Flip Operation Research Articles

On the skew-symmetric binary sequences and the merit factor problem

The merit factor problem is of practical importance to manifold domains, such as digital communications engineering, radars, system modulation, system testing, information theory, physics, chemistry. In this work, some useful mathematical properties related to the flip operation of the skew-symmetric binary sequences are presented. By exploiting those properties, the space complexity of state-of-the-art stochastic merit factor optimization algorithms could be reduced from O(n2) to O(n). As a proof of concept, a lightweight stochastic algorithm was constructed, which can optimize pseudo-randomly generated skew-symmetric binary sequences with long lengths (up to 105+1) to skew-symmetric binary sequences with a merit factor greater than 5. An approximation of the required time is also provided. The numerical experiments suggest that the algorithm is universal and could be applied to skew-symmetric binary sequences with arbitrary lengths.

On the Independent Uphill Domination Polynomial of a Graph

Objectives: The concept of independent uphill domination polynomial is newly defined to deal with the present graph theory in this paper. It is characterized and analyzed within various contexts and types of graphs, its roots are discovered, its relation to different graph transforms is discussed and the study of this graph can help reveal new structures of graphs. Methods: The independent uphill domination polynomial is defined as is an independent uphill dominating set of size in . The uphill paths are used in identifying the criterion of independent uphill dominating sets. The computation of specific values of the polynomial is performed for basic graphs, and the polynomial’s response to various flip operations is observed. Findings: Checking the standard graphs for some properties of the independent uphill dominance polynomial shows the features of the independent uphill dominance polynomial as an uphill dominance polynomial of a certain type of digraph. Families of polynomials can be best understood when it comes to stability and characteristics by analyzing their roots on different graphical planes. They demonstrate how the structure of the graph and the polynomial change as a result of the different graph operations. Novelty: Incorporating uphill paths into independent dominating sets extends common domination polynomials and provides a distinct perspective distinct from previous investigations on graph dominance. Hence, this work enriches the subject and suggests new avenues for studying related polynomials and their uses by encompassing more structural properties of graphs. Keywords: Domination, Polynomial, Uphill domination, Independent domination, Root, Book graph, Independent uphill domination polynomial

Road Crack Detection by Combining Dynamic Snake Convolution and Attention Mechanism

As one of the early manifestations of road pavement structure degradation, road cracks will accelerate the deterioration of the road if not detected and repaired in time. Aiming at the problems of low recall and incomplete crack detection in current road detection, based on the U-Net network, this paper proposed an Attention-Dynamic Snake Convolution U-Net (ADSC-U-Net) network. Firstly, the dynamic snake-shaped convolution was added to the normal downsampling process to make the network adaptively focus on the slender and curved local features, which can solve the problem of low accuracy of small crack detection. Secondly, the attention mechanism was used to pay better attention to the significant features of positive samples under the condition of a large proportion gap between positive and negative samples, which solved the problem of the poor crack integrity detection effect. Finally, the dataset was expanded by random vertical and horizontal flip operations, which solved the problem of network training overfitting caused by the small-scale datasets. The experimental results showed that, when the input image had a resolution of 480 × 320, evaluation indices P, R, and F1 of ADSC-U-Net on the self-built dataset were 74.44%, 68.77%, and 69.42%, respectively. Compared to SegNet, DeepLab, and DeepCrack, the P was improved by 1.90%, 2.49%, and 11.64%, respectively; the R was improved by 8.01%, 4.70%, and 59.58%, respectively; and the comprehensive evaluation index F1 was improved by 5.73%, 4.02%, and 55.87%, respectively, which proves the effectiveness of the proposed method.

Multiparticle states in braided lightlike κ -Minkowski noncommutative QFT

In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar quantum field theory on the noncommutative spacetime known as lightlike κ-Minkowski. The associated κ-Poincaré quantum group of isometries is triangular, and its quantum R matrix enables the definition of a braided algebra of N points that retains κ-Poincaré invariance. Leveraging our recent findings, we can now represent the generators of the deformed oscillator algebra as nonlinear redefinitions of undeformed oscillators, which are nonlocal in momentum space. The deformations manifest at the multiparticle level, as the one-particle states are identical to the undeformed ones. We successfully introduce a covariant and involutive deformed flip operator using the R matrix. The corresponding deformed (anti)symmetrization operators are covariant and idempotent, allowing for a well-posed definition of multiparticle states, a result long sought in quantum field theory on κ-Minkowski. We find that P and T are not symmetries of the theory, although PT (and hence CPT) is. We conclude by noticing that identical particles appear distinguishable in the new theory, and discuss the fate of the Pauli exclusion principle in this setting. Published by the American Physical Society 2024

A reduction of the separability problem to SPC states in the filter normal form

It was recently suggested that a solution to the separability problem for states that remain positive under partial transpose composed with realignment (the so-called symmetric with positive coefficients states or simply SPC states) could shed light on entanglement in general. Here we show that such a solution would solve the problem completely.Given a state in $ \mathcal{M}_k\otimes\mathcal{M}_m$, we build a SPC state in $ \mathcal{M}_{k+m}\otimes\mathcal{M}_{k+m}$ with the same Schmidt number. It is known that this type of state can be put in the filter normal form retaining its type. A solution to the separability problem in $\mathcal{M}_k\otimes\mathcal{M}_m$ could be obtained by solving the same problem for SPC states in the filter normal form within $\mathcal{M}_{k+m}\otimes\mathcal{M}_{k+m}$. This SPC state can be built arbitrarily close to the orthogonal projection on the symmetric subspace of $ C^{k+m}\otimes C^{k+m}$. All the information required to understand entanglement in $ \mathcal{M}_s\otimes\mathcal{M}_t$ $(s+t\leq k+m)$ lies inside an arbitrarily small ball around that projection. We also show that the Schmidt number of any state $\gamma\in\mathcal{M}_n\otimes\mathcal{M}_n$ which commutes with the flip operator and lies inside a small ball around that projection cannot exceed $\lfloor\frac{n}{2}\rfloor$.

The sojourn times of one dimensional discrete-time quantum walks

In the existing literature, a sojourn time of a discrete-time quantum walk is not a random variable. To solve this problem, we redefine the sojourn time of a quantum walk where its coin evolution operator can be general. We first discuss a class of quantum walks governed by flip operators. We cumulatively calculate how much time a walker spends in the set of non-negative integers up to a fixed evolution time. Whether a walker makes a left or right evolution, we add up the staying times as long as it stays within the target set. We define a sojourn time as the total amount of the staying times. Compared with existing definitions, we show that this definition can satisfy the probability normalization. From this, we define a random variable about the sojourn time and discuss its probability distribution. We build a mathematical model to characterize a sojourn time that is embedded into a quantum walk. These results are also valid for a class of quantum walks governed by general coin operators. We also give a method for calculating the sojourn time and analyze the shape features of its probability distribution.

Reconfiguration of Hamiltonian Cycles in Rectangular Grid Graphs

We study reconfiguration of simple Hamiltonian cycles in a rectangular grid graph [Formula: see text], where the Hamiltonian cycle in each step of the reconfiguration connects every internal vertex of [Formula: see text] to a boundary vertex by a single straight line segment. We introduce two operations, flip and transpose, which are local to the grid. We show that any simple cycle of [Formula: see text] can be reconfigured to any other simple cycle of [Formula: see text] using [Formula: see text] flip and transpose operations. Our result proves that the simple Hamiltonian cycle graph [Formula: see text] is connected with respect to those two operations and has diameter [Formula: see text].

Sampling planar tanglegrams and pairs of disjoint triangulations

A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that the problem of generating planar tanglegrams uniformly at random reduces to the corresponding problem for irreducible planar tanglegram layouts, which are known to be in bijection with pairs of disjoint triangulations of a convex polygon. We extend the flip operation on a single triangulation to a flip operation on pairs of disjoint triangulations. Interestingly, the resulting flip graph is both connected and regular, and hence a random walk on this graph converges to the uniform distribution. We also show that the restriction of the flip graph to the pairs with a fixed triangulation in either coordinate is connected, and give diameter bounds that are near optimal. Our results furthermore yield new insight into the flip graph of triangulations of a convex n-gon with a geometric interpretation on the associahedron.

Stagnation Detection with Randomized Local Search.

Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called SD-(1+1) EA introduced by Rajabi and Witt (Algorithmica 2022) adds stagnation detection to the classical (1+1) EA with standard bit mutation. This algorithm flips each bit independently with some mutation rate, and stagnation detection raises the rate when the algorithm is likely to have encountered a local optimum. In this paper, we investigate stagnation detection in the context of the k-bit flip operator of randomized local search that flips k bits chosen uniformly at random and let stagnation detection adjust the parameter k. We obtain improved runtime results compared to the SD-(1+1) EA amounting to a speedup of at least (1-o(1))2πm, where m is the so-called gap size, i. e., the distance to the next improvement. Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of k due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the k-bit flip operator with stagnation detection.

Complexity results on untangling red-blue matchings

Given a matching between n red points and n blue points by line segments in the plane, we consider the problem of obtaining a crossing-free matching through flip operations that replace two crossing segments by two non-crossing ones. We first show that (i) it is NP-hard to α-approximate the shortest flip sequence, for any constant α. Second, we show that when the red points are collinear, (ii) given a matching, a flip sequence of length at most (n2) always exists, and (iii) the number of flips in any sequence never exceeds (n2)n+46. Finally, we present (iv) a lower bounding flip sequence with roughly 1.5(n2) flips, which shows that the (n2) flips attained in the convex case are not the maximum, and (v) a convex matching from which any flip sequence has roughly 1.5n flips. The last four results, based on novel analyses, improve the constants of state-of-the-art bounds.

Enhancing quantum teleportation fidelity under decoherence via weak measurement with flips

Noiseless quantum channels are critical to share a pure maximally entangled state for performing an ideal teleportation protocol. However, in reality the shared entanglement severely degraded due to decoherence. In this paper, we propose a quantum teleportation channel protection scheme to enhance the teleportation fidelity in presence of decoherence. Before the entangled pair enters the decoherence channel, the weak measurement and flip operations are applied to transfer the qubit to a more robust state to the effects of the noise. After the decoherence channel the reversed flip operations and weak measurement reversal are applied to recover the initial state. We illustrate our protected teleportation scheme and compare it with a protocol based on weak measurement reversal. The numerical results show that the average teleportation fidelity of our proposed scheme can be significantly improved. Although the proposed entanglement protection scheme is probabilistic, after a successful entanglement transmission, we use the standard teleportation protocol which has probability one.

Influence of coin symmetry on infinite hitting times in quantum walks

Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other vertex in finite time, provided they are connected. Discrete-time quantum walks on finite connected graphs however, can have infinite hitting times. This phenomenon is related to graph symmetry, as previously characterized by the group of direction-preserving graph automorphisms that trivially affect the coin Hilbert space. If a graph is symmetric enough (in a particular sense) then the associated quantum walk unitary will contain eigenvectors that do not overlap a set of target vertices, for any coin flip operator. These eigenvectors span the Infinite Hitting Time (IHT) subspace. Quantum states in the IHT subspace never reach the target vertices, leading to infinite hitting times. However, this is not the whole story: the graph of the 3D cube does not satisfy this symmetry constraint, yet quantum walks on this graph with certain symmetric coins can exhibit infinite hitting times. We study the effect of coin symmetry by analyzing the group of coin-permutation symmetries (CPS): graph automorphisms that act nontrivially on the coin Hilbert space but leave the coin operator invariant. Unitaries using highly symmetric coins with large CPS groups, such as the permutation-invariant Grover coin, are associated with higher probabilities of never arriving, as a result of their larger IHT subspaces.

Protected Quantum Teleportation Through Noisy Channel by Weak Measurement and Environment-Assisted Measurement

Quantum teleportation as a key protocol for quantum communication and quantum computing demonstrates the stark difference between quantum and classical information transmission. An ideal teleportation protocol requires pure maximally entangled state as the teleportation channel, while in real implementations the shared entanglement is severely degraded due to decoherence. In this letter, we propose a scheme to protect the quantum teleportation from decoherence by means of environment assisted measurement with weak measurements and flip operations. We show that the teleportation fidelity of our proposed scheme is significantly improved compared to teleportation with no protection and a teleportation protocol based on quantum measurement reversal. Also, the explicit formula of average teleportation fidelity and success probability of the entanglement protection are derived.

Low-Complexity Switch Scheduling Algorithms: Delay Optimality in Heavy Traffic

Motivated by applications in data center networks, in this paper, we study the problem of scheduling in an input queued switch. While throughput maximizing algorithms in a switch are well-understood, delay analysis was developed only recently. It was recently shown that the well-known MaxWeight algorithm achieves optimal scaling of mean queue lengths in steady state in the heavy-traffic regime, and is within a factor less than $2$ of a universal lower bound. However, MaxWeight is not used in practice because of its high time complexity. In this paper, we study several low complexity algorithms and show that their heavy-traffic performance is identical to that of MaxWeight. We first present a negative result that picking a random schedule does not have optimal heavy-traffic scaling of queue lengths even under uniform traffic. We then show that if one picks the best among two matchings or modifies a random matching even a little, using the so-called flip operation, it leads to MaxWeight like heavy-traffic performance under uniform traffic. We then focus on the case of non-uniform traffic and show that a large class of low time complexity algorithms have the same heavy-traffic performance as MaxWeight, as long as it is ensured that a MaxWeight matching is picked often enough. We also briefly discuss the performance of these algorithms in the large scale heavy-traffic regime when the size of the switch increases simultaneously with the load. Finally, we perform empirical study on a new algorithm to compare its performance with some existing algorithms.

An efficient method to improve the quality of tetrahedron mesh with MFRC

In this paper, we proposed a novel operation to reconstruction tetrahedrons within a certain region, which we call MFRC (Multi-face reconstruction). During the existing tetrahedral mesh improvement methods, the flip operation is one of the very important components. However, due to the limited area affected by the flip, the improvement of the mesh quality by the flip operation is also very limited. The proposed MFRC algorithm solves this problem. MFRC can reconstruct the local mesh in a larger range and can find the optimal tetrahedron division in the target area within acceptable time complexity. Therefore, based on the MFRC algorithm, we combined other operations including smoothing, edge removal, face removal, and vertex insertion/deletion to develop an effective mesh quality improvement method. Numerical experiments of dozens of meshes show that the algorithm can effectively improve the low-quality elements in the tetrahedral mesh, and can effectively reduce the running time, which has important significance for the quality improvement of large-scale mesh.

Human Gait Recognition: A Single Stream Optimal Deep Learning Features Fusion.

Human Gait Recognition (HGR) is a biometric technique that has been utilized for security purposes for the last decade. The performance of gait recognition can be influenced by various factors such as wearing clothes, carrying a bag, and the walking surfaces. Furthermore, identification from differing views is a significant difficulty in HGR. Many techniques have been introduced in the literature for HGR using conventional and deep learning techniques. However, the traditional methods are not suitable for large datasets. Therefore, a new framework is proposed for human gait recognition using deep learning and best feature selection. The proposed framework includes data augmentation, feature extraction, feature selection, feature fusion, and classification. In the augmentation step, three flip operations were used. In the feature extraction step, two pre-trained models were employed, Inception-ResNet-V2 and NASNet Mobile. Both models were fine-tuned and trained using transfer learning on the CASIA B gait dataset. The features of the selected deep models were optimized using a modified three-step whale optimization algorithm and the best features were chosen. The selected best features were fused using the modified mean absolute deviation extended serial fusion (MDeSF) approach. Then, the final classification was performed using several classification algorithms. The experimental process was conducted on the entire CASIA B dataset and achieved an average accuracy of 89.0. Comparison with existing techniques showed an improvement in accuracy, recall rate, and computational time.

An efficient dual-layer cross-coupled chaotic map security-based multi-image encryption system

This paper proposes an effective image encryption method to encrypt several images in one encryption process. The proposed encryption scheme differs from the current multiple image encryption schemes because of their two-layer cross-coupled chaotic map-based permutation-diffusion operation. Block-shuffling, left–right (L–R) flipping and then bit-XOR diffusion operations are carried out in the first layer using one set of cross-coupled chaotic map. Block-shuffling, up–down (U–D) flipping and then bit-XOR diffusion operations are performed with another set of cross-coupled chaotic maps in the second layer. The two different layers of permutation-diffusion make the proposed algorithm more efficient than the existing multi-image encryption algorithms. Moreover, the combination of block-based shuffling and flip operation decreases the algorithm’s computational complexity, which means enhancing the time efficiency of the algorithm. In cross-coupling operation, the use of a single fixed-type one-dimensional chaotic map-piece-wise linear chaotic map (PWLCM) makes the algorithm efficient both in hardware and in software. PWLCM’s initial values and system parameters (keys) are generated by means of the hash values of original images that resist the algorithm against the attacks of chosen-plaintext and known-plaintext. Results of simulation and comparative security analysis reveal that the suggested scheme is more effective in encryption and resists better against all widely used attacks.

Rank/select queries over mutable bitmaps

The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the case where one is allowed to modify the bitmap via a flip(i) operation that toggles its ith bit. By adapting and properly extending some results concerning prefix-sum data structures, we present a practical solution to the problem, tailored for modern CPU instruction sets. Compared to the state-of-the-art, our solution improves runtime with no space degradation. Moreover, it does not incur in a significant runtime penalty when compared to the fastest immutable indexes, while providing even lower space overhead.

Automatic segmentation of coronary lumen and external elastic membrane in intravascular ultrasound images using 8-layer U-Net

BackgroundIntravascular ultrasound (IVUS) is the golden standard in accessing the coronary lesions, stenosis, and atherosclerosis plaques. In this paper, a fully automatic approach by an 8-layer U-Net is developed to segment the coronary artery lumen and the area bounded by external elastic membrane (EEM), i.e., cross-sectional area (EEM-CSA). The database comprises single-vendor and single-frequency IVUS data. Particularly, the proposed data augmentation of MeshGrid combined with flip and rotation operations is implemented, improving the model performance without pre- or post-processing of the raw IVUS images.ResultsThe mean intersection of union (MIoU) of 0.937 and 0.804 for the lumen and EEM-CSA, respectively, were achieved, which exceeded the manual labeling accuracy of the clinician.ConclusionThe accuracy shown by the proposed method is sufficient for subsequent reconstruction of 3D-IVUS images, which is essential for doctors’ diagnosis in the tissue characterization of coronary artery walls and plaque compositions, qualitatively and quantitatively.

On flips in planar matchings

In this paper we investigate the structure of flip graphs on non-crossing perfect matchings in the plane. Specifically, consider all non-crossing straight-line perfect matchings on a set of 2n points that are placed equidistantly on the unit circle. A flip operation on such a matching replaces two matching edges that span an empty quadrilateral with the other two edges of the quadrilateral, and the flip is called centered if the quadrilateral contains the center of the unit circle. The graph Gn has those matchings as vertices, and an edge between any two matchings that differ in a flip, and it is known to have many interesting properties. In this paper we focus on the spanning subgraph Hn of Gn obtained by taking all edges that correspond to centered flips, omitting edges that correspond to non-centered flips. We show that the graph Hn is connected for odd n, but has exponentially many small connected components for even n, which we characterize and count via Catalan and generalized Narayana numbers. For odd n, we also prove that the diameter of Hn is linear in n. Furthermore, we determine the minimum and maximum degrees of Hn for all n, and characterize and count the corresponding vertices. Our results imply the non-existence of certain rainbow cycles in Gn, and they resolve several open questions and conjectures raised in a recent paper by Felsner, Kleist, Mütze, and Sering.