A Robust Discontinuous Phase Unwrapping Based on Least-Squares Orientation Estimator

Weighted least-squares (WLS) phase unwrapping is widely used in optical engineering. However, this technique still has issues in coping with discontinuity as well as noise. In this paper, a new WLS phase unwrapping algorithm based on the least-squares orientation estimator (LSOE) is proposed to improve phase unwrapping robustness. Specifically, the proposed LSOE employs a quadratic error norm to constrain the distance between gradients and orientation vectors. The estimated orientation is then used to indicate the wrapped phase quality, which is in terms of a weight mask. The weight mask is calculated by post-processing, including a bilateral filter, STDS, and numerical relabeling. Simulation results show that the proposed method can work in a scenario in which the noise variance is 1.5. Comparisons with the four WLS phase unwrapping methods indicate that the proposed method provides the best accuracy in terms of segmentation mean error under the noisy patterns.

Unconventional Thermal and Magnetic-Field-Driven Changes of a Bipartite Entanglement of a Mixed Spin-(1/2,S) Heisenberg Dimer with an Uniaxial Single-Ion Anisotropy

The concept of negativity is adapted in order to explore the quantum and thermal entanglement of the mixed spin-(1/2,S) Heisenberg dimers in presence of an external magnetic field. The mutual interplay between the spin size S, XXZ exchange and uniaxial single-ion anisotropy is thoroughly examined with a goal to tune the degree and thermal stability of the pairwise entanglement. It turns out that the antiferromagnetic spin-(1/2,S) Heisenberg dimers exhibit higher degree of entanglement and higher threshold temperature in comparison with their ferromagnetic counterparts when assuming the same set of model parameters. The increasing spin magnitude S accompanied with an easy-plane uniaxial single-ion anisotropy can enhance not only the thermal stability but simultaneously the degree of entanglement. It is additionally shown that the further enhancement of a bipartite entanglement can be achieved in the mixed spin-(1/2,S) Heisenberg dimers, involving half-odd-integer spins S. Under this condition the thermal negativity saturates at low-enough temperatures in its maximal value regardless of the magnitude of half-odd-integer spin S. The magnetic field induces consecutive discontinuous phase transitions in the mixed spin-(1/2,S) Heisenberg dimers with S>1, which are manifested in a surprising oscillating magnetic-field dependence of the negativity observed at low enough temperature.

A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang–Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule. Graphicabstract

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ q c = q a = q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ k ⟩ ≤ 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ q a ≥ q c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.

Higher-order simplicial synchronization of coupled topological signals

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of simplicial complexes. In particular we consider topological signals, i.e., dynamical signals defined on simplices of different dimension, here taken to be nodes and links for simplicity. We show that coupling between signals defined on nodes and links leads to explosive topological synchronization in which phases defined on nodes synchronize simultaneously to phases defined on links at a discontinuous phase transition. We study the model on real connectomes and on simplicial complexes and network models. Finally, we provide a comprehensive theoretical approach that captures this transition on fully connected networks and on random networks treated within the annealed approximation, establishing the conditions for observing a closed hysteresis loop in the large network limit.

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

Aspects of Hyperscaling Violating geometries at finite cutoff

Recently, it was proposed that a $$ T\overline{T} $$ T T ¯ deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: it is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound EW ≥ $$ \frac{I}{2} $$ I 2 for all values of the cutoff.