Related papers: On cyclically shifted strings

Spin chains have been proposed as a reliable and convenient way of transferring information and entanglement in a quantum computational context. Nonetheless, it has to be expected that any physical implementation of these systems will be…

There have been many remarkable developments in our understanding of superstring theory in the past few years, a period that has been described as ``the second superstring revolution.'' Several of them are discussed here. The presentation…

When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…

We argue that the light particles in string theory obey an effective quantum mechanics modified by the inclusion of a quantum-gravitational friction term, induced by unavoidable couplings to unobserved massive string states in the…

In this thesis time-dependent configurations are studied in the formalism of first-quantized string. These configurations are exact: solutions of the corresponding two-dimensional conformal field theory can be found. We can compute…

String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…

In this paper we discuss symmetry breaking in string theory. Spacetime symmetries are implemented as inner automorphisms of the underlying superconformal algebra. Conserved currents generate unbroken spacetime symmetries. As we deform the…

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

In synchronous rewriting, the productions of two rewriting systems are paired and applied synchronously in the derivation of a pair of strings. We present a new synchronous rewriting system and argue that it can handle certain phenomena…

We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical…

The quantum grassmannian is known to be a graded quantum algebra with a straightening law when the poset of generating quantum minors is endowed with the standard partial ordering. In this paper it is shown that this result remains true…

Currently, string theory represents the only advanced approach to a unification of all interactions, including gravity. In spite of the more than thirty years of its existence it did not make any empirically testable predictions. And it is…

We study properties of an array of numbers, called "the triangle," in which each row is formed by rotating all the numbers in the previous row to the left by $m$ positions in cyclical fashion, then appending a number to the end of the row.…

We explain how fractional spin and statistics are relevant to (super)strings in a three-dimensional (3D) Minkowski spacetime.

Our knowledge on the nucleon spin structure has greatly improved over the last twenty years or so, but still many fundamental questions remain unsolved. I will try to review some of the puzzling aspects of the origin of the nucleon spin. I…

In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…

Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…

We study the following combinatorial problem. Given a set of $n$ y-monotone curves, which we call wires, a tangle determines the order of the wires on a number of horizontal layers such that any two consecutive layers differ only in swaps…

An order-preserving square in a string is a fragment of the form $uv$ where $u\neq v$ and $u$ is order-isomorphic to $v$. We show that a string $w$ of length $n$ over an alphabet of size $\sigma$ contains $\mathcal{O}(\sigma n)$…