Convolutional Adaptive Network for Link Prediction in Knowledge Bases

Knowledge bases (KBs) have become an integral element in digitalization strategies for intelligent engineering and manufacturing. Existing KBs consist of entities and relations and deal with issues of newly added knowledge and completeness. To predict missing information, we introduce an expressive multi-layer network link prediction framework—namely, the convolutional adaptive network (CANet)—which facilitates adaptive feature recalibration by networks to improve the method’s representational power. In CANet, each entity and relation is encoded into a low-dimensional continuous embedding space, and an interaction operation is adopted to generate multiple specific embeddings. These embeddings are concatenated into input matrices, and an attention mechanism is integrated into the convolutional operation. Finally, we use a score function to measure the likelihood of candidate information and a cross-entropy loss function to speed up computation by reducing the convolution operations. Using five real-world KBs, the experimental results indicate that the proposed method achieves state-of-the-art performance.

On the fractional p-Laplacian problems

This paper deals with nonlocal fractional p-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractional p-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next show that there exists a limit sequence of a sequence of weak solutions for finite-dimensional problems, and this limit sequence is a sequence of the solutions of our problems. We get this result by the estimate of the energy functional and the compactness property of continuous embedding inclusions between some special spaces.

Continuous embedding between P-de Branges spaces

In this paper we study the continuity of the embedding operator ℓ : ℋ p (E) ↪ ℋ q (E) when 0 < p < q ⩽ ∞. The necessary and sufficient condition has already been described in [10] if p > 1. In this work, we address the problem when p = 1, using a new approach, but asking some additional hypothesis about the Hermite-Biehler function E. We give also a different proof for the case p > 1.

Embeddings for the space on sets of finite perimeter

Given an open set with finite perimeter $\Omega \subset {\open R}^n$, we consider the space $LD_\gamma ^{p}(\Omega )$, $1\les p<\infty $, of functions with pth-integrable deformation tensor on Ω and with pth-integrable trace value on the essential boundary of Ω. We establish the continuous embedding $LD_\gamma ^{p}(\Omega )\subset L^{pN/(N-1)}(\Omega )$. The space $LD_\gamma ^{p}(\Omega )$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.

Existence of solutions for a higher order fractional boundary value problem posed on the half-line

The aim of this paper is to study the existence and uniqueness of solutions for a boundary value problem associated with a fractional nonlinear differential equation with higher order posed on the half-line. An appropriate continuous embedding for suitable Banach spaces are proved and the Minty–Browder theorem for monotone operators is used in the proof of existence of solutions for a boundary value problem of fractional order posed on the half-line.

ON TYPICALITY OF TRANSLATION FLOWS WHICH ARE DISJOINT WITH THEIR INVERSE

In this paper we prove that the set of translation structures for which the corresponding vertical translation flows are disjoint with its inverse contains a $G_{\unicode[STIX]{x1D6FF}}$-dense subset in every non-hyperelliptic connected component of the moduli space ${\mathcal{M}}$. This is in contrast to hyperelliptic case, where for every translation structure the associated vertical flow is reversible, i.e., it is isomorphic to its inverse by an involution. To prove the main result, we study limits of the off-diagonal 3-joinings of special representations of vertical translation flows. Moreover, we construct a locally defined continuous embedding of the moduli space into the space of measure-preserving flows to obtain the $G_{\unicode[STIX]{x1D6FF}}$-condition. Moreover, as a by-product we get that in every non-hyperelliptic connected component of the moduli space there is a dense subset of translation structures whose vertical flow is reversible.

Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions

In this paper, we study the dynamics and bifurcation properties of a three-parameter family of 1D Gompertz's growth functions, which are defined by the population size functions of the Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box” fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation cascades for 1D Gompertz's growth functions. Moreover, this work concerns the description of some bifurcation properties of a Hénon's map type embedding: a “continuous” embedding of 1D Gompertz's growth functions into a 2D diffeomorphism. More particularly, properties that characterize the big bang bifurcations are considered in relation with this coupling of two population size functions, varying the embedding parameter. The existence of communication areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.

Banach algebra of the Fourier multipliers on weighted Banach function spaces

Let MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w), thenMX,w(ℝ) is continuously embedded into L∞(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L∞(ℝ) is that MX,w(ℝ) is a Banach algebra.

Generalized homogeneous Besov spaces associated with the Riemann–Liouville operator

We define and study generalized homogeneous Besov spaces connected with the Riemann–Liouville operator. We establish some results of density of subspaces, completeness and continuous embedding. Also, a discrete equivalent norm is examined.