Conditions For Embedding Research Articles

Optimization of Size of Pixel Blocks for Orthogonal Transform in Optical Watermarking Technique

We previously proposed a novel technology with which the images of real objects with no copyright protection could contain invisible digital watermarking, using spatially modulated illumination. In this “optical watermarking” technology, we used orthogonal transforms, such as a discrete cosine transform (DCT) or a Walsh-Hadamard transform (WHT), to produce watermarked images, where 1-b binary information was embedded into each pixel block. In this paper, we propose an optimal condition for a technique of robust optical watermarking that varies the size of pixel blocks by using a trade-off in the efficiency of embedded watermarking. We conducted experiments where 4 × 4, 8 × 8, and 16 × 16 pixels were used in one block. A detection accuracy of 100% was obtained by using a block with 16 × 16 pixels when embedded watermarking was extremely weak, although the accuracy did not necessarily reach 100% by using blocks with 4 × 4 or 8 × 8 pixels under the same embedding conditions. We also examined the effectiveness of using a Haar discrete wavelet transform (Haar DWT) as an orthogonal transform under the same experimental condition, and the results showed that the accuracy of detection was slightly inferior to DCT and WHT under very weak embedding conditions. The results from experiments revealed the effectiveness of our new proposal.

Haefliger’s codimension-one singular foliations, open books and twisted open books in dimension 3

We consider singular foliations of codimension one on 3-manifolds, in the sense defined by Andre Haefliger as being Γ1-structures. We prove that under the obvious linear embedding condition, they are Γ1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity Cr, r ≥ 1. In particular, in dimension 3, this gives a very simple proof of Thurston’s 1976 regularization theorem without using Mather’s homology equivalence.

Completing a solution of the embedding problem for incomplete idempotent latin squares when numerical conditions suffice

Building upon the work of several previous papers, necessary and sufficient conditions are obtained for an incomplete idempotent latin square R of order n to be embedded in an idempotent latin square of order 2n. This work extends known necessary and sufficient conditions for embeddings into idempotent latin squares of order t≥2n+1, thereby pushing the bounds down to the point where subsequent developments must handle additional conditions that involve the arrangement of symbols on the given square.

ON A WEAKLY UNIFORMLY ROTUND DUAL OF A BANACH SPACE

Every Banach space with separable second dual can be equivalently renormed to have weakly uniformly rotund dual. Under certain embedding conditions a Banach space with weakly uniformly rotund dual is reflexive.

Nested spline–wavelet decompositions

We consider conditions for embedding of (generally speaking, discontinuous and nonpolynomial) spline spaces obtained by a removal of grid points (nests). For such spaces we present the wavelet decomposition, construct the embedding and extension matrices, and derive the corresponding decomposition and reconstruction formulas. We also consider the decomposition and restoration operators in spaces of finite sequences (flows). Bibliography: 1 title.

Lateral Soil Resistance for On-bottom Pipeline Design on Clayey Seabed

A series of physical model tests were conducted to investigate the lateral resistance of a partially embedded pipe in soft clay under various embedment and loading conditions at both small and large lateral displacements. Computational limit analyses using a technique called Discontinuity Layout Optimisation (DLO) were conducted to back-analyse and compare with the experimental results. It was found that pipes with different over-penetration ratios show different failure modes and pipe trajectories during lateral movements. Based on the numerical and experimental results, a set of design equations are proposed for the predictions of the lateral resistance of a partially embedded pipe under combined vertical and horizontal loads, which can be used by pipeline engineers to predict the post-buckling configuration given the structural properties of the pipeline.

Tikhonov regularization for nonparametric instrumental variable estimators

We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivatives. After showing its consistency in the Sobolev norm and uniform consistency under an embedding condition, we derive the expression of the asymptotic Mean Integrated Square Error and the rate of convergence. The optimal value of the regularization parameter is characterized in two examples. We illustrate our theoretical findings and the small sample properties with simulation results. Finally, we provide an empirical application to estimation of an Engel curve, and discuss a data driven selection procedure for the regularization parameter.

Lectins for histochemical demonstration of glycans

Lectins have been proven to be invaluable reagents for the histochemical detection of glycans in cells and tissues by light and electron microscopy. This technical review deals with the conditions of tissue fixation and embedding for lectin labeling, as well as various markers and related labeling techniques. Furthermore, protocols for lectin labeling of sections from paraffin and resin-embedded tissues are detailed together with various controls to demonstrate the specificity of the labeling by lectins.

Improved protocol for processing stented porcine coronary arteries for immunostaining

Percutaneous coronary intervention has resulted in a paradigm shift in the treatment of coronary artery disease and myocardial infarction. However, neither bare-metal stents nor polymer-coated drug-eluting stents represent ideal therapies at this time due to the undesired in-stent stenosis or delayed thrombosis. Hence there is pressing clinical need for greater understanding of the cellular mechanisms involved. It is hoped that this in turn will provide insight into designing and developing the next generation of stents. Although immunohistochemistry and immunofluorescence are appropriate tools in understanding the molecular histology, performing these techniques on stented blood vessels is technically challenging because of poor permeability of antibodies into the stented blood vessels which are embedded in methacrylate-based resins and inadequate image resolution due to autofluorescence. Hence there is a need to develop techniques which can facilitate immunohistochemistry/immunofluorescence procedures on stented blood vessel cross-sections. In this study we describe an improved protocol for processing stented porcine coronary arteries for immunostaining with smooth muscle cell, endothelial cell, monocyte and macrophage markers. We first identified the optimal conditions for resin embedding of stented artery and cross sectioned the vessels using high speed precision wafering diamond blade. The sections were then ground using two levels of water sandpaper on a Metaserve 2000 grinder to achieve the desired thickness. For immunostaining, we developed a novel deplasticization protocol which favors optimal antibody permeabilization. Our protocol not only provides feasibility of improved immunostaining of stented artery sections but also results in high quality images.

Optimization of Entrapping Conditions of Nitrifying Bacteria and Selection of Entrapping Agent

Sodium alginate and polyvinyl alcohol were selected as entrapping agents to immobilize nitrifying microbia. Through orthogonal tests, optimal conditions of entrapping nitrifying bacteria by the two agents were determined by ammonia nitrogen removal efficiency. The properties of the two immobilized microbial beads produced under their optimum embedding conditions were compared. Results indicate that the optimum embedding conditions of calcium alginate beads (briefly CA beads) were 10ml of nitrifying bacteria, 4% of sodium alginate content, 3mm in bead diameter and 24-hr crosslinking time. The optimum embedding conditions of polyvinyl alcohol beads (briefly PVA beads) were 10ml of nitrifying bacteria, 10% of PVA content, 3mm in bead diameter and 24-hr crosslinking time. Comprehensive comparisons on mechanical strength, stability, mass transfer property and ammonia nitrogen removal efficiency of the two immobilized microbial beads indicate that polyvinyl alcohol is a better embedding agent for nitrifying bacteria in wastewater treatment compared with sodium alginate.

Optimal Embeddings of Spaces of Generalized Smoothness in the Critical Case

We study necessary and sufficient conditions for embeddings of Besov and Triebel-Lizorkin spaces of generalized smoothness \(B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n})\) and \(F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n})\), respectively, into generalized Holder spaces \(\Lambda_{\infty,r}^{\mu(\cdot)}(\ensuremath {\ensuremath {\mathbb {R}}^{n}})\). In particular, we are able to characterize optimal embeddings for this class of spaces provided q>1. These results improve the embedding assertions given by the continuity envelopes of \(B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n})\) and \(F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n})\), which were obtained recently solving an open problem of D.D. Haroske in the classical setting.

Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the p(x)-Laplacian and its critical exponent

We give a sucient condition for the compact embedding from W k;p(¢) 0 (›) to L q(¢) (›) in case essinfx2›(Np(x)=(N i kp(x)) i q(x)) = 0, where › is a bounded open set in R N. As an application, we find a nontrivial nonnegative weak solution of the nonlinear elliptic equation idiv ‡ jru(x)j p(x)i2 ru(x) · = ju(x)j q(x)i2 u(x) in ›, u(x) = 0 on @›. We also consider the existence of a weak solution to the problem above even if the embedding is not compact.

L p -Poincaré inequality for general symmetric forms

Lp Poincare inequalities for general symmetric forms are established by new Cheeger’s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger’s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.

Pure subrings of the rings

Pure subrings of finite rank in the -adic completion of the ring of integers and in its homomorphic images are considered. Certain properties of these rings are studied (existence of an identity element, decomposability into a direct sum of essentially indecomposable ideals, condition for embeddability into a csp-ring, etc.). Additive groups of these rings and conditions under which these rings are subrings of algebraic number fields are described.Bibliography: 12 titles.

Pure subrings of the rings Z{sub {chi}}

Pure subrings of finite rank in the Z-adic completion of the ring of integers and in its homomorphic images are considered. Certain properties of these rings are studied (existence of an identity element, decomposability into a direct sum of essentially indecomposable ideals, condition for embeddability into a csp-ring, etc.). Additive groups of these rings and conditions under which these rings are subrings of algebraic number fields are described. Bibliography: 12 titles.

When do people start to recognize signs?

The aim of this paper is to examine when signers start to recognize the lexical meaning of a sign. This is studied with movies of 32 mono-morphemic signs of Sign Language of the Netherlands (SLN). Signs were presented in isolation or with preceding fidgets (e.g., rubbing your nose). Signers watched these movies at normal playing speed and had to respond as soon as they recognized a sign, which they were able to do, on average, about 850 ms after the coded beginning of the sign. By subtracting the time participants need to generate a motor response to a visible event, which was 310 ms on average, sign recognition was estimated to occur after around 540 ms. The results were further analyzed in relation to the sign’s movement phases (preparation, nucleus, and recovery) and for effects of participant characteristics, sign characteristics, and embedding conditions. The current findings are compared with earlier work on the time course of lexical sign recognition. Moreover, they are compared with findings from an earlier experiment on detecting the beginning of a sign (Arendsen et al., 2007) to study possible interference of lexical recognition with sign detection by signers.

Protein folding invariants

This article discusses the topological invariants associated with an augmented ribbon model of single domain protein. The model is a triple (S, G, J) in S3 where S is a 2-manifold with boundary, G is a circle-with-chords, and J is an arc. The surfaces satisfy an embedding condition called laundry. The invariants are necessary and sufficient conditions for two triples to be equivalent by ambient isotopy. The model describes the native state, the unfolded state, and a unique folding pathway as a single mathematical entity. This may help illuminate some of the remarkable properties of protein. Twist transitions are introduced that allow the surface to pass through itself. A new arithmetic involving the complex numbers is used to represent variable linking numbers.

Note on Embedding a Class of Finite Planar Spaces into 3-Dimensional Projective Spaces

Let \(S = ({\mathcal{P}},{\mathcal{L}},{\mathcal{H}})\) be a finite planar space such that any two planes intersect in a line. Such planar spaces are interesting, since they provide examples for a class of finite geometries which is conjectured to be embeddable in a finite projective geometry (see e.g. [3,6]). In this paper, a new embedding condition for a class of these finite planar spaces is given.

The relationship between the Einstein and Yang-Mills equations

In this paper we prove that special requirements to Yang-Mills equations on a 4-dimensional conformally connected manifold allow one to reduce them to a system of Einstein equations and additional ones that bind components of the energy-impulse tensor. We propose an algorithm that gives conditions for the embedding of the metric of the gravitational field into a special (uncharged) Yang-Mills conformally connected manifold. As an application of the algorithm, we prove that the metric of any Einstein space and the Robertson-Walker metric are embeddable into the specified manifold.

Optimal Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving k-Modulus of Smoothness

We establish necessary and sufficient conditions for embeddings of Bessel potential spaces H σ X(IR n ) with order of smoothness σ ∈ (0, n), modelled upon rearrangement invariant Banach function spaces X(IR n ), into generalized Holder spaces (involving k-modulus of smoothness). We apply our results to the case when X(IR n ) is the Lorentz-Karamata space \(L_{p,q;b}({{\rm I\kern-.17em R}}^n)\). In particular, we are able to characterize optimal embeddings of Bessel potential spaces \(H^{\sigma}L_{p,q;b}({{\rm I\kern-.17em R}}^n)\) into generalized Holder spaces. Applications cover both superlimiting and limiting cases. We also show that our results yield new and sharp embeddings of Sobolev-Orlicz spaces W k + 1 L n/k(logL) α (IR n ) and W k L n/k(logL) α (IR n ) into generalized Holder spaces.