Number Of Free Parameters Research Articles

Site-Specific Amino Acid Distributions Follow a Universal Shape.

In many applications of evolutionary inference, a model of protein evolution needs to be fitted to the amino acid variation at individual sites in a multiple sequence alignment. Most existing models fall into one of two extremes: Either they provide a coarse-grained description that lacks biophysical realism (e.g., dN/dS models), or they require a large number of parameters to be fitted (e.g., mutation-selection models). Here, we ask whether a middle ground is possible: Can we obtain a realistic description of site-specific amino acid frequencies while severely restricting the number of free parameters in the model? We show that a distribution with a single free parameter can accurately capture the variation in amino acid frequency at most sites in an alignment, as long as we are willing to restrict our analysis to predicting amino acid frequencies by rank rather than by amino acid identity. This result holds equally well both in alignments of empirical protein sequences and of sequences evolved under a biophysically realistic all-atom force field. Our analysis reveals a near universal shape of the frequency distributions of amino acids. This insight has the potential to lead to new models of evolution that have both increased realism and a limited number of free parameters.

Phylosymmetric Algebras: Mathematical Properties of a New Tool in Phylogenetics

In phylogenetics, it is of interest for rate matrix sets to satisfy closure under matrix multiplication as this makes finding the set of corresponding transition matrices possible without having to compute matrix exponentials. It is also advantageous to have a small number of free parameters as this, in applications, will result in a reduction in computation time. We explore a method of building a rate matrix set from a rooted tree structure by assigning rates to internal tree nodes and states to the leaves, then defining the rate of change between two states as the rate assigned to the most recent common ancestor of those two states. We investigate the properties of these matrix sets from both a linear algebra and a graph theory perspective and show that any rate matrix set generated this way is closed under matrix multiplication. The consequences of setting two rates assigned to internal tree nodes to be equal are then considered. This methodology could be used to develop parameterised models of amino acid substitution which have a small number of parameters but convey biological meaning.

Temporal Learning in Video Data Using Deep Learning and Gaussian Processes

This paper presents an approach for data-driven modeling of hidden, stationary temporal dynamics in sequential images or videos using deep learning and Bayesian non-parametric techniques. In particular, a deep Convolutional Neural Network (CNN) is used to extract spatial features in an unsupervised fashion from individual images and then, a Gaussian process is used to model the temporal dynamics of the spatial features extracted by the deep CNN. By decomposing the spatial and temporal components and utilizing the strengths of deep learning and Gaussian processes for the respective sub-problems, we are able to construct a model that is able to capture complex spatio-temporal phenomena while using relatively small number of free parameters. The proposed approach is tested on high-speed grey-scale video data obtained of combustion flames in a swirl-stabilized combustor, where certain protocols are used to induce instability in combustion process. The proposed approach is then used to detect and predict the transition of the combustion process from stable to unstable regime. It is demonstrated that the proposed approach is able to detect unstable flame conditions using very few frames from high-speed video. This is useful as early detection of unstable combustion can lead to better control strategies to mitigate instability. Results from the proposed approach are compared and contrasted with several baselines and recent work in this area. The performance of the proposed approach is found to be significantly better in terms of detection accuracy, model complexity and lead-time to detection.

The confrontation of the shock-powered synchrotron maser model with the Galactic FRB 200428

ABSTRACT The association of FRB 200428 with an X-ray burst (XRB) from the Galactic magnetar SGR 1935+2154 offers important implications for the physical processes responsible for the fast radio burst (FRB) phenomena. By assuming that the XRB emission is produced in the magnetosphere, we investigate the possibility that the FRB emission is produced by shock-powered synchrotron maser (SM), which is phenomenologically described with a number of free parameters. The observational constraints on the model parameters indicate that the model can in principle be consistent with the FRB 200428 observations, if the ejecta lunched by magnetar activities can have appropriate ingredients and structures and the shock processes occur on the line of sight. To be specific, a complete burst ejecta should consist of an ultra-relativistic and extremely highly collimated e± component and a sub-relativistic and wide-spreading baryonic component. The internal shocks producing the FRB emission arise from a collision between the e± ejecta and the remnant of a previous baryonic ejecta at the same direction. The parameter constraints depend on the uncertain spectrum and efficiency of the SM emission. While the spectrum is tentatively described by a spectral index of −2, we estimate the emission efficiency to be around 10−4 by requiring that the synchrotron emission of the shocked material cannot be much brighter than the magnetosphere XRB emission.

Kinetics of the reductive amination of 1-undecanal in thermomorphic multicomponent system

The homogenously rhodium-catalyzed reductive amination reaction of 1-undecanal was performed in two solvent systems to provide a building block for the kinetic description of the industrially relevant hydroaminomethylation. Therefore, the reductive amination was analyzed in detail by experimental, computational and simulations studies. Initially, a network analysis was carried out, which allowed a kinetic modeling including water influence. Thermodynamic data provided by Density Functional Theory calculations enabled a detailed analysis of the dependence of thermodynamic and kinetic parameters on reaction conditions. Thus, the number of free parameters that had to be determined by kinetic experiments was significantly reduced. Partial pressure, composition of the solvents, temperature as well as water influence were studied by performing dynamic experiments. Simulation results with estimated parameters were found to be in good agreement with experiments. The kinetic model allows further process development and optimization as well as the kinetic description of the hydroaminomethylation by coupling hydroformylation and reductive amination.

Surprise Acts as a Reducer of Outcome Value in Human Reinforcement Learning.

Surprise occurs because of differences between a decision outcome and its predicted outcome (prediction error), regardless of whether the error is positive or negative. It has recently been postulated that surprise affects the reward value of the action outcome; studies have indicated that increasing surprise as an absolute value of prediction error decreases the value of the outcome. However, how surprise affects the value of the outcome and subsequent decision making is unclear. We suggest that, on the assumption that surprise decreases the outcome value, agents will increase their risk-averse choices when an outcome is often surprising. Here, we propose the surprise-sensitive utility model, a reinforcement learning model that states that surprise decreases the outcome value, to explain how surprise affects subsequent decision making. To investigate the properties of the proposed model, we compare the model with previous reinforcement learning models on two probabilistic learning tasks by simulations. As a result, the proposed model explains the risk-averse choices like the previous models, and the risk-averse choices increase as the surprise-based modulation parameter of outcome value increases. We also performed statistical model selection by using two experimental datasets with different tasks. The proposed model fits these datasets better than the other models with the same number of free parameters, indicating that the model can better capture the trial-by-trial dynamics of choice behavior.

Regularized models of audiovisual integration of speech with predictive power for sparse behavioral data

Audiovisual integration can facilitate speech comprehension by integrating information from lip-reading with auditory speech perception. When incongruent acoustic speech is dubbed onto a video of a talking face, this integration can lead to the McGurk illusion of hearing a different phoneme than that spoken by the voice. Several computational models of the information integration process underlying these phenomena exist. All are based on the assumption that the integration process is, in some sense, optimal. They differ, however, in assuming that it is based on either continuous or categorical internal representations. Here we develop models of audiovisual integration of the phonetic information represented on an internal representation that is continuous and cyclical. We compare these models to the Fuzzy Logical Model of Perception (FLMP), which is based on a categorical internal representation. Using cross-validation, we show that model evaluation criteria based on the goodness-of-fit are poor measures of the models’ generalization error even if they take the number of free parameters into account. We also show that the predictive power of all the models benefit from regularization that limits the precision of the internal representation. Finally, we show that, unlike the FLMP, models based on a continuous internal representation have good predictive power when properly regularized.

Modular symmetry origin of texture zeros and quark-lepton unification

The even weight modular forms of level $N$ can be arranged into the common irreducible representations of the inhomogeneous finite modular group $\Gamma_N$ and the homogeneous finite modular group $\Gamma'_N$ which is the double covering of $\Gamma_N$, and the odd weight modular forms of level $N$ transform in the new representations of $\Gamma'_N$. We find that the above structure of modular forms can naturally generate texture zeros of the fermion mass matrices if we properly assign the representations and weights of the matter fields under the modular group. We perform a comprehensive analysis for the $\Gamma'_3\cong T'$ modular symmetry. The three generations of left-handed quarks are assumed to transform as a doublet and a singlet of $T'$, we find six possible texture zeros structures of quark mass matrix up to row and column permutations. We present five benchmark quark models which can produce very good fit to the experimental data. These quark models are further extended to include lepton sector, the resulting models can give a unified description of both quark and lepton masses and flavor mixing simultaneously although they contain less number of free parameters than the observables.

Covert symmetries in the neutrino mass matrix

The flavour neutrino puzzle is often addressed by considering neutrino mass matrices m with a certain number of vanishing entries (mij = 0 for some values of the indices), since a reduction in the number of free parameters increases the predictive power. Symmetries that can enforce textures zero can also enforce a more general type of conditions f(mij) = 0 with f some function of the matrix elements mij. In this case m can have all entries non-vanishing with no reduction in its predictive power. We classify all generation-dependent U(1) symmetries which, in the presence of two leptonic Higgs doublets, can reduce the number of independent high-energy parameters of type-I seesaw to the minimum number compatible with non-vanishing neutrino mixings and CP violation. These symmetries are broken above the scale where the effective operator is generated and can thus remain covert, in the sense that no explicit evidence of the symmetry can be read off the neutrino mass matrix, and different symmetries can give rise to the same low-energy structure. We find that only two cases are viable: one yields a structure with two zero-textures already considered in the literature, the other has no zero-textures and has never been considered before. It predicts normal ordering, a lightest neutrino mass ∼ 10 meV, a Dirac phase δ ∼ frac{3pi }{2} and definite values for the Majorana phases.

Using hypothesis testing on the mass-transfer effect with sulfate removal as an application

ABSTRACT Sulfate and chemical oxygen demand removal by an anaerobic batch reactor treating of acid mine drainage is modelled. Available models are abundant but excessively complex, with large numbers of free parameters. Here, maximum likelihood and chi-squared hypothesis tests are applied to three simple models, with Malthus-Monod and Fick description, in increasing order of complexity: (i) planktonic single population (of sulfate-reducing bacteria); (ii) planktonic double-competing populations (adding fermentative bacteria); (iii) granule bound double-competing populations. The data set consists of 6 time profiles, sampled from 120 days of operation after stabilization of the reactor in pH 4. Single population is refuted by all profiles, in which the sulfate reduction is larger than fermentatives. The planktonic double-competing population description is refuted at 119 days, with inner granule diffusion rate as low as of the previous period. The results showed that, after an operation time, the influence of mass transfer became more evident and the incorporation of Fick's law in the model was fundamental to the description of this trend. All tests and inferences are performed at the confidence interval due to large systematic uncertainties in the data.

Energy of fermionic ground states with low-entanglement single-reference expansions, and tensor-based strong-coupling extensions of the coupled-cluster method

We consider a fermionic system for which there exist a single-reference configuration-interaction (CI) expansion of the ground state wave function that converges, albeit not necessarily rapidly, with respect to excitation number. We show that, if the coefficients of Slater determinants (SD) with $l\leq k$ excitations can be defined with a number of free parameters $N_{\leq k}$ bounded polynomially in $k$, the ground state energy $E$ only depends on a small fraction of all the wave function parameters, and is the solution of equations of the coupled-cluster (CC) form. This generalizes the standard CC method, for which $N_{\leq k}$ is bounded by a constant. Based on that result and low-rank tensor decompositions (LRTD), we discuss two possible extensions of the CC approach for wave functions with general polynomial bound for $N_{\leq k}$. First, one can use LRTD to represent the amplitudes of the CC cluster operator $T$ which, unlike in the CC case, is not truncated with respect to excitation number, and the energy and tensor parameters are given by a LRTD-adapted version of standard CC equations. Second, the LRTD can also be used to directly parametrize the CI coefficients, which involves different equations of the CC form. We derive those equations for up to quadruple-excitation coefficients, using a different type of excitation operator in the CC wave function ansatz, and a Hamiltonian representation in terms of excited particle and hole operators. We complete the proposed CC extensions by constructing compact tensor representations of coefficients, or $T$-amplitudes, using superpositions of tree tensor networks which take into account different possible types of entanglement between excited particles and holes. Finally, we discuss why the proposed extensions are theoretically applicable at larger coupling strengths than those treatable by the standard CC method.

Effective theory approach to new physics with flavour: general framework and a leptoquark example

Extending the Standard Model with higher-dimensional operators in an effective field theory (EFT) approach provides a systematic framework to study new physics (NP) effects from a bottom-up perspective, as long as the NP scale is sufficiently large compared to the energies probed in the experimental observables. However, when taking into account the different quark and lepton flavours, the number of free parameters in- creases dramatically, which makes generic studies of the NP flavour structure infeasible. In this paper, we address this issue in view of the recently observed “flavour anomalies” in B-meson decays, which we take as a motivation to develop a general framework that allows us to systematically reduce the number of flavour parameters in the EFT. This framework can be easily used in global fits to flavour observables at Belle II and LHCb as well as in analyses of flavour-dependent collider signatures at the LHC. Our formalism represents an extension of the well-known minimal-flavour-violation approach, and uses Froggatt-Nielsen charges to define the flavour power-counting. As a relevant illustration of the formalism, we apply it to the flavour structures which could be induced by a U1 vector leptoquark, which represents one of the possible explanations for the recent hints of flavour non-universality in semileptonic B-decays. We study the phenomenological viability of this specific framework performing a fit to low-energy flavour observables.

Dark Matter and Baryons (Surplus Quarks) Generated by Oblique Confinement of Quarks

For surplus quarks (and baryons) to emerge after Big Bang, a nonequilibrium binding and superconductor-like condensation of quark-antiquark pairs must occur before the electroweak (EW) symmetry breakdown (similar for leptons). The formerly unknown dimensionless coupling to the Ginsburg-Landau like potential and the scale parameter in the EW theory then become microscopic functions of the massive quark and antiquark fields, thus defining the matter-antimatter asymmetry and the dark matter content in the Universe at correct orders of magnitude. Thereby also the number of free parameters in the Standard Model is reduced.

Superstrong photospheric magnetic fields in sunspot penumbrae

Context. Recently, there have been some reports of unusually strong photospheric magnetic fields (which can reach values of over 7 kG) inferred from Hinode SOT/SP sunspot observations within penumbral regions. These superstrong penumbral fields are even larger than the strongest umbral fields on record and appear to be associated with supersonic downflows. The finding of such fields has been controversial since they seem to show up only when spatially coupled inversions are performed. Aims. Here, we investigate and discuss the reliability of those findings by studying in detail observed spectra associated with particularly strong magnetic fields at the inner edge of the penumbra of active region 10930. Methods. We applied classical diagnostic methods and various inversions with different model atmospheres to the observed Stokes profiles in two selected pixels with superstrong magnetic fields, and compared the results with a magnetohydrodynamic simulation of a sunspot whose penumbra contains localized regions with strong fields (nearly 5 kG at τ = 1) associated with supersonic downflows. Results. The different inversions provide different results: while the SPINOR 2D inversions consider a height-dependent single-component model and return B > 7 kG and supersonic positive vLOS (corresponding to a counter-Evershed flow), height-dependent two-component inversions suggest the presence of an umbral component (almost at rest) with field strengths ∼4 − 4.2 kG and a penumbral component with vLOS ∼ 16 − 18 km s−1 and field strengths up to ∼5.8 kG. Likewise, height-independent two-component inversions find a solution for an umbral component and a strongly redshifted (vLOS ∼ 15 − 17 km s−1) penumbral component with B ∼ 4 kG. According to a Bayesian information criterion, the inversions providing a better balance between the quality of the fits and the number of free parameters considered by the models are the height-independent two-component inversions, but they lie only slightly above the SPINOR 2D inversions. Since it is expected that the physical parameters all display considerable gradients with height, as supported by magnetohydrodynamic (MHD) sunspot simulations, the SPINOR 2D inversions are the preferred ones. Conclusions. According to the MHD sunspot simulation analyzed here, the presence of counter-Evershed flows in the photospheric penumbra can lead to the necessary conditions for the observation of ∼5 kG fields at the inner penumbra. Although a definite conclusion about the potential existence of fields in excess of 7 kG cannot be given, their nature could be explained (based on the simulation results) as the consequence of the extreme dynamical effects introduced by highly supersonic counter-Evershed flows (vLOS > 10 km s−1 and up to ∼30 km s−1 according to SPINOR 2D). The latter are much faster and more compressive downflows than those found in the MHD simulations and therefore could lead to field intensification up to considerably stronger fields. Also, a lower gas density would lead to a deeper depression of the τ = 1 surface, making possible the observation of deeper-lying stronger fields. The superstrong magnetic fields are expected to be nearly force-free, meaning that they can attain much larger strengths than expected when considering only balance between magnetic pressure and the local gas pressure.

On the Goldberg–Sachs theorem in six dimensions

We study the “shear-free” part of the Goldberg–Sachs theorem for type II and D six-dimensional Einstein spacetimes. A spacetime is of the type II or D if it admits a double Weyl aligned null direction (WAND). The Goldberg–Sachs theorem then restricts geometric properties of double WANDs. This restriction can be expressed in terms of constraints on the form of the “optical matrix” defining the expansion, rotation, and shear of the double WAND. We show that a rank-four and rank-three optical matrix is orthogonally similar to one of three canonical forms, reducing the number of free parameters of the optical matrix from ten to five.

A genetic algorithm for astroparticle physics studies

Precision measurements of charged cosmic rays have recently been carried out by space-born (e.g. AMS-02), or ground experiments (e.g. HESS). These measured data are important for the studies of astro-physical phenomena, including supernova remnants, cosmic ray propagation, solar physics and dark matter. Those scenarios usually contain a number of free parameters that need to be adjusted by observed data. Some techniques, such as Markov Chain Monte Carlo and MultiNest, are developed in order to solve the above problem. However, it is usually required a computing farm to apply those tools. In this paper, a genetic algorithm for finding the optimum parameters for cosmic ray injection and propagation is presented. We find that this algorithm gives us the same best fit results as the Markov Chain Monte Carlo but consuming less computing power by nearly 2 orders of magnitudes. Program summaryOperating system: LinuxProgramming Language: CSoftware Package: ROOTLibraries: cmath, cstdio, cstdlib, ctimeOptional Software Package: DRAGON

Assessment of reliability-based design of stable slopes

The viability of applying reliability-based design in the limit equilibrium evaluation of slope stability is assessed. Two model slopes are designed according to the limit states specification of European standard EN 1997:2004 and reliability assessed using full Monte Carlo calculation with 106trials. Comparison of these results with reliability estimates obtained via a spectrum of different analysis techniques, broadly grouped into first-order reliability methods (FORM) and performance function moment estimation methods, indicates that FORM-based techniques are superior, with a first-order response surface method found to provide the best combination of accuracy, stability, and speed of convergence. In this way, accurate reliability indices for nonclosed form problems of the nature considered here can be obtained within 20–30 function calls, depending on the number of free parameters and required precision.

The NMSSM is within reach of the LHC: mass correlations & decay signatures

The Next-to-Minimal Supersymmetric Standard Model (NMSSM), the singlet extension of the MSSM which fixes many of the MSSM’s shortcomings, is shown to be within reach of the upcoming runs of the Large Hadron Collider (LHC). A systematic treatment of the various Higgs decay channels and their interplay has been lacking due to the seemingly large number of free parameters in the NMSSM’s Higgs sector. We demonstrate that due to the SM-like nature of the observed Higgs boson, the NMSSM’s Higgs and neutralino sectors have highly correlated masses and couplings and can effectively be described by four physically intuitive parameters: the physical masses of the two CP-odd states and their mixing angle, and tan β, which plays a minor role. The heavy Higgs bosons in the NMSSM have large branching ratios into pairs of lighter Higgs bosons or a light Higgs and a Z boson. Search channels arising via these Higgs cascades are unique to models like the NMSSM with a Higgs sector larger than that of the MSSM. In order to cover as much of the NMSSM parameter space as possible, one must combine conventional search strategies employing decays of the additional Higgs bosons into pairs of SM particles with Higgs cascade channels. We demonstrate that such a combination would allow a significant fraction of the viable NMSSM parameter space containing additional Higgs bosons with masses below 1 TeV to be probed at future runs of the LHC.

Likelihood approximations of implied weights parsimony can be selected over the Mk model by the Akaike information criterion.

A likelihood method that approximates the behaviour of implied weighting is described. This approach provides a likelihood perspective on several aspects of implied weighting, such as guidance for the choice of concavity values, a justification to use different concavities for different numbers of taxa, and a natural basis for extended implied weighting. In this approach, the number of free parameters in the estimation depends on C, the number of characters (in contrast to the standard Mk model, which estimates 2T-3 parameters for T taxa). Depending on the characteristics of the dataset, the likelihood obtained with this approach may in some cases be similar or superior to that of the Mk model, but with fewer parameters being adjusted. Because of that tradeoff, testing against the Mk model by means of the Akaike information criterion on a set of 182 morphological datasets indicated many cases (36) in which the likelihood approximation to implied weighting is the best method, from an information-theoretic point of view. Given that it is expected to produce (almost) the same results as this maximum-likelihood approximation, implied weighting can therefore be seen as a valid alternative to the Mk model often used for morphological datasets, on the basis of a criterion for model fit widely advocated by likelihoodists.

Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler–Bernoulli beam equations

This paper presents a number of finite difference time domain (FDTD) schemes to simulate the vibration of prestressed beams to various degrees of accuracy. The Timoshenko, shear and Euler–Bernoulli models are investigated, with a focus on the numerical modelling for the Timoshenko system. The conservation of a discrete Hamiltonian to machine accuracy ensures stability and convergence of the numerical schemes. The difference equations are in the form of theta schemes, which depend on a number of free parameters that can be tuned in order to reduce numerical dispersion. Although the schemes are built by means of second-order accurate finite difference operators only, fully fourth-order accurate schemes may be designed through modified equation techniques, and wideband-accurate schemes are also possible. The latter are schemes designed to maximise the resolving power at all wavelengths. Investigation of beams of cross section varying from slender to thick allows a thorough comparison between the various schemes, for the three beam models.