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The counter-rotating pair of wake vortices shed by flying aircraft can pose a threat to ensuing aircraft, particularly on landing approach. To allow adequate time for the vortices to disperse/decay, landing aircraft are required to maintain certain fixed separation distances. The Aircraft Vortex Spacing System (AVOSS), under development at NASA, is designed to prescribe safe aircraft landing approach separation distances appropriate to the ambient weather conditions. A key component of the AVOSS is a ground sensor, to ensure, safety by making wake observations to verify predicted behavior. This task requires knowledge of a flowfield strength metric which gauges the severity of disturbance an encountering aircraft could potentially experience. Several proposed strength metric concepts are defined and evaluated for various combinations of metric parameters and sensor line-of-sight elevation angles. Representative populations of generating and following aircraft types are selected, and their associated wake flowfields are modeled using various wake geometry definitions. Strength metric candidates are then rated and compared based on the correspondence of their computed values to associated aircraft response values, using basic statistical analyses.

This manual describes the operation and theory of the PC-CARES (Personal Computer-Ceramic Analysis and Reliability Evaluation of Structures) computer program for the IBM PC and compatibles running PC-DOS/MS-DOR OR IBM/MS-OS/2 (version 1.1 or higher) operating systems. The primary purpose of this code is to estimate Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities. Included in the manual is the description of the calculation of shape and scale parameters of the two-parameter Weibull distribution using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. The methods for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull line, as well as the techniques for calculating the Batdorf flaw-density constants are also described.

Fracture data from five series of four point bend tests of beam and spin tests of flat annular disks were reanalyzed. Silicon nitride and graphite were the test materials. The experimental fracture strengths of the disks were compared with the predicted strengths based on both volume flaw and surface flaw analyses of four point bend data. Volume flaw analysis resulted in a better correlation between disks and beams in three of the five test series than did surface flaw analysis. The Weibull (moduli) and characteristic gage strengths for the disks and beams were also compared. Differences in the experimental Weibull slopes were not statistically significant. It was shown that results from the beam tests can predict the fracture strength of rotating disks.

The calculation of shape and scale parametes of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by using the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

The choice of a unique Nash equilibrium (NE) is crucial in theoretical classical and quantum games. The Eiswer-Wilkens-Lewenstein quantization scheme solves the prisoner's dilemma only for high entanglement. At medium entanglement, there are multiple NEs. We investigate the selection of a unique NE in the quantum prisoner's dilemma with variable dilemma strength parameters. The risk-dominance criterion is used. The influence of the dilemma strength parameters and entanglement is emphasized. We found that entanglement completely controls the risk-dominant equilibrium. Entanglement promotes quantum-cooperation in the risk-dominant equilibrium and thus improves its outcome., Comment: 17 pages

We perform a parameter sensitivity analysis of the mapped interacting boson model (IBM) and boson-fermion-fermion model (IBFFM) description of $\beta$-decay properties of the neutron-rich even-even $^{96-110}$Zr and $^{98-110}$Mo nuclei, and neutron-deficient odd-odd $^{68,70}$As and even-even $^{78}$Ge nuclei. Based on the self-consistent mean-field calculations with a given energy density functional and a pairing interaction, strength parameters for the interacting-boson Hamiltonian describing even-even nuclei, single-particle energies and occupation probabilities for odd particles, which are needed to build the Gamow-Teller and Fermi transition operators as well as the IBFFM Hamiltonian, are completely determined. It is found that the calculated $\log{}_{10}ft$ values for the $\beta^+$ decay of $^{68}$As are particularly sensitive to the quadrupole-quadrupole interaction strength for the even-even boson core of the odd-odd nucleus, $^{68}$As, as in the case of the neutron-rich Zr isotopes studied previously. We further incorporate higher-order terms in the one-nucleon transfer operators in the boson system, and find that while their effects are non-negligible, they do not significantly alter qualitative features of $\beta$-decay properties. We report a novel application of the mapped IBM framework to compute $\beta$-decay half-lives, and show that the observed trend along isotopic chains are reasonably reproduced., Comment: 17 pages, 13 figures, 2 tables

Influences of the octupole shape degree of freedom on low-energy spectra of neutron-rich odd-mass xenon isotopes are studied within the interacting boson-fermion model that is based on the nuclear density functional theory. The interacting-boson Hamiltonian describing low-energy quadrupole and octupole collective states of the even-even nuclei $^{140,142,144}$Xe, single-particle energies, and occupation probabilities for an unpaired neutron in the odd-mass nuclei $^{141,143,145}$Xe, are determined based on the axially symmetric quadrupole-octupole deformation-constrained self-consistent mean-field calculations with a choice of the energy density functional and pairing interaction. Strength parameters of the boson-fermion interactions are empirically determined to reproduce a few low-lying levels of each odd-mass nucleus. The mean-field calculation predicts for $^{142}$Xe a potential energy surface that is notably soft in the octupole deformation with a non-zero octupole global minimum. The octupole correlations are shown to be relevant in positive-parity excited states of $^{143,145}$Xe., Comment: 13 pages, 9 figures, 9 tables

We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected, the results calculated with the contact terms multiplied by the fitted strength parameters yield an improved description of the elastic Nd scattering observables in a wide range of incoming nucleon energies below the pion production threshold., Comment: 43 pages, 13 figures

Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has been studied and debated extensively in recent years. Under this assumption, the hot spots and cold spots of the CMB are expected to be uniformly distributed over a 2-sphere. We use the orientation matrix, first proposed by Watson (1965) and Scheidegger (1965) and associated shape and strength parameters (Woodcock, 1977) to analyse whether the hot and cold spots of the observed CMB temperature anisotropy field are uniformly placed. We demonstrate the usefulness of our estimators by using simulated toy models containing non-uniform data. We apply our method on several foreground minimized CMB maps observed by WMAP and Planck over large angular scales. The shape and strength parameters constrain geometric features of possible deviations from uniformity (isotropy) and the power of the anomalous signal. We find that distributions of hot or cold spots in cleaned maps show no unusual signature of clustering or girdling. Instead, we notice a strikingly uniform distribution of hot spots over the full sky. The signal remains robust with respect to the four cleaned maps used and presence or absence of the non-Gaussian cold spot (NGCS). On the partial sky with WMAP KQ75 and Planck U73 masks we find anomalously low strength of non-uniformity for cold spots which is found to be robust with respect to various cleaning methods, masks applied, instruments, frequencies, and the presence or absence of the NGCS. Interestingly we find that the signal of anomalously weak non-uniformity could be due to contributions from the quadrupole and octupole and may be related with the low CMB temperature variance anomaly., Comment: 25 pages, 11 figures

Musculoskeletal (MSK) models offer a non-invasive way to understand biomechanical loads on joints and tendons, which are difficult to measure directly. Variations in muscle strength, especially relative differences between muscles, significantly impact model outcomes. Typically, scaled generic MSK models use maximum isometric forces that are not adjusted for different demographics, raising concerns about their accuracy. This review provides an overview on experimentally derived strength parameters, including physiological cross-sectional area (PCSA), muscle mass (Mm), and relative muscle mass (%Mm), which is the relative distribution of muscle mass across the leg. We analysed differences by age and sex, and compared open-source lower limb MSK model parameters with experimental data from 57 studies. Our dataset, with records dating back to 1884, shows that uniformly increasing all maximum isometric forces in MSK models does not capture key muscle ratio differences due to age and sex. Males have a higher proportion of muscle mass in the rectus femoris and semimembranosus muscles, while females have a greater relative muscle mass in the pelvic (gluteus maximus and medius) and ankle muscles (tibialis anterior, tibialis posterior, and extensor digitorum longus). Older adults have a higher relative muscle mass in the gluteus medius, while younger individuals show more in the gastrocnemius. Current MSK models do not accurately represent muscle mass distribution for specific age or sex groups, and none of them accurately reflect female muscle mass distribution. Further research is needed to explore musculotendon age- and sex differences.

What factors contribute to the success of national teams in the Men's Ice Hockey World Championships and the Men's Ice Hockey World Junior Championships? This study examines whether hosting the tournament provides a home advantage; the influence of past tournament performances; the impact of players' physical characteristics such as height, weight, and age; and the value of experience from the World Championships compared to the NHL and other leagues. We employ a dynamic ranking model based on the Plackett-Luce distribution with time-varying strength parameters driven by the score. Additionally, we conduct a forecasting analysis to predict the probabilities of winning the tournament, earning a medal, and advancing to the playoff phase.

Motivated by the recent studies of acoustically driven electron spin resonance applied to diamond nitrogen-vacancy (NV) centers, we investigate the interaction of an electronic spin-triplet state with periodically time-dependent oscillating strain fields. On the basis of a lowest-lying two-level system, we show the importance of two-phonon transition probabilities controlled by rotating an applied magnetic field using the Floquet theory. In particular, we demonstrate how to evaluate coupling-strength parameters in the spin--strain interaction for the $C_{3v}$ point group considering the NV spin states. The level splitting of spin states can be adjusted by changing the field directions relative to the NV axis to obtain lower phonon resonance frequencies suitable for practical applications. Focusing on a field-rotation angle for the vanishment of a longitudinal phonon-mediated transition, we show that the magnetoacoustic resonance presented here provides useful information as a new probe of unquantified spin--strain couplings possessed by NV defects., Comment: 12 pages, 11 figures

Failure of earthen slopes is a very recurrent phenomenon, credited mainly due to the excess rainfall and application of surfeit surcharge. However, most of the analyses regarding slope stability were performed without considering the unsaturated state of the soil. The prime purpose of the present manuscript is to address the stability of unsaturated homogeneous slopes subjected to surcharge load and pseudo-static seismic forces under different climatic conditions. The upper bound limit analysis technique was used based on the log-spiral failure mechanism. The suction stress-based effective stress approach was used to capture the effect of the unsaturated zone of the slope. The suction stress is modelled using Gardner's one-parameter hydraulic conductivity function and van-Genuchten's soil water characteristics curve. An extensive parametric study is carried out to assess the combined effect of slope geometry, soil-strength parameters, hydro-mechanical parameters, depth of water table, various flow conditions, surcharge load, and seismic loading. A few stability charts are proposed to show the impact of surcharge load and seismic load separately on unsaturated homogeneous slopes subjected to various climatic conditions. The present computed solutions match quite well with the available solutions prescribed in the literature.

We present an analytical and numerical study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding ($W$) of the polar angle ($\varphi$), upon a sequence of $N$ weak measurements of increased magnitude ($c$), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement induced geometric phase by a full analytic derivation, valid in the quasicontinuous limit ($N \rightarrow \infty$), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite-$N$ interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol., Comment: 11 pages, 8 figures

We explain the ATOMKI anomaly with a very light $Z'$ state that features non-anomalous and non-flavour-universal vector and axial-vector couplings to all leptons. This $Z'$ comes from a theoretical framework with a spontaneously broken $U(1)'$ symmetry in addition to the Standard Model (SM) gauge group and is compliant with current measurements of the anomalous magnetic moments of the electron and the muon as well as beam dump experiments. The lepton flavour structure of this model allows for $Z'$ couplings to all light neutrinos, suggesting the possibility of $Z'$-mediated Non-Standard Interactions (NSIs) of neutrinos in matter, so that measurements of the strength parameters of the NSIs can constrain the value of the couplings. We use experimental constraints on NSIs of neutrinos using older TEXONO data and newer IceCube data. The IceCube data, in particular, strongly constrain the flavour universality of the leptonic vector current. The constraints enable us to define the region of parameter space of this theoretical scenario that can be pursued in further phenomenological analyses.

While contact binary objects are common in the solar system, their formation mechanism is unclear. In this work we examine several contact binaries and calculate the necessary strength parameters that allow the two lobes to merge without the smaller of the two being gravitationally destroyed by the larger. We find a small but non-zero amount of cohesion or a large friction angle is required for the smaller lobe to survive the merging process, consistent with observations. This means it is possible for two previously separated rubble piles to experience a collapse of their mutual orbit and form a contact binary. The necessary strength required to survive this merger depends on the relative size, shape, and density of the body, with prolate shapes requiring more cohesion than oblate shapes., Comment: Accepted to Astrophysical Journal Letters

We present a comprehensive investigation on the possibility of the search for new force mediator $X$ boson in $e^+e^-$ collision and $J/\psi$ decay at the BESIII experiment. The typical interactions of $X$ boson coupling to leptons and quarks are explored. The production and decay properties of this $X$ particle, the product/decay chains $e^+e^-\to X\gamma \to e^+e^-\gamma$ and $J/\psi \to X\gamma\to\mu^+\mu^-\gamma$, and exclusion limits on the reduced coupling strength parameters as functions of $X$ boson mass are presented. With the data set of tens of fb$^{-1}~e^+e^-$ or $10^{10}~J/\psi$, we find that the exclusion limits on the coupling strength parameters fall in the range of $10^{-3}\sim10^{-4}$, depending on $m_X$ assuming the decay width 10 eV$<\Gamma_X<$100 eV reasonably, for various hypotheses in the literature. According to our estimation, the search for new force mediator $X$ boson in both $e^+e^-$ collision and $J/\psi$ decay are accessible in nowadays BESIII experiment., Comment: To appear in EPJC; 26 pages, 13 figures; Fig.s (5, 6, 9, 11, 12, 13) are reploted and their discussion are updated; three paragraphs, two equations and 1 table are added; two errors are corrected

Grain-grain collisions shape the 3-dimensional size and velocity distribution of the inner Zodiacal Cloud and the impact rates of dust on inner planets, yet they remain the least understood sink of zodiacal dust grains. For the first time, we combine the collisional grooming method combined with a dynamical meteoroid model of Jupiter-family comets (JFCs) that covers four orders of magnitude in particle diameter to investigate the consequences of grain-grain collisions in the inner Zodiacal Cloud. We compare this model to a suite of observational constraints from meteor radars, the Infrared Astronomical Satellite (IRAS), mass fluxes at Earth, and inner solar probes, and use it to derive the population and collisional strength parameters for the JFC dust cloud. We derive a critical specific energy of $Q^*_D=5\times10^5 \pm 4\times10^5 R_\mathrm{met}^{-0.24}$ J kg$^{-1}$ for particles from Jupiter-family comet particles, making them 2-3 orders of magnitude more resistant to collisions than previously assumed. We find that the differential power law size index $-4.2\pm0.1$ for particles generated by JFCs provides a good match to observed data. Our model provides a good match to the mass production rates derived from the Parker Solar Probe observations and their scaling with the heliocentric distance. The higher resistance to collisions of dust particles might have strong implications to models of collisions in solar and exo-solar dust clouds. The migration via Poynting-Roberson drag might be more important for denser clouds, the mass production rates of astrophysical debris disks might be overestimated, and the mass of the source populations might be underestimated. Our models and code are freely available online., Comment: 41 pages, 14 figures, 1 table - Submitted to The Planetary Science Journal (PSJ) - After 2nd review

This paper presents a method for finding ram-pressure stripped (RPS) galaxy candidates by performing a morphological analysis of galaxy images obtained from the Legacy survey. We consider a sample of about 600 galaxies located in different environments such as groups and clusters, tidally interacting pairs and the field. The sample includes 160 RPS previously classified in the literature into classes from J1 to J5, based on the increasing level of disturbances. Our morphological analysis was done using the {\sc astromorphlib} software followed by the inspection of diagnostic diagrams involving combinations of different parameters like the asymmetry ($A$), concentration ($C$), S\'ersic index ($n$), and bulge strength parameters $F(G,\,M_{20})$. We found that some of those diagrams display a distinct region in which galaxies classified as J3, J4 and J5 decouples from isolated galaxies. We call this region as the morphological transition zone and we also found that tidally interacting galaxies in pairs are predominant within this zone. Nevertheless, after visually inspecting the objects in the morphological transition zone to discard obvious contaminants, we ended up with 33 bonafide new RPS candidates in the studied nearby groups and clusters (Hydra, Fornax, and CLoGS sample), of which one-third show clear evidence of unwinding arms. Future works may potentially further increase significantly the samples of known RPS using such method., Comment: 17 pages, 9 figures

We consider heat operators on a bounded domain $\Omega \subseteq \mathbb{R}^n$, with a critically singular potential diverging as the inverse square of the distance to $\partial \Omega$. While null boundary controllability for such operators was recently proved in all dimensions in arXiv:2112.04457, it crucially assumed (i) $\Omega$ was convex, (ii) the control must be prescribed along all of $\partial \Omega$, and (iii) the strength of the singular potential must be restricted to a particular subrange. In this article, we prove instead a definitive approximate boundary control result for these operators, in that we (i) do not assume convexity of $\Omega$, (ii) allow for the control to be localized near any $x_0 \in \partial \Omega$, and (iii) treat the full range of strength parameters for the singular potential. Morever, we lower the regularity required for $\partial \Omega$ and the lower-order coefficients. The key novelty is a local Carleman estimate near $x_0$, with a carefully chosen weight that takes into account both the appropriate boundary conditions and the local geometry of $\partial \Omega$., Comment: Accepted version

The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions for Bayesian inference of the strength parameters based on the paired comparison results. We evaluate them according to four desiderata motivated by the use of inferred Bradley-Terry parameters to rate teams on the basis of outcomes of a set of games: invariance under interchange of teams, invariance under interchange of winning and losing, normalizability and invariance under elimination of teams. We consider various proposals which fail to satisfy one or more of these desiderata, and illustrate two proposals which satisfy them. Both are one-parameter independent distributions for the logarithms of the team strengths: 1) Gaussian and 2) Type III generalized logistic., Comment: 22 pages, 3 figures, formatted for submission to the Electronic Journal of Statistics

Resonances of Schr\"odinger Hamiltonians with point interactions are considered. The main object under the study is the resonance free region under the assumption that the centers, where the point interactions are located, are known and the associated 'strength' parameters are unknown and allowed to bear additional dissipative effects. To this end we consider the boundary of the resonance free region as a Pareto optimal frontier and study the corresponding optimization problem for resonances. It is shown that upper logarithmic bound on resonances can be made uniform with respect to the strength parameters. The necessary conditions on optimality are obtained in terms of first principal minors of the characteristic determinant. We demonstrate the applicability of these optimality conditions on the case of 4 equidistant centers by computing explicitly the resonances of minimal decay for all frequencies. This example shows that a resonance of minimal decay is not necessarily simple, and in some cases it is generated by an infinite family of feasible resonators., Comment: 23 pages, 1 figure, several typos corrected, acknowledgements updated, these results were reported during the summer school "Modeling, Analysis, and Approximation Theory toward applications in tomography and inverse problems" (L\"ubeck, July 31 - August 4, 2017)

In this paper we revisit the classical fluctuation-dissipation theorem with derivations and interpretations based on quantum electrodynamics (QED). As a starting point we take the widely cited semiclassical expression of the theorem connecting the absorption coefficient with the correlation spectra of a radiating molecular dipole. The literature is suggesting how this connection can be derived in terms of quantum mechanical statistical averages, but the corresponding results in terms of QED seems to be very difficult to trace in detail. The problem is therefore addressed here based on first principles. Interestingly, it turns out that the QED approach applied to the aforementioned statistical averages does not only prove the validity of the fluctuation-dissipation theorem, but it also provides a derivation and a quantum mechanical interpretation of Schwarzschild's equation for radiative transfer. In particular, it is found that the classical Beer-Bouguer-Lambert law is due to absorption as well as of stimulated emission, and furthermore that the source term in Schwarzschild's equation (Kirchhoff's law) is due solely to spontaneous emission. The significance of the fluctuation-dissipation theorem is finally elaborated on in terms of the appropriate scaling of line strength parameters (including line mixing) which is relevant in far infrared and millimeter wave broadband applications.

We demonstrate the recent designs of Safe Extremum Seeking (Safe ES) on the 1 kilometer-long charged particle accelerator at the Los Alamos Neutron Science Center (LANSCE). Safe ES is a modification of ES which, in addition to minimizing an analytically unknown cost, also employs a safety filter based on an analytically unknown control barrier function (CBF) safety metric. Accelerator tuning is necessitated by the accelerators being large, with many drifting parameters due to thermal effects and degradation. At the same time, safe operation (the maintenance of state constraints) is crucial, as damage brings astronomical costs, both financially and in operation downtime. Our measured (but analytically unknown) safety metric is the beam current. We perform multivariable Safe ES on three accelerator applications, in which we adapt 4, 6, and 3 magnet strength parameters, respectively. Two of the three applications are for validated simulation models of beamlines at LANSCE: the first for the Proton Radiography (pRad) beamline of 800 MeV protons for spot size tuning; the second on a high performance code, HPSim, for tuning the low energy beam transport (LEBT) region of of 750 keV protons. The third is an experimental tuning of the steering magnets in the LEBT at LANSCE.

Integral equation theories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in 2D systems, a relevant inter-domain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equation for this novel system: Rogers-Young (RY), Modified Hypernetted Chain (MHNC), and Variational Modified Hypernetted Chain (VMHNC). For the last two closures the bridge function of a reference system is required, being the hard disk the most convenient reference system. Given that in 2D there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick approximation (PY), and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke parameterization (LB). The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is only satisfactory for low-structured regimes. MHNC and VMHNC closures perform globally well and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB--based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB--based closures do not have a solution for all studied interaction strength parameters, and, in general, PY--based closures are numerically preferable., Comment: 9 pages, 4 figures

In this article, we proposed an inverse Lindley distribution and studied its fundamental properties such as quantiles, mode, stochastic ordering and entropy measure. The proposed distribution is observed to be a heavy-tailed distribution and has a upside-down bathtub shape for its failure rate. Further, we proposed its applicability as a stress-strength reliability model for survival data analysis. The estimation of stress-strength parameters and $R=P[X>Y]$, the stress-strength reliability has been approached by both classical and Bayesian paradigms. Under Bayesian set-up, non-informative (Jeffrey) and informative (gamma) priors are considered under a symmetric (squared error) and a asymmetric (entropy) loss functions, and a Lindley-approximation technique is used for Bayesian computation. The proposed estimators are compared in terms of their mean squared errors through a simulation study. Two real data sets representing survival of Head and Neck cancer patients are fitted using the inverse Lindley distribution and used to estimate the stress-strength parameters and reliability., Comment: 17 pages, 4 figures, 9 tables

Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to EEG. However, this approach lacks a reliable method to determine the initial filter conditions and assumes that the distribution of states remains Gaussian. This study presents an alternative, data-driven method to track the states and parameters of neural mass models (NMMs) from EEG recordings using deep learning techniques, specifically an LSTM neural network. Approach An LSTM filter was trained on simulated EEG data generated by a neural mass model using a wide range of parameters. With an appropriately customised loss function, the LSTM filter can learn the behaviour of NMMs. As a result, it can output the state vector and parameters of NMMs given observation data as the input. Main Results Test results using simulated data yielded correlations with R squared of around 0.99 and verified that the method is robust to noise and can be more accurate than a nonlinear Kalman filter when the initial conditions of the Kalman filter are not accurate. As an example of real-world application, the LSTM filter was also applied to real EEG data that included epileptic seizures, and revealed changes in connectivity strength parameters at the beginnings of seizures. Significance Tracking the state vector and parameters of mathematical brain models is of great importance in the area of brain modelling, monitoring, imaging and control. This approach has no need to specify the initial state vector and parameters, which is very difficult to do in practice because many of the variables being estimated cannot be measured directly in physiological experiments. This method may be applied using any neural mass model and, therefore, provides a general, novel, efficient approach to estimate brain model variables that are often difficult to measure.

We consider effects of the Non-Standard Interactions (NSI) on oscillations of the high energy atmospheric neutrinos. The \nu_\mu-oscillograms are constructed and their dependence on the NSI strength parameters \epsilon_{\alpha \beta} studied. We computed zenith angle distributions of the \nu_\mu-events in the presence of NSI in different energy regions. The distributions are confronted with the IceCube-79 (high energy sample) and the DeepCore (low energy sample) data and constraints on the strength parameters |\epsilon_{\mu \tau}| < 6x10^-3 and |\epsilon_{\mu\mu}-\epsilon_{\tau\tau}| < 3x10^-2 (90% C.L.) have been obtained. Future measurements of the zenith angle distributions by DeepCore in smaller energy bins will allow to improve the bounds by factor 2 - 3. We discuss the signatures of NSI in zenith angle and energy distributions of events which allow to discriminate them from the effects of sterile neutrinos., Comment: 30 pages, 15 figures; v2: Typos corrected, several comments added

We study the possible gravitational wave signal and the viability of baryogenesis arising from the electroweak phase transition in an extension of the Standard Model (SM) by a scalar singlet field without a $\mathbb{Z}_2$ symmetry. We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken $\mathbb{Z}_2$ symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters $\alpha \lesssim 0.05$, and the Chapman-Jouguet velocity defines the maximum velocity for which the wall is stopped by the friction from the plasma. We further provide an analytical approximation to the wall velocity in the general scalar singlet scenario without $\mathbb{Z}_2$ symmetry and test it against the results of a detailed calculation, finding good agreement. We show that in the singlet scenario with a spontaneously broken $\mathbb{Z}_2$ symmetry, the phase transition is always weak and we see no hope for baryogenesis. In contrast, in the case with explicit $\mathbb{Z}_2$ breaking there is a region of the parameter space producing a promising baryon yield in the presence of CP violating interactions via an effective operator involving the singlet scalar and the SM top quarks. Yet, we find that this region yields unobservable gravitational waves. Finally, we show that the promising region for baryogenesis in this model may be fully tested by direct searches for singlet-like scalars in di-boson final states at the HL-LHC, combined with present and future measurements of the electron electric dipole moment.