Four-dimensional Representation Research Articles

On a Four-Dimensional Representation of DNA Primary Sequences [J. Chem. Inf. Comput. Sci. 43, 532−539 (2003)

On a Four-Dimensional Representation of DNA Primary Sequences [<i>J. </i><i>Chem. Inf. Comput. Sci</i>. <i>43</i>, 532−539 (2003)

PSEUDO-CUNTZ ALGEBRA AND RECURSIVE FP GHOST SYSTEM IN STRING THEORY

Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo-Cuntz algebra, which is a *-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pseudo-Cuntz algebra recursively in two different ways. Restricting a certain permutation representation of the pseudo-Cuntz algebra, representations of these two recursive FP ghost systems are obtained. With respect to the zero-mode operators of FP (anti)ghosts, it is shown that one corresponds to the four-dimensional representation found recently by one of the present authors (M. Abe) and Nakanishi, while the other corresponds to the two-dimensional one by Kato and Ogawa.

On a four-dimensional representation of DNA primary sequences.

We consider a four-dimensional representation of DNA primary sequences by assigning to each of the four basic amino acids A, T, G, C directions along the four orthogonal coordinate axes. Advantages and limitations of the novel representation of DNA primary sequences are discussed, and the use of the 4-D representation is illustrated by constructing novel sequence invariants. Comparisons with the similarity/dissimilarity results based on 2-D and 3-D representations for a set of eight short DNA sequences corresponding to the first exon of beta globin in eight species, including human, are considered to illustrate the use of our novel sequence invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.

Point form electrodynamics and the Gupta–Bleuler formalism

The Gupta–Bleuler formalism for photons is generalized by choosing the representation of the little group for massless particles, the two-dimensional Euclidean group, to be the four-dimensional nonunitary representation obtained by restricting elements of the Lorentz group to the Euclidean group. Though the little group representation is nonunitary, it is shown that the representation of the Poincaré group is unitary. Under Lorentz transformations photon creation and annihilation operators transform as irreducible representations of massless particles, and not as four-vectors. As a consequence the polarization vector, which connects the four-vector potential with creation and annihilation operators, is given in terms of boosts, coset representatives of the Lorentz group with respect to the Euclidean group. Several polarization vectors (boost choices) are worked out, including a front form polarization vector. The different boost choices are shown to be related by the analogue of Melosh rotations, namely Euclidean group transformations

Nuclear tetrahedral symmetry: possibly present throughout the periodic table.

More than half a century after the fundamental, spherical shell structure in nuclei had been established, theoretical predictions indicated that the shell gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the TD(d) ("double-tetrahedral") symmetry group. Strong shell-gap structure is enhanced by the existence of the four-dimensional irreducible representations of TD(d); it can be seen as a geometrical effect that does not depend on a particular realization of the mean field. Possibilities of discovering the TD(d) symmetry in experiment are discussed.

A Strong Schottky Lemma for Nonpositively Curved Singular Spaces

Motivated by the question of faithfulness of the four-dimensional Burau representation, we study a generalization of the Schottky Lemma which is useful for studying actions on affine buildings.

Noncrystallographic Coxeter groupH4inE8

The E8 lattice is constructed in terms of icosians by matching two sets of F4 lattices described by quaternions. Embedding the noncrystallographic group H4 into the Weyl group W(E8) has been described using matrix generators with an emphasis on the relevant Coxeter elements. The conjugacy classes of H4 in terms of quaternions and the characters of the two four-dimensional irreducible representations are explicitly calculated.

U q [sl (2| ∧ 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra Uq[sl(2|∧1)] are constructed for arbitrary level k=α, where α≠0,−1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-α highest weight Fock–Wakimoto modules. Screen currents which commute with the action of Uq[sl(2|∧1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed.

The conventionality of pictorial representation in interstellar messages

Pictorial messages have previously been advocated for interstellar communication because such messages are presumed to be capable of presenting information in a non-arbitrary and easily intelligible manner. In contrast to this view, pictorial messages actually represent information in a partially conventional way. This point is demonstrated by examining pictorial representations of human beings from a range of cultures. While such representations may be understood quite readily by individuals familiar with the conventions of a particular culture, to the uninitiated outsider, such representations can be unintelligible. In spite of the partially arbitrary nature of pictorial representation, we may be able to construct messages that would teach extraterrestrial intelligence (ETI) some of the conventions by which we view pictures. One such approach is to pair numerical information about geometrical objects with pictorial representations of the same objects. Problems of conventionality can also be addressed in part through use of (1) multiple representations of the same object, (2) contextual cues, (3) three- and four-dimensional representations and (4) non-visual representations.

Integral method to study transition radiation from surfaces with arbitrary profile

Transition radiation is produced when an electron moving at constant speed crosses the boundary separating two media with different optical properties. We propose an alternative description of this phenomenon, based on an integral representation of the electromagnetic field and show that the approach gives known results for a flat surface. Compared to previously published methods, based either on the reciprocity theorem in electromagnetism or on a four-dimensional Fourier representation of the field generated by the moving electron, this method has the advantage that it can be applied to general boundary geometries.

Temporal distribution of information for human consonant recognition in VCV utterances

The temporal distribution of perceptually relevant information for consonant recognition in British English VCVs is investigated. The information distribution in the vicinity of consonantal closure and release was measured by presenting initial and final portions, respectively, of naturally produced VCV utterances to listeners for categorization. A multidimensional scaling analysis of the results provided highly interpretable, four-dimensional geometrical representations of the confusion patterns in the categorization data. In addition, transmitted information as a function of truncation point was calculated for the features manner place and voicing. The effects of speaker, vowel context, stress, and distinctive feature on the resulting information distributions were tested statistically. It was found that, although all factors are significant, the location and spread of the distributions depends principally on the distinctive feature, i.e., the temporal distribution of perceptually relevant information is very different for the features manner, place, and voicing.

On the construction and solution of [formula omitted]-symmetric models

The U q( gl ′(2,1; C)) symmetric R-matrix, acting on the direct product of a four-dimensional representation of this algebra with itself, constructed by Gould et al., is generalized to the case of two different four-dimensional not necessarily unitary representations and to the case of a product of these with the fundamental one. The latter is used in the algebraic Bethe ansatz solution of some models. Together with the R-matrix acting on the product of the fundamental representation with itself, these fundamental R-matrices form the starting point of an infinite fusion hierarchy of exactly solvable models. A number of these are constructed explicitly. Some Bethe ansatz equations for the eigenvalues of their transfer matrices are derived.

Maxwell stress dyadic in differential-form formalism

The classical Maxwell stress tensor (or stress-energy-momentum tensor) is revisited by introducing the dyadic formalism to that of differential forms. Dyadics, as originally introduced by Gibbs to vector analysis, appear suitable companions to differential forms because of their co-ordinate-free character. Basic properties of dyadics together with some useful identities are first derived. It is shown that, in terms of the identities, the Maxwell stress tensor can be given a particularly simple dyadic form. This requires that the Lorentz force density be first expressed as a dyadic quantity mapping trivectors to vectors and, in four-dimensional representation, the Lorentz force-power density as a dyadic mapping from quadrivectors to vectors. Finally, it is shown that to be able to define the force density in terms of a stress dyadic, the macroscopic electromagnetic medium (assumed linear, homogeneous and time-independent) must satisfy a certain symmetry condition which turns out to equal the Lorentz reciprocity condition for time-harmonic fields.

On the Exact Solution of Models Based¶on Non-Standard Representations

The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their quantum deformations respectively. It is, however, very difficult to apply it to models based on higher dimensional representations of these algebras in auxiliary space, which are not of fusion type. A systematic approach to this problem is presented here. It is illustrated by the diagonalization of a transfer-matrix of a model based on the product of two different four-dimensional representations of $U_{q}(\hat{gl}'(2,1;C))$.

Four-dimensional model calculation of torsional levels of cyclic water tetramer

Quantum four-dimensional model calculations of the coupled intermolecular torsional vibrations of the cyclic homodromic water tetramers (H2O)4 and (D2O)4 are presented, based on the analytical modEPEN4B potential energy surface [S. Graf and S. Leutwyler, J. Chem. Phys. 109, 5393 (1998), preceding paper] and a four-dimensional discrete variable representation approach. The lowest 50 torsional levels were calculated up to 420 and 500 cm−1 for (D2O)4 and (H2O)4, respectively. For both clusters, the torsional ground state is split by a synchronous O–H torsional inversion process, similar to inversion tunneling in ammonia, with calculated tunnel splittings of 21.8 and 0.000 12 MHz for (H2O)4 and (D2O)4, respectively. As for the cyclic water trimer and pentamer, the four torsional fundamentals of the tetramer lie above the torsional interconversion barriers, between 185–200 cm−1 for (D2O)4 and 229–242 cm−1 for (H2O)4, but also lie below the one-dimensional torsionally adiabatic barriers. The anharmonic fundamental frequencies lie both above and below the normal-mode frequencies, by up to 33%. Slightly above the fundamental torsional excitations, at 257–260 and 280–281 cm−1 for (H2O)4 and (D2O)4, respectively, lie four states corresponding to four versions of the {uudd} isomer, which form a pseudorotational manifold; the torsional interconversion occurs by a sequence of double O–H flips. Higher excited pseudorotational states are calculated up to a vibrational angular momentum of k=3. At ≈295 and ≈300 cm−1, a further group of eight states is found, corresponding to the eight permutationally equivalent versions of yet another isomer, the {uuud} structure. The four {uudd} and eight {uuud} states of (H2O)4 exhibit inverse isotope effects, and lie at lower energy than their (D2O)4 counterparts.

Universal R-matrix and graded Hopf algebra structure of

An explicit formula for the universal R-matrix of is given using Drinfeld's basis. Its generators are chosen according to a non-standard set of positive simple roots. The expression implies an extension of the standard graded Hopf algebra defined in terms of its Chevalley generators to . In addition to a four-dimensional vector representation, an infinite-dimensional representation of suitable for the description of a model related to the integer quantum Hall transition is considered.

Defining Johnson-Neyman Regions of Significance in the Three-Covariate ANCOVA Using Mathematica

The Johnson-Neyman ANCOVA, used when nonhomogeneity of within-group regressions is present, poses special computational and plotting problems when three covariates are used. These problems can be overcome by using (a) an appropriate design and contrast matrix for the general linear model and (b) the Mathematica software system of computation to handle the symbolic and graphical processing requirements. Four-dimensional graphical representation of the polynomials which result are contour plotted in a three-dimensional space in order to define the regions of significance for contrasts. It is also shown that for some values of the covariate orthogonal contrasts are produced.

Transformation of black-hole hair under duality and supersymmetry

We study the transformation under the full string theory duality group of the observable charges (including mass, angular momentum, NUT charge, electric, magnetic and different scalar charges) of four-dimensional point-like objects whose asymptotic behavior constitutes a subclass closed under duality. We find that those charges fall into two complex four-dimensional representations of the duality group. T- duality (including Buscher's transformations) has an O(1, 2) action on them and S- duality a U(1) action. The generalized Bogomol'nyi bound is an U(2, 2)- invariant built out of one representation while the other representation (which includes the angular momentum) never appears in it. The bound is manifestly duality-invariant. Consistency between T- duality and supersymmetry seems to require that primary scalar hair is included in the generalized Bogomol'nyi bound. We also find that all known four-dimensional supersymmetric massless black holes are the T- duals in the time direction of the usual massive supersymmetric black holes. Non-extreme massless “black holes” can be found as the T- duals of the non-extreme black holes. All of them have primary scalar hair and naked singularities.

A new algebraic Bethe ansatz forgl(2,1) invariant vertex models

The algebraic Bethe ansatz for the integrable vertex model constructed from the four-dimensional representation of the superalgebra gl(2,1) is calculated using a ferromagnetic reference state. This Bethe ansatz was known only for the three-dimensional representation leading to the supersymmetric t-J model. The necessary modification of the nested algebraic Bethe ansatz scheme and generalizations to related models are discussed.

Quasicrystals and strong interactions between square modes

We analyze the possibility of finding almost hexagonal and quasicrystalline patterns, in finite square containers, as the result of the nonlinear interaction of four-dimensional and eight-dimensional representations of ${D}_{4}$. We report the possibility of sustained oscillations between simple and nonsimple squares as the result of these interactions.