that determines the matrix element of the corresponding quark string operator. The distribution for a transversally polarised photon admits a spectral representation which can be continued to the on-shell region $p^2 =0$. The resulting model Ioffe-time distribution turns out to be larger than parametrisations of the available $F_2^{\gamma}$ data. This result is linked to the slope of the quark distribution at the origin, which comes out too large as well.

D-branes and the conifold singularity

We analyze in detail the description of type IIB theory on a Calabi-Yau three-fold near a conifold singularity in terms of intersecting D-branes. In particular, we study the singularity structure of higher derivative F-terms of the form F g W 2 g where W is the gravitational superfield. This singularity is expected to be due to a one-loop contribution from a charged soliton hypermultiplet becoming massless at the conifold point. In the intersecting D-brane description this soliton is described by an open string stretched between the two D-branes. After identifying the graviphoton vertex as a closed string operator we show that F g 's have the expected singularity structure in the limit of vanishing soliton mass.

STRING FIELD THEORY OF TWO-DIMENSIONAL QCD ON A CYLINDER: A REALIZATION OF W∞ CURRENT ALGEBRA

We consider two-dimensional QCD on a cylinder, where space is a circle of length L. We formulate the theory in terms of gauge-invariant gluon operators and multiple-winding meson (open string) operators. The meson bilocal operators satisfy a W∞ current algebra. The gluon sector (closed strings) contains purely quantum-mechanical degrees of freedom. The description of this sector in terms of nonrelativistic fermions leads to a W∞ algebra. The spectrum of excitations of the full theory is therefore organized according to two different algebras: a wedge subalgebra of W∞ current algebra in the meson sector and a wedge subalgebra of W∞ algebra in the glueball sector. In the large N limit the theory becomes semiclassical and an effective description for the gluon degrees of freedom can be obtained. We have solved the effective theory of the gluons in the small L limit. We get a glueball spectrum which coincides with the “discrete states” of the (Euclidean) c=1 string theory. We remark on the implications of these results for (a) QCD at finite temperature and (b) string theory.

Design of a safe string library for C

AbstractThe C programming language provides no bounds‐checking for arrays. As a result, string operations provided in the standard C library are potentially unsafe. A solution, in the form of a safe string library, is presented. The design goals are safety, inter‐operability with existing safe and unsafe routines, debugging help and ease of use.

Critical and non-critical strings

Nilpotent BRST operators for higher-spin strings, with currents of spins 2 and s, have recently been constructed for s=4, 5 and 6. In the case of , this operator can be understood as being the BRST operator for the critical string. In this paper, we construct a generalized BRST operator that can be associated with a non-critical string, in which matter is coupled to the gravity of the critical case. We also obtain the complete cohomology of the critical BRST operator, and investigate the physical spectra of the s=5 and s=6 string theories.

Strategy Acquisition of the 3-D Packing Problem in Multiagent Environment. GA-based Hierarchical Tuning.

In this paper, a new approach to solving automatic 3-D packing problems is proposed. This problem is a well-known complex combinatorial problem. In particular, the difficulties of this problem are compounded in a multiagent environment in which there are multiple agents that perform the packing of corresponding containers. Here, we attempt to establish the mechanism by which the 3-D packing strategy is automatically tuned and the appropriate packing solution is obtained in a multiagent environment, by applying genetic algorithms which mimic the process of a natural evolution system. It this paper, a 3-D packing strategy is acquired through hierarchical tuning. This is achieved by an agent strategy tuning layer and a supervisor strategy tuning layer. First, each agent acquires the individual packing strategy related to the corresponding container. An agent packing strategy is controlled by two evaluation functions which dominate the selection of the next allocation position and box. To find the near-optimal strategy, the weighted coefficients of the evaluation functions are tuned by applying genetic operators such as conventional reproduction, crossover and mutation. Next a supervisor strategy is implemented as a priority sequence of agents. The supervisor strategy is also tuned by modified genetic operators for order-based strings. Based on the proposed method, a 3-D packing simulator was constructed and numerical experiments were carried out. The results of the experiments show the usefulness of the proposed method.

On Aggregation and Computation on Domain Values

<p>Query languages often allow a limited amount of anthmetic and string operations on domain values, and sometimes sets of values can be dealt with through aggregation and sometimes even set comparisons. We address the question of how these facilities can be added to a relational language in a natural way. Our discussions lead us to reconsider the definition of the standard operators, and we introduce a new way of thinking about relational algebra computations.</p><p>We define a language FC, which has an iteration mechanism as its basis. A tuple language is used to carry out almost all computations. We prove equivalence results relating FC to relational algebra under various circumstances.</p>

A CONSTRUCTIVE QUANTUM FIELD THEORETIC APPROACH TO CHERN-SIMONS THEORY

Chern-Simons theory is formulated quantum field theoretically in terms of string operators, which are localized on finite non-selfintersecting paths in the zero-time plane R2. It is shown how the Weyl algebra approach to the abelian Chern-Simons theory leads to a bundle theoretic construction of these ‘Chern-Simons string operators’. To proceed to the non-abelian case topological Chern-Simons theory is considered as a specific model of a more general theory describing the quantum kinematics of coloured framed Plek ton s inR2. This theory allows the construction of string operators as pair-creation operators, mapping n-Plekton states into (n+2)-Plekton states. Link invariants are obtained as vacuum correlation functions of string operators and obey a natural version of reflection positivity. The vacuum sector of such a purely kinematical Plekton theory may be recovered from the link invariants by Osterwalder-Schrader reconstruction. To make the theory work one needs the structures of a ribbon graph category, for which the representations of a quasi-triangular quasi-Hopf algebra may serve as a specific realization.

MASS AND ENERGY-MOMENTUM TENSOR OF QUANTUM STRINGS IN GRAVITATIONAL SHOCK-WAVES

We investigate at the quantum level the nonlinear transformation relating the string operators (zero modes and oscillators) and Fock space states before and after the collision with gravitational shock waves. This throws light on the rôle of the space–time geometry in this problem. We do all the treatment for a general shock wave space–time of any localized source. We compute the exact expectation values of the total number (N) and mass ( M 2) operators and show that they are finite, which generalize our previous results in the Aichelburg–Sexl geometry. We study the energy-momentum tensor of the string and compute the exact expectation values of all its components. We analyze vacuum polarization and quadratic fluctuations. All these physical magnitudes are finite. We express all of them in terms of exact integral representations in which the role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) are clearly exhibited. The presence of such poles is not at all related to the structure of the space–time geometry (which may or may not be singular).