Trivial Constraints Research Articles

A differential representation for holographic correlators

We present a differential representation for holographic four-point correlators. In this representation, the correlators are given by acting differential operators on certain seed functions. The number of these functions is much smaller than what is normally seen in known examples of holographic correlators, and all of them have simple Mellin amplitudes. This representation establishes a direct connection between correlators in position space and their Mellin space counterpart. The existence of this representation also imposes non- trivial constraints on the structure of holographic correlators. We illustrate these ideas by correlators in AdS5 × S5 and AdS5 × S3.

Internet of Cross-Chains: Model-Driven Cross-Chain as a Service Platform for the Internet of Everything in Smart City

Modern consumer electronics included consumer robots, which are made by heterogeneous Internet of Things, and Internet of robotics things are integral members of the Internet of Everything (IoE . IoE plays an incumbent role in smart cities and generates big data. Moreover, smart city IoE maintains various levels of security provisions. However, those are still vulnerable to security and privacy breaches. Nonetheless, mobility increases the risk of security and privacy breaches. As a result, in the internet era, providing seamless security and privacy for inter and intra communication of heterogeneous things is a significant challenge. Furthermore, blockchain is one of the established communication techniques that ensure both security and privacy. On the other hand, blockchain inherits trivial constraints with respect to scalability, latency, and interoperability. Cross-chain is a blockchain concept that aims to alleviate the aforementioned concerns. Therefore, we proposed a multifactor aware (privacy, security, interoperability, and scalability model-driven reference architecture for the Internet of cross-chains, also known as cross-chain as a service platform.

Data-driven suppression of short-period multiples from laterally varying thin-layered overburden structures

Marchenko multiple elimination methods remove all orders of overburden-generated internal multiples in a data-driven way. In the presence of thin beds, however, these methods have been shown to underperform. This is because the underlying inverse problem requires the information about short-period internal multiple (SPIM) imprint on the inverse transmission to be correctly constrained. This has been addressed in 1.5D media with energy conservation and minimum-phase reconstruction. Extending the applications to two dimensions and, hence, making the step toward field data were believed to be hampered by the need for a multidimensional minimum-phase reconstruction which is (1) not unique and (2) no algorithm has been found to perform this in practice on band-limited data. Here, we address both of these problems with an approach that includes solving the Marchenko equation with a trivial constraint, evaluating the energy conservation condition of its solutions to find the spatially dependent error syndrome, using the 1.5D minimum-phase reconstruction for each shot gather to find the spatially dependent constraint, and finally using that inside another run of the Marchenko equation solver to find a much-improved result. We find that the method works because in 2D media the expression of SPIMs in the inverse transmission coda is approximately 1.5D. We then investigate a class of models and synthetic data sets to verify where the 1.5D approximation starts breaking down. Our analysis indicates that this approach could perform very well in settings with moderate lateral variations, which also is where the (short-period) internal multiples are most difficult to differentiate from primary reflections.

The dual polyhedron to the chordal graph polytope and the rebuttal of the chordal graph conjecture

The integer linear programming approach to structural learning of decomposable graphical models led us earlier to the concept of a chordal graph polytope. An open mathematical question motivated by this research is what is the minimal set of linear inequalities defining this polytope, i.e. what are its facet-defining inequalities, and we came up in 2016 with a specific conjecture that it is the collection of so-called clutter inequalities. In this theoretical paper we give an implicit characterization of the minimal set of inequalities. Specifically, we introduce a dual polyhedron (to the chordal graph polytope) defined by trivial equality constraints, simple monotonicity inequalities and certain inequalities assigned to incomplete chordal graphs. Our main result is that the vertices of this polyhedron yield the facet-defining inequalities for the chordal graph polytope. We also show that the original conjecture is equivalent to the condition that all vertices of the dual polyhedron are zero-one vectors. Using that result we disprove the original conjecture: we find a vector in the dual polyhedron which is not in the convex hull of zero-one vectors from the dual polyhedron.

Classification of primary constraints for new general relativity in the premetric approach

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients [Formula: see text] appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients [Formula: see text]. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).

Automatic Differentiation for Solid Mechanics

Automatic differentiation (AD) is an ensemble of techniques that allow to evaluate accurate numerical derivatives of a mathematical function expressed in a computer programming language. In this paper we use AD for stating and solving solid mechanics problems. Given a finite element discretization of the domain, we evaluate the free energy of the solid as the integral of its strain energy density, and we make use of AD for directly obtaining the residual force vector and the tangent stiffness matrix of the problem, as the gradient and the Hessian of the free energy respectively. The result is a remarkable simplification in the statement and the solution of complex problems involving non trivial constraints systems and both geometrical and material non linearities. Together with the continuum mechanics theoretical basis, and with a description of the specific AD technique adopted, the paper illustrates the solution of a number of solid mechanics problems, with the aim of presenting a convenient numerical implementation approach, made easily available by recent programming languages, to the solid mechanics community.

Trivial constraints on orbital-free kinetic energy density functionals

Approximate kinetic energy density functionals (KEDFs) are central to orbital-free density functional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We identify a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows that validity for arbitrary v-representable densities is not restored by appeal to the density-potential bijection.

Equivalence between the Lovelock\u2013Cartan action and a constrained gauge theory

We show that the four-dimensional Lovelock–Cartan action can be derived from a massless gauge theory for the SO(1, 3) group with an additional BRST trivial part. The model is originally composed of a topological sector and a BRST exact piece and has no explicit dependence on the metric, the vierbein or a mass parameter. The vierbein is introduced together with a mass parameter through some BRST trivial constraints. The effect of the constraints is to identify the vierbein with some of the additional fields, transforming the original action into the Lovelock–Cartan one. In this scenario, the mass parameter is identified with Newton’s constant, while the gauge field is identified with the spin connection. The symmetries of the model are also explored. Moreover, the extension of the model to a quantum version is qualitatively discussed.

A possible explanation of low energy γ-ray excess from galactic centre and Fermi bubble by a Dark Matter model with two real scalars

We promote the idea of multi-component Dark Matter (DM) to explain results from both direct and indirect detection experiments. In these models as contribution of each DM candidate to relic abundance is summed up to meet WMAP/Planck measurements of ΩDM, these candidates have larger annihilation cross-sections compared to the single-component DM models. We illustrate this fact by introducing an extra scalar to the popular single real scalar DM model. We also present detailed calculations for the vacuum stability bounds, perturbative unitarity and triviality constraints on this model. As direct detection experimental results still show some conflict, we kept our options open, discussing different scenarios with different DM mass zones. In the framework of our model we make an interesting observation: the existing direct detection experiments like CDMS II, CoGeNT, CRESST II, XENON 100 or LUX together with the observation of excess low energy γ-ray from galactic centre and Fermi bubble by Fermi Gamma-ray Space Telescope (FGST) already have the capability to distinguish between different DM halo profiles.

An energy-conserving second order numerical scheme for nonlinear hyperbolic equation with an exponential nonlinear term

We present a second order accurate numerical scheme for a nonlinear hyperbolic equation with an exponential nonlinear term. The solution to such an equation is proven to have a conservative nonlinear energy. Due to the special nature of the nonlinear term, the positivity is proven to be preserved under a periodic boundary condition for the solution. For the numerical scheme, a highly nonlinear fractional term is involved, for the theoretical justification of the energy stability. We propose a linear iteration algorithm to solve this nonlinear numerical scheme. A theoretical analysis shows a contraction mapping property of such a linear iteration under a trivial constraint for the time step. We also provide a detailed convergence analysis for the second order scheme, in the ℓ∞(0,T;ℓ∞) norm. Such an error estimate in the maximum norm can be obtained by performing a higher order consistency analysis using asymptotic expansions for the numerical solution. As a result, instead of the standard comparison between the exact and numerical solutions, an error estimate between the numerical solution and the constructed approximate solution yields an O(Δt3+h4) convergence in ℓ∞(0,T;ℓ2) norm, which leads to the necessary ℓ∞ error estimate using the inverse inequality, under a standard constraint Δt≤Ch. A numerical accuracy check is given and some numerical simulation results are also presented.

Observational constraint on the varying speed of light theory

The varying speed of light (VSL) theory is controversial. It succeeds in explaining some cosmological problems, but on the other hand it is excluded by mainstream physics because it will shake the foundation of physics. In the present paper, we devote ourselves to test whether the speed of light is varying from the observational data of the type Ia Supernova, Baryon Acoustic Oscillation, Observational $H(z)$ data and Cosmic Microwave Background (CMB). We select the common form $c(t)=c_0a^n(t)$ with the contribution of dark energy and matter, where $c_0$ is the current value of speed of light, $n$ is a constant, and consequently construct a varying speed of light dark energy model (VSLDE). The combined observational data show a much trivial constraint $n=-0.0033 \pm 0.0045$ at 68.3\% confidence level, which indicates that the speed of light may be a constant with high significance. By reconstructing the time-variable $c(t)$, we find that the speed of light almost has no variation for redshift $z < 10^{-1}$. For high-$z$ observations, they are more sensitive to the VSLDE model, but the variation of speed of light is only in order of $10^{-2}$. We also introduce the geometrical diagnostic $Om (z)$ to show the difference between the VSLDE and $\Lambda$CDM model. The result shows that the current data are difficult to differentiate them. All the results show that the observational data favor the constant speed of light.

SiON metrology using angular and energy distributions of photoelectrons

Angle-resolved X-ray photoelectron spectroscopy (ARXPS) is a useful tool for non-destructive in-depth analysis of near surface regions. However, the reconstruction of depth profile from ARXPS data is an ill-posed mathematical problem. Thus, the main goal of this work was to develop a new, iterative algorithm based on the least square fitting which allows to solve this problem. The depth profiles were restored by dividing sample in thin virtual box shaped layers each with a different concentration. To extract information on the depth distribution, this algorithm is based on the analysis of the angular peak intensities along with the inelastic background. In addition, the physically trivial constraint of atomic fractions adding up to unity was imposed. The model takes into account the effect of elastic scattering and anisotropy of the photoelectric cross section. To test the algorithm, experimental spectrum for SiON samples on Si substrate were measured with a Thermo Theta Probe electron spectrometer for off-normal emission angles in the range between 25° and 75°. A very good agreement was found between the measured spectra and obtained spectra from the algorithm.

On the Higgs mass generation mechanism in the Standard Model

The mass-generation mechanism is the most urgent problem of modern particle physics. The discovery and study of the Higgs boson with the Large Hadron Collider at CERN are the highest priority steps to solve the problem. In this paper, the Standard Model Higgs mechanism of elementary particle mass generation is reviewed with pedagogical details. The discussion of the Higgs quadric self-coupling λ parameter and the bounds to the Higgs boson mass are presented. In particular, the unitarity, triviality, and stability constraints on the Higgs boson mass are discussed. The generation of a finite value for the λ parameter due to quantum corrections via effective potential is illustrated. Some simple predictions for the top quark and the Higgs boson masses are given when both the top Yukawa coupling and the Higgs self-coupling λ are equal to 1.

10.1007/s11496-008-1002-9

The mass-generation mechanism is the most urgent problem of modern particle physics. The discovery and study of the Higgs boson with the Large Hadron Collider at CERN are the highest priority steps to solve the problem. In this paper, the Standard Model Higgs mechanism of elementary particle mass generation is reviewed with pedagogical details. The discussion of the Higgs quadric self-coupling λ parameter and the bounds to the Higgs boson mass are presented. In particular, the unitarity, triviality, and stability constraints on the Higgs boson mass are discussed. The generation of a finite value for the λ parameter due to quantum corrections via effective potential is illustrated. Some simple predictions for the top quark and the Higgs boson masses are given when both the top Yukawa coupling and the Higgs self-coupling λ are equal to 1.

On survivable network polyhedra

Given an undirected network G = ( V , E ) , a vector of nonnegative integers r = ( r ( v ) : v ∈ V ) associated with the nodes of G and weights on the edges of G, the survivable network design problem is to determine a minimum-weight subnetwork of G such that between every two nodes u , v of V , there are at least min { r ( u ) , r ( v ) } edge-disjoint paths. In this paper we study the polytope associated with the solutions to that problem. We show that when the underlying network is series–parallel and r ( v ) is even for all v ∈ V , the polytope is completely described by the trivial constraints and the so-called cut constraints. As a consequence, we obtain a polynomial time algorithm for the survivable network design problem in that class of networks. This generalizes and unifies known results in the literature. We also obtain a linear description of the polyhedron associated with the problem in the same class of networks when the use of more than one copy of an edge is allowed.

$k$-Colour Partitions of Acyclic Tournaments

Let $G_{1}$ be the acyclic tournament with the topological sort $0 &lt; 1 &lt; 2 &lt; \dots &lt; n &lt; n+1$ defined on node set $N\cup \{0,n+1\}$, where $N=\{1,2,\dots,n\}$. For integer $k\geq 2$, let $G_{k}$ be the graph obtained by taking $k$ copies of every arc in $G_{1}$ and colouring every copy with one of $k$ different colours. A $k$-colour partition of $N$ is a set of $k$ paths from 0 to $n+1$ such that all arcs of each path have the same colour, different paths have different colours, and every node of $N$ is included in exactly one path. If there are costs associated with the arcs of $G_{k}$, the cost of a $k$-colour partition is the sum of the costs of its arcs. For determining minimum cost $k$-colour partitions we describe an $O(k^{2}n^{2k})$ algorithm, and show this is an NP-$hard$ problem. We also study the convex hull of the incidence vectors of $k$-colour partitions. We derive the dimension, and establish a minimal equality set. For $k&gt;2$ we identify a class of facet inducing inequalities. For $k=2$ we show that these inequalities turn out to be equations, and that no other facet defining inequalities exists besides the trivial nonnegativity constraints.

Steiner k-Edge Connected Subgraph Polyhedra

In this paper we consider the Steiner k-edge survivable network problem. We discuss the polytope associated with the solutions to that problem. We show that when the graph is series-parallel and k is even, the polytope is completely described by the trivial constraints and the so called Steiner-cut constraints. This generalizes recent work of Baiou and Mahjoub, SIAM J. Discrete Mathematics, vol. 10, pp. 505–514, 1997 for the case k = 2. As a consequence, we obtain in this case a linear description of the polyhedron associated with the problem when multiple copies of an edge are allowed.

Stability and Performance of List Scheduling With ExternalProcess Delays

Non-preemptive static priority list scheduling is a simple, low-overhead approach to scheduling precedence-constrained tasks in real-time multiprocessor systems. However, it is vulnerable to anomalous timing behavior caused by variations in task durations. Specifically, reducing the duration of one task can delay the starting time of another task. This phenomenon, called Scheduling Instability, can make it difficult or impossible to guarantee real-time deadlines. Several heuristic solutions to handle scheduling instability have been reported. This paper addresses three main limitations in the state of the art in schedule stabilization. First, each stabilization technique only applies to a narrowly defined class of systems. To alleviate this constraint, we present an Extended Scheduling Model encompassing a wide range of assumptions about the scheduling environment, and address the stability problem under this model. Second, existing stabilization methods are heuristics based on a partial understanding of the causes of instability. We therefore derive a set of General Instability Conditions which are both necessary and sufficient for instability to occur. Third, solutions to scheduling instability range from trivial constraints on the run-time dispatcher through complex transformations of the precedence graph. We present scheduling simulation results comparing the average performance of several inherently stable run-time dispatchers of widely varying levels of complexity. Results show that for representative real-time workloads, simple low-overhead dispatchers perform nearly as well as a complex ’’minimally stabilized‘‘ dispatcher. Thus, complex schedule stabilization methods may be unnecessary, or even detrimental, due to their high computational overhead.

Making light of keeping color categories in the dark: Some arguments against Saunders and van Brakel's notions of trivial constraints in color nomenclature

Saunders &amp; van Brakel prematurely reject the idea of nontrivial constraints in color nomenclature. Their claim that the universality of color naming is caused by Western contact and cultural dominance is inadequate because of the great variety of terminology systems still found in the world. The complex interactions of hue, brightness, and saturation can be studied rigorously. If we discard the standard models of color nomenclature because of some discrepancies and anomalies, we will not be able to explain the vast array of remaining data that is consistent with current theories.

Cohomological construction of quantized universal enveloping algebras

Given an associative algebra A A and the category C \mathcal C of its finite dimensional modules, additional structures on the algebra A A induce corresponding ones on the category C \mathcal C . Thus, the structure of a rigid quasi-tensor (braided monoidal) category on R e p A Rep_{A} is induced by an algebra homomorphism A → A ⊗ A A\to A\otimes A (comultiplication), coassociative up to conjugation by Φ ∈ A ⊗ 3 \Phi \in A^{\otimes 3} (associativity constraint) and cocommutative up to conjugation by R ∈ A ⊗ 2 \mathcal R \in A^{\otimes 2} (commutativity constraint), together with an antiautomorphism (antipode) S S of A A satisfying the compatibility conditions. A morphism of quasi-tensor structures is given by an element F ∈ A ⊗ 2 F\in A^{\otimes 2} with suitable induced actions on Φ \Phi , R \mathcal R and S S . Drinfeld defined such a structure on A = U ( G ) [ [ h ] ] A=U(\mathcal G )[[h]] for any semisimple Lie algebra G \mathcal {G} with the usual comultiplication and antipode but nontrivial R \mathcal R and Φ \Phi , and proved that the corresponding quasi-tensor category is isomomorphic to the category of representations of the Drinfeld-Jimbo (DJ) quantum universal enveloping algebra (QUE), U h ( G ) U_{h}(\mathcal G ) . In the paper we give a direct cohomological construction of the F F which reduces Φ \Phi to the trivial associativity constraint, without any assumption on the prior existence of a strictly coassociative QUE. Thus we get a new approach to the DJ quantization. We prove that F F can be chosen to satisfy some additional invariance conditions under (anti)automorphisms of U ( G ) [ [ h ] ] U(\mathcal G )[[h]] , in particular, F F gives an isomorphism of rigid quasi-tensor categories. Moreover, we prove that for pure imaginary values of the deformation parameter, the elements F F , R R and Φ \Phi can be chosen to be formal unitary operators on the second and third tensor powers of the regular representation of the Lie group associated to G \mathcal G with Φ \Phi depending only on even powers of the deformation parameter. In addition, we consider some extra properties of these elements and give their interpretation in terms of additional structures on the relevant categories.