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The aim of this work is to compare symbolic and ordinary powers of monomial ideals using commutative algebra and combinatorics. Monomial ideals whose symbolic and ordinary powers coincide are called Simis ideals. Weighted monomial ideals are defined by assigning linear weights to monomials. We examine Simis and normally torsion-free ideals, relate some of the properties of monomial ideals and weighted monomial ideals, and present a structure theorem for edge ideals of $d$-uniform clutters whose ideal of covers is Simis in degree $d$. One of our main results is a combinatorial classification of when the dual of the edge ideal of a weighted oriented graph is Simis in degree $2$., Comment: 22 pages

We go through several previous corrections and contributions to the muon $g-2$, starting from the dark photon hypothesis to the dark Z. We explore the inputs from a dark Z boson virtual mediator in a first order loop. We consider not only the QED like contributions in the theory but also weak interactions. We obtain a new factor that adds corrections to the form factor associated with the anomalous magnetic moment. We show our result is favorable in new unexplored windows in the mass-coupling parameter space., Comment: 10 pages, 4 figures

We study the possibility to describe dark matter in a model of the universe with two scale factors and a non-standard Poisson bracket structure characterized by the deformation parameter \kappa. The dark matter evolution is analyzed in the early stages of the universe, and its relic density is obtained via the Freeze-In and Freeze-Out mechanism. We show that by fixing \k{appa} and the initial ratio of energy densities present in the different sectors of the universe, the space of thermal average annihilation cross-sections and dark matter masses compatible with the standard cosmology prior to Big Bang Nucleosynthesis (BBN), is enlarged. This feature of the model is compatible with non-standard cosmology.

We analyze the early stage of evolution of a universe with two scale factors proposed in [1] when matter is present. The scale factors describe two causally disconnected patches of the universe interacting trough a non-trivial Poisson bracket structure in the momentum sector characterized by one parameter \kappa. We studied two scenarios in which one of the patches is always filled with relativistic matter while the other contains relativistic matter in one case, and non-relativistic matter in the second case. By solving numerically the set of equations governing the dynamics, we found that the energy content of one sector drains to the other and from here it is possible to constraint the deformation parameter \kappa by imposing that the decay of the energy density happens, at most, at the Big Bang Nucleosynthesis temperature in order to return to the usual behavior of radiation. The relation with Non Standard Cosmologies is also addressed.

In the context of gravity in the strong-coupling regime, the propagation amplitude of gravity coupled to relativistic particles undergoing geodesic separation is calculated exactly. Geodesic separation gives rise to boundary terms associated with the h_\times and h_+ graviton components. At low temperatures the propagation amplitude vanishes, implying no graviton propagation in this regime., Comment: 7 pages

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. A critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom (DOFs), tolerance settings and the approximate time taken per cycle for each model., Comment: 22 pages, 7 figures, 2 tables

Bikesharing schemes are transportation systems that not only provide an efficient mode of transportation in congested urban areas, but also improve last-mile connectivity with public transportation and local accessibility. Bikesharing schemes around the globe generate detailed trip data sets with spatial and temporal dimensions, which, with proper mining and analysis, reveal valuable information on urban mobility patterns. In this paper, we study the London bicycle sharing dataset to explore community structures. Using a novel clustering technique, we derive distinctive behavioural patterns and assess community interactions and spatio-temporal dynamics. The analyses reveal self-contained, interconnected and hybrid clusters that mimic London's physical structure. Exploring changes over time, we find geographically isolated and specialized communities to be relatively consistent, while the remaining system exhibits volatility, especially during and around peak commuting times. By increasing our understanding of the collective behaviour of the bikesharing users, this analysis supports policy appraisal, operational decision-making and motivates improvements in infrastructure design and management., Comment: 7th International Workshop on Pervasive Urban Applications, UbiComp '18 ACM International Joint Conference on Pervasive and Ubiquitous Computing; 7 pages, 4 figures

We consider a model of dark quantum electrodynamics which is coupled with a visible photon through a kinetic mixing term. After checking of consistency properties, we compute the $g_w-2$, where $g_w$ is the gyromagnetic factor for a dark fermion. The $g_w-2$ and $g-2$ of quantum electrodynamics are related by the kinetic mixing factor. We analyse the $g_w-2$ in terms of the ratio $\kappa =m_\gamma/m_\chi$ where $m_\gamma$ and $m_\chi$ are the masses of the dark photon and the dark fermion and we discuss how light and heavy fermions become very different for $m_\gamma \leq10^{-5}\,$ eV. This analysis is also carried out using different available data., Comment: Small changes in the introduction

We point out that a cold dark matter condensate made of gauge bosons from an extra hidden U(1) sector - dubbed hidden- photons - can create a small, oscillating electric density current. Thus, they could also be searched for in the recently proposed LC-circuit setup conceived for axion cold dark matter search by Sikivie, Sullivan and Tanner. We estimate the sensitivity of this setup for hidden-photon cold dark matter and we find it could cover a sizable, so far unexplored parameter space., Comment: 2 columns, 4 pages, 2 figures, v2: some clarifications added, version accepted by EPJC

The scattering of neutrinos assuming a "secret" interaction at low energy is considered. To leading order in energy, the two-body potential is a $\delta$-potential, and it is used as a motivation to study generic short-range elastic interactions between neutrinos. The scattering cross section and Sommerfeld enhancement depend on two phenomenological parameters deriving from the exact form of the potential, akin to "renormalized" coupling constants. Repulsive potentials lead to a decrease in the total cross section, resulting in an enhancement of the neutrino density. For attractive potentials of the right form, substantial Sommerfeld enhancement can appear., Comment: This paper supersedes the earlier version of our paper. Extensive revision of the earlier material with two new sections incorporating a general discussion of short-range potentials as well as an appendix are included and the title is changed to match with the version to appear in PRD

We discuss the contribution of axion-like excitations (ALE) to the vacuum birrefringence in the limit $m_A \gtrsim \omega$, where $m_A$ is the mass of the excitation and $\omega$ the energy of test photons interacting with an external (intense) magnetic field. The relevance of this term with respect to the QED contribution depends on the ratio $g_A/m_A$ and, from present bounds on the mass and the coupling constant $g_A$, we find that in the present low energy regime, it ranges from $10^{-14}$ to $10^2$ suggesting an interesting alternative to explore., Comment: References adde and section II rewritten. MPLA in press

Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed, Comment: Contribution to the Fifth International Conference on Mathematical Methods in Physics, Rio de Janeiro, April 24-28 2006

We analyze the consequences of violation of Lorentz and $CPT$ invariance in the massless neutrino sector by deforming the canonical anti-commutation relations for the fields. We show that, for particular choices of the deformation, oscillation between massless neutrino species takes place when only Lorentz invariance is violated. On the other hand, if both Lorentz and $CPT$ invariances are violated, we show that there is no oscillation between massless neutrino species. Comparing with the existing experimental data on neutrino oscillations, we obtain bounds on the parameter for Lorentz invariance violation., Comment: Several portions of the paper was completely re-written and new references added. To appear in PLB

We explore the possibility of baryogenesis without departure from thermal equilibrium. A possible scenario is found, though it contains strong constraints on the size of the $CPT$ violation ($CPTV$) effects and on the role of the $B$ (baryon number) nonconserving interactions which are needed for it., Comment: Revtex, 4pages