Related papers: Binary strings of finite VC dimension
We study the partial orderings of the form $\langle {\mathbb P} ({\mathbb X}), \subset \rangle $, where ${\mathbb X}$ is a binary relational structure with the connectivity components isomorphic to a strongly connected structure ${\mathbb…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints Str(M^0)=0 and Str(M^2)=\Lambda at tree level, where \Lambda is the one-loop string…
We extend the notion of a strong backdoor from the CSP setting to the Valued CSP setting (VCSP, for short). This provides a means for augmenting a class of tractable VCSP instances to instances that are outside the class but of small…
The evidence for string/string-duality can be extended from the matching of the vector couplings to gravitational couplings. In this note this is shown in the rank three example, the closest stringy analog of the Seiberg/Witten-setup, which…
The well known N=2 string theory describes self-dual gravity, as was shown by Ooguri and Vafa sometime ago. In search of a variant of this theory which would describe self-dual supergravity in 2+2 dimensions, we have constructed two new N=2…
We consider some unitary representations of infinite dimensional Lie algebras motivated by string theory on AdS_3. These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first…
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
We show that bounded families of global classical relativistic strings that can be written as graphs are relatively compact in C0 topology, but their accumulation points include many non relativistic strings. We also provide an alternative…
In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity…
We argue that apart from the standard closed and open strings one may consider a third possibility that we call monodromic strings. The monodromic string propagating on a target looks like an ordinary open string (a mapping from a segment…
We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies…
We show that the nuclear dimension of a (twisted) group C*-algebra of a virtually polycyclic group is finite. This prompts us to make a conjecture relating finite nuclear dimension of group C*-algebras and finite Hirsch length, which we…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
Recently there has been considerable interest in studying the length and the depth of finite groups, algebraic groups and Lie groups. In this paper we introduce and study similar notions for algebras. Let $k$ be a field and let $A$ be an…
A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of…
We review some examples of heterotic/type II string duality which shed light on the infrared dynamics of string compactifications with N=2 and N=1 supersymmetry in four dimensions.
The space-time dimensions transverse to a static straight cosmic string with a sufficiently large tension (supermassive cosmic strings) are compact and typically have a singularity at a finite distance form the core. In this paper, we…
One cannot yet point to any firm string prediction. While many approximate string ground states are known with interesting properties, we do not have any argument that one or another describes what we observe around us, and for reasons…