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In the first part of this article, we review a formalism of local zeta integrals attached to spherical reductive prehomogeneous vector spaces, which partially extends M. Sato's theory by incorporating the generalized matrix coefficients of admissible representations. We summarize the basic properties of these integrals such as the convergence, meromorphic continuation and an abstract functional equation. In the second part, we prove a generalization that accommodates certain non-spherical spaces with spherical quotients. As an application, the resulting theory applies to the prehomogeneous vector space underlying Bhargava's cubes, which is also considered by F. Sato and Suzuki–Wakatsuki in their study of toric periods.

This chapter deals with an approach towards a physical description of the spreading of pollution in a turbulent atmosphere. We may witness this phenomenon quite commonly by, e.g., following the smoke of a chimney or the steam emerging from a power plant. It is remarkable that the equations to quantify atmospheric turbulence reveal close similarities with the formalism provided by the Fick’s diffusion laws. This is not only true for passive constituents (like smoke or moisture) but also for the turbulent diffusion of heat and momentum. Modelling of atmospheric turbulences, however, is still based on two conceptions which describe the same phenomenon from different perspectives. The development of an all-embracing view has thus remained a challenging task for the future.

The effective field theory motivated relativistic mean-field (E-RMF) formalism is employed to study the equation of state (EoS) for the infinite symmetric nuclear matter (SNM) at finite temperature using the recently developed forces FSUGarnet, IOPB-I, G3, and the well known NL3 force parameter. The EoS is then used to estimate the critical temperature T c, pressure P c and density ρ c of the SNM for the liquid–gas phase transition. As T c is not a constrained parameter in both experiments and theoretical calculations, there is a large uncertainty around its value. Although, the critical parameters are correlated among themselves. It is revealed that vector self-coupling ζ 0 of used forces play determining role in EoS in finite temperature limit. Keeping the incompressibility in acceptable limit i.e. 240 ± 20 MeV, the lower value of ζ 0 gives a better result of T c when compared to the several experimental data. The critical parameters however show weak correlation with the properties at saturation density at zero temperature. The compressibility factors calculated with these parameters are in agreement with the universal value of liquid–gas systems. Stability conditions are examined along with binodal and spinodal regions. Besides this, the thermodynamic properties like specific heat and latent heat are also worked out. We have carried out detailed consistency check of our calculations using critical exponents and standard scaling laws. All the exponents are well within the theoretical mean-field results.

Many systems in life sciences have been modeled by reaction–diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events, etc) such that an appropriate formalism like impulsive reaction–diffusion equations is necessary to analyze them. While several works tackled the issue of traveling waves for monotone reaction–diffusion equations and the computation of spreading speeds, very little has been done in the case of monotone impulsive reaction–diffusion equations. Based on vector-valued recursion equations theory, we aim to present in this paper results that address two main issues of monotone impulsive reaction–diffusion equations. Our first result deals with the existence of traveling waves for monotone systems of impulsive reaction–diffusion equations. Our second result tackles the computation of spreading speeds for monotone systems of impulsive reaction–diffusion equations. We apply our methodology to a planar system of impulsive reaction–diffusion equations that models tree–grass interactions in fire-prone savannas. Numerical simulations, including numerical approximations of spreading speeds, are finally provided in order to illustrate our theoretical results and support the discussion.

In recent years, great efforts have been made to analyse biological systems to understand the long-run behaviours. As a well-established formalism for modelling real-life biological systems, Boolean networks (BNs) allow their representation and analysis using formal reasoning and tools. Most biological systems are robust - they can withstand the loss of links and cope with external environmental perturbations. Hence, the BNs used to model such systems are necessarily large and dense, and yet modular. However, existing analysis methods only work well on networks of moderate size. Thus, there is a great need for efficient methods that can handle large-scale BNs and for doing so it is inevitable to exploit both the structural and dynamic properties of the networks. In this paper, we propose a method towards the optimal decomposition of BNs to balance the relation between the structure and dynamics of a network. We show that our method can greatly improve the existing decomposition-based attractor detection by analysing a number of large real-life biological networks.

The generalized learning algorithm can be efficiently used as control strategy, but it has some drawbacks such as: sensitivity to the training dataset, poor robustness against changes in the system, difficulty to generate the control signals without destabilising the plant, tuning of the controller, etc. To overcome some of these issues, in this work a new switched neural adaptive control strategy is proposed. It is based on the combination of an adaptive artificial neural network, a PID regulator, an estimated inverse model of the plant and two switches to route the signals properly in the control scheme. The technique is described using the hybrid automata formalism. In order to test the validity of this proposal, it is applied to the control of a quadrotor unmanned aerial vehicle (UAV), subjected to changes in its mass and wind disturbances. Simulation results show how the on-line learning increases the robustness of the controller, reducing the effects of the mass change and of the wind on the UAV stabilization, thus improving the UAV trajectory tracking.

Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple files from $ \mathsf {n}$ non-communicating servers by downloading quantum systems without revealing which file is retrieved. As variants of QPIR with stronger security requirements, symmetric QPIR is a protocol in which no other files than the target file are leaked to the user, and $ \mathsf {t}$ -private QPIR is a protocol in which the identity of the target file is kept secret even if at most $ \mathsf {t}$ servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the file size to the size of downloaded quantum systems, and we prove that the symmetric $ \mathsf {t}$ -private QPIR capacity is $\min \{1,2( \mathsf {n}- \mathsf {t})/ \mathsf {n}\}$ for any $1\leq \mathsf {t} . We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.

Linking complex, multigenic traits to protein activity is an important challenge in current biology, including applications in the medical sciences, agriculture, or forestry. Two simple algorithms are presented here to establish that link. The first one describes synergistic interactions of n proteins in shaping a complex trait ('weak emergence') as opposed to a simply additive 'modular' contribution of these proteins. A coefficient κ is defined that allows to quantify the degree of emergent interaction. For cases of strong emergence a separate formalism is introduced, implying that a number of n proteins at concentrations exceeding individual threshold values are required to spontaneously form a new, complex trait. Threshold concentrations are allowed to vary, depending on the concentrations of the other constitutive proteins. The experimental effort is estimated to provide a corresponding database for applying both formalisms, including high-throughput phenomics, and manipulation of protein concentrations using the molecular toolbox. Future efforts will be directed to overcome current limitations of the models that ignore the dynamics of protein-trait relationships with time, and the importance of the spatial arrangement of proteins for emergent interaction.

In this paper, we derive analytical time-dependent Green's functions in a two-dimensional, anisotropic elastic, and infinite solid. It is based on the Stroh formalism combined with application of the Cauchy's residue theorem. Final expressions of the Green's function are in terms of simple finite line integral from 0 to 2π. The time-dependence of the line forces can be impulsive, Heaviside, or within a given time duration. The space-dependence of the line force is very general, including concentrated or uniformly distributed sources within a given line interval. Green's functions of both displacements and stresses are derived in analytical forms, and are verified against existing results. Numerical examples are presented to demonstrate the effect of source types and material anisotropy on the Green's functions.

The paper presents the formalism of an intelligent decision-making system based on multi-agent neurocognitive architectures, which has an architectural similarity to the human brain. An invariant of the organizational and functional structure of the intellectual decision-making process based on the multi-agent neurocognitive architecture is developed. An algorithm for teaching intelligent decision-making systems based on the self-organization of the invariant of multi-agent neurocognitive architectures is presented. Using this algorithm, an intelligent agent was trained and the architecture of the learning process was built on the basis of an invariant of neurocognitive architecture. Further research is related to training an intelligent agent in more complex behavior and expanding the capabilities of an intelligent decision-making system based on multi-agent neurocognitive architectures.

A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types, all within a unified, sheaf-theoretic formalism. We take robotic systems as an exemplar of complex systems and rigorously describe actuators, sensors, and algorithms using this framework., Comment: In Proceedings ACT 2020, arXiv:2101.07888. arXiv admin note: substantial text overlap with arXiv:2005.04715

Kinetic formalisms of metabolism link metabolic fluxes to enzyme levels, metabolite concentrations and their allosteric regulatory interactions. Though they require the identification of physiologically relevant values for numerous parameters, kinetic formalisms uniquely establish a mechanistic link across heterogeneous omics datasets and provide an overarching vantage point to effectively inform metabolic engineering strategies. Advances in computational power, gene annotation coverage, and formalism standardization have led to significant progress over the past few years. However, careful interpretation of model predictions, limited metabolic flux datasets, and assessment of parameter sensitivity remain as challenges. In this review we highlight fundamental considerations which influence model quality and prediction, advances in methodologies, and success stories of deploying kinetic models to guide metabolic engineering.

Al, Ca, and Zn are representative commercial alloying elements for Mg alloys. To investigate the effects of these elements on the deformation and recrystallization behaviors of Mg alloys, we develop interatomic potentials for the Al–Ca, Al–Zn, Mg–Al–Ca and Mg–Al–Zn systems based on the second nearest-neighbor modified embedded-atom method formalism. The developed potentials describe structural, elastic, and thermodynamic properties of compounds and solutions of associated alloy systems in reasonable agreement with experimental data and higher-level calculations. The applicability of these potentials to the present investigation is confirmed by calculating the generalized stacking fault energy for various slip systems and the segregation energy on twin boundaries of the Mg–Al–Ca and Mg–Al–Zn alloys, accompanied with the thermal expansion coefficient and crystal structure maintenance of stable compounds in those alloys.

We study the norm potentials of Holder continuous \begin{document}$ \text{GL}_2(\mathbb{R}) $\end{document} -cocycles over hyperbolic systems whose canonical holonomies converge and are Holder continuous. Such cocycles include locally constant \begin{document}$ \text{GL}_2(\mathbb{R}) $\end{document} -cocycles as well as fiber-bunched \begin{document}$ \text{GL}_2(\mathbb{R}) $\end{document} -cocycles. We show that the norm potentials of irreducible such cocycles have unique equilibrium states. Among the reducible cocycles, we provide a characterization for cocycles whose norm potentials have more than one equilibrium states.

As the field of ionic liquids matures to more industrially implemented applications, robust models of their physico-chemical properties become necessary for process optimization. Viscosity is a particularly difficult property to model since there is no generally accepted theory for the viscosity of liquids. This paper aims to review the viscosity models developed or adapted to ionic liquids and their mixtures that are available in the literature. The scope of application and limitations of these models are discussed. In particular, the mixing rules' current formalism for ionic liquids is analysed in light of established knowledge from the inorganic molten salt community.

Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error probability. We derive one-shot bounds on the optimal average codeword length by proposing two new information quantities; namely, the conditional and unconditional $\varepsilon$-cutoff entropies. Using these one-shot bounds, we obtain the second-order asymptotics of the problem under two different formalisms---the average and maximum probabilities of error over the realization of the side-information. While the first-order terms in the asymptotic expansions for both formalisms are identical, we find that the source dispersion under the average error formalism is, in most cases, strictly smaller than its maximum error counterpart. Applications to a certain class of guessing problems, previously studied by Kuzuoka [\emph{{IEEE} Trans.\ Inf.\ Theory}, vol.~66, no.~3, pp.~1674--1690, 2020], are also discussed., Comment: 23 pages, accepted for publication in IEEE Transactions on Information Theory

Identifying patient-specific flow of signal transduction perturbed by multiple single-nucleotide alterations is critical for improving patient outcomes in cancer cases. However, accurate estimation of mutational effects at the pathway level for such patients remains an open problem. While probabilistic pathway topology methods are gaining interest among the scientific community, the overwhelming majority do not account for network perturbation effects from multiple single-nucleotide alterations. Here we present an improvement of the mutational forks formalism to infer the patient-specific flow of signal transduction based on multiple single-nucleotide alterations, including non-synonymous and synonymous mutations. The lung adenocarcinoma and skin cutaneous melanoma datasets from TCGA Pan-Cancer Atlas have been employed to show the utility of the proposed method. We have comprehensively characterized six mutational forks. The number of mutated nodes ranged from one to four depending on the topological characteristics of a fork. Transitional confidences (TCs) have been computed for every possible combination of single-nucleotide alterations in the fork. The performed analysis demonstrated the capacity of the mutational forks formalism to follow a biologically explainable logic in the identification of high-likelihood signaling routes in lung adenocarcinoma and skin cutaneous melanoma patients. The findings have been largely supported by the evidence from the biomedical literature. We conclude that the formalism has a great chance to enable an assessment of patient-specific flow by leveraging information from multiple single-nucleotide alterations to adjust the transitional likelihoods that are solely based on the canonical view of a disease.

Answer Set Programming (ASP) is a successful rule-based formalism for modeling and solving knowledge-intense combinatorial (optimization) problems. Despite its success in both academic and industry, open challenges like automatic source code optimization, and software engineering remains. This is because a problem encoded into an ASP might not have the desired solving performance compared to an equivalent representation. Motivated by these two challenges, this paper has three main contributions. First, we propose a developing process towards a methodology to implement ASP programs, being faithful to existing methods. Second, we present ASP encodings that serve as the basis from the developing process. Third, we demonstrate the use of ASP to reverse the standard solving process. That is, knowing answer sets in advance, and desired strong equivalent properties, “we” exhaustively reconstruct ASP programs if they exist. This paper was originally motivated by the search of propositional formulas (if they exist) that represent the semantics of a new aggregate operator. Particularly, a parity aggregate. This aggregate comes as an improvement from the already existing parity ( xor ) constraints from xorro, where lacks expressiveness, even though these constraints fit perfectly for reasoning modes like sampling or model counting. To this end, this extended version covers the fundaments from parity constraints as well as the xorro system. Hence, we delve a little more in the examples and the proposed methodology over parity constraints. Finally, we discuss our results by showing the only representation available, that satisfies different properties from the classical logic xor operator, which is also consistent with the semantics of parity constraints from xorro.

Purpose To examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT). Materials and methods For nine non-small-cell carcinoma cell (NSCLC) lines, the linear-quadratic (LQ) and USC models were used to calculate the EUD of a set of hypothetical two-compartment tumor dose–volume histogram (DVH) models. The dose was varied by ±5%, ±10%, and ±20% about the prescription dose (60 Gy/3 fractions) to the first compartment, with fraction volume varying from 1% and 5% to 30%. Clinical DVHs of 21 SBRT treatments of NSCLC prescribed to the 70–83% isodose lines were also considered. The EUD of non-standard SBRT dose fractionation (EUDSBRT) was further converted to standard fractionation of 2 Gy (EUDCFRT) using the LQ and USC models to facilitate comparisons between different SBRT dose fractionations. Tumor control probability (TCP) was then estimated from the LQ- and USC-EUDCFRT. Results For non-standard SBRT fractionation, the deviation of the USC- from the LQ-EUDSBRT is largely limited to 5% in the presence of dose variation up to ±20% to fractional tumor volume up to 30% in all NSCLC cell lines. Linear regression with zero constant yielded USC-EUDSBRT = 0.96 × LQ-EUDSBRT (r2 = 0.99) for the clinical DVHs. Converting EUDSBRT into standard 2‑Gy fractions by the LQ formalism produced significantly larger EUDCFRT than the USC formalism, particularly for low $$\alpha /\beta$$ α / β ratios and large fraction dose. Simplified two-compartment DVH models illustrated that both the LQ- and USC-EUDCFRT values were sensitive to cold spot below the prescription dose with little volume dependence. Their deviations were almost constant for up to 30% dose increase above the prescription. Linear regression with zero constant yielded USC-EUDCFRT = 1.56 × LQ-EUDCFRT (r2 = 0.99) for the clinical DVHs. The clinical LQ-EUDCFRT resulted in median TCP of almost 100% vs. 93.8% with USC-EUDCFRT. Conclusion A uniform formalism of EUD should be defined among the SBRT community in order to apply it as a single metric for dose reporting and dose–response modeling in high-dose-gradient SBRT because its value depends on the underlying cell survival model and the model parameters. Further investigations of the optimal formalism to derive the EUD through clinical correlations are warranted.

Rotational Profiler provides an analytical algorithm to compute sets of classical torsional dihedral parameters by fitting an empirical energy profile to a reference one that can be obtained experimentally or by quantum-mechanical methods. The resulting profiles are compatible with the functional forms in the most widely used biomolecular force fields (e.g., GROMOS, AMBER, OPLS, and CHARMM). The linear least-squares regression method is used to generate sets of parameters that best satisfy the fitting. Rotational Profiler is free to use, analytical, and force field/package independent. The formalism is herein described, and its usage, in an interactive and automated manner, is made available as a Web server at http://rotprof.lncc.br.

Connections between the Görling-Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew-Burke-Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.

The equations of motion for the parametrized post-Newtonian (PPN) formalism for several S-stars close to the relativistic compact object Sgr A* at the center of the galaxy are examined. The effect of the difference in the periods of Newtonian and post-Newtonian orbits is taken into account. The period of the best approximation to the PN-orbit of the star S2 exceeds the period of the Newtonian orbit by 16 days. The PPN parameters βPPN and γPPN are measured. Bayesian methods are used for fitting the trajectories of the PPN motion. Posterior estimates of βPPN and γPPN $$ {0.97}_{-0.65}^{+0.42} $$ and $$ {0.81}_{-0.60}^{+0.46} $$ are obtained, respectively. This result confirms the prediction of the general theory of relativity for the post-Newtonian equations of motion under conditions close to Sgr A*.

While the SAFT equation of state, based on extensions and simplifications of Wertheim’s multi-density perturbation theory for associating molecules, has found wide application in industry and acade...

Periodic photonic lattices constitute a fundamental pillar of physics supporting a plethora of scientific concepts and applications. The advent of metamaterials and metastructures is grounded in a ...

In this paper a general study of NV center internal state in diamond is presented. This study is based on experimental and theoretical findingsfound in literature. First, a Hamiltonian model for center NV internal state is proposed in terms of a complete set of commuting observables(CSCO), which consist of angular momentum ^L, spin momentum ^ S, total angular momentum ^ J = ^L+ ^ S and spin momentum on z-direction^ Sz. The second quantization formalism –in steady-state (conservative model)– is used. The creation and annihilation operators are used todescribed the steady spin-levels structure and in dynamic-state (non-conservative model) and can also describe the system dynamic betweendifferent spin-levels transitions. Finally, a discussion is presented about the application of this study in the photochromism phenomenon andsolid-state quantum bit (qubit).

In this paper a stochastic formulation for describing the dynamics of an epidemic is established. We state our model in the language of a compartmental scheme of three sites (susceptible, infected and recovered) SIR, for which the parameters model are extended to be statistical distributions of time. It is established a master equation for governing the dynamics of the probability density P of finding the system in the state characterized by the values of the aleatory variables S, I, R and time t. Our stochastic formalism allow us to recover the associated deterministic model in terms of the expected values of S, I and R; whereas the second momenta of P provide us statistical standard deviations for these three variables which delimit the region in which most of the particular realizations are to be expected. We have applied the analysis developed here, for studying the specific case of the influenza AH1N1 that took place in Mexico in 2009. The reported data by the main Mexican Health institution are in good agreement with the predictions of our model for the standard deviation of the aleatory variables.

Al-Ti complex deoxidation equilibria in high Cr stainless steels were studied by measuring the thermodynamic behavior of O in the Fe-Cr-Al-O, Fe-Cr-Ti-O, and Fe-Cr-Al-Ti-O melts. The present deoxidation experiments were thermodynamically analyzed along with available data in the literature using Wagner’s formalism. The compatible set of parameters for the multicomponent Fe-Cr-Al-Ti-O system was selected, and its applicable concentration and temperature limits were discussed. The parameter set successfully reproduced the present experimental results and literature data of deoxidation equilibria in the Fe-Cr-Al-O and Fe-Cr-Ti-O alloy melts over the wide Cr concentration up to 40 mass pct at 1823 K to 1996 K (1550 °C to 1723 °C). The validity of the parameters was also checked by carrying out the Al-Ti complex deoxidation experiments with the construction of the predominance diagram for inclusions in the Fe-Cr-Al-Ti-O melts at 1873 K (1600 °C).

In this paper we present two performance models of a web-based sales system, one without the presence of an attack and the other with the presence of a denial of service attack. Models are formulated using the PEPA formalism. The PEPA eclipse plug-in is used to support the creation of the PEPA models for the web-based sales system and the automatic calculation of the performance measures identified to evaluate the models. The evaluation of the models illustrates how the performance of the warehouse's sale is negatively affected by denial of service attack through preventing some or all customers' orders from being fulfilled. The resultant delay on selling perishable products would result on products being discarded.

Why proteins are fuzzy? Constant adaptation to the cellular environment requires a wide range of changes in protein structure and interactions. Conformational ensembles of disordered proteins in particular exhibit large shifts to activate or inhibit alternative pathways. Fuzziness is critical for liquid–liquid phase separation and conversion of biomolecular condensates into fibrils. Interpretation of these phenomena presents a challenge for the classical structure-function paradigm. Here I discuss a multi-valued formalism, based on fuzzy logic, which can be applied to describe complex cellular behavior of proteins.

Gravitational waves from supermassive black hole binary mergers along with an electromagnetic counterpart have the potential to shed ‘light’ on the nature of dark energy in the intermediate redshift regime. Accurate measurement of dark energy parameters at intermediate redshift is extremely essential to improve our understanding of dark energy, and to possibly resolve a couple of tensions involving cosmological parameters. We present a Fisher matrix forecast analysis in the context of eLISA to predict the errors for three different cases: the non-interacting dark energy with constant and evolving equation of state (EoS), and the interacting dark sectors with a generalized parametrization. In all three cases, we perform the analysis for two separate formalisms, namely, the standard EoS formalism and the Om parametrization which is a model-independent null diagnostic for a wide range of fiducial values in both phantom and non-phantom regions, to make a comparative analysis between the prospects of these two diagnostics in eLISA. Our analysis reveals that it is wiser and more effective to probe the null diagnostic instead of the standard EoS parameters for any possible signature of dark energy at intermediate redshift measurements like eLISA.

On the basis of the study of air flight control, as well as the need to take into account the regional parameters of the airspace, the expediency and the need for mathematical modeling of the air navigation environment were identified. The article deals with the features of the model of air navigation environment, in which the base of the study adopted the basic information used to describe the plan for the execution of air flight. In the study, it was found that in navigation main feature is the geodesic of abstraction, however, such information was found, is not complete for the plan for air flight. The study emphasized the role of taking into account all the restrictions by which certain prohibitions on the use of specific volumes of airspace are imposed. Based on the results obtained, a graph of the geometric representation of the airspace with constraints was constructed. The results of the study allow us to conclude that the construction of a mathematical model of the air navigation environment allows us to achieve the following results: optimization of the distribution of the EAP loads by sectors, visualization of the air navigation situation in the region, the establishment of critical load directions, the collection of data on the load, the study of the factor effects on the regularity and safety of the aircraft movement. The mathematical model of the aeronautical situation was built with the help of a composition of hierarchical type. As a result of such construction of mathematical model its transformation with addition of new models is possible. Using the proposed mathematical model in the framework of discrete event systems can be used to simulate complex air navigation environment with a large number of aircraft. The use of the formalism presented in this study allows a clear distinction between the mechanism of information processing and the information itself in the process of modeling.

The neutron temperature at different irradiation positions in the research reactor FRM II was measured using thermometer labels together with lutetium standards. This was the first time to measure the local temperature at the irradiation positions with this combination. The simplified Westcott formalism was used to calculate the neutron temperature using Lu and g(Tn) factors from different data sources. The results showed agreement between neutron temperature according to the Lu method and the temperature showed on the labels. They can be used as a reliable alternative to determine the neutron temperature instead of using Lu standards in the extended k0 NAA.

Ethical and explainable artificial intelligence is an interdisciplinary research area involving computer science, philosophy, logic, and social sciences, etc. For an ethical autonomous system, the ability to justify and explain its decision-making is a crucial aspect of transparency and trustworthiness. This paper takes a Value-Driven Agent (VDA) as an example, explicitly representing implicit knowledge of a machine learning-based autonomous agent and using this formalism to justify and explain the decisions of the agent. For this purpose, we introduce a novel formalism to describe the intrinsic knowledge and solutions of a VDA in each situation. Based on this formalism, we formulate an approach to justify and explain the decision-making process of a VDA, in terms of a typical argumentation formalism, Assumption-based Argumentation (ABA). As a result, a VDA in a given situation is mapped onto an argumentation framework in which arguments are defined by the notion of deduction. Justified actions with respect to semantics from argumentation correspond to solutions of the VDA. The acceptance (rejection) of arguments and their premises in the framework provides an explanation for why an action was selected (or not). Furthermore, we go beyond the existing version of VDA, considering not only practical reasoning, but also epistemic reasoning, such that the inconsistency of knowledge of the VDA can be identified, handled, and explained.

In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Sciama-Kibble (ECSK) gravity. We consider different possibilities on how torsion is affected by Weyl transformations and discuss how this translates into the interpolation between two different Weyl transformations of the spin connection, parameterized with a zero-form parameter λ. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conservation of the mimetic stress-energy tensor and show that the trace of the total stress-energy tensor is not null but depends on both, the value of λ and spacetime torsion., P. M. is supported by Agencia Nacional de Investigaci´on (ANID) through the grant 21161574. OV acknowledges VRIIP UNAP for financial support through Project VRIIP0062-19 and Becas Chile grant 74200062. FI ad PS acknowledges financial support from the Chilean government through Fondecyt grant 1180681. NM, acknowledges Fondecyt grant 11180894.

Since the pioneering works of Newton (1643&ndash, 1727), Mechanics has been constantly reinventing itself: reformulated in particular by Lagrange (1736&ndash, 1813) then Hamilton (1805&ndash, 1865), it now offers powerful conceptual and mathematical tools for the exploration of dynamical systems, essentially via the action-angle variables formulation and more generally through the theory of canonical transformations. We propose to the (graduate) reader an overview of these different formulations through the well-known example of Foucault&rsquo, s pendulum, a device created by Foucault (1819&ndash, 1868) and first installed in the Panth&eacute, on (Paris, France) in 1851 to display the Earth&rsquo, s rotation. The apparent simplicity of Foucault&rsquo, s pendulum is indeed an open door to the most contemporary ramifications of classical mechanics. We stress that adopting the formalism of action-angle variables is not necessary to understand the dynamics of Foucault&rsquo, s pendulum. The latter is simply taken as well-known and simple dynamical system used to exemplify and illustrate modern concepts that are crucial in order to understand more complicated dynamical systems. The Foucault&rsquo, s pendulum first installed in 2005 in the collegiate church of Sainte-Waudru (Mons, Belgium) will allow us to numerically estimate the different quantities introduced.

The exact solutions of either spherical or deformed mean-field plus various types of pairing models are briefly reviewed. It is shown that, besides the standard pairing model, there are several special types of pairing interaction that can be solved exactly. In comparison to the standard pairing, the results of several pairing-driven quantities, such as pairing excitation energies, even–odd mass differences, the moment of inertia, etc., show that these types of pairing interaction can indeed be used to describe pairing correlations in nuclei either more accurately or efficiently. Moreover, the shape phase transitional behaviors of nuclei described by the consistent-Q formalism of the interacting boson model are summarized.

The third part of our survey series concerning the evaluation of matrix elements (MEs) of the unitary group generators and of their products in the electronic Gel’fand–Tsetlin basis of the two-column irreps of U(n)—which are essential in the unitary group approach (UGA) to the many-electron correlation problem as handled by the configuration interaction (CI) and the coupled cluster (CC) approaches—relies on what we refer to as the Green-Gould (G-G) approach. In addition to the CI and CC methods, the G-G formalism proved to be very helpful in a number of other tasks, particularly in handling of the spin-dependent operators, the density matrices, or partitioned basis sets adapted to a chosen group chain.

The objective of this series of papers is to survey important techniques for the evaluation of matrix elements (MEs) of unitary group generators and their products in the electronic Gel’fand–Tsetlin basis of two-column irreps of U(n) that are essential to the unitary group approach (UGA) to the many-electron correlation problem as handled by configuration interaction and coupled cluster approaches. Attention is also paid to the MEs of one-body spin-dependent operators and of their relationship to a standard spin-independent UGA formalism. The principal goal is to outline basic principles, concepts, and ideas without getting buried in technical details and thus to help an interested reader to follow the detailed developments in the original literature. In this first instalment we focus on tensorial techniques, particularly those designed specifically for UGA purposes, which exploit the spin-adapted tensorial analogues of the standard creation and annihilation operators of the ubiquitous second-quantization formalism. Subsequent instalments will address techniques based on the graphical methods of spin-algebras and on the Green–Gould polynomial formalism. In the “Appendix A” we then provide a succinct historical outline of the origins of the Lie group and Lie algebra concepts.

High-temperature treatment of γ-Al2 O3 can lead to a series of polymorphic transformations, including the formation of δ-Al2 O3 and θ-Al2 O3 . Quantification of the microstructure in the range where δ- and θ-Al2 O3 are formed represents a formidable challenge, as both phases accommodate a high degree of structural disorder. In this work, we explore the use of an XRD recursive-stacking formalism for the quantification of high-temperature transition aluminas. We formulate the recursive-stacking methodology for modelling of disorder in δ-Al2 O3 and twinning in θ-Al2 O3 and show that explicitly accounting for the disorder is necessary to reliably model the XRD patterns of high-temperature transition alumina. We also use the recursive stacking approach to study phase transformation during high-temperature (1050 °C) treatment. We show that the two different intergrowth modes of δ-Al2 O3 have different transformation characteristics and that a significant portion of δ-Al2 O3 is stabilized with θ-Al2 O3 even after prolonged high-temperature exposures.

The present contribution elucidates the non-covalent interactions present within the molecular frameworks of a miscellany of mono and dihalo-salicylic acid derivatives from the viewpoint of the “atoms-in-molecule” (AIM) formalism. The pivotal roles of hydrogen bonds (HBs) and other short-contact non-covalent interactions, such as H···H and O···O/O···X (X = F, Cl, Br), toward the conformational preferences of the studied aromatic systems have been depicted in detail. Moreover, the modulations of the π-aromaticity of the studied systems in the presence of the concerned non-covalent interactions have been ascertained employing the nucleus-independent chemical shift (NICS) descriptor.

Answer Set Programming (ASP) is a declarative logic formalism that allows to encode computational problems via logic programs. Despite the declarative nature of the formalism, some advanced expertise is required, in general, for designing an ASP encoding that can be efficiently evaluated by an actual ASP system. A common way for trying to reduce the burden of manually tweaking an ASP program consists in automatically rewriting the input encoding according to suitable techniques, for producing alternative, yet semantically equivalent, ASP programs. However, rewriting does not always grant benefits in terms of performance; hence, proper means are needed for predicting their effects with this respect. In this paper we describe an approach based on Machine Learning (ML) to automatically decide whether to rewrite. In particular, given an ASP program and a set of input facts, our approach chooses whether and how to rewrite input rules based on a set of features measuring their structural properties and domain information. To this end, a Multilayer Perceptrons model has then been trained to guide the ASP grounder I-DLV on rewriting input rules. We report and discuss the results of an experimental evaluation over a prototypical implementation., Comment: In Proceedings ICLP 2020, arXiv:2009.09158

We provide an entirely new approach to the theory of thermodynamic formalism for entire functions of bounded type. The key point is that we introduce an integral means spectrum for logarithmic tracts which takes care of the fractal behavior of the boundary of the tract near infinity. It turns out that this spectrum behaves well as soon as the tracts have some sufficiently nice geometry which, for example, is the case for quasidisks, John, or Hölder tracts. In these cases we get a good control of the corresponding transfer operators, leading to full thermodynamic formalism along with its applications such as exponential decay of correlations, central limit theorem, and a Bowen’s formula for the Hausdorff dimension of radial Julia sets. This approach covers all entire functions for which thermodynamic formalism has been so far established and goes far beyond. It applies, in particular, to every hyperbolic function from any Erëmenko–Lyubich analytic family of Speiser class S \mathcal {S} provided this family contains at least one function with Hölder tracts. The latter is, for example, the case if the family contains a Poincaré linearizer.

We consider radiation emitted by colour-charged and massive particles crossing strong plane wave backgrounds in gauge theory and gravity. These backgrounds are treated exactly and non-perturbatively throughout. We compute the back-reaction on these fields from the radiation emitted by the probe particles: classically through background-coupled worldline theories, and at tree-level in the quantum theory through three-point amplitudes. Consistency of these two methods is established explicitly. We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds. Finally, we demonstrate that in four-dimensions these calculations can be carried out with a background-dressed version of the massive spinor-helicity formalism., 34 pages, 1 figure. v2: published version, improvements to section 4.1

A new reactive force field based on the ReaxFF formalism is effectively parametrized against an extended training set of quantum chemistry data (containing more than 120 different structures) to describe accurately silver and silver-thiolate systems. The results obtained with this novel representation demonstrate that the novel ReaxFF paradigm is a powerful methodology to reproduce more appropriately average geometric and energetic properties of metal clusters and slabs when compared to the earlier ReaxFF parametrizations dealing with silver and gold. ReaxFF cannot describe adequately specific geometrical features such as the observed shorter distances between the under-coordinated atoms at the cluster edges. Geometric and energetic properties of thiolates adsorbed on a silver Ag20 pyramid are correctly represented by the new ReaxFF and compared with results for gold. The simulation of self-assembled monolayers of thiolates on a silver (111) surface does not indicate the formation of staples in contrast to the results for gold-thiolate systems.

We develop the quantizer–dequantizer formalism for the probability and mean-value representations of qubits and qutrits. In these representations, the elements of symbols of operators are measurable physical quantities. We derive the star-product kernels, which lead to explicit expressions of the associative product of the symbols of the density operators and quantum observables for qubits. The extension of the quantizer–dequantizer formalism associated with the probability and mean-value descriptions of qudit states is discussed.

This paper is devoted to investigating the description of the q-deformed multiple-trapping equation for charge carrier transport in amorphous semiconductors. For this, we at first modified the multi–trapping model (MTM) of charge carriers in amorphous semiconductors from time-of-flight (TOF) transient photo-current in the framework of the q-derivative formalism, and then, we have constructed, our simulated current by using a method based on the Laplace method. This method is implemented in a program proposed recently by [14] which allows us to construct a current using the Padé approximation expansion.

In 2004, Dharam Vir Ahluwalia and Daniel Grumiller discovered a dark matter candidate called Elko: spin one-half fermions with mass dimension one. These fermions are described by a spinorial Klein-Gordon formalism and very different from electrons or neutrinos. In this review, we give a brief introduction to the localization of Elko spinor fields on branes. First, we briefly review some brane-world theories and the localization of bulk matter fields on branes. Then, after a brief introduction to Elko spinor fields, we focus on the localization of Elko fields on branes in three cases: the free Elko fields, the Elko fields with Yukawa-like coupling, and finally, the Elko fields with non-minimal coupling.

Let $T \in C^{2+ \varepsilon} (S^{1} \setminus \{x_{b} \})$, $\varepsilon> 0 $, be a circle homeomorphism with one break point $x_{b}$, at which $ T'(x) $ has a discontinuity of the first kind and both one-sided derivatives at the point $x_{b} $ are strictly positive. Assume that the rotation number $\rho_{T}$ is irrational and its decomposition into a continued fraction beginning from a certain place coincides with the golden mean, i.e., $\rho_{T}=[m_{1}, m_{2}, \ldots, m_{l}, \, m_{l + 1}, \ldots] $, $ m_{s} = 1$, $s> l> 0$. Since the rotation number is irrational, the map $ T $ is strictly ergodic, that is, possesses a unique probability invariant measure $\mu_{T}$. A.A. Dzhalilov and K.M. Khanin proved that the probability invariant measure $ \mu_{G} $ of any circle homeomorphism $ G \in C^{2+ \varepsilon} (S^{1} \setminus \{x_{b} \})$, $\varepsilon> 0$, with one break point $ x_{b} $ and the irrational rotation number $ \rho_{G} $ is singular with respect to the Lebesgue measure $ \lambda $ on the circle, i.e., there is a measurable subset of $ A \subset S^{1} $ such that $ \mu_ {G} (A) = 1 $ and $ \lambda (A) = 0$. We will construct a thermodynamic formalism for homeomorphisms $ T_{b} \in C^{2+ \varepsilon} (S^{1} \setminus \{x_{b} \})$, $\varepsilon> 0 $, with one break at the point $ x_{b} $ and rotation number equal to the golden mean, i.e., $ \rho_{T}:= \frac {\sqrt{5} -1}{2} $. Using the constructed thermodynamic formalism, we study the exponents of singularity of the invariant measure $ \mu_{T} $ of homeomorphism $ T $.