Related papers: Dual formulation of spin network evolution
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
We study the cosmological evolution of domain wall networks in two and three spatial dimensions in the radiation and matter eras using a large number of high-resolution field theory simulations with a large dynamical range. We investigate…
We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the…
We present a novel logic-based concept called Space Explanations for classifying neural networks that gives provable guarantees of the behavior of the network in continuous areas of the input feature space. To automatically generate space…
It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…
Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's, superstrings, five-branes, F-theory,…
In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers,…
To solve the path integral for quantum gravity, one needs to regularise the space-times that are summed over. This regularisation usually is a discretisation, which makes it necessary to give up some paradigms or symmetries of continuum…
Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed…
We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of…
Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a map from a generally covariant…
In this paper it is studied a space-time duality web that maps electric into magnetic (and magnetic into electric) charged classical stationary rotating solutions for $2+1$-dimensional Abelian Einstein Maxwell Chern-Simons theories. A first…
We introduce bio-inspired artificial neural networks consisting of neurons that are additionally characterized by spatial positions. To simulate properties of biological systems we add the costs penalizing long connections and the proximity…
In recent years, there has been a growing recognition that higher-order structures are important features in real-world networks. A particular class of structures that has gained prominence is known as a simplicial complex. Despite their…
We introduce and explore the notion of "spaces of input histories", a broad family of combinatorial objects which can be used to model input-dependent, dynamical causal order. We motivate our definition with reference to traditional partial…
We study the formation and evolution of an interconnected string network in large-scale field-theory numerical simulations, both in flat spacetime and in expanding universe. The network consists of gauge U(1) strings of two different kinds…
The distinct models that describe spin 1 and 2 massive excitations in 2+1 dimensions are analized, showing their equivalence (between models of same spin) and analogies (between models of different spin). Topics as spontaneous symmetry…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…