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Journal articles on the topic 'Embedding formalism'

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Published: 25 May 2024

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1

ABREU, E. M. C., A. C. R. MENDES, C. NEVES, W. OLIVEIRA, and F. I. TAKAKURA. "DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM." International Journal of Modern Physics A 22, no. 21 (August 20, 2007): 3605–20. http://dx.doi.org/10.1142/s0217751x07036932.

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In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.
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Mikura, Yusuke, and Yuichiro Tada. "On UV-completion of Palatini-Higgs inflation." Journal of Cosmology and Astroparticle Physics 2022, no. 05 (May 1, 2022): 035. http://dx.doi.org/10.1088/1475-7516/2022/05/035.

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Abstract We investigate the UV-completion of the Higgs inflation in the metric and the Palatini formalisms. It is known that the cutoff scales for the perturbative unitarity of these inflation models become much smaller than the Planck scale to be consistent with observations. Expecting that the low cutoff scales originate in the curvature of a field-space spanned by the Higgs fields, we consider embedding the curved field-space into a higher dimensional flat space and apply this procedure to the metric-Higgs and the Palatini-Higgs scenarios. The new field introduced in this way successfully flattens the field-space and UV-completes the Higgs inflation in the metric formalism. However, in the Palatini formalism, the new field cannot uplift the cutoff up to the Planck scale. We also discuss the unavoidable low cutoff in the Palatini formalism in the context of the local conformal symmetry.
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Abreu, E. M. C., J. Ananias Neto, A. C. R. Mendes, C. Neves, and W. Oliveira. "Obtaining gauge invariant actions via symplectic embedding formalism." Annalen der Physik 524, no. 8 (June 18, 2012): 434–55. http://dx.doi.org/10.1002/andp.201100199.

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HONG, SOON-TAE, and YOUNG-JAI PARK. "BFT HAMILTONIAN EMBEDDING FOR SU(3) SKYRMION." Modern Physics Letters A 15, no. 14 (May 10, 2000): 913–23. http://dx.doi.org/10.1142/s0217732300000918.

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We apply the Batalin, Fradkin and Tyutin (BFT) formalism to the SU (3) flavor Skyrmion model to investigate the Weyl ordering correction to the structure of the hyperfine splittings of strange baryons. On the other hand, the Berry phases and Casimir effects are also discussed.
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Banerjee, R., and J. Barcelos-Neto. "Reducible Systems and Embedding Procedures in the Canonical Formalism." Annals of Physics 265, no. 2 (May 1998): 134–54. http://dx.doi.org/10.1006/aphy.1997.9998.

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Pernal, Katarzyna. "Reduced density matrix embedding. General formalism and inter-domain correlation functional." Physical Chemistry Chemical Physics 18, no. 31 (2016): 21111–21. http://dx.doi.org/10.1039/c6cp00524a.

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MONEMZADEH, M., and M. TAKI. "HAMILTONIAN EMBEDDING OF NONCOMMUTATIVE D-BRANE SYSTEM." International Journal of Modern Physics A 26, no. 06 (March 10, 2011): 1035–43. http://dx.doi.org/10.1142/s0217751x11051597.

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We choose the mechanical action of open string in the presence of constant B-fields, which allows us to build up constraint structures. In an open string theory, the secondary constraints give rise to noncommutativity of the string coordinates on the boundaries. We find that applying the Batalin–Fradkin–Fradkina–Tyutin (BFFT) formalism to this noncommutative system converts it to a commutative one and makes new local gauge symmetries.
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Pavanello, Michele, and Johannes Neugebauer. "Modelling charge transfer reactions with the frozen density embedding formalism." Journal of Chemical Physics 135, no. 23 (December 21, 2011): 234103. http://dx.doi.org/10.1063/1.3666005.

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9

Kopeikin, Sergei. "Beyond the standard IAU framework." Proceedings of the International Astronomical Union 5, S261 (April 2009): 7–15. http://dx.doi.org/10.1017/s1743921309990081.

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AbstractWe discuss three conceivable scenarios of extension and/or modification of the IAU relativistic resolutions on time scales and spatial coordinates beyond the Standard IAU Framework. These scenarios include: (1) the formalism of the monopole and dipole moment transformations of the metric tensor replacing the scale transformations of time and space coordinates; (2) implementing the parameterized post-Newtonian formalism with two PPN parameters – β and γ; (3) embedding the post-Newtonian barycentric reference system to the Friedman-Robertson-Walker cosmological model.
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MONEMZADEH, M., and AGHILEH S. EBRAHIMI. "EMBEDDING OF NONCOMMUTATIVE MASSIVE QED." Modern Physics Letters A 27, no. 14 (May 5, 2012): 1250081. http://dx.doi.org/10.1142/s0217732312500812.

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In this paper, BFT formalism of Proca model in noncommutative space is investigated. Considering that all theories with first class constraint are gauge theories, Proca model in noncommutative space is not a gauge theory in general due to the appearance of second class constraints in it. In present research, the Proca model is converted into a gauge theory using BFT approach by introducing several auxiliary variables which in turn manage to convert the second class constraints to first class ones. Consequently, we apply modified BFT that preserve the chain structure of constraints. Modified BFT has the benefit that it gives less number of independent gauge parameters and we obtain gauge generating function and infinitesimal gauge variation of fields in Proca model. As results, we investigate partition function of this model and embedded noncommutative Proca is ready to quantize in usual way.
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Grishin, Evgeni, and Dimitri Veras. "Embedding planetesimals into white dwarf discs from large distances." Monthly Notices of the Royal Astronomical Society 489, no. 1 (August 5, 2019): 168–75. http://dx.doi.org/10.1093/mnras/stz2148.

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ABSTRACT The discovery of the intact minor planet embedded in the debris disc orbiting SDSS J1228+1040 raises questions about the dynamical history of the system. Further, the recent passage of the potentially interstellar object 1I/’Oumuamua within the Solar system has re-ignited interest in minor body flux through exoplanetary systems. Here, we utilize the new analytical formalism from Grishin et al. (2019) to estimate the rate at which the gaseous components of typical white dwarf discs trap an exo-planetesimal. We compare the types of captured orbits which arise from planetesimals originating from the interstellar medium, exo-Kuiper belts, and exo-Oort clouds. We find that the rate of interstellar medium injection is negligible, whereas capture of both exo-Kuiper and exo-Oort cloud planetesimals is viable, but strongly size-dependent. For a gaseous disc which extends much beyond its Roche limit, capture is more probable than disruption at the Roche limit. We find that the capture probability linearly increases with the radial extent of the disc. Even in systems without minor planets, capture of smaller bodies will change the disc size distribution and potentially its temporal variability. Our formalism is general enough to be applied to future discoveries of embedded planetesimals in white dwarf debris discs.
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12

Faber, C., P. Boulanger, C. Attaccalite, I. Duchemin, and X. Blase. "Excited states properties of organic molecules: from density functional theory to the GW and Bethe–Salpeter Green's function formalisms." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2011 (March 13, 2014): 20130271. http://dx.doi.org/10.1098/rsta.2013.0271.

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Many-body Green's function perturbation theories, such as the GW and Bethe–Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line of range-separated hybrid functionals within the generalized Kohn–Sham formalism designed to provide correct excitation energies. We give an overview and compare these approaches with examples drawn from the study of gas phase organic systems such as fullerenes, porphyrins, bacteriochlorophylls or nucleobases molecules. The perspectives and challenges that many-body perturbation theory is facing, such as the role of self-consistency, the calculation of forces and potential energy surfaces in the excited states, or the development of embedding techniques specific to the GW and Bethe–Salpeter equation formalisms, are outlined.
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Paston, S. A., and E. N. Semenova. "External time canonical formalism for gravity in terms of embedding theory." Gravitation and Cosmology 21, no. 3 (July 2015): 181–90. http://dx.doi.org/10.1134/s020228931503007x.

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NATIVIDADE, C. P., H. BOSCHI-FILHO, and L. V. BELVEDERE. "BFFT FORMALISM APPLIED TO THE MINIMAL CHIRAL SCHWINGER MODEL." Modern Physics Letters A 19, no. 39 (December 21, 2004): 2957–69. http://dx.doi.org/10.1142/s0217732304014069.

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We consider the minimal chiral Schwinger model, by embedding the gauge non-invariant formulation into a gauge theory following the Batalin–Fradkin–Fradkina–Tyutin point of view. Within the BFFT procedure, the second-class constraints are converted into strongly involutive first-class ones, leading to an extended gauge-invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess–Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge non-invariant action.
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15

Behr, Nicolas, Giuseppe Dattoli, Ambra Lattanzi, and Silvia Licciardi. "Dual Numbers and Operational Umbral Methods." Axioms 8, no. 3 (July 2, 2019): 77. http://dx.doi.org/10.3390/axioms8030077.

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Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view, embedding dual numbers within a formalism reminiscent of operational umbral calculus.
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Duchemin, Ivan, Ciro A. Guido, Denis Jacquemin, and Xavier Blase. "The Bethe–Salpeter formalism with polarisable continuum embedding: reconciling linear-response and state-specific features." Chemical Science 9, no. 19 (2018): 4430–43. http://dx.doi.org/10.1039/c8sc00529j.

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17

HONG, SOON-TAE, YONG-WAN KIM, YOUNG-JAI PARK, and K. D. ROTHE. "SYMPLECTIC EMBEDDING AND HAMILTON–JACOBI ANALYSIS OF PROCA MODEL." Modern Physics Letters A 17, no. 08 (March 14, 2002): 435–51. http://dx.doi.org/10.1142/s0217732302006746.

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Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess–Zumino and gauge fixing terms of BRST-invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton–Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.
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18

Gaona, Alejandro, and J. Antonio García. "BFT embedding of the Green-Schwarz superstring and the pure spinor formalism." Journal of High Energy Physics 2005, no. 09 (September 30, 2005): 083. http://dx.doi.org/10.1088/1126-6708/2005/09/083.

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19

Banerjee, R., and J. Barcelos-Neto. "Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism." Nuclear Physics B 499, no. 1-2 (August 1997): 453–78. http://dx.doi.org/10.1016/s0550-3213(97)00296-4.

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20

Gitman, D. M., P. Yu Moshin, and A. A. Reshetnyak. "An embedding of the BV quantization into an N=1 local superfield formalism." Physics Letters B 621, no. 3-4 (August 2005): 295–308. http://dx.doi.org/10.1016/j.physletb.2005.06.071.

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21

ABREU, E. M. C., A. C. R. MENDES, C. NEVES, W. OLIVEIRA, C. WOTZASEK, and L. M. V. XAVIER. "NEW CONSIDERATIONS ABOUT THE MAXWELL–PODOLSKY-LIKE THEORY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM." Modern Physics Letters A 25, no. 13 (April 30, 2010): 1115–27. http://dx.doi.org/10.1142/s0217732310032330.

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The Podolsky theory can be modified by changing the sign of the Maxwell term. In this case we have a Podolsky-like action with a different spectrum. This new theory was already analyzed by the literature at the propagator level. However, we believe that the results are inconclusive since a precise and entire comprehension, at the Lagrangian level, of this theory is still lacking. In this paper we show in an exact way, using the symplectic embedding formalism, that this Podolsky-like action is in fact dual equivalent to the Proca theory showing the same physical features.
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22

RIESEN, KASPAR, and HORST BUNKE. "GRAPH CLASSIFICATION BASED ON VECTOR SPACE EMBEDDING." International Journal of Pattern Recognition and Artificial Intelligence 23, no. 06 (September 2009): 1053–81. http://dx.doi.org/10.1142/s021800140900748x.

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Graphs provide us with a powerful and flexible representation formalism for pattern classification. Many classification algorithms have been proposed in the literature. However, the vast majority of these algorithms rely on vectorial data descriptions and cannot directly be applied to graphs. Recently, a growing interest in graph kernel methods can be observed. Graph kernels aim at bridging the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. In the present paper, we propose an approach transforming graphs into n-dimensional real vectors by means of prototype selection and graph edit distance computation. This approach allows one to build graph kernels in a straightforward way. It is not only applicable to graphs, but also to other kind of symbolic data in conjunction with any kind of dissimilarity measure. Thus it is characterized by a high degree of flexibility. With several experimental results, we prove the robustness and flexibility of our new method and show that our approach outperforms other graph classification methods on several graph data sets of diverse nature.
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23

Elias, Watheq, M. Elliott, and C. C. Matthai. "Electrical transport of zig-zag and folded graphene nanoribbons." MRS Proceedings 1549 (2013): 41–46. http://dx.doi.org/10.1557/opl.2013.950.

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ABSTRACTIn recent years, there has been much interest in modelling graphene nanoribbons as they have great potential for use in molecular electronics. We have employed the NEGF formalism to determine the conductivity of graphene nanoribbons in various configurations. The electronic structure calculations were performed within the framework of the Extended Huckel Approximation. Both zigzag and armchair nanoribbons have been considered. In addition, we have also computed the transmission and conductance using the non-equilibrium Greens function formalism for these structures. We also investigated the effect of defects by considering a zigzag nanoribbon with six carbon atoms removed. Finally, the effect of embedding boron nitride aromatic molecules in the nanoribbon has been considered. The results of our calculations are compared with that obtained from recent work carried out using tight-binding model Hamiltonians.
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GONŢA, DENIS. "EFFECTIVE EQUATIONS ON THE 3-BRANE WORLD FROM TYPE IIB STRING." International Journal of Modern Physics A 21, no. 01 (January 10, 2006): 83–108. http://dx.doi.org/10.1142/s0217751x06024281.

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The effective field equations on a 3-brane are established considering the massless bosonic sector of the type IIB string compactified on S5. The covariant embedding formalism in a space endowed with Z2-symmetry is applied. Recently the derivation of the effective equations on the 3-brane, where only gravity penetrates in the bulk was performed by Shiromizu, Maeda, and Sasaki. We extend this approach to the situation when the bulk contains a set of fields given by the type IIB string. The notion of the Einstein–Cartan space is considered in order to avoid extra suppositions about the embedding of these fields. The interactions between the brane and the bulk fields are understood in a purely geometric way, which fixes the form of these interactions. Finally, we present the dynamically equivalent effective equations expressed completely in Riemannian terms and make conclusions.
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Lorenzi, Roberta Maria, Alice Geminiani, Yann Zerlaut, Marialaura De Grazia, Alain Destexhe, Claudia A. M. Gandini Wheeler-Kingshott, Fulvia Palesi, Claudia Casellato, and Egidio D’Angelo. "A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics." PLOS Computational Biology 19, no. 9 (September 1, 2023): e1011434. http://dx.doi.org/10.1371/journal.pcbi.1011434.

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Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.
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de Bono, B., S. Safaei, P. Grenon, and P. Hunter. "Meeting the multiscale challenge: representing physiology processes over ApiNATOMY circuits using bond graphs." Interface Focus 8, no. 1 (December 15, 2017): 20170026. http://dx.doi.org/10.1098/rsfs.2017.0026.

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We introduce, and provide examples of, the application of the bond graph formalism to explicitly represent biophysical processes between and within modular biological compartments in ApiNATOMY. In particular, we focus on modelling scenarios from acid–base physiology to link distinct process modalities as bond graphs over an ApiNATOMY circuit of multiscale compartments. The embedding of bond graphs onto ApiNATOMY compartments provides a semantically and mathematically explicit basis for the coherent representation, integration and visualisation of multiscale physiology processes together with the compartmental topology of those biological structures that convey these processes.
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27

Dattoli, Giuseppe, Silvia Licciardi, and Rosa Maria Pidatella. "Inverse Derivative Operator and Umbral Methods for the Harmonic Numbers and Telescopic Series Study." Symmetry 13, no. 5 (May 1, 2021): 781. http://dx.doi.org/10.3390/sym13050781.

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The formalism of differ-integral calculus, initially developed to treat differential operators of fractional order, realizes a complete symmetry between differential and integral operators. This possibility has opened new and interesting scenarios, once extended to positive and negative order derivatives. The associated rules offer an elegant, yet powerful, tool to deal with integral operators, viewed as derivatives of order-1. Although it is well known that the integration is the inverse of the derivative operation, the aforementioned rules offer a new mean to obtain either an explicit iteration of the integration by parts or a general formula to obtain the primitive of any infinitely differentiable function. We show that the method provides an unexpected link with generalized telescoping series, yields new useful tools for the relevant treatment, and allows a practically unexhausted tool to derive identities involving harmonic numbers and the associated generalized forms. It is eventually shown that embedding the differ-integral point of view with techniques of umbral algebraic nature offers a new insight into, and the possibility of, establishing a new and more powerful formalism.
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Tanhayi, M. Reza. "Particle creation in global de Sitter space: Bulk space consideration." International Journal of Modern Physics D 24, no. 07 (May 27, 2015): 1550052. http://dx.doi.org/10.1142/s0218271815500522.

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Recently in [P. R. Anderson and E. Mottola, Phys. Rev. D 89 (2014) 104039, arXiv:1310.1963 [gr-qc] and P. R. Anderson and E. Mottola, Phys. Rev. D 89 (2014) 104038, arXiv:1310.0030 [gr-qc].], it was shown that global de Sitter space is unstable even to the massive particle creation with no self-interactions. In this paper, we study the instability by making use of the coordinate-independent plane wave in de Sitter space. Within this formalism, we show that the previous results of instability of de Sitter space due to the particle creation can be generalized to higher-spin fields in a straightforward way. The so-called plane wave is defined globally in de Sitter space and de Sitter invariance is manifest since such modes are deduced from the group theoretical point of view by means of the Casimir operators. In fact, we employ the symmetry of embedding space namely the 4 + 1-dimensional flat space to write the field equations and the solutions can be obtained in terms of the plane wave in embedding space.
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Krejčí, Pavel, and Adrien Petrov. "A mathematical model for the third-body concept." Mathematics and Mechanics of Solids 23, no. 3 (November 28, 2017): 420–32. http://dx.doi.org/10.1177/1081286517732827.

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The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.
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Shaposhnyk, Olha, Kenneth Lai, Gregor Wolbring, Vlad Shmerko, and Svetlana Yanushkevich. "Next Generation Computing and Communication Hub for First Responders in Smart Cities." Sensors 24, no. 7 (April 8, 2024): 2366. http://dx.doi.org/10.3390/s24072366.

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This paper contributes to the development of a Next Generation First Responder (NGFR) communication platform with the key goal of embedding it into a smart city technology infrastructure. The framework of this approach is a concept known as SmartHub, developed by the US Department of Homeland Security. The proposed embedding methodology complies with the standard categories and indicators of smart city performance. This paper offers two practice-centered extensions of the NGFR hub, which are also the main results: first, a cognitive workload monitoring of first responders as a basis for their performance assessment, monitoring, and improvement; and second, a highly sensitive problem of human society, the emergency assistance tools for individuals with disabilities. Both extensions explore various technological-societal dimensions of smart cities, including interoperability, standardization, and accessibility to assistive technologies for people with disabilities. Regarding cognitive workload monitoring, the core result is a novel AI formalism, an ensemble of machine learning processes aggregated using machine reasoning. This ensemble enables predictive situation assessment and self-aware computing, which is the basis of the digital twin concept. We experimentally demonstrate a specific component of a digital twin of an NGFR, a near-real-time monitoring of the NGFR cognitive workload. Regarding our second result, a problem of emergency assistance for individuals with disabilities that originated as accessibility to assistive technologies to promote disability inclusion, we provide the NGFR specification focusing on interactions based on AI formalism and using a unified hub platform. This paper also discusses a technology roadmap using the notion of the Emergency Management Cycle (EMC), a commonly accepted doctrine for managing disasters through the steps of mitigation, preparedness, response, and recovery. It positions the NGFR hub as a benchmark of the smart city emergency service.
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Paston, Sergey, Elizaveta Semenova, and Anton Sheykin. "Canonical Description for Formulation of Embedding Gravity as a Field Theory in a Flat Spacetime." Symmetry 12, no. 5 (May 3, 2020): 722. http://dx.doi.org/10.3390/sym12050722.

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We consider the approach to gravity in which four-dimensional curved spacetime is represented by a surface in a flat Minkowski space of higher dimension. After a short overview of the ideas and results of such an approach we concentrate on the study of the so-called splitting gravity, a form of this description in which constant value surface of a set of scalar fields in the ambient flat space-time defines the embedded surface. We construct a form of action which is invariant w.r.t. all symmetries of this theory. We construct the canonical formalism for splitting gravity. The resulting theory turns out to be free of constraints. However, the Hamiltonian of this theory is an implicit function of canonical variables. Finally, we discuss the path integral quantization of such a theory.
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de Abreu, E. M. C., J. Ananias Neto, A. C. R. Mendes, and G. Oliveira-Neto. "Non-Abelian BFFT embedding, Schrödinger quantization and the field–antifield anomaly of the O(N) nonlinear sigma model." International Journal of Modern Physics A 31, no. 01 (January 10, 2016): 1550225. http://dx.doi.org/10.1142/s0217751x15502255.

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We have embedded the [Formula: see text] nonlinear sigma model in a non-Abelian gauge theory. After that as a first class-system, it was quantized using two different approaches: the functional Schrödinger method and the nonlocal field–antifield procedure. First, the quantization was performed with the functional Schrödinger method, for [Formula: see text], obtaining the wave functionals for the ground and excited states. Second, using the well-known BV formalism, we have computed the one-loop anomaly. This result shows that the classical gauge symmetries, which appear due to the conversion via BFFT method, are broken at the quantum level.
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33

Corli, Sebastiano, Lorenzo Moro, Davide E. Galli, and Enrico Prati. "Casting Rubik’s Group into a Unitary Representation for Reinforcement Learning." Journal of Physics: Conference Series 2533, no. 1 (June 1, 2023): 012006. http://dx.doi.org/10.1088/1742-6596/2533/1/012006.

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Abstract Rubik’s Cube is one of the most famous combinatorial puzzles involving nearly 4.3 × 1019 possible configurations. However, only a single configuration matches the solved one. Its mathematical description is expressed by the Rubik’s group, whose elements define how its layers rotate. We develop a unitary representation of the Rubik’s group and a quantum formalism to describe the Cube based on its geometrical constraints. Using single particle quantum states, we describe the cubies as bosons for corners and fermions for edges. By introducing a set of four Ising-like Hamiltonians, we managed to set the solved configuration of the Cube as the global ground state for all the Hamiltonians. To reach the ground state of all the Hamiltonian operators, we made use of a Deep Reinforcement Learning algorithm based on a Hamiltonian reward. The Rubik’s Cube is successfully solved through four phases, each phase driven by a corresponding Hamiltonian reward based on its energy spectrum. We call our algorithm QUBE, as it employs quantum mechanics to tackle the combinatorial problem of solving the Rubik’s Cube. Embedding combinatorial problems into the quantum mechanics formalism suggests new possible algorithms and future implementations on quantum hardware.
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34

Ignatenko, A. V., A. A. Kuznetsova, A. S. Kvasikova, A. V. Glushkov, and M. Yu Gurskaya. "NONLINEAR CHAOTIC DYNAMICS OF ATOMIC AND MOLECULAR SYSTEMS IN AN ELECTROMAGNETIC FIELD." Photoelectronics, no. 25 (December 26, 2016): 79–84. http://dx.doi.org/10.18524/0235-2435.2016.25.157626.

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It has been numerically studied a chaotic dynamics of diatomic molecules (on example of the GeO molecule in an infrared field) and some laser systems. An advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov exponent’s (LE) analysis, and surrogate data method, prediction models etc is used. It has been shown that systems exhibit a nonlinear behaviour with elements of a low-or high-dimensional chaos. There are firstly presented the numerical data on topological and dynamical invariants of chaotic systems, in particular, the correlation, embedding, Kaplan-York dimensions, LE, Kolmogorov’s entropy etc for GeO molecule in an electromagnetic infrared field in the chaotic regime.
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35

Hirpara, Ravish H., and Shambhu N. Sharma. "Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation." Transactions of the Institute of Measurement and Control 43, no. 14 (June 14, 2021): 3181–94. http://dx.doi.org/10.1177/01423312211019662.

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This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.
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36

Ha¨usler, Christoph, Cun-Fa Gao, and Herbert Balke. "Collinear and Periodic Electrode-Ceramic Interfacial Cracks in Piezoelectric Bimaterials." Journal of Applied Mechanics 71, no. 4 (July 1, 2004): 486–92. http://dx.doi.org/10.1115/1.1767168.

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Field singularities of collinear and collinear periodic interface cracks between an electrode and a piezoelectric matrix are studied in terms of the Stroh formalism for mixed boundary conditions. In contrast to the relevant work done previously on this subject, the problem is solved based on the assumption that the upper and lower planes embedding the electrode consist of two arbitrary piezoelectric materials, and the cracks are assumed to be permeable. The problem is reduced to an interfacial crack problem equivalent to that in purely elastic media. Explicit expressions are presented for the complex potentials and field intensity factors. All the field variables exhibit oscillatory singularities, and their intensities are dependent on the material properties and the applied mechanical loads, but not on the applied electric loads.
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37

Bereciartua, P. J., F. J. Zuñiga, J. M. Perez-Mato, V. Petříček, E. Vila, A. Castro, J. Rodríguez-Carvajal, and S. Doyle. "Structure refinement and superspace description of the system Bi2(n + 2)Mo n O6(n + 1) (n = 3, 4, 5 and 6)." Acta Crystallographica Section B Structural Science 68, no. 4 (June 28, 2012): 323–40. http://dx.doi.org/10.1107/s0108768112017478.

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The system Bi2(n + 2)Mo n O6(n + 1) is described within the superspace formalism. Two superspace models are proposed for the different members of this family, depending on the parity of the parameter n. The superspace model for the odd members is constructed through the embedding of the cationic distribution of the member with n = 3, and the modification of a superspace model previously proposed for the compound Bi2MoO6. However, this model cannot be applied to the even members of the family. Performing the appropriate transformations, a suitable superspace model for the even members is obtained. The atomic structure of the different compounds of the family have been refined through the Rietveld method combining synchrotron X-ray and neutron powder diffraction data.
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38

Schleif, Frank-Michael, and Peter Tino. "Indefinite Proximity Learning: A Review." Neural Computation 27, no. 10 (October 2015): 2039–96. http://dx.doi.org/10.1162/neco_a_00770.

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Efficient learning of a data analysis task strongly depends on the data representation. Most methods rely on (symmetric) similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel or branch-and-bound approaches. Similarities and dissimilarities are, however, often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms. Major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data. We provide a comprehensive survey for the field of learning with nonmetric proximities. First, we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data. Second, we provide a systematization of the various approaches. For each category of approaches, we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties. In a summarizing section, we provide a larger experimental study for the majority of the algorithms on standard data sets. We also address the problem of large-scale proximity learning, which is often overlooked in this context and of major importance to make the method relevant in practice. The algorithms we discuss are in general applicable for proximity-based clustering, one-class classification, classification, regression, and embedding approaches. In the experimental part, we focus on classification tasks.
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39

BALDWIN, JOHN T. "FORMALIZATION, PRIMITIVE CONCEPTS, AND PURITY." Review of Symbolic Logic 6, no. 1 (September 19, 2012): 87–128. http://dx.doi.org/10.1017/s1755020312000263.

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AbstractWe emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedy’s notion of ‘formalism freeness’ in the context of various schools in model theory. Then we clarify some of the mathematical issues in recent discussions of purity in the proof of the Desargues proposition. We note that the conclusion of ‘spatial content’ from the Desargues proposition involves arguments which are algebraic and even metamathematical. Hilbert showed that the Desargues proposition implies the coordinatizing ring is associative, which in turn implies the existence of a three-dimensional geometry in which the given plane can be embedded. With W. Howard we give a new proof, removing Hilbert’s ‘detour’ through algebra, of the ‘geometric’ embedding theorem.Finally, our investigation of purity leads to the conclusion that even the introduction of explicit definitions in a proof can violate purity. We argue that although both involve explicit definition, our proof of the embedding theorem is pure while Hilbert’s is not. Thus the determination of whether an argument is pure turns on the content of the particular proof. Moreover, formalizing the situation does not provide a tool for characterizing purity.
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40

DAVIDSON, AHARON, and DAVID KARASIK. "QUANTUM GRAVITY OF A BRANE-LIKE UNIVERSE." Modern Physics Letters A 13, no. 27 (September 7, 1998): 2187–92. http://dx.doi.org/10.1142/s0217732398002321.

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Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge–Teitelboim embedding of Arnowitt–Deser–Misner formalism, parametrized by the coordinates yA(t,xi), is governed by some ρAB(y,y′,y″). Invoking a novel Lagrange multiplier λ, accompanying the lapse function N and the shift vector Ni, we derive the quadratic Hamiltonian [Formula: see text] The inclusion of mattter resembles minimal coupling. Setting PA=-i(δ/δyA), we derive a bifurcated Wheeler–Dewitt-like equation. Einstein gravity, associated with λ being a certain fourfold degenerate eigenvalue of ρAB, is characterized by a vanishing center-of-mass momentum ∫PAd3x=0. Troublesome (ρ-λI)-1 is then replaced by regular M-1, such that M-1(ρ-λI) defines a projection operator, modifying the Hamiltonian accordingly.
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41

BANDOS, IGOR A., and WOLFGANG KUMMER. "p-BRANES, POISSON-SIGMA MODELS AND EMBEDDING APPROACH TO (p+1)-DIMENSIONAL GRAVITY." International Journal of Modern Physics A 14, no. 31 (December 20, 1999): 4881–914. http://dx.doi.org/10.1142/s0217751x99002311.

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A generalization of the embedding approach for d-dimensional gravity based upon p-brane theories is proposed. We prove that the D-dimensional p-brane coupled to an antisymmetric tensor field of rank (p+1) provides the dynamical basis for the description of d=(p+1)-dimensional gravity in the isometric embedding formalism. By that we mean that the equations of motion following from this action describe any (p+1)-dimensional space–time (at least locally) once the antisymmetric tensor field is chosen appropriately. "Physical" matter appears in such an approach as a manifestation of a D-dimensional antisymmetric tensor (generalized Kalb–Ramond) background. For the simplest case, the Lorentz harmonic formulation of the bosonic string in a Kalb–Ramond background and its relation to a first order Einstein–Cartan approach for (d=2)-dimensional gravity is analyzed in some detail. We show that a general Poisson-sigma model structure emerges in this case. For the minimal choice of a free D=3 string an interesting "dual" formulation is found which has the structure of a Jackiw–Teitelboim theory, coupled minimally to a massive scalar field. Our approach is intended to serve as a preparation for the study of d-dimensional supergravity theory, either starting from the generalized action of free supersymmetric (d-1)-branes or D(d-1)-branes, or from the corresponding geometric equations ("rheotropic" conditions).
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42

BAKAS, IOANNIS, and DIDIER A. DEPIREUX. "THE ORIGIN OF GAUGE SYMMETRIES IN INTEGRABLE SYSTEMS OF THE KdV TYPE." International Journal of Modern Physics A 07, no. 08 (March 30, 1992): 1767–92. http://dx.doi.org/10.1142/s0217751x92000764.

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Generalized systems of integrable nonlinear differential equations of the KdV type are considered from the point of view of self-dual Yang-Mills theory in space-times with signature (2, 2). We present a systematic method for embedding the rth flows of the SL (N) KdV hierarchy with N≥2 and r<N in the dimensionally reduced self-dual system using SL (N) as gauge group. We also find that for r>N the corresponding equations can be described in a similar fashion, provided that (in general) the rank of the gauge group increases accordingly. Certain connections of this formalism with WN algebras are also discussed. Finally, we obtain a new class of nonlinear systems in two dimensions by introducing self-dual Ansätze associated with the [Formula: see text] algebras of Bershadsky and Polyakov.
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43

Lahoche, Vincent, Dine Ousmane Samary, and Mohamed Tamaazousti. "Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking." Symmetry 14, no. 3 (February 28, 2022): 486. http://dx.doi.org/10.3390/sym14030486.

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The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using the renormalization group from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to provide a complementary point of view on standard methods used in data science, especially for open issues. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in Entropy, 23(9), 1132 to reproduce experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with Z2-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes.
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44

Gallerati, Antonio. "Constructing black hole solutions in supergravity theories." International Journal of Modern Physics A 34, no. 35 (December 20, 2019): 1930017. http://dx.doi.org/10.1142/s0217751x19300175.

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We perform a detailed analysis of black hole solutions in supergravity models. After a general introduction on black holes in general relativity and supersymmetric theories, we provide a detailed description of ungauged extended supergravities and their dualities. Therefore, we analyze the general form of black hole configurations for these models, their near-horizon behavior and characteristic of the solution. An explicit construction of a black hole solution with its physical implications is given for the STU-model. The second part of this review is dedicated to gauged supergravity theories. We describe a step-by-step gauging procedure involving the embedding tensor formalism to be used to obtain a gauged model starting from an ungauged one. Finally, we analyze general black hole solutions in gauged models, providing an explicit example for the [Formula: see text], [Formula: see text] case. A brief review on special geometry is also provided, with explicit results and relations for supersymmetric black hole solutions.
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45

Ignatenko, A. V., T. B. Tkach, and I. V. Ivanova. "Chaotic dynamics of diatomic systems in an electromagnetic field: Dynamical and topological invariants." Physics of Aerodisperse Systems, no. 61 (December 9, 2023): 158–64. http://dx.doi.org/10.18524/0367-1631.2023.61.291841.

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An advanced combined quantum-dynamic and chaos-geometric method for analysis, modelling, and forecasting of the chaotic dynamics of diatomic molecules in an intense electromagnetic field is presented. The method is based on the use of the non-stationary theory of the Schrödinger equation in the approximation of the density functional and the methods of the theory of chaos and dynamic systems for the analysis of time series of polarization and other characteristics of diatomic molecules in an intense electromagnetic field. In particular, the latter includes the Gottwald-Melbourne test, the correlation integral method , fractal and multifractal formalism, average mutual information, false nearest neighbours, surrogate data algorithms, analysis on the basis of the Lyapunov's exponents, Kolmogorov entropy, nonlinear forecast models based on algorithms of optimized predicted trajectories, B-spline approximations. As an illustration, the advanced data for the dynamical and topological invariants (correlation dimension, embedding dimension, Kaplan-York dimension, Lyapunov's exponents, Kolmogorov entropy, etc.) for the diatomic ZrO molecule in a linearly polarized electromagnetic field are listed.
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46

IONESCU, D. C., E. ZIO, and A. C. CONSTANTINESCU. "Embedding Monte Carlo simulation within the stochastic Petri network formalism for the evaluation of the availability of a nuclear safety system." Risk, Decision and Policy 8, no. 2-3 (May 2003): 133–42. http://dx.doi.org/10.1080/713926642.

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47

Schiffel, S., and M. Thielscher. "Representing and Reasoning About the Rules of General Games With Imperfect Information." Journal of Artificial Intelligence Research 49 (February 14, 2014): 171–206. http://dx.doi.org/10.1613/jair.4115.

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A general game player is a system that can play previously unknown games just by being given their rules. For this purpose, the Game Description Language (GDL) has been developed as a high-level knowledge representation formalism to communicate game rules to players. In this paper, we address a fundamental limitation of state-of-the-art methods and systems for General Game Playing, namely, their being confined to deterministic games with complete information about the game state. We develop a simple yet expressive extension of standard GDL that allows for formalising the rules of arbitrary finite, n-player games with randomness and incomplete state knowledge. In the second part of the paper, we address the intricate reasoning challenge for general game-playing systems that comes with the new description language. We develop a full embedding of extended GDL into the Situation Calculus augmented by Scherl and Levesque's knowledge fluent. We formally prove that this provides a sound and complete reasoning method for players' knowledge about game states as well as about the knowledge of the other players.
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48

DODARO, CARMINE, and FRANCESCO RICCA. "The External Interface for Extending WASP." Theory and Practice of Logic Programming 20, no. 2 (December 10, 2018): 225–48. http://dx.doi.org/10.1017/s1471068418000558.

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Answer set programming (ASP) is a successful declarative formalism for knowledge representation and reasoning. The evaluation of ASP programs is nowadays based on the conflict-driven clause learning (CDCL) backtracking search algorithm. Recent work suggested that the performance of CDCL-based implementations can be considerably improved on specific benchmarks by extending their solving capabilities with custom heuristics and propagators. However, embedding such algorithms into existing systems requires expert knowledge of the internals of ASP implementations. The development of effective solver extensions can be made easier by providing suitable programming interfaces. In this paper, we present the interface for extending the CDCL-based ASP solver wasp. The interface is both general, that is, it can be used for providing either new branching heuristics or propagators, and external, that is, the implementation of new algorithms requires no internal modifications of wasp. Moreover, we review the applications of the interface witnessing it can be successfully used to extend wasp for solving effectively hard instances of both real-world and synthetic problems.
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49

Reinholdt, Peter, Morten S. Nørby, and Jacob Kongsted. "Modeling of Magnetic Circular Dichroism and UV/Vis Absorption Spectra Using Fluctuating Charges or Polarizable Embedding within a Resonant-Convergent Response Theory Formalism." Journal of Chemical Theory and Computation 14, no. 12 (November 8, 2018): 6391–404. http://dx.doi.org/10.1021/acs.jctc.8b00660.

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50

Glushkov, A. V., E. R. Gubanova, O. Yu Khetselius, G. P. Prepelitsa, A. A. Svinarenko, Yu Ya Bunyakova, and V. V. Buyadzhi. "Analysis and forecast of the environmental radioactivity dynamics based on methods of chaos theory: general scheme and some application." Ukrainian hydrometeorological journal, no. 16 (October 29, 2017): 40–45. http://dx.doi.org/10.31481/uhmj.16.2015.05.

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We present firstly a new whole technique of analysis, processing and forecasting environmental radioactivity dynamics, which has been earlier developed for the atmospheric pollution dynamics analysis and investigation of chaotic feature sin dynamics of the typical hydroecological systems. The general formalism include: a) A general qualitative analysis of dynamical problem of the environmental radioactivity dynamics (including a qualitative analysis from the viewpoint of ordinary differential equations, the “Arnold-analysis”); b) checking for the presence of a chaotic (stochastic) features and regimes (the Gottwald-Melbourne’s test; the method of correlation dimension); c) Reducing the phase space (choice of the time delay, the definition of the embedding space by methods of correlation dimension algorithm and false nearest neighbor points); d) Determination of the dynamic invariants of a chaotic system (Computation of the global Lyapunov dimension λa; determination of the Kaplan-York dimension dL and average limits of predictability Prmax on the basis of the advanced algorithms; e) A non-linear prediction (forecasting) of an dynamical evolution of the system. The last block indeed includes new (in a theory of environmental radioactivity dynamics) methods and algorithms of nonlinear prediction such as methods of predicted trajectories, stochastic propagators and neural networks modelling, renorm-analysis with blocks of the polynomial approximations, wavelet-expansions etc.
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