Journal articles on the topic 'Observable canonical forms'

We discuss the observables that have been recently put forth to describe quarks and gluons orbital angular momentum distributions. Starting from a standard parameterization of the energy momentum tensor in QCD one can single out two forms of angular momentum, a so-called kinetic term – Ji decomposition – or a canonical term – Jaffe-Manohar decomposition. Orbital angular momentum has been connected in each decomposition to a different observable, a Generalized Transverse Momentum Distribution (GTMD), for the canonical term, and a twist three Generalized Parton Distribution (GPD) for the kinetic term. While the latter appears as an azimuthal angular modulation in the longitudinal target spin asymmetry in deeply virtual Compton scattering, due to parity constraints, the GTMD associated with canonical angular momentum cannot be measured in a similar set of experiments.

New possibilities of Gramian computation, by means of canonical transformations into diagonal, controllable, and observable canonical forms, are shown. Using such a technique, the Gramian matrices can be represented as products of the Hadamard matrices of multipliers and the matrices of the transformed right-hand sides of Lyapunov equations. It is shown that these multiplier matrices are invariant under various canonical transformations of linear continuous systems. The modal Lyapunov equations for continuous SISO LTI systems in diagonal form are obtained, and their new solutions based on Hadamard decomposition are proposed. New algorithms for the element-by-element computation of Gramian matrices for stable, continuous MIMO LTI systems are developed. New algorithms for the computation of controllability Gramians in the form of Xiao matrices are developed for continuous SISO LTI systems, given by the equations of state in the controllable and observable canonical forms. The application of transformations to the canonical forms of controllability and observability allowed us to simplify the formulas of the spectral decompositions of the Gramians. In this paper, new spectral expansions in the form of Hadamard products for solutions to the algebraic and differential Sylvester equations of MIMO LTI systems are obtained, including spectral expansions of the finite and infinite cross - Gramians of continuous MIMO LTI systems. Recommendations on the use of the obtained results are given.

New approaches to the transformations of the uncontrollable and unobservable matrices of linear systems to their canonical forms are proposed. It is shown that the uncontrollable pair (A,B) and unobservable pair (A,C) of linear systems can be transform to their controllable (A,B), and observable (A,C) canonical forms by suitable choice of nonsingular matrix M satisfying the condition M[AB]=[AB] and M=[A,B] , respectively. It is also shown that by suitable choice of the gain matrix K of the feedbacks of the derivative of the state vector it is possible to reduce the descriptor system to the standard one.

Although a large literature on delegation exists, few models have pushed beyond a core set of canonical assumptions. This approach may be justified on grounds of tractability, but the failure to grasp the significance of different assumptions and push beyond specific models has limited our understanding of the incentives for delegation. Consequently, the justifications for delegation that have received recent scrutiny and testing differ from some of the more plausible justifications offered by informal studies of delegation. We show that surprisingly few results in the literature hinge on risk aversion, and surprisingly many turn on the ignored, though equally canonical, technological assumption that uncertainty is fixed (relative to policies). Relaxing the key assumptions about dimensionality and functional forms provides a clearer intuition about delegation—one that is closer to classical treatments. The theory allows us to relate different institutional features (commitment, specialization costs, monitoring, multiple principals) to delegation's observable properties.

A recurrent idea in Indian philosophical, theological, and mythological systems is that of a universe manifested through a sequence of emanations. Diverse traditions of doctrine and practice share this vision of the progression from the one to the many. Temple designs often embody the same pattern. Within the diverse traditions of Indian temple architecture, an emanatory scheme is observable both in the formal structure of individual temple designs, which express a dynamic sequence of emergence and growth, and in the way in which temple forms develop throughout the course of such traditions. The canonical Sanskrit texts on architecture (Vastu Shastras) share this emanatory way of thinking, presenting varied temple typologies in which designs develop from simple to complex, emerging sequentially one from another. These texts provide a framework for design that demands interpretation and improvisation, while leading to results that are only partly determined by the individual architect. This contributes to a sense, powerfully established by the unfolding potential of the tradition of architectural practice, that a new temple design is svayambhu (self-manifesting) appearing through a cosmic process from a supra-human source.

The study is devoted to Russian pronouns which children use in grammatical position of a direct object. The aim of the research is to consider the distinctive features of the pronouns belonging to different semantic groups. Additionally, the paper is an effort to answer the question if the connection between the position of the object in the sentence and the semantics of the pronoun is relevant when mastering the language, i.e. to discover pronouns of what classes are more likely to be associated with the object syntactic function in children’s speech. Corpus recordings of children’s speech, namely the data from longitudinal observations of children’s speech, comprise the material of the study. The basic research method employed is the functional-semantic analysis of utterances. As a result of the performed study, it was found that direct objects denoted by pronouns in the accusative case appear in most children’s speech in the third year of life. As for the frequency of occurrence of accusative case forms in a child’s speech, pronoun classes differ from one another; this is partly caused by their semantics. There is a clear distinction between deictic pronouns and quantifiers: children use the latter (negative, indefinite, universal) more often in the object position. Four semantic characteristics are associated with the frequency of occurrence of object forms. The first one is inanimateness: inanimate pronouns and pronouns referring to inanimate referents take the object position more often than animate pronouns. The next characteristic is anaphoricity or the anaphoric nature of pronouns: pronouns referring to another word in a child’s speech are more often in the accusative case than other pronouns. The non-concreteness or lack of reference to a concrete referent which is directly observable in the communication situation also influences the frequency of occurrence: indefinite and negative pronouns turn out to be the most "objective" for children. Finally, another characteristic is generalisation, or a reference to a group of referents: the pronoun vsyo (all, everything) occupies a prominent position on the "object" scale. The influence of semantic factors is not noted when using adjective pronouns incorporated into nominal groups dependent on nouns in the accusative case and also when using non-canonical objects (the adverbs kak (how), tak (so) and subordinate complement clauses (sentential actants) with relative pronouns.

We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or T4, they describe an equivalent class of a trio of the Einstein-Kähler forms (the hyperkähler forms). We calculate the dimensions of these moduli spaces by using the Atiyah-Singer Index theorem. We mention the partition function and the possibility of the observables in the Witten-type topological half-flat gravity model case.

Abstract Purpose: During development and homeostatic processes such as wound repair, certain cells undergo a remarkable process where they radically transform in cell shape and state, from epithelial to mesenchymal cells. This ability is referred to as ‘Epithelial-Mesenchymal Plasticity’ (EMP), triggered by both mechanical (i.e. loss of cell-cell contact) and soluble cues (i.e. TGFβ), and is absolutely essential in both embryonic and adult organisms. Dysregulation of EMP also occurs in cancer; where tumor cells undergo EMP to become metastatic, stem-like, and drug resistant. Critically, increased EMP correlates with increased cancer severity. However, it is largely a black box as to how EMP is regulated and how epithelial cells sense physical, geometrical, and soluble cues in their environment to assume a mesenchymal fate. This work inferred that cell shape is a determinant of not only fates – but of long-term outcomes. That is, we provide mechanistic explanations between cell context, environment, and cancer severity. In this work, we investigated how mechanical and soluble cues are coupled to the dynamics of signaling pathways that regulate transcriptional and post-transcriptional events that underpin EMP. Especially with regards to mechanical cues, we attempt to unlock the ‘black box’ as to how changes in adhesion, ECM (Extracellular Matrix) stiffness, and environment geometry are coupled to the transcriptional events that drive EMP. Results: We show that changes in cell and nuclear shape result from the actions of the cytoskeleton and important drivers of EMP in upregulating ‘interlocking’ networks that promote EMP-driving inflammation and suppressing insulin signaling. Using a combination of cell biology, proteomics, and new statistical methods, we provide a systems biology model demonstrating: Cell shape → MT bound Kinesin-1 activity and nuclear shape → inflammation (IKK, JNK), insulin signaling (IRS), and YAP/TAZ → EMP Our work connects observable changes in phenotype to causal changes in signaling network architecture and cell fates. We used an integrative -omic approach to analyze tumors from breast cancer patients. We identified a novel tumor suppressor – JAM3 – whose loss is associated with altered nuclear shape in vivo, inhibiting JAM3 in cells, or stimulation with canonical EMP inducer TGFβ to promote EMP, and thus changes the organization of microtubules and alters nuclear shape. During EMP we observe there is upregulation of a pro-inflammatory, insulin resistant, signaling network that is predictive of mesenchymal states across cancer. EMP following JAM3 depletion and/or TGFβ stimulation is rescued by inhibition of Kinesin-1 motors. This rescue is explained by changes in inflammatory and insulin signaling. We show that while Kinesin-1 activity is responsible for upregulation in canonical signalling and network ‘hubs’, changes in nuclear shape upregulate ‘effectors’ of these hubs. Thus, microtubules and nuclei differentially regulate different parts of ‘interlocking’ networks. Conclusions: This work has integrated image-omics, comprehensive global proteomics, and quantitative cell biology to provide a mechanistic ¬and systems-level understanding of how epithelial cells differentiate into mesenchymal forms during disease development and progression. This work is of major significance for three reasons. First, it shows how cell shape can mechanistically regulate cell fates on an unprecedented systems-level. Second, we identify an EMP network that is conserved across cancers and may indeed be conserved across both normal and diseased mesenchymal cells. Indeed, we speculate that different types of diseased cells may all share the same network. Finally, we introduce the concept of interlocking networks – where hubs and effectors are regulated by different cellular components. Our work has been extensively validated, using chemical and genetic approaches and in vivo model of in human breast cancer. Citation Format: Zheng Yin. Epithelial-Mesenchymal Plasticity is Regulated by Inflammatory Signaling Networks Coupled to Cell Morphology [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr P5-11-01.

For pure Yang-Mills theory on Minkowski space-time, formulated in functional spaces where the covariant divergence is an elliptic operator without zero modes, and for a trivial principal bundle over the fixed time Euclidean space with a compact, semisimple, connected and simply connected structure Lie group, a Green function for the covariant divergence has been found. It allows one to solve the first class constraints associated with Gauss’ laws and to identify a connection-dependent coordinatization of the trivial principal bundle. In a neighborhood of the global identity section, by using canonical coordinates of the first kind on the fibers, one has a symplectic implementation of the Lie algebra of the small gauge transformations generated by Gauss’ laws and one can make a generalized Hodge decomposition of the gauge potential one-forms based on the BRST operator. This decomposition singles out a pure gauge background connection (the BRST ghost as Maurer-Cartan one-form on the group of gauge transformations) and a transverse gauge-covariant magnetic gauge potential. After an analogous decomposition of the electric field strength into the transverse and the longitudinal part, Dirac’s observables associated with the transverse electric and magnetic components are identified as their restriction to the global identity section of the trivial principal bundle. The longitudinal part of the electric field can be re-expressed in terms of these electric and magnetic transverse parts and of the constraints without Gribov ambiguity. The physical Lagrangian, Hamiltonian, non-Abelian and topological charges have been obtained in terms of transverse Dirac’s observables, also in the presence of fermion fields, after a symplectic decoupling of the gauge degrees of freedom; one has an explicit realization of the abstract “Riemannian metric” on the orbit space. Both the Lagrangian and the Hamiltonian are nonlocal and nonpolynomial; like in the Coulomb gauge they are not Lorentz-invariant, but the invariance can be enforced on them if one introduces Wigner covariance of the observables by analyzing the various kinds of Poincare orbits of the system and by reformulating the theory on suitable spacelike hypersurfaces, following Dirac. By extending to classical relativistic field theory the problems associated with the Lorentz noncovariance of the canonical (presymplectic) center of mass for extended relativistic systems, in the sector of the field theory with P2>0 and W2≠0 one identifies a classical invariant intrinsic unit of length, determined by the Poincare Casimirs, whose quantum counterpart is the ultraviolet cutoff looked for by Dirac and Yukawa: it is the Compton wavelength of the field configuration (in an irreducible Poincare representation) multiplied by the value of its spin.

An elaborated review with proofs of Schmidt canonical decomposition of any bipartite state vector is approached through general subsystem basis expansion. The upgraded forms of Schmidt decomposition in terms of correlation operator and twin observables are presented in detail. The discussion is extended to distant measurement, Einstein–Podolsky–Rosen states and Schrödinger's steering. All claims and proofs are given in standard form unlike in the previous articles of the author where all results were obtained utilizing the very rarely used antilinear Hilbert–Schmidt maps of one subsystem state space into the other. For practical reasons the formalism of partial traces with their rules and reduced density operators together with correlation operator are used.Quanta 2018; 7: 19–39.

We extend the three-dimensional noncommutative relations of the position and momentum operators to those in the four dimension. Using the Seiberg-Witten (SW) map, we give the Heisenberg representation of these noncommutative algebras and endow the noncommutative parameters associated with the Planck constant, Planck length and cosmological constant. As an analog with the electromagnetic gauge potential, the noncommutative effect can be interpreted as an effective gauge field, which depends on the Plank constant and cosmological constant. Based on these noncommutative relations, we give the Klein-Gordon (KG) equation and its corresponding current continuity equation in the noncommutative phase space including the canonical and Hamiltonian forms and their novel properties beyond the conventional KG equation. We analyze the symmetries of the KG equations and some observables such as velocity and force of free particles in the noncommutative phase space. We give the perturbation solution of the KG equation.

ABSTRACT Asymptotic giant branch (AGB) stars are, together with supernovae, the main contributors of stellar dust to the interstellar medium (ISM). Dust grains formed by AGB stars are thought to be large. However, as dust nucleation and growth within their outflows are still not understood, the dust-grain size distribution (GSD) is unknown. This is an important uncertainty regarding our knowledge of the chemical and physical history of interstellar dust, as AGB dust forms ${\sim} 70{{\ \rm per\ cent}}$ of the starting point of its evolution. We expand on our chemical kinetics model, which uniquely includes a comprehensive dust–gas chemistry. The GSD is now allowed to deviate from the commonly assumed canonical Mathis, Rumpl & Nordsieck distribution. We find that the specific GSD can significantly influence the dust–gas chemistry within the outflow. Our results show that the level of depletion of gas-phase species depends on the average grain surface area of the GSD. Gas-phase abundance profiles and their possible depletions can be retrieved from observations of molecular emission lines when using a range of transitions. Because of degeneracies within the prescription of GSD, specific parameters cannot be retrieved, only (a lower limit to) the average grain surface area. None the less, this can discriminate between dust composed of predominantly large or small grains. We show that when combined with other observables such as the spectral energy distribution and polarized light, depletion levels from molecular gas-phase abundance profiles can constrain the elusive GSD of the dust delivered to the ISM by AGB outflows.

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its "purification". As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein–Gordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its "purification" induces on the one-particle space of the quantized system a topology which coincides with that given by the two-point functions of quasifree Hadamard states. These findings will be shown to lead to new results concerning the structure of the local (von Neumann) observable-algebras in representations of quasifree Hadamard states of the Klein–Gordon field in an arbitrary globally hyperbolic spacetime, such as local definiteness, local primarity and Haag-duality (and also split- and type III1-properties). A brief review of this circle of notions, as well as of properties of Hadamard states, forms part of the article.

AbstractWe generalize Lévy’s lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a much more general class of measures, so-called GAP measures. For any given density matrix $$\rho $$ ρ on a separable Hilbert space $${\mathcal {H}}$$ H , $${\textrm{GAP}}(\rho )$$ GAP ( ρ ) is the most spread-out probability measure on the unit sphere of $${\mathcal {H}}$$ H that has density matrix $$\rho $$ ρ and thus forms the natural generalization of the uniform distribution. We prove concentration-of-measure whenever the largest eigenvalue $$\Vert \rho \Vert $$ ‖ ρ ‖ of $$\rho $$ ρ is small. We use this fact to generalize and improve well-known and important typicality results of quantum statistical mechanics to GAP measures, namely canonical typicality and dynamical typicality. Canonical typicality is the statement that for “most” pure states $$\psi $$ ψ of a given ensemble, the reduced density matrix of a sufficiently small subsystem is very close to a $$\psi $$ ψ -independent matrix. Dynamical typicality is the statement that for any observable and any unitary time evolution, for “most” pure states $$\psi $$ ψ from a given ensemble the (coarse-grained) Born distribution of that observable in the time-evolved state $$\psi _t$$ ψ t is very close to a $$\psi $$ ψ -independent distribution. So far, canonical typicality and dynamical typicality were known for the uniform distribution on finite-dimensional spheres, corresponding to the micro-canonical ensemble, and for rather special mean-value ensembles. Our result shows that these typicality results hold also for $${\textrm{GAP}}(\rho )$$ GAP ( ρ ) , provided the density matrix $$\rho $$ ρ has small eigenvalues. Since certain GAP measures are quantum analogs of the canonical ensemble of classical mechanics, our results can also be regarded as a version of equivalence of ensembles.

Abstract The amplituhedron determines scattering amplitudes in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills by a single “positive geometry” in the space of kinematic and loop variables. We study a closely related definition of the amplituhedron for the simplest case of four-particle scattering, given as a sum over complementary “negative geometries”, which provides a natural geometric understanding of the exponentiation of infrared (IR) divergences, as well as a new geometric definition of an IR finite observable $$ \mathcal{F} $$ F (g, z) — dually interpreted as the expectation value of the null polygonal Wilson loop with a single Lagrangian insertion — which is directly determined by these negative geometries. This provides a long-sought direct link between canonical forms for positive (negative) geometries, and a completely IR finite post-loop-integration observable depending on a single kinematical variable z, from which the cusp anomalous dimension Γcusp(g) can also be straightforwardly obtained. We study an especially simple class of negative geometries at all loop orders, associated with a “tree” structure in the negativity conditions, for which the contributions to $$ \mathcal{F} $$ F (g, z) and Γcusp can easily be determined by an interesting non-linear differential equation immediately following from the combinatorics of negative geometries. This lets us compute these “tree” contributions to $$ \mathcal{F} $$ F (g, z) and Γcusp for all values of the ‘t Hooft coupling. The result for Γcusp remarkably shares all main qualitative characteristics of the known exact results obtained using integrability.

International audience Our aim is to apply some tools of control to fishing population systems. In this paper we construct a non linear observer for the continuous stage structured model of an exploited fish population, using the fishing effort as a control term, the age classes as a states and the quantity of captured fish as a measured output. Under some biological satisfied assumptions we formulate the observer corresponding to this system and show its exponential convergence. With the Lie derivative transformation, we show that the model can be transformed to a canonical observable form; then we give the explicit gain of the estimation. Le but de ce travail est d'appliquer des outils de contrôle aux systèmes de population de pêche. on construit un observateurpour un modèle continu structuré en age de population de pêche exploitée qui tient compte des pré-recrutés. Les variables dumodèle: l'effort de pêche, les classes d'age et la capture sont considérés respectivement comme contrôleur, états du systèmes et sa sortie mesurée. Le changement de variables basé sur les dérivés de Lie nous a permis de mettre le système sous une forme canonique observable. La forme explicite de l'observateur est finalement donnée.