Model-independent Method Research Articles

X-Ray Crystal Truncation Rod Studies of Electrochemical Double Layers

Electrochemical double layers (EDL) is traditionally described as diffuse distributions of cations and anions, proposed in Gouy and Chapman (GC) model[1] and further developed extensively over decades largely based on voltammetry measurements. However, the GC model is suspected to break down at large potentials, because it predicts the unlimited rise in differential capacitance. Stern suggested long ago that there should be a layer with a finite ion density, known as ‘Stern layer’[2]. While it is generally accepted that Gouy-Chapman model or its modified versions describe well electrochemical interphase structures, recent studies of Pt(111) surface in CsF solution using a model-independent direct inversion method[3] have shown that Stern layer forms over the large double-layer potential range on Pt(111) surface.[4]In this talk, we present synchrotron x-ray observation of Electrochemical Stern layers on the surfaces of RuO2 single crystals in 0.1 M CsF electrolyte. It is of fundamental importance to study if Stern layer forms on electrode surfaces other than Pt(111). In this case, we will examine RuO2 surfaces and compare the results to that of Pt(111) surface. RuO2 is chosen for several reasons. First, it is a well-studied system because of its oxygen evolution reactions and we are familiar with the structure because of our previous studies.[5,6] Second, it is an oxide with oxygen terminated while Pt is a pure metal. Third, the surfaces of RuO2 are squares or rectangles while that Pt(111) surface is triangles. The Stern layers formed at the interfaces of RuO2 (110) and (100) are compared to the previously reported Stern layer on Pt(111). [4] While the Cs+ density profiles at the potentials close to hydrogen evolution reactions are similar, the hydration layers intervening the surface and the Cs+ layer are significantly denser on RuO2 surfaces than that on Pt(111) surface, reflecting the oxygen termination of RuO2 surfaces. The overall similarities between Stern layers on ruthenium surfaces and platinum surface suggest the universal presence of Stern layers in all well-defined solid-electrolyte interfaces.[1] Bard, A. J.; Faulkner, L. R., Electrochemical methods: fundamentals and applications. 2nd ed.; John Wiley: New York, 2001.[2] Stern, O., The theory of the electrolytic double layer. Zeitschrift Für Elektrochemie 1924, 30, 508.[3] Kawaguchi, T. et al., J. Appl. Cryst., 2018 51, 679.[4] Liu, Y.; Kawaguchi, T.; Pierce, M.S.; Komanicky, V.; You, H., Layering and Ordering in Electrochemical Double Layers, J Phys Chem Lett, 2018, 9, 1265.[5] Y.S. Chu, T.E. Lister, W.G. Cullen, H. You, Z. Nagy, Physical Review Letters 2001, 86, 3364.[6] Rao, R.R. et al., Journal of Physical Chemistry C, 2018, 122, 17802

The angular scale of homogeneity with SDSS-IV DR16 luminous red galaxies

We report measurements of the angular scale of cosmic homogeneity (θH ) using the recently released luminous red galaxy sample of the sixteenth data release of the Sloan Digital Sky Survey (SDSS-IV LRG DR16). It consists of a model-independent method, as we only use the celestial coordinates of these objects to carry out such an analysis. The observational data is divided into thin redshift bins, namely 0.67 < z < 0.68, 0.70 < z < 0.71, and 0.73 < z < 0.74, in order to avoid projection biases, and we estimate our uncertainties through a bootstrap method and a suite of mock catalogues. We find that the LRGs exhibit an angular scale of homogeneity consistent with the predictions of the standard cosmology within the redshift interval studied. Considering the bootstrap method, in which the measurements are obtained in a model-independent way, we found at 1σ level that θH boot(0.675) = 7.57 ± 2.91 deg, θH boot (0.705) = 7.49 ± 2.63 deg and θH boot (0.735) = 8.88 ± 2.81 deg. Such results are in good agreement with the ones obtained using mock catalogues built under the assumption of the standard cosmological model.

Active Fault-Tolerant Control for Quadrotor UAV against Sensor Fault Diagnosed by the Auto Sequential Random Forest

Active disturbance rejection control (ADRC) is a model-independent method widely used in passive fault-tolerant control of the quadrotor unmanned aerial vehicle. While ADRC’s effectiveness in actuator fault treatment has been proven, its tolerance to sensor faults requires improvements. In this paper, an ADRC-based active fault-tolerant control (AFTC) scheme is proposed to control the flying attitude against sensor fault for reliability enhancement. Specifically, a semi-model-dependent state tracker is raised to reduce the influence of slow tracking, and accentuate the sensor fault even in varying maneuvers. Derived from the random forest, an enhanced method named auto sequential random forest is designed and applied to isolate and identify faults in real time. Once the tolerance compensation is generated with the fault information, a high-performance AFTC is achieved. The simulation results show that the proposed method can effectively follow the residual when a sensor fault and a change of maneuver occur concurrently. Precise fault information is obtained within 0.04 s, even for small faults on the noise level. The diagnosis accuracy is greater than 86.05% (100% when small faults are excluded), and the identification precision exceeds 97.25%. The short settling time (0.176 s when the small fault is excluded) and modest steady-state error validate the advanced and robust tolerance performance of the proposed AFTC method.

Beyond prediction: methods for interpreting complex models of soil variation

• Describe a set of methods for the interpretation of complex mapping models. • Methods are not dependent on a specific type of model. • Reveal global model functioning and local drivers of soil variation. • Provide new insights into complex mapping models. • Might assist formulating hypotheses on the mechanisms driving soil variation. Understanding the spatial variation of soil properties is central to many sub-disciplines of soil science. Commonly in soil mapping studies, a soil map is constructed through prediction by a statistical or non-statistical model calibrated with measured values of the soil property and environmental covariates of which maps are available. In recent years, the field has gradually shifted attention towards more complex statistical and algorithmic tools from the field of machine learning. These models are particularly useful for their predictive capabilities and are often more accurate than classical models, but they lack interpretability and their functioning cannot be readily visualized. There is a need to understand how these models can be used for purposes other than making accurate prediction and whether it is possible to extract information on the relationships among variables found by the models. In this paper we describe and evaluate a set of methods for the interpretation of complex models of soil variation. An overview is presented of how model-independent methods can serve the purpose of interpreting and visualizing different aspects of the model. We illustrate the methods with the interpretation of two mapping models in a case study mapping topsoil organic carbon in France. We reveal the importance of each driver of soil variation, their interaction, as well as the functional form of the association between environmental covariate and the soil property. Interpretation is also conducted locally for an area and two spatial locations with distinct land use and climate. We show that in all cases important insights can be obtained, both into the overall model functioning and into the decision made by the model for a prediction at a location. This underpins the importance of going beyond accurate prediction in soil mapping studies. Interpretation of mapping models reveal how the predictions are made and can help us formulating hypotheses on the underlying soil processes and mechanisms driving soil variation.

F(T) cosmology against the cosmographic method: A new study using mock and observational data

ABSTRACT In this paper, we study the power-law f(T) model using Hubble diagrams of type Ia supernovae (SNIa), quasars (QSOs), gamma-ray bursts (GRBs), and the measurements from baryonic acoustic oscillations (BAO) in the framework of the cosmographic method. Using mock data for SNIa, QSOs, and GRBs generated based on the power-law f(T) model, we show whether different cosmographic methods are suitable to reconstruct the distance modulus or not. In particular, we investigate the rational PADE polynomials (3,2) and (2,2) in addition to the fourth- and fifth-order Taylor series. We show that PADE (3,2) is the best approximation that can be used in the cosmographic method to reconstruct the distance modulus at both low and high redshifts. In the context of PADE (3,2) cosmographic method, we show that the power-law f(T) model is well consistent with the real observational data from the Hubble diagrams of SNIa, QSOs, and GRBs. Moreover, we find that the combination of the Hubble diagram of SNIa and the BAO observation leads to better consistency between the model-independent cosmographic method and the power-law f(T) model. Finally, our observational constraints on the parameter of the effective equation of state of DE described by the power-law f(T) model show the phantom-like behaviour, especially when the BAO observations are included in our analysis.

A Novel MSFED Feature for the Intelligent Fault Diagnosis of Rotating Machines

The vibration energy distribution pattern usually changes with the rotating machine’s health state and is a good indicator for intelligent fault diagnosis (IFD). The existing initial features such as RMS are less effective in revealing the vibration energy distribution pattern, and the frequency spectrum cannot provide a rich and hierarchical description of the vibration energy distribution pattern. Addressing this issue, we proposed a multi-scale frequency energy distribution (MSFED) feature for the IFD of rotating machines. The MSFED feature can reveal the vibration energy distribution patterns in the frequency domain in a multi-scale manner, and its one-dimensional vector and two-dimensional map formats make it usable for most IFD models. Experimental validation on the gearbox and bearing datasets verified that the MSFED feature achieved the highest diagnostic accuracy among commonly used initial features, in typical fault diagnosis scenarios except for the variable-load scenario. Furthermore, the separability and transferability of the MSFED feature were evaluated by distance-based metrics, and the results were in agreement with the features’ diagnostic performance. This work provides an important reference for the IFD of rotating machines, not only proposing a novel MSFED feature but also opening a new avenue for model-independent methods of the initial quality evaluation.

Hunting for vampires and other unlikely forms of parity violation at the Large Hadron Collider

Non-Standard-Model parity violation may be occurring in LHC collisions. Any such violation would go unseen, however, as searches for it are not currently performed. One barrier to searches for parity violation is the lack of model-independent methods sensitive to all of its forms. We remove this barrier by demonstrating an effective and model-independent way to search for parity-violating physics at the LHC. The method is data-driven and makes no reference to any particular parity-violating model. Instead, it inspects data to construct sensitive parity-odd event variables (using machine learning tools), and uses these variables to test for parity asymmetry in independent data. We demonstrate the efficacy of this method by testing it on data simulated from the Standard Model and from a non-standard parity-violating model. This result enables the possibility of investigating a variety of previously unexplored forms of parity violation in particle physics.Data and software are shared at https://zenodo.org/record/6827724.

A New Way to Explore Cosmological Tensions Using Gravitational Waves and Strong Gravitational Lensing

In recent years, a crisis in the standard cosmology has been caused by inconsistencies in the measurements of some key cosmological parameters, the Hubble constant H 0 and cosmic curvature parameter Ω K , for example. It is necessary to remeasure them with the cosmological model-independent methods. In this paper, based on the distance sum rule, we present such a way to constrain H 0 and Ω K simultaneously in the late universe from strong gravitational lensing time-delay (SGLTD) data and gravitational wave (GW) standard siren data simulated from the future observation of the Einstein Telescope (ET). Based on the data for six currently observed SGLTDs, we find that the constraint precision of H 0 from the combined 100 GW events can be comparable with the measurement from the SH0ES collaboration. As the number of GW events increases to 700, the constraint precision of H 0 will exceed that of the Planck 2018 results. Considering 1000 GW events as the conservative estimation of ET in the 10 yr observation, we obtain H 0 = 73.69 ± 0.36 km s−1 Mpc−1 with a 0.5% uncertainty and . In addition, we simulate 55 strong gravitational lensing (SGL) systems with a 6.6% uncertainty for the measurement of time-delay distance. By combining with 1000 GWs, we infer that H 0 = 73.65 ± 0.35 km s−1 Mpc−1 and Ω K = 0.008 ± 0.048. Our results suggest that this approach can play an important role in exploring cosmological tensions.

Raman spectroscopy of thermally perturbed carbon fibers: Discriminating spectral responses of modulus classes and defect types

The mechanical strength properties of carbon fibers are generally thought to be correlated with the presence of underlying atomic-level defects. These defects serve to break the underlying translational symmetry of the graphitic or graphene subunits of the fiber construction, resulting in the emergence of new Raman-active spectral features. However, historical attempts to classify the precise origin of defect contributions to the Raman spectra have been challenging because of indistinct and overlapping features in the carbon fiber Raman spectra. Further, while substantial research exists on high-temperature exposure in inert atmospheres for carbon fiber composites, comparatively less addresses microscale behaviors and Raman spectral alterations to monofilament carbon fibers exposed to high-temperature atmospheric environments. Here, we report Raman spectral responses of nine commercially available high-performance, polyacrylonitrile-based carbon fibers exposed to various atmospheric heat treatments. We introduce a model-independent characterization method, the integrated absolute difference, to quantify the spectral responses to heat treatment of different fiber modulus classes. We combine this new method with a newly reported strategy to standardize spectral fitting for carbon fibers. With this approach, we show that atomic-scale defects in the underlying fiber microstructure manifest in measurably distinct manners and have distinct responses to thermal perturbation. These combined approaches may lay the foundation for disentangling contributions from specific defects in the Raman spectra of carbon fibers.

Disentangling long and short distances in momentum-space TMDs

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in ΛQCD/kT. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over {k}_Tle {k}_T^{mathrm{cut}} in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near {k}_T^{mathrm{cut}} , such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.

Model-independent determination of the gap function of nearly localized superconductors

The gap function $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ carries essential information on both, the pairing glue as well as the pair-breaking processes in a superconductor. Unfortunately, in nearly localized superconductors with a nonconstant density of states in the normal state, the standard procedure for extraction of $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ cannot be applied. Here we introduce a model-independent method that makes it possible to extract $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ also in this case. The feasibility of the procedure is demonstrated on the tunneling data for the disordered thin films of TiN. We find an unconventional feature of $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ which suggests that the electrons in TiN are coupled to a very soft pair-breaking mode.

Multiple Measurements of Gravitational Waves Acting as Standard Probes: Model-independent Constraints on the Cosmic Curvature with DECIGO

Although the spatial curvature has been precisely determined via observations of the cosmic microwave background by the Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which will allow us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter Ω k in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with the future generation of the space-based Decihertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of ΔΩ k = 0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon sample of Type Ia supernovae, which shows no evidence for a deviation from a flat universe at z ∼ 2.3. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution of Ω k with redshift, through direct measurements of cosmic curvature at different redshifts (z ∼ 5). Such a model-independent Ω k reconstruction to the distant past could become a milestone in gravitational-wave cosmology.

Development and Validation of the HPLC Method for Quantification of the Innovative Drug DD217, Factor Xa Inhibitor, in Rat Plasma for a Pharmacokinetic Study

Introductio n . Nowadays, discovery and development of innovative drugs represent a relevant goal for the pharmaceutical market. One of such drugs is N-(5-chloropyridine-2-yl)-2-({4-[ethanimidoyl(methyl)benzoyl}amino)-5-methylbenzamide hydrochloride (hereinafter DD217), an innovative drug that belongs to the class of anticoagulants, namely factor Xa inhibitors. Aim. The aim of this study was to develop and validate a method for DD217 determination in rat plasma by means of high-performance liquid chromatography–tandem mass spectrometry (HPLC-MS/MS) to carry out pharmacokinetic studies. Materials and methods. Outbred Wistar rats were used in the study. Rats received a single dose of DD217 substance solution intragastrically at a dose of 5, 15, 30 mg/kg. The validated HPLC-MS/MS method was employed for DD217 determination in rat plasma. Nebivolol was chosen as the internal standard of the method. Chromatographic separation involved the use of Phenomenex Luna С8 column (3 µm, 50 × 4.6 mm) and gradient elution with water-acetonitrile solution containing 0.1 % formic acid. The total run time of each sample was equal to 2.0 min. DD217 and nebivolol were detected in positive electrospray ionization mode, the ion transitions monitored were m/z 436,1 → 119,9 and 406,0 → 151,0, respectively. Pharmacokinetic parameters and descriptive statistics were calculated through model-independent method in IBM SPSS Statistics v27 and Julia v1.6.0 (MixedModels v3.8.0, ClinicalTrialUtilities v0.5.1) software. Results and discussion. Method was validated by linearity, lower limit of quantification, selectivity, accuracy and precision, dilution integrity, matrix effect, recovery, carry-over, and stability. The lower limit of quantification of DD217 in rat plasma was 2.0 ng/mL. The method was successfully applied for establishing the pharmacokinetic parameters of DD217 substance in rat plasma after intragastric administration at a dose of 5, 15, 30 mg/kg. Conclusion. HPLC-MS/MS method for DD217 determination in plasma was developed, validated and applied in order to evaluate pharmacokinetic parameters of DD217 substance in rat plasma.

General Markovian equation for scalar fields in a slowly evolving background

We present a general and model-independent method to obtain an effective Markovian quantum kinetic equation for the expectation value of a slowly evolving scalar field in an adiabatically evolving background from first principles of nonequilibrium quantum field theory. The method requires almost no assumptions about the field's interactions and the composition of the background, except that 1) the coupling constants shall be small enough for perturbation theory to be applicable, 2) there is a clear separation between microphysical time scales and the rate at which bulk properties change, and 3) higher time derivatives of the field remain small. The resulting Markovian equation of motion is expressed in terms of an effective potential and friction coefficients. Motivated by cosmological applications we focus on spatially homogeneous and isotropic systems, but the approach could also be applied to spatial gradients.

Relativistic, model-independent determination of electromagnetic finite-size effects beyond the pointlike approximation

We present a relativistic and model-independent method to derive structure-dependent electromagnetic finite-size effects. This is a systematic procedure, particularly well-suited for automation, which works at arbitrarily high orders in the large-volume expansion. Structure-dependent coefficients appear as zero-momentum derivatives of physical form factors which can be obtained through experimental measurements or auxiliary lattice calculations. As an application we derive the electromagnetic finite-size effects on the pseudoscalar meson mass and leptonic decay amplitude, through orders $\mathcal{O}(1/{L}^{3})$ and $\mathcal{O}(1/{L}^{2})$, respectively. The structure dependence appears at this order through the meson charge radius and the real radiative leptonic amplitude, which are known experimentally.

DISSOLUTION PROFILE SIMILARITY ANALYSES-STATISTICAL PRINCIPLES, METHODS AND CONSIDERATIONS.

The pharmaceutical industry and regulatory agencies rely on dissolution similarity testing to make critical product decisions as part of drug product life cycle management. Accordingly, the application of mathematical approaches to evaluate dissolution profile similarity is described in regulatory guidance with the emphasis given to the similarity factor f2 with little discussion of alternative methods. In an effort to highlight current practices to assess dissolution profile similarity and to strive toward global harmonization, a workshop entitled "In Vitro Dissolution Similarity Assessment in Support of Drug Product Quality: What, How, When" was held on May 21-22, 2019 at the University of Maryland, Baltimore. This manuscript provides in-depth discussion of the mathematical principles of the model-independent statistical methods for dissolution profile similarity analyses presented in the workshop. Deeper understanding of the testing objective and statistical properties of the available statistical methods is essential to identify methods which are appropriate for application in practice. A decision tree is provided to aid in the selection of an appropriate statistical method based on the underlying characteristics of the drug product. Finally, the design of dissolution profile studies is addressed regarding analytical and statistical recommendations to sufficiently power the study. This includes a detailed discussion on evaluation of dissolution profile data for which several batches per reference and/or test product are available.

Anisotropy of the gravitational-wave standard sirens and its cosmological applications

We analyze the anisotropic factors present in the gravitational wave signal, such as the peculiar velocity of the observer and the inhomogeneous distribution of matter in the universe. We model the gravitational wave source as a standard siren, extract the anisotropic part of its luminosity distance d_L, and obtain the Hubble parameter H(z) by direct calculation instead of integration. Finally, we derive the equation of state w_mathrm{DE}(z) for the dark energy by both model-dependent and model-independent methods, and further investigate the cosmological significance of the simulated H(z) measurements. The advantage of this approach is that it makes full use of the anisotropic part of the d_L data, which directly gives the value of H(z) at certain redshifts. This approach is sensitive to the local features of H(z) and does not depend on the cosmological model.

Powered Prosthesis Locomotion on Varying Terrains: Model-Dependent Control With Real-Time Force Sensing

Lower-limb prosthesis wearers are more prone to falling than non-amputees. Powered prostheses can reduce this instability of passive prostheses. While shown to be more stable in practice, powered prostheses generally use model-independent control methods that lack formal guarantees of stability and rely on heuristic tuning. Recent work overcame one of the limitations of model-based prosthesis control by developing a class of provably stable prosthesis controllers that only require the human interaction forces with the prosthesis, yet these controllers have not been realized with sensing of these forces in the control loop. Our work realizes the first model-dependent prosthesis knee controller that uses in-the-loop on-board real-time force sensing at the interface between the human and prosthesis and at the ground. The result is an optimization-based control methodology that formally guarantees stability while enabling human-prosthesis walking on a variety of terrain types. Experimental results demonstrate this force-based controller outperforms similar controllers not using force sensors, improving tracking across 4 terrain types.

Study of pharmacokinetic of new peptide drug 1-deamino-arginine-vasotocin for hypernatremia correction

Introduction: The pharmacokinetics studies are some of the necessary parts of the drugs preclinical investigations. Pharmacokinetic properties of new peptide drug 1-deamino-arginine-vasotocin (dAVT) in the form of an injection solution for intravenous and intramuscular administration for hypernatremia correction were investigated.&#x0D; Materials and methods: The study was carried out on male rats and rabbits with a single intravenous administration of the drug in three doses, a single intramuscular administration in one dose and multiple administration to rats in one dose. To determine natriiuretic peptide concentration in blood plasma, tissues, and excretes, assays based on a sodium level change measurement using a biochemical analyzer have been developed and validated. Pharmacokinetic parameters were calculated by the model-independent method of statistical moments.&#x0D; Results and discussion: The pharmacokinetics of the drug was found to be linear after a single administration of dAVT drug in the dose range 3–10 μg/kg for rats and rabbits. The relative bioavailability of dAVT after intramuscular and intravenous administrations was more than 30%. After a biomarker content change, the active substance was intensively distributed into highly vascularized organs (spleen), the organs that provide metabolism and subsequent excretion (liver and kidneys), whereas it hardly reached moderately and weakly vascularized tissues (muscles, omentum). Less than 10% dAVT was excreted with urine; no dAVT was determined in feces; and repeated administration did not lead to its cumulation.&#x0D; Conclusion: Pharmacokinetics parameters of new nonapeptide drug 1-deamino-arginine-vasotocin were evaluated after original analytical biomarker approach. The study included all main areas necessary to characterize the original drug pharmacokinetic.

Lattice calculation of χ c0 → 2γ decay width * *Support by NSFC of China (12070131001) and also the support by CAS Interdisciplinary Innovation Team and NSFC of China (11935017), NSFC of China (12047505) and State Key Laboratory of Nuclear Physics and Technology, Peking University

We perform a lattice QCD calculation of the decay width using a model-independent method that does not require the momentum extrapolation of corresponding off-shell form factors. The simulation is performed on ensembles of twisted mass lattice QCD gauge configurations with three different lattice spacings. After the continuum extrapolation, the decay width is obtained to be . Regardless of this large statistical error, our result is compatible with the experimental results within 1.3σ. Potential improvements of the lattice calculation in the future are also discussed.