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Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries…
Complex networked systems in fields such as physics, biology, and social sciences often involve interactions that extend beyond simple pairwise ones. Hypergraphs serve as powerful modeling tools for describing and analyzing the intricate…
The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
We examine the holographic entanglement entropy in hyperscaling violating backgrounds. Precisely in such theories by semi-analytic computation, we use holographic methods to derive the universal terms of entanglement entropy in various…
Lifshitz and hyperscaling violating geometries, which provide a holographic description of non-relativistic field theories, generically have a singularity in the infrared region of the geometry, where tidal forces for freely falling…
In the context of the AdS$_3$/CFT$_2$, the boundary causal development and the entanglement wedge of any boundary spacelike interval can be mapped to a thermal CFT$_2$ and a Rindler $\widetilde{\text{AdS}_3}$ respectively via certain…
Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
We propose an analogue of the Ryu-Takayanagi formula for holographic entanglement entropy applicable to non-relativistic holographic dualities involving Horava gravity. This is a powerful tool for the duality to have, as topological order…
We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for…
The signature of noncommutativity on various measures of entanglement has been observed by considering the holographic dual of noncommutative super Yang-Mills theory. We have followed a systematic analytical approach in order to compute the…
The assumption of using a static graph to represent multivariate time-varying signals oversimplifies the complexity of modeling their interactions over time. We propose a Dynamic Multi-hop model that captures dynamic interactions among…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…
We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical…
In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in…
The Hamiltonian analysis for a 3-dimensional connection dynamics of $\frak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01}, L_{02}, L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the…