AutoSVD++: An Efficient Hybrid Collaborative Filtering Model via Contractive Auto-encoders

Collaborative filtering (CF) has been successfully used to provide users with personalized products and services. However, dealing with the increasing sparseness of user-item matrix still remains a challenge. To tackle such issue, hybrid CF such as combining with content based filtering and leveraging side information of users and items has been extensively studied to enhance performance. However, most of these approaches depend on hand-crafted feature engineering, which are usually noise-prone and biased by different feature extraction and selection schemes. In this paper, we propose a new hybrid model by generalizing contractive auto-encoder paradigm into matrix factorization framework with good scalability and computational efficiency, which jointly model content information as representations of effectiveness and compactness, and leverage implicit user feedback to make accurate recommendations. Extensive experiments conducted over three large scale real datasets indicate the proposed approach outperforms the compared methods for item recommendation.Comment: 4 pages, 3 figure

Quantitative Volume Space Form Rigidity Under Lower Ricci Curvature Bound

Let $M$ be a compact $n$-manifold of $\operatorname{Ric}_M\ge (n-1)H$ ($H$ is a constant). We are concerned with the following space form rigidity: $M$ is isometric to a space form of constant curvature $H$ under either of the following conditions: (i) There is $\rho>0$ such that for any $x\in M$, the open $\rho$-ball at $x^*$ in the (local) Riemannian universal covering space, $(U^*_\rho,x^*)\to (B_\rho(x),x)$, has the maximal volume i.e., the volume of a $\rho$-ball in the simply connected $n$-space form of curvature $H$. (ii) For $H=-1$, the volume entropy of $M$ is maximal i.e. $n-1$ ([LW1]). The main results of this paper are quantitative space form rigidity i.e., statements that $M$ is diffeomorphic and close in the Gromov-Hausdorff topology to a space form of constant curvature $H$, if $M$ almost satisfies, under some additional condition, the above maximal volume condition. For $H=1$, the quantitative spherical space form rigidity improves and generalizes the diffeomorphic sphere theorem in [CC2].Comment: The only change from the early version is an improvement on Theorem A: we replace the non-collapsing condition on $M$ by on $\tilde M$ (the Riemannian universal cover), and the corresponding modification is adding "subsection c" in Section

Two Rules on the Protein-Ligand Interaction

So far, we still lack a clear molecular mechanism to explain the protein-ligand interaction on the basis of electronic structure of a protein. By combining the calculation of the full electronic structure of a protein along with its hydrophobic pocket and the perturbation theory, we found out two rules on the protein-ligand interaction. One rule is the interaction only occurs between the lowest unoccupied molecular orbitals (LUMOs) of a protein and the highest occupied molecular orbital (HOMO) of its ligand, not between the HOMOs of a protein and the LUMO of its ligand. The other rule is only those residues or atoms located both on the LUMOs of a protein and in a surface pocket of a protein are activity residues or activity atoms of the protein and the corresponding pocket is the ligand binding site. These two rules are derived from the characteristics of energy levels of a protein and might be an important criterion of drug design

Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound

The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $n$-manifold with a negative lower Ricci curvature bound and a upper diameter bound, it was known that it admits an almost maximal volume entropy if and only if it is diffeomorphic and Gromov-Hausdorff close to a hyperbolic space form. We prove the quantitative rigidity of almost maximal volume entropy for $\operatorname{RCD}$-spaces with a negative lower Ricci curvature bound and Riemannian manifolds with a negative $L^p$-integral Ricci curvature lower bound.Comment: 21 page

Therapeutic efficacy of a combination of mesalazine and Bifid Triple Viable Capsules (BTVCs) on ulcerative colitis patients, and its effect on inflammation and oxidative stress

Purpose: To determine the curative impact of mesalazine (MSZ)-BTVCs combination on ulcerative colitis (UC), and its influence on inflammation and oxidative stress in the patients.Methods: 100 UC patients were randomely assigned to a control group given MSZ capsule treatment only, and a combination group treated with BTVCs and MSZ. Treatment effectiveness, inflammatory response, and oxidative stress in the two groups before and after treatment were compared.Results: The combination group had higher total effectiveness than the control group. The serum levels of MDA, high-sensitivity C-reactive protein (hs-CRP), TNF-α and interleukin-6 (IL-6) were lower, while serum levels of superoxide dismutase (SOD) and interleukin-10 (IL-10) were markedly increased in patients given combination treatment, when compared with controls. Pre-drug exposure UC disease activity index (UC-DAI) and clinical symptom scores were similar in both cohorts of patients, but the post-treatment scores were statistically decreased, especially in the combination group.Conclusion: The combined use of MSZ and BTVCs was more effective against UC than monotherapy, as it effectively relieved inflammation and oxidative stress in patients, resulting in better clinical efficacy

Well-posedness of the martingale problem for super-Brownian motion with interactive branching

In this paper a martingale problem for super-Brownian motion with interactive branching is derived. The uniqueness of the solution to the martingale problem is obtained by using the pathwise uniqueness of the solution to a corresponding system of SPDEs with proper boundary conditions. The existence of the solution to the martingale problem and the local H\"{o}lder continuity of the density process are also studied

A Geometric Approach to the Modified Milnor Problem

The Milnor Problem (modified) in the theory of group growth asks whether any finite presented group of vanishing algebraic entropy has at most polynomial growth. We show that a positive answer to the Milnor Problem (modified) is equivalent to the Nilpotency Conjecture in Riemannian geometry: given $n, d>0$, there exists a constant $\epsilon(n,d)>0$ such that if a compact Riemannian $n$-manifold $M$ satisfies that Ricci curvature \op{Ric}_M\ge -(n-1), diameter d\ge \op{diam}(M) and volume entropy $h(M)<\epsilon(n,d)$, then the fundamental group $\pi_1(M)$ is virtually nilpotent. We will verify the Nilpotency Conjecture in some cases, and we will verify the vanishing gap phenomena for more cases i.e., if $h(M)<\epsilon(n,d)$, then $h(M)=0$.Comment: 25 page