Basis Of Representation Research Articles

State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions.

Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.

Ladder operators approach to representation classification problem for Jordan-Schwinger image of su(2) algebra

The eigenvalues of the complete commuting set of self-adjoint operators determine the classification of states. We construct a classification for the image of the Jordan-Schwinger mapping of the su(2) algebra. We use the ladder operator approach to construct a canonical basis of irreducible representations and define the self-adjoint operators of the complete commuting set.

Quantifying Spatio-Temporal Boundary Condition Uncertainty for the North American Deglaciation

Ice sheet models are used to study the deglaciation of North America at the end of the last ice age (past 21,000 years), so that we might understand whether and how existing ice sheets may reduce or disappear under climate change. Though ice sheet models have a few parameters controlling physical behaviour of the ice mass, they also require boundary conditions for climate (spatio-temporal fields of temperature and precipitation, typically on regular grids and at monthly intervals). The behaviour of the ice sheet is highly sensitive to these fields, and there is relatively little data from geological records to constrain them as the land was covered with ice. We develop a methodology for generating a range of plausible boundary conditions, using a low-dimensional basis representation of the spatio-temporal input. We derive this basis by combining key patterns, extracted from a small ensemble of climate model simulations of the deglaciation, with sparse spatio-temporal observations. By jointly varying the ice sheet parameters and basis vector coefficients, we run ensembles of the Glimmer ice sheet model that simultaneously explore both climate and ice sheet model uncertainties. We use these to calibrate the ice sheet physics and boundary conditions for Glimmer, by ruling out regions of the joint coefficient and parameter space via history matching. We use binary ice/no ice observations from reconstructions of past ice sheet margin position to constrain this space by introducing a novel metric for history matching to binary data.

Local orbital formulation of the Floquet theory of projectile electronic stopping

A recently proposed theoretical framework for the description of electronic quantum friction for constant-velocity nuclear projectiles traversing periodic crystals is here implemented using a local basis representation. The theory requires a change of reference frame to that of the projectile, and a basis set transformation for the target basis functions to a gliding basis is presented, which is time-periodic but does not displace in space with respect to the projectile, allowing a local-basis Floquet impurity-scattering formalism to be used. It is illustrated for a one-dimensional single-band tight-binding model, as the simplest paradigmatic example, displaying the qualitative behaviour of the formalism. The time-dependent non-orthogonality of the gliding basis requires care in the proper (simplest) definition of a local projectile perturbation. The Fermi level is tilted with a slope given by the projectile velocity, which complicates integration over occupied states. It is solved by a recurrent application of the Lippmann-Schwinger equation, in analogy with previous non-equilibrium treatment of electron ballistic transport. Aiming towards a first-principles mean-field-like implementation, the final result is the time-periodic particle density in the region around the projectile, describing the stroboscopically stationary perturbation cloud around the projectile, out of which other quantities can be obtained, such as the electronic stopping power.

Construction of human bone surface model

For the local area shape after feature segmentation, the feature contour line is used to reconstruct the feature area surface, and the transition surface is combined to create a complete femoral surface model. This not only improves the reconstruction accuracy of the femoral surface model, but also simplifies the model data structure and improves the model weight. At the same time, it provides a basis for the semantic representation and editing of the femoral model in the subsequent processes.

Jucys–Murphy elements and Grothendieck groups for generalized rook monoids

We consider a tower of generalized rook monoid algebras over the field \mathbb{C} of complex numbers and observe that the Bratteli diagram associated to this tower is a simple graph. We construct simple modules and describe Jucys–Murphy elements for generalized rook monoid algebras. Over an algebraically closed field \Bbbk of positive characteristic p , utilizing Jucys–Murphy elements of rook monoid algebras, for 0\leq i\leq p-1 we define the corresponding i -restriction and i -induction functors along with two extra functors. On the direct sum \mathcal{G}_{\mathbb{C}} of the Grothendieck groups of module categories over rook monoid algebras over \Bbbk , these functors induce an action of the tensor product of the universal enveloping algebra U(\widehat{\mathfrak{sl}}_p(\mathbb{C})) and the monoid algebra \mathbb{C}[\mathcal{B}] of the bicyclic monoid \mathcal{B} . Furthermore, we prove that \mathcal{G}_{\mathbb{C}} is isomorphic to the tensor product of the basic representation of U(\widehat{\mathfrak{sl}}_{p}(\mathbb{C})) and the unique infinite-dimensional simple module over \mathbb{C}[\mathcal{B}] , and also exhibit that \mathcal{G}_{\mathbb{C}} is a bialgebra. Under some natural restrictions on the characteristic of \Bbbk , we outline the corresponding result for generalized rook monoids.

Discrete Lehmann representation of imaginary time Green's functions

We present an efficient basis for imaginary time Green's functions based on a low-rank decomposition of the spectral Lehmann representation. The basis functions are simply a set of well-chosen exponentials, so the corresponding expansion may be thought of as a discrete form of the Lehmann representation using an effective spectral density which is a sum of $\ensuremath{\delta}$ functions. The basis is determined only by an upper bound on the product $\ensuremath{\beta}{\ensuremath{\omega}}_{max}$, with $\ensuremath{\beta}$ the inverse temperature and ${\ensuremath{\omega}}_{max}$ an energy cutoff, and a user-defined error tolerance $\ensuremath{\epsilon}$. The number $r$ of basis functions scales as $O(log(\ensuremath{\beta}{\ensuremath{\omega}}_{max})log(1/\ensuremath{\epsilon}))$. The discrete Lehmann representation of a particular imaginary time Green's function can be recovered by interpolation at a set of $r$ imaginary time nodes. Both the basis functions and the interpolation nodes can be obtained rapidly using standard numerical linear algebra routines. Due to the simple form of the basis, the discrete Lehmann representation of a Green's function can be explicitly transformed to the Matsubara frequency domain, or obtained directly by interpolation on a Matsubara frequency grid. We benchmark the efficiency of the representation on simple cases, and with a high-precision solution of the Sachdev-Ye-Kitaev equation at low temperature. We compare our approach with the related intermediate representation method, and introduce an improved algorithm to build the intermediate representation basis and a corresponding sampling grid.

State Regulation of Energy Transition and Economic Development

Government regulation with respect to the reduction of greenhouse gas emissions has been actively developing in the world in the past three decades, mainly in form of carbon taxation and emission trading systems with a carbon price as their basic representation. With more than 50 countries already applying such regulation and many others looking in that direction due to their obligations under the Paris Agreement, the question of suitable carbon price is still open. The aim of this paper is to form groups of countries according to the chosen economic, environmental and regulation factors to facilitate decision-making regarding the formation of energy transition regulation policies. Clustering analysis was carried out to identify countries with similar features in the research area. Five clusters with average carbon price ranging from USD 5.3 to 49.2 per t were obtained. The hypothesis of the study regarding direct connection between the level of economic development and state regulation was partially confirmed. It was revealed that most of the countries with active carbon regulation depend on the external supply of fossil energy sources. The results of the clustering could serve as a benchmark for the countries with similar indicators.

The nature of security: A conceptual framework for integral-comprehensive modeling of IT security and cybersecurity

Cybersecurity is a broadly defined concept comprising security for many different types of elements. Dealing with cybersecurity is a multidimensional problem, and the damage generated by cyberattacks can be very diverse. Reports about cybersecurity show recurrent problems, or increasing on their frequency of appearance, with no clear approach for solving them. Existing models deal with cybersecurity in several different but general ways, and results are not better. Consequently, managing cybersecurity deserves consideration of a new approach. Our approach is based on the nature of security. Security services are modeled around three basic security concepts, namely isolation, interaction, and representation. With these three concepts, a cybersecurity development starts with security objectives for overcoming the cybersecurity challenges, and also has a security representation to achieve integral and comprehensive security results. We propose an architecture-based security conceptual framework having three components, namely a system representation model kind, a security representation model kind, and a security process model kind, to accomplish the security process for a system. The security process is fully guided and supported with security objectives from the beginning to the end. The framework proposes several models, based on data structures for representing the system, the security, and the process itself. The models are scalable to represent systems of any size, from tiny to huge technology infrastructures, and with support for automation of the security process. The scope of the framework is the security of IT systems and cybersecurity, including information, software, virtual resources, hardware, IT devices, money, people, and other related physical objects being represented digitally. The framework was developed while creating a university cloud infrastructure, and consolidated while supporting the security of several national wide software and infrastructure applications for digital signature in Costa Rica. We aim to provide a new and innovative way for doing cybersecurity, by directly targeting the actual security requirements; with a simple, systemic, structured and potentially automated security process, and for achieving integral and comprehensive security solutions.

Coarse-grained intermolecular interactions on quantum processors

Variational quantum algorithms (VQAs) are increasingly being applied in simulations of strongly bound (covalently bonded) systems using full molecular orbital basis representations. The application of quantum computers to the weakly bound intermolecular and noncovalently bonded regime, however, has remained largely unexplored. In this work, we develop a coarse-grained representation of the electronic response that is ideally suited for determining the ground state of weakly interacting molecules using a VQA. We require qubit numbers that grow linearly with the number of molecules and derive scaling behavior for the number of circuits and measurements required, which compare favorably to traditional variational quantum eigensolver methods. We demonstrate our method on IBM superconducting quantum processors and show its capability to resolve the dispersion energy as a function of separation for a pair of nonpolar molecules---thereby establishing a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, we conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but nevertheless chemically ubiquitous and biologically important regime. Finally, we perform experiments on simulated and real quantum computers for systems of three, four, and five oscillators as well as oscillators with anharmonic onsite binding potentials; the consequences of the latter are unexamined in large systems using classical computational methods but can be incorporated here with low computational overhead.

A Comparative Study of Time Domain Compressed Sensing Techniques for Optoacoustic Imaging

Speeding up data acquisition and reducing the complexity of the detection system are among the central goals for advancing optoacoustic imaging. In this way, new reconstruction algorithms using the compressed sensing (CS) formalism have received considerable interest in recent years. This work presents a comparative study of reconstruction algorithms using time-domain CS schemes for optoacoustic tomography. This is motivated by the well-known capabilities of the CS paradigm in achieving good reconstruction performance even with limited sensing capabilities. Formulation of the mathematical problem is provided along with simulation results, where the performance of different representation basis used in time-domain CS strategies are analyzed in a qualitative and quantitative fashion. Comparison with a well-established optoacoustic tomography reconstruction technique as backprojection is also provided. These experiments show the suitability of time-domain CS techniques for this application and point out that the use of the canonical basis for the representation of the optoacoustic measurements is well suited in comparison with other more sophisticated basis.

Representation of gender-specific vocabulary through sociocultural transformations of linguistic identity

The article reconsiders the sociolinguistic basis of gender-specific vocabulary representation within the context of linguistic identity’s sociocultural transformations. The comprehension of language interaction is postulated as an indispensable precondition for understanding linguistic identity to affect their sociocultural development. It is also connected with the influence of sociocultural transformations on the features of cognitive processes. The study primarily follows selection, descriptive, and synthesis methods. The strategies of gender-specific vocabulary usage as a rate of male and female’s differentiation are essential in the study of linguistic identity. It is important in the sense that the gender category determines the psychological and social development of individuals, especially their verbal behaviour. Gender-specific vocabulary circulation in the context of the evolution of linguistic identity is the result of such sociocultural processes as a focus on gender-sensitive communication patterns, avoidance of language gender imbalance, and social dynamics. Gender-specific vocabulary may serve as a modifier of an individual’s verbal behaviour and speech internalisation processes. Such kinds of lexis may act as tools for constructing the linguistic view of the world and defining the language ontologisation options. In the context of the last years’ social and cultural changes, the development of linguistic identity explicates the idea of verbal behaviour and sociocultural processes’ interdependence. Linguistic identity has been revealed as a representative of identity in general to reflect social and cultural levels of existence which are shown through the language. Keywords: speaker, communication, social parity, verbalisation, gender, behavioural pattern.

A generalised smoothing approach for continuous, planar, inverse kinematics problems

Bayesian methods have recently been proposed to solve inverse kinematics problems for marker based motion capture. The objective is to find the posterior distribution, a probabilistic summary of our knowledge and corresponding uncertainty about the model parameters such as joint angles, segment angles, segment translations, and marker positions. To date, Bayesian inverse kinematics models have focused on a frame by frame solution, which if repeatedly applied gives estimates that are discontinuous in time. We propose to overcome this limitation for continuous, planar inverse kinematics problems via the use of finite basis representations to model latent kinematic quantities as smooth, continuous functions. Our generalised smoothing approach is able to accurately approximate the solution to planar inverse kinematics problems defined by simple systems of ordinary differential equations in addition to considerably more complex systems such as a planar analysis of human gait. Improvements in accuracy are considerable with a decrease in average RMSE of 0.025 rad observed when estimating ankle joint angle for a randomly selected running stride with the proposed generalised smoothing approach compared to previous time-independent approaches. In addition, the generalised smoothing approach is able to effectively estimate kinematic parameters in the presence of missing data along with derivatives of kinematic quantities without the need for prior filtering or gap-filling of data.

Machine Learning Applications for Chemical Reactions.

Machine learning (ML) approaches have enabled rapid and efficient molecular property predictions as well as the design of new novel materials. In addition to great success for molecular problems, ML techniques are applied to various chemical reaction problems that require huge costs to solve with the existing experimental and simulation methods. In this review, starting with basic representations of chemical reactions, we summarized recent achievements of ML studies on two different problems; predicting reaction properties and synthetic routes. The various ML models are used to predict physical properties related to chemical reaction properties (e. g. thermodynamic changes, activation barriers, and reaction rates). Furthermore, the predictions of reactivity, self‐optimization of reaction, and designing retrosynthetic reaction paths are also tackled by ML approaches. Herein we illustrate various ML strategies utilized in the various context of chemical reaction studies.

Food-Porn: Philosophical and Psychoanalytic Approach to Contemporary Alimentary Practices

The paper deals with two contemporary alimentary phenomena (food porn and mukbang) in order to understand the basis for researching such phenomena in the social and anthropological sciences about food. As conceptual approaches, we choose the conception of hyperreality of J. Baudrillard and the modern version of psychoanalysis (structural psychoanalysis of J. Lacan). Based on these two approaches, we demonstrated one of the key complexities of the methodology of contemporary research on alimentary practices. It consists in the problematic choice between the search for basis in the global representation of society or in anthropological models. We also need to consider such phenomena not only in the perspective of meaning, but also in terms of pleasure.

Transfer learning using attentions across atomic systems with graph neural networks (TAAG).

Recent advances in Graph Neural Networks (GNNs) have transformed the space of molecular and catalyst discovery. Despite the fact that the underlying physics across these domains remain the same, most prior work has focused on building domain-specific models either in small molecules or in materials. However, building large datasets across all domains is computationally expensive; therefore, the use of transfer learning (TL) to generalize to different domains is a promising but under-explored approach to this problem. To evaluate this hypothesis, we use a model that is pretrained on the Open Catalyst Dataset (OC20), and we study the model's behavior when fine-tuned for a set of different datasets and tasks. This includes MD17, the *CO adsorbate dataset, and OC20 across different tasks. Through extensive TL experiments, we demonstrate that the initial layers of GNNs learn a more basic representation that is consistent across domains, whereas the final layers learn more task-specific features. Moreover, these well-known strategies show significant improvement over the non-pretrained models for in-domain tasks with improvements of 53% and 17% for the *CO dataset and across the Open Catalyst Project (OCP) task, respectively. TL approaches result in up to 4× speedup in model training depending on the target data and task. However, these do not perform well for the MD17 dataset, resulting in worse performance than the non-pretrained model for few molecules. Based on these observations, we propose transfer learning using attentions across atomic systems with graph Neural Networks (TAAG), an attention-based approach that adapts to prioritize and transfer important features from the interaction layers of GNNs. The proposed method outperforms the best TL approach for out-of-domain datasets, such as MD17, and gives a mean improvement of 6% over a model trained from scratch.

The Gelfand–Tsetlin basis for infinite-dimensional representations of

We consider the problem of determination of the Gelfand–Tsetlin basis for unitary principal series representations of the Lie algebra . The Gelfand–Tsetlin basis for an infinite-dimensional representation can be defined as the basis of common eigenfunctions of corner quantum minors of the corresponding L-operator. The construction is based on the induction with respect to the rank of the algebra: an element of the basis for is expressed in terms of a Mellin–Barnes type integral of an element of the basis for . The integration variables are the parameters (in other words, the quantum numbers) setting the eigenfunction. Explicit results are obtained for ranks 3 and 4, and the orthogonality of constructed sets of basis elements is demonstrated. For the kernel of the integral is expressed in terms of gamma-functions of the parameters of eigenfunctions, and in the case of —in terms of a hypergeometric function of the complex field at unity. The formulas presented for an arbitrary rank make it possible to obtain the system of finite-difference equations for the kernel. They include expressions for the quantum minors of L-operator via the minors of L-operator for the principal series representations, as well as formulas for action of some non-corner minors on the eigenfunctions of corner ones. The latter hold for any representation of (not only principal series) in which the corner minors of the L-operator can be diagonalized.

Risk Cost Measurement of Value for Money Evaluation Based on Case-Based Reasoning and Ontology: A Case Study of the Urban Rail Transit Public-Private Partnership Projects in China

Risk is demonstrated as one of the most crucial drivers of value for money (VFM) in public–private partnerships (PPP), but in previous studies, the risk cost estimation of the quantitative evaluation of VFM was still a dilemma that strongly depended on specialist discretion or had low methodological operability. This paper establishes a prediction model for estimating the risk cost in the phase of VFM evaluation through a combination of case-based reasoning (CBR) and ontology technology. PPP information ontology was established to provide the technical basis of knowledge representation for the CBR cycle. Then, according to whether the information data were quantitative or qualitative, similarity calculation methods were used for the retrieval of similar cases. The conceptual semantic similarity algorithm based on the ontology tree structure was well implemented to compare abstract information. After the most similar cases were extracted, a revision mechanism was followed when there were deviations in the similar cases. Finally, the risk costs of the target case were obtained by weighting the extracted similar cases based on the similarity. An empirical analysis was performed with 18 historical projects from the China Public–Private Partnerships Center. The results showed that the relative errors between the estimated and actual costs of total risk and retained risk were 11.05% and 2.41%, respectively. This indicates that the estimation model could achieve a better risk cost prediction with small errors, which validates the availability of the model. Based on the proposed model, this research establishes an extensible PPP information ontology model. It promotes the integration and interoperability of information knowledge in the PPP domain, which can be further expanded according to the requirements. Coherent accuracy is provided by the whole CBR-based measurement process, which has offered a systematic and objective method for the risk costs measurement of PPP projects.

Gelfand–Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions

We generalize the famous weight basis constructions of the finite-dimensional irreducible representations of sl(n,C) obtained by Gelfand and Tsetlin in 1950. Using combinatorial methods, we construct one such basis for each finite-dimensional representation of sl(n,C) associated to a given skew Schur function. Our constructions use diamond-colored distributive lattices of skew-shaped semistandard tableaux that generalize some classical Gelfand–Tsetlin (GT) lattices. Our constructions take place within the context of a certain programmatic study of poset models for semisimple Lie algebra representations and Weyl group symmetric functions undertaken by the first-named author and others. Some key aspects of the methodology of that program are recapitulated here.Combinatorial and representation-theoretic applications of our constructions are pursued here and elsewhere. Here, we extend combinatorial results about classical GT lattices to our more general lattices. We also use classical GT lattices to construct new and combinatorially distinctive weight bases for certain families of irreducible representations of the orthogonal Lie algebras. In another paper, via an entirely similar approach using the non-classical lattices of this paper, we obtain explicit weight bases for some infinite families of irreducible representations of the exceptional simple Lie algebras of types E6 and E7. Other combinatorial applications and generalizations are pursued in companion papers.

Input-Latency Free Versatile Bit-Serial GF(2 m ) Polynomial Basis Multiplication

Cryptography and error correction codes are widely used for information security and data integrity services in modern digital computing and communications systems. A number of standardized and published cryptography, and error correction algorithms utilize arithmetic operations over <inline-formula> <tex-math notation="LaTeX">$\text {GF}(2^{m})$ </tex-math></inline-formula>. The polynomial basis (PB) representation of <inline-formula> <tex-math notation="LaTeX">$\text {GF}(2^{m})$ </tex-math></inline-formula> elements is suitable for the support of multiple <inline-formula> <tex-math notation="LaTeX">$\text {GF}(2^{m})$ </tex-math></inline-formula> fields (that is, versatility). This article considers the problem of reduced hardware efficiency of versatile <inline-formula> <tex-math notation="LaTeX">$\text {GF}(2^{m})$ </tex-math></inline-formula> PB multipliers as a result of increased loading latency of the inputs and irreducible polynomial. In this context, to the best of our knowledge, this article proposes the first input-latency free versatile bit-serial <inline-formula> <tex-math notation="LaTeX">$\text {GF}(2^{m})$ </tex-math></inline-formula> multiplier using PB. The superiority of the proposed versatile PB multiplier is demonstrated for the case where the multiplication&#x2019;s inputs arrive serially in terms of higher output throughput and hardware efficiency compared to existing versatile PB and Gaussian normal basis (GNB) counterparts based on the application-specific integrated circuit (ASIC) and field-programmable gate array (FPGA) realizations, respectively. The proposed versatile PB multiplier improves hardware efficiency by factors of 1.8 and 2.5, respectively, compared to the versatile PB and versatile GNB counterparts.