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In this paper, we present a revision of the discrete symmetries (C, P, T, CP, and CPT), within an approach that treats 2-component Weyl spinors as the fundamental building blocks. Then, we discuss some salient aspects of the discrete symmetries within quantum field theory (QFT). Besides the generic discussion, we also consider aspects arising within specific renormalizable theories (such as QED and YM). As a new application of the chiral formulation, we discuss the discrete symmetries for the Rarita-Schwinger (RS) spin-$\frac{3}{2}$ field. For the sake of completeness, the elements of linearized gravity (LG) and RS theories are discussed, as they are fundamental to Supergravity (SUGRA). We also discuss the advantages of using the 2-component spinors as the basic building blocks for the formulation of CPT-violating QFTs. Following this formalism, we establish an extension of the general RS theory with terms that violate the Lorentz symmetry and/or CPT symmetry, as well as the one already established in LG., Comment: 27 pages, 0 figures

The proposed system consists of a two-stage cascade. The first stage performs a rough heartbeat detection while the second stage refines the previous one, improving the temporal localization and also classifying the heartbeats into types S1 and S2. The first contribution is a novel approach that combines the dissimilarity matrix with the frame-level spectral divergence to locate heartbeats using the repetitiveness shown by the heart sounds and the temporal relationships between the intervals defined by the events S1/S2 and non-S1/S2 (systole and diastole). The second contribution is a verification-correction-classification process based on a sliding window that allows the preservation of the temporal structure of the cardiac cycle in order to be applied in the heart sound classification. The proposed method has been assessed using the open access databases PASCAL, CirCor DigiScope Phonocardiogram and an additional sound mixing procedure considering both Additive White Gaussian Noise (AWGN) and different kinds of clinical ambient noises from a commercial database. The proposed method provides the best detection/classification performance in realistic scenarios where the presence of cardiac anomalies as well as different types of clinical environmental noises are active in the PCG signal. Of note, the promising modelling of the temporal structures of the heart provided by the dissimilarity matrix together with the frame-level spectral divergence, as well as the removal of a significant number of spurious heart events and recovery of missing heart events, both corrected by the proposed verification-correction-classification algorithm, suggest that our proposal is a successful tool to be applied in heart segmentation.

We present a study on the possibility of observing a hypothetical particle known as the Flavon $H_F$, which is predicted in an extension of the standard model that includes the so-called Froggatt-Nielsen mechanism. The proposed decay channel is through a $b\bar{b}h$ final state, where the Higgs boson $(h)$ decays to a pair of photons or a pair of $b$ quarks $(h\to \gamma\gamma,\,b\bar{b})$. We found that, under special scenarios of the model parameter space, the processes analyzed could provide evidence for the existence of the Flavon in the next stage of the LHC: the High Luminosity LHC. Specifically, we predict a \textit{signal significance} of $5\sigma$ ($2\sigma$) in the $h\to b\bar{b}$ ($h\to\gamma\gamma$) channel for a Flavon mass of $800$ ($900$) GeV and an integrated luminosity of $2500$ ($3000$) fb$^{-1}$., Comment: arXiv admin note: text overlap with arXiv:2205.12641

Industrial particle accelerators typically operate in dirtier environments than research accelerators, leading to increased noise in RF and electronic systems. Furthermore, given that industrial accelerators are mass produced, less attention is given to optimizing the performance of individual systems. As a result, industrial accelerators tend to underperform their own hardware capabilities. Improving signal processing for these machines will improve cost and time margins for deployment, helping to meet the growing demand for accelerators for medical sterilization, food irradiation, cancer treatment, and imaging. Our work focuses on using machine learning techniques to reduce noise in RF signals used for pulse-to-pulse feedback in industrial accelerators. Here we review our algorithms and observed results for simulated RF systems, and discuss next steps with the ultimate goal of deployment on industrial systems., Comment: 9 pages, 6 figures, accepted for publication in Journal of Instrumentation (J. Inst., pending)

Modeling and Simulation (M&S) for system design and prototyping is practiced today both in the industry and academia. M&S are two different areas altogether and have specific objectives. However, most of the times these two separate areas are taken together. The developed code is tightly woven around both the model and the underlying simulator that executes it. This constraints both the model development and the simulation engine that impacts scalability of the developed code. Furthermore, a lot of time is spent in development of a model because it needs both domain knowledge and simulation techniques, which also requires communication among users and developers. Unified Modeling Language (UML) is widely accepted in the industry, whereas Discrete Event Specification (DEVS) based modeling that separates the model and the simulator, provides a cleaner methodology to develop models and is much used in academia. DEVS today is used by engineers who understand discrete event modeling at a much detailed level and are able to translate requirements to DEVS modeling code. There have been earlier efforts to integrate UML and DEVS but they haven't succeeded in providing a transformation mechanism due to inherent differences in these two modeling paradigms. This paper presents an integrated approach towards crosstransformations between UML and DEVS using the proposed eUDEVS, which stands for executable UML based on DEVS. Further, we will also show that the obtained DEVS models belong to a specific class of DEVS models called Finite Deterministic DEVS (FD-DEVS) that is available as a W3C XML Schema in XFD-DEVS. We also put the proposed eUDEVS in a much larger unifying framework called DEVS Unified Process that allows bifurcated model-continuity based lifecycle methodology for systems M&S. Finally, we demonstrate the laid concepts with a complete example.

In this paper, we study the coupling of the gravity supermultiplet (graviton and gravitino) of minimal $\mathcal{N}=1$ SUGRA following a constructive approach. Firstly, we use the master formulae that follows from considering the scaling behavior of the spinor variables under the little group. Secondly, we derive the 4-point couplings using BFCW. Then, we verify these results for the general 3-point interactions that can be derived using the KLT-type relations, i.e., they can be written as the square of the coupling of the gluons and gluinos. Finally, we consider SUGRA Compton effect for graviton-gravitino. For completeness, we present in the appendix the $\mathcal{N}=1$ Sugra lagrangian in the 2-component Weyl formalism, including the proofs of SUSY and gauge invariance., Comment: 28 pages, 5 figures, 1 table, minor typos fixed, reference added

The use of e-learning systems has a long tradition, where students can study online helped by a system. In this context, the use of recommender systems is relatively new. In our research project, we investigated various ways to create a recommender system. They all aim at facilitating the learning and understanding of a student. We present a common concept of the learning path and its learning indicators and embed 5 different recommenders in this context.

The singular parametric oscillators obtained from the one-parameter Darboux deformation/transformation effected upon the classical harmonic oscillator are introduced and discussed in some detail using sin(omega_0 t) and cos(omega_0 t) as seed solutions. The corresponding Ermakov-Lewis integrability problem of these parametric oscillators is also studied. It is shown that the Ermakov-Lewis invariants do not depend on the deformation parameter and are singularity-free., Comment: 16 pages, 10 figures, 35 references, published version, a few remaining misprints corrected

Structural and tectonic features in the Pacific Coast of Mexico generate a high level of seismic activity in the Jalisco block (JB) region, making it one of the most attractive areas of the world for geophysical investigations. The Rivera North America contact zone has been the object of different tectonic studies in recent years framed within the TsuJal project. To this day, this project is generating numerous crucial geophysical results, which significantly improve our understanding of the region. Our study is focused on the interaction between the south of the JB and Rivera plate (RP), which crosses the Middle America trench. We also cover an offshore onshore transect of 130 km length between the eastern Rivera fracture zone and La Huerta region, in the Jalisco state. To characterize this region,we interpreted wide angle seismic, multichannel seismic, and multibeam bathymetry data. The integration of these results, with the local and regional seismicity recorded by the Jalisco Seismic Accelerometric Telemetric Network and by the Mapping the Rivera Subduction Zone experiment, provides new insights into the geometry of the southern RP, which is dipping 12 14 degrees under the JB in the northeast southwest direction. Moreover, our results provide new seismic images of the accretionary wedge, the shallow crust, the deep crust, and the upper-mantle structure along this profile., Comment: Seismological Research Letters 2019

Industrial particle accelerators inherently operate in much dirtier environments than typical research accelerators. This leads to an increase in noise both in the RF system and in other electronic systems. Combined with the fact that industrial accelerators are mass produced, there is less attention given to optimizing the performance of an individual system. As a result, industrial systems tend to under perform considering their hardware hardware capabilities. With the growing demand for accelerators for medical sterilization, food irradiation, cancer treatment, and imaging, improving the signal processing of these machines will increase the margin for the deployment of these systems. Our work is focusing on using machine learning techniques to reduce the noise of RF signals used for pulse-to-pulse feedback in industrial accelerators. We will review our algorithms, simulation results, and results working with measured data. We will then discuss next steps for deployment and testing on an industrial system., Comment: Talk presented at LLRF Workshop 2023 (LLRF2023, arXiv: 2310.03199)

The discovery of a light Higgs boson means that whatever form new physics takes, it should keep stable the Higgs mass. Besides the well-known solutions to the naturalness problem (Supersymmetry, Conformal symmetry, Compositeness, etc), models that include heavy particles with feeble couplings to the Standard Model (SM) can be considered natural, since the corrections to the Higgs mass remains of the order of the electroweak (EW) scale. This solution can be used for model building too, with realizations that include the see-saw mechanism for neutrino masses and FIMP dark matter models, but it also holds for generic sectors that have Planck-suppressed couplings with the SM. One can also incorporate this solution within the SMEFT framework; the corresponding higher-dimensional operators induce small corrections to both the Higgs mass and its self-coupling, a prediction that can be tested at a future Higgs factory. We present a natural extension of the SMEFT that describes corrections to the SM, while also including a Feeble Coupled Sector aimed to account for the dark cosmos, with predictions for new signals that can be tested too., Comment: 7 pages

The non-conservation of the lepton number has been explored at the LHC through the Lepton-Flavor Violating (LFV) Higgs decays $h\to\ell_a\ell_b$, with $\ell_{a,\,b}=e,\,\mu,\,\tau$ $(a \neq b)$. Current limits on these decays are a source of valuable information on the structure of the Yukawa and Higgs sectors. The LFV Higgs couplings can arise within the general Two-Higgs Doublet Model (2HDM); the predicted rates for these decay modes depend on the specific Yukawa structure being considered, ranging from a vanishing branching ratio at tree-level for some versions (2HDM-I, II, X, Y), up to large and detectable ratios within the general 2HDM-III. An attractive scenario is given by the texturized version of the model (2HDM-Tx), with the Yukawa matrices having some texture zeros, such as the minimal version with the so-called Cheng-Sher ansazt. We study the constraints on the parameter space of the 2HDM provided by experimental and theoretical restrictions, and use them to study the detection of LFV Higgs modes at LHC. We find several encouraging scenarios to the search for the decay $h \to\tau\mu$ that could be achieved in the High-Luminosity LHC. On the other hand, LFV Higgs couplings can also be induced at one-loop level in the 2HDM with neutrino masses, with the loops being mediated by neutrino interactions; we find that the resulting branching ratios are of order $10^{-7}$ at best, which is out of the reach of current and future phases of the LHC., Comment: Version accepted to be published in IJMPA

The detection of a single Higgs boson at the Large Hadron Collider (LHC) has allowed one to probe some properties of it, including the Yukawa and gauge couplings. However, in order to probe the Higgs potential, one has to rely on new production mechanisms, such as Higgs pair production. In this paper, we show that such a channel is also sensitive to the production and decay of a so-called `Flavon' field ($H_F$), a new scalar state that arises in models that attempt to explain the hierarchy of the Standard Model (SM) fermion masses. Our analysis also focuses on the other decay channels involving the Flavon particle, specifically the decay of the Flavon to a pair of $Z$ bosons ($H_F \to Z Z$) and the concurrent production of a top quark and charm quark ($H_F\to tc$), having one or more leptons in the final states. In particular, we show that, with 3000 fb$^{-1}$ of accumulated data at 14 TeV (the Run 3 stage) of the LHC an heavy Flavon $H_F$ with mass $M_{H_F} \simeq 2m_t $ can be explored with $3\sigma -5\sigma $ significance through these channels., Comment: 39 pages, 21 figures

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.

Aspects of top quark physics can be studied at a future Circular Electron-Positron Collider (CEPC). In particular, Flavor-Changing Neutral Current interactions (FCNC) of the top quark can be studied even with a center-of-mass energy from $\sqrt{s}\gtrsim m_t$ to $\sqrt{s}=240$ GeV, through the production a single top quark in association with a charm quark, which can arise in several scenarios of new physics. We explore here this signal within the Left-Right Mirror Model, which is a Left-Right model that includes mirror fermions; this model is motivated as a possible solution to the strong CP problem and by its rich phenomenology. We find that for particular scenarios of the model parameters, which are in agreement with the most up-to-date experimental constraints, the signal coming from the process $e^+e^-\to V \to tc$ ($V=Z,\,Z^{\prime}$) provide a detectable signal and thus it can give evidence for FCNC interactions; in these scenarios the mass of a new neutral gauge boson can be as high as $m_{Z'}=7$ TeV., Comment: 14 pages and 11 figures, to be published in The European Physical Journal Plus

In this paper we present general formulae for the calculation of LFV Higgs decays $H_r \to l_a l_b$ at one-loop, with $H_r$ being part of the Higgs spectrum of a generic multi-scalar extension of the Standard Model (SM) with neutrino masses. We develop a method based on a classification of the particles appearing in the loop diagrams (scalars, fermions and vectors), and by identifying the corresponding couplings, we are able to present compact expressions for the form factors involved in the amplitudes. Our results are applicable to models where Flavor Changing Neutral Currents (FCNC) are forbidden at tree-level, but change of flavor is induced by charged currents. Then, as applications of our formalism, we evaluate the branching ratio for the mode $h \to l_a l_b$, for two specific models: the See-Saw Type I-$\nu$SM and the Scotogenic model (here $h = H_1$ corresponds to the SM-like Higgs boson); we find that the largest branching ratio for SM-like Higgs $h$ boson within the $\nu$SM is of the order $\mathcal{BR}(h\to \mu \tau)\simeq 10^{-12}$, while for the Scotogenic model we find $\mathcal{BR}(h\to l_a l_b)\lesssim 10^{-9}$, which satisfy the latest experimental LHC results., Comment: 46 pages, 15 figures

Experiments were performed at the Fermilab Accelerator Science and Technology (FAST) facility to elucidate the effects of long-range wakefields (LRWs) in TESLA-type superconducting rf cavities. In particular, we investigated the higher-order modes (HOMs) generated in the eight cavities of a cryomodule (CM) due to off-axis steering with correctors located ~4 m upstream of the CM. We have observed correlated submacropulse centroid slews of a few-hundred microns and centroid oscillations at ~240 kHz in the rf BPM data after the CM. The entrance energy into the CM was 25 MeV, and the exit energy was 100 MeV with 125 pC/b and 400 pC/b in 50-bunch pulse trains. These experimental results were evaluated for machine learning training aspects which will be used to inform the commissioning plan for the Linac Coherent Light Source-II injector CM.

Warps are observed in a large fraction of disc galaxies, and can be due to a large number of different processes. Some of these processes might also cause vertical heating and flaring. Using a sample of galaxies simulated in their cosmological context, we study the connection between warping and disc heating. We analyse the vertical stellar density structure within warped stellar discs, and monitor the evolution of the scale-heights of the mono-age populations and the geometrical thin and thick disc during the warp's lifetime. We also compare the overall thickness and the vertical velocity dispersion in the disc before and after the warp. We find that for warps made of pre-existing stellar particles shifted off-plane, the scale-heights do not change within the disc's warped region: discs tilt rigidly. For warps made of off-plane new stellar material (either born in-situ or accreted), the warped region of the disc is not well described by a double $\mathrm{sech^2}$ density profile. Yet, once the warp is gone, the thin and thick disc structure is recovered, with their scale-heights following the same trends as in the region that was never warped. Finally, we find that the overall thickness and vertical velocity dispersion do not increase during a warp, regardless of the warp's origin. This holds even for warps triggered by interactions with satellites, which cause disc heating but before the warp forms. Our findings suggest that the vertical structure of galaxies does not hold any memory of past warps., Comment: 10 pages, 7 figures, 1 table. Submitted to MNRAS

We study the accelerated motion of mirrors and the photonic Unruh effect. The solutions of Maxwell's equations with appropriate boundary conditions in Rindler coordinates are found. The canonical quantization of the field is carried out properly. Important consequences arise from the presence of mirrors or polarizers. It is shown that a single reflective surface produces frequency quantization due to Dirichlet conditions applied to the $-1/(\alpha x)^2$ anomalous potential for non-inertial observers. The number of photons per accelerated mode is estimated via Hankel functions., Comment: 5 pages, 1 figure

In this paper we study the coupling of scalar (Higgs) particles ($\phi$) with gravitons ($h$) and their possible effects. The general form of the 3-point interaction $\phi(p) h(1)h(2)$ can be derived using the scaling behavior of the spinor variables under the little group; the resulting vertices exhibit such simplicity, that some simplifications should be hidden in the expressions obtained from the extended scalar action. To investigate this, we study an extended Einstein-Hilbert action that besides the minimal coupling, it also includes terms of the form $\phi R^2$, $\phi R^{\mu\nu} R_{\mu\nu}$ and $\phi R^{\mu\nu\rho\sigma} R_{\mu\nu\rho\sigma}$, as well as the term $\epsilon_{\mu\nu \alpha\beta} \phi_5 R^{\mu\nu}_{\rho\sigma} R^{\alpha\beta\rho\sigma}$ for the case of a pseudo-scalar ($\phi_5$). The resulting vertices satisfy KLT-type relations, i.e., they can be written as the square of the coupling of the Higgs with gluons. We find that the amplitude for the Higgs decay into a pair of gravitons (on-shell) only receives a contribution coming from the square of the Riemann tensor. Similar results are obtained for the 3-body decay $\phi \to h h^* (\to XX)$, with an off-shell graviton ($h^*$) that goes into the final state $XX$. One could expect that these quadratic terms can produce new loop effects, however we find that the new contribution from this non-minimal coupling to the graviton self-energy, also vanishes for on-shell gravitons., Comment: 16 pages, 1 figure

We use the Holder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is two-dimensional and periodic in the two Cartesian directions, with the symmetry group $P_{4mm}$. The resulting parametric isospectral potential display a P_m symmetry for values of the parameter moderately close to the singular value gamma_s. However, at large values of the parameter, visually around gamma=gamma_s+110, the original symmetry is recovered. For a much higher precision value of the parameter for this symmetry recovery, we show that the multifractal spectrum of the parametric potential can be conveniently used. In the latter case, we obtain gamma=gamma_s+201.085 for three decimal digits precision., Comment: 6 pages, 4 figures with subfigures, accepted at Materials Letters

This paper presents a new chaotic system having four attractors, including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial conditions, Lyapunov spectrum, strangeness measure, attraction basin, including the class and size of it, existence of strange attractor, bifurcation analysis, multistability, electronic circuit design, and hardware implementation, are rigorously treated. Numerical computations are used to compute the basin of attraction and show that the system has a far-reaching composite basin of attraction. Such a basin of attraction is vital for engineering applications. Moreover, a circuit model of the system is realized using analog electronic components. A procedure is detailed for converting the system parameters into corresponding electronic component values such as the circuital resistances while ensuring the dynamic ranges are bounded. Besides, the system is used as the source of control inputs for independent navigation of a differential drive mobile robot, which is subject to the Pfaffian velocity constraint. Due to the properties of sensitivity on initial conditions and topological mixing, the robot's path becomes unpredictable and guaranteed to scan the workspace, respectively., Comment: 12 pages, 13 figures, in revision

Motivated by the fermion mass hierarchy we study the phenomenology of two flavorful two-Higgs-doublet model (2HDM) scenarios. By virtue of the flavor or singular alignment ansatz it is possible to link the mass of a subset of fermions to the vacuum-expectation-value (VEV) of a unique Higgs doublet and to simultaneously avoid flavor-changing-neutral-currents at tree-level. We explicitly construct two models called Type-A and B. There, either the top quark alone or all third generation fermions couple to the doublet with the larger VEV. The other fermions acquire their masses through the small VEV of the other doublet. Thus, more natural values for the Yukawa couplings can be obtained. The main differences between these models and conventional ones are studied including a discussion of both their structure and phenomenological consequences. In particular, as distinctive deviations for the Yukawa couplings of the light fermions are predicted we discuss possible tests at the LHC based on searches for $h\to J/\Psi + \gamma$, $h\to\mu\mu$, and heavy scalar resonances decaying to muon pairs. We find that for a wide region of parameter space this specific set of signatures can be used to distinguish among the new proposed types and the conventional ones., Comment: 13 pages, 5 tables, 9 figures; new references added and major improvements; version accepted by Phys. Rev. D

This paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In order to overcome this difficulty we propose to approximate the set of all solutions by means of a limited precision approach based on White's multi-objective value-iteration dynamic programming algorithm. We prove that the number of calculated solutions is tractable and show experimentally that the solutions obtained are a good approximation of the true Pareto front.

Without a vaccine, the fight against the spreading of the coronavirus has focused on maintaining physical distance. To study the impact of such measures on inter-municipality traffic, we analyze a mobile dataset with the daily flow of people in Portugal in March and April 2020. We find that the reduction in inter-municipality traffic depends strongly on its initial outflow. In municipalities where the mobility is low, the outflow reduced by $10-20\%$ and this decrease was independent of the population size. Whereas, for municipalities of high mobility, the reduction was a monotonic increasing function of the population size and it even exceeded $60\%$ for the largest municipalities. As a consequence of such heterogeneities, there were significant structural changes on the most probable paths for the spreading of the virus, which must be considered when modeling the impact of control measures.

The Large Hadron Collider (LHC) has measured the Higgs boson couplings with the heavier particles of the Standard Model (SM), and they seem to lay on a single line as function of the particle mass, as predicted in the SM. However a complete test of this property must involve the lighter generations, and the coming measurements at LHC, or future colliders, may reveal hidden patterns associated with physics beyond the SM. In renormalizable multi-Higgs models, the Higgs-fermion couplings could still be linear, but they could lay on multiple lines. Then, the angle subtended by these lines, with respect to the SM line, can be used to characterize different models, as it is shown here for the Two-Higgs doublet Model (2HDM). Models where fermion masses arise from higher-dimensional operators, may also result in large deviations from the SM values for the Higgs couplings, which would show an irregular pattern as a function of the fermion masses. In the case of neutrino masses, when they arise from the see-saw mechanism, one finds that the Higgs Yukawa couplings will show a non-linear mass relation., Comment: 6 pages, 4 figures, 1 table

In this work we study the annihilation of fermionic dark matter, considering it as a neutral particle with non-vanishing magnetic ($M$) and electric ($D$) dipole moments. Effective cross section of the process $\chi \overline{\chi} \rightarrow \gamma \gamma$ is computed starting from a general form of the coupling $\chi \overline{\chi} \gamma$ in the framework of an extension of the Standard Model. By taking into account the annihilation of dark matter pairs into mono-energetic photons, we found that for masses of $O(10^2)$ GeV, an electric dipole moment $\sim 10^{-16}\, \textrm{e cm}$ is required to satisfy the current relic density inferences. Additionally, in order to pin down models viable to describe the physics of dark matter in the early Universe, we also constrain our model according to recent measurements of the temperature anisotropies of the cosmic microwave background radiation, and report constraints to the electric and magnetic dipole moments for a range of masses within our model., Comment: 20 pages, 6 figures

We present a review of Higgs physics in the SM and beyond, including the tests of the Higgs boson properties that have been performed at LHC and have permitted to delineate its profile. After presenting the essential features of the BEH mechanism, and its implementation in the SM, we discuss how the Higgs mass limits developed over the years. These constraints in turn helped to classify the Higgs phenomenology (decays and production mechanisms), which provided the right direction to search for the Higgs particle, an enterprise that culminated with its discovery at LHC. So far, the constraints on the couplings of the Higgs particle, point towards a SM interpretation. However, the SM has open ends that suggest the need to look for extensions of the model. We discuss in general the connection of the Higgs sector with some new physics (e.g. supersymmetry, flavor and Dark matter), with special focus on a more flavored Higgs sector. Thus is realized in the most general 2HDM, and its textured version, which we study in general, and for its various limits, which contain distinctive flavor-violating signals that could be searched at current and future colliders., Comment: 34 pages, 13 figures, 5 tables, updated references, version to match published version

The elementary Euclidean concept of circumcenter has recently been employed to improve two aspects of the classical Douglas--Rachford method for projecting onto the intersection of affine subspaces. The so-called circumcentered-reflection method is able to both accelerate the average reflection scheme by the Douglas--Rachford method and cope with the intersection of more than two affine subspaces. We now introduce the technique of circumcentering in blocks, which, more than just an option over the basic algorithm of circumcenters, turns out to be an elegant manner of generalizing the method of alternating projections. Linear convergence for this novel block-wise circumcenter framework is derived and illustrated numerically. Furthermore, we prove that the original circumcentered-reflection method essentially finds the best approximation solution in one single step if the given affine subspaces are hyperplanes.