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We explore the relationship between renormalization group (RG) flow and error correction by constructing quantum algorithms that exactly recognize 1D symmetry-protected topological (SPT) phases protected by finite internal Abelian…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
Redox biology underpins signalling, metabolism, immunity, and adaptation, yet lacks a unifying theoretical framework capable of formalising structure, function, and dynamics. Current interpretations rely on descriptive catalogues of…
The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
The dynamics of monitored systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling phases, tuned by the measurement rate. When the dynamics obeys a continuous symmetry, the entangling phase…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
In self-consuming generative models that train on their own outputs, alignment with user preferences becomes a recursive rather than one-time process. We provide the first formal foundation for analyzing the long-term effects of such…
At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing…
We employ the state-of-the-art molecular dynamics simulations to study the kinetics of phase separation and aging phenomena of segregating binary fluid mixtures imbibed in porous materials. Different random porous structures are considered…
Uniquely among primates, humans possess a remarkable capacity to recognize and manipulate abstract structure in the service of task goals across a broad range of behaviors. One illustration of this is in the visual perception of geometric…
General conditions controlling formation of incommensurate phases (IPs) in crystals undergoing reconstructive phase transitions (RPTs) are analyzed in the framework of a model free phenomenological approach. A universal trend to stabilizing…
Phase reconstruction, which estimates phase from a given amplitude spectrogram, is an active research field in acoustical signal processing with many applications including audio synthesis. To take advantage of rich knowledge from data,…
Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
We study numerically transitional coherent structures in a boundary-layer flow with homogeneous suction at the wall (the so-called asymptotic suction boundary layer ASBL). The dynamics restricted to the laminar-turbulent separatrix is…
The recently developed 3D graphic statics (3DGS) lacks a rigorous mathematical definition relating the geometrical and topological properties of the reciprocal polyhedral diagrams as well as a precise method for the geometric construction…
We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…
Manipulating the global $PT$ symmetry of a non-Hermitian composite system is a rather significative and challenging task. Here, we investigate Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides with transverse…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…