Abstract Purpose Since their introduction, intrauterine devices (IUDs) have been associated with various complications. Avery rare complication is the perforation of the cervix by the strings of the IUD. Purpose of the current study is to present a novel case of cervical perforation by the strings of a copper IUD and to perform a systematic review of the literature. Materials and Methods The patient a 43-year-old attended the gynecology clinic in order to remove her copper IUD. Speculum examination revealed that both the strings of the IUD perforated the anterior lip of the cervix. Management options were offered, the patient opted for a hysteroscopic removal. We searched the electronic databases: MEDLINE, Cochrane Library,Google Scholar,EBSCO for similar cases. Results Electronic search yielded 1821 articles; 8 were selected for inclusion. Mean age of the women was 35,37±7,781, range (26-47) years. One woman (12.5%) was nulligravida;3 women were multigravida (37,5%). Seven women (87,5%) were asymptomatic. Three IUDs (37,5%) were LNG-IUS; 5 IUDs (62,5%) contained copper. Conclusions Cervical perforation by the strings of IUD is an extremely rare clinical entity. It is asymptomatic in general and in most cases the strings of the IUD may be returned back to the endocervical canal after surgical maneuvers.

Cosmic strings can arise from spontaneous phase transitions during the inflationary period and are describable as disclination topological defects in spacetime. Analytical integration of the geodesic equations for a particle around a cosmic string reveals distinct orbit patterns dependent on the disclination intensity $\beta_{0}$. After its interaction with the cosmic string, the particle's behavior becomes random. To categorize these patterns, we describe the geodesic motion as iterated maps of a discrete parameter. Through the stabilization values of these functions, we correlate the scattering angle and the number of loops for the particle with $\beta_{0}$. Therefore, we interpret the gravitational field mathematically as an instructor of a particle's next position, given its previous one. We find that the radial function in the small displacement limit is similar to the logistic map. This leads us to conjecture the potential of the discrete parameter being a multiple of Planck's time, suggesting a method for the geometric discretization of spacetime around a cosmic string.

Physics and neuroscience share overlapping objectives, the major of which is probably the attempt to reduce the observed universe to a set of rules. The approaches are complementary, attempting to find a reduced description of the universe or of the observer, respectively. We propose here that combining the two approaches within an observer-inclusive physical scheme, bears significant advantages. In such a scheme, the same set of rules applies to the universe and its observers, and the two descriptions are entangled. We show here that analyzing special relativity in an observer-inclusive framework can resolve its contradiction with the observed non-locality of physical interactions. The contradiction is resolved by reducing the universe (including the observer) to a dynamic distribution of closed strings (“ceons”) whose vibration waves travel at c. This ceons model is consistent with general relativity, non-locality, the holographic principle and loop quantum gravity; it also eliminates Zeno’s motion paradoxes. Yet, the model entails several new empirical predictions. Finally, the ceons model suggests a fundamental physical implementation of active biological perception. Paraphrasing Torricelli, this paper suggests that we live submerged in a c of light.

There has been observational evidence about spin axes of quasars in large quasar groups correlated over hundreds of Mpc. This is seen in the radio spectrum as well as in the optical range. There is not yet a satisfactory explanation of this "spooky" alignment. This alignment cannot be explained by mutual interaction at the time that quasars manifest themselves optically. A cosmological explanation could be possible in the formation of superconducting vortices (cosmic strings) in the early universe, just after the symmetry-breaking phase of the universe. We gathered from the NASA/IPAC and SIMBAD extragalactic databases the right ascension, declination, inclination, position angle and eccentricity of the host galaxies of 3 large quasar groups to obtain the azimuthal and polar angle of the spin vectors. The alignment of the azimuthal angle of the spin vectors of quasars in their host galaxy is confirmed in the large quasar group U1.27 and compared with two other groups in the vicinity, i.e., U1.11 and U1.28. It is well possible that the azimuthal angle alignment fits the predicted azimuthal angle dependency in the theoretical model of the formation of general relativistic superconducting vortices, where the initial axially symmetry is broken just after the symmetry breaking of the scalar-gauge field.} \keyword{quasar groups; alignment spin vectors; host galaxy; cosmic strings; symmetry breaking; scalar-gauge field.

This article will continue ansatz gage matrix of Iyer Markoulakis Helmholtz Hamiltonian mechanics points’ fields gage to Pauli Dirac monopole particle fields ansatz gage general formalism at Planck level, by constructing a Pauli Dirac Planck circuit matrix field gradient of particle monopole flow loop. This circuit assembly gage (PDPcag) that maybe operating at the quantum level, demonstrates the power of point fields matrix theoretical quantum general formalism of Iyer Markoulakis Helmholtz Hamiltonian mechanics transformed to Coulomb gage metrics, to form eigenvector fields of magnetic monopoles as well as electron positron particle gage metrics fields. Eigenvector calculations performed based on Iyer Markoulakis quantum general formalism are substituted for gage values of typical eigenvectors of dipolar magnetically biased monopoles with their conjugate eigenvectors, as well as eigenvector fields that are of the electron and positron particles. Then they are compiled to form combinatorial eigenvector matrix bundle of the monopole particle circuit field constructs assembly. Evaluation of this monopole particle fields matrix provided eigenvector fields results like SUSY, having Hermitian quantum matrix with electron-positron annihilation alongside north and south monopoles collapsing to dipolar “stable” magnetism, representing electromagnetic gaging typical metrics fields. Applying experimental observations on magnetic poles with measuring magnetic forces John Hodge’s results were showing asymmetrical pole forces; author has mathematically constructed asymmetric\strings\gage\metrics to characterize electromagnetic gravity, putting together while integrating with stringmetrics gravity that author has been reporting in earlier published articles. Physical Analysis with generalization of mass-charge and charge-fields gage metrics to quantum relativity gage metrics fields are proposed based on author’s proof formalism paper providing derivational algorithmic steps, to determine gage parametric values within the equation of Coulomb gage. Vortex fields’ wavefunctions and the scalar potential characterized by a function and a coupling constant having quantum density matrix together define the gage metrics quantifiable observable measurement physics of electron-positron cross-diagonal fields; contrastingly, diagonal terms of PDPcag matrix characterizes electron-positron particle eigenvector fields, while Hilbert Higgs mass metrics characterizes eigen-matter. Author is already working with Christopher O’Neill about magic square symmetry configurations to quantitatively understand symmetry, structure, and the real space geometry that are expected to form out of vacuum quanta point fields’ quantitative quantum general formalism theory of Iyer Markoulakis. In addition, author is currently collaborating with Manuel Malaver’s astrophysical Einstein Minkowski modified space time metrics evaluations of the sense-time-space relativistic general metrics to have means to account for curving or shaping of spacetime topology of a five-dimensional sense-time-space. Manuel Malaver’s specialization with modified Einstein Maxwell equations for modeling galaxies and stars cosmological physics, utilizing Einstein-Maxwell-Tolman- Schwarzschild and Reissner-Nordström spacetime and black holes theoretical formalisms have author of this paper collaboratively model quantum astrophysics of dark energy Star’s theory with Einstein-Gauss-Bonnet gravity equations.

There are two reasons to have an efficient algorithm for identifying all maximal Lyndon substrings of a string: firstly, Bannai et al. introduced in 2015 a linear algorithm to compute all runs of a string that relies on knowing all maximal Lyndon substrings of the input string, and secondly, Franek et al. showed in 2017 a linear equivalence of sorting suffixes and sorting maximal Lyndon substrings of a string, inspired by a novel suffix sorting algorithm of Baier. In 2016, Franek et al. presented a brief overview of algorithms for computing the Lyndon array that encodes the knowledge of maximal Lyndon substrings of the input string. Among the presented were two well-known algorithms for computing the Lyndon array: a quadratic in-place algorithm based on iterated Duval's algorithm for Lyndon factorization, and a linear algorithmic scheme based on linear suffix sorting, computing inverse suffix array, and applying to it the Next Smaller Value algorithm. Duval's algorithm works for strings over any ordered alphabet, while for linear suffix sorting, a constant or an integer alphabet is required. The authors at that time were not aware of Baier's algorithm. In 2017, our research group proposed a novel algorithm for the Lyndon array. Though the proposed algorithm is linear in the average case and has O(n log(n)) worst-case complexity, it is interesting as it emulates the fast Fourier algorithm's recursive approach and introduces tau-reduction that might be of independent interest. In 2018, we presented a linear algorithm to compute the Lyndon array of a string inspired by Phase I of Baier's algorithm for suffix sorting. This paper presents theoretical analysis of these two algorithms and provides empirical comparisons of both their C++ implementations with respect to iterated Duval's algorithm.