### A family of semitoric systems with four focus-focus singularities and two double pinched tori. (arXiv:1911.11883v1 [math.DS])

We construct a 1-parameter family $F_t=(J, H_t)_{0 \leq t \leq 1}$ of integrable systems on a compact $4$-dimensional symplectic manifold $(M, \omega)$ that changes smoothly from a toric system $F_0$ with eight elliptic-elliptic singular points via toric type systems to a semitoric system $F_t$ for $t^- < t < t^+$. These semitoric systems $F_t$…

### K-MACE and Kernel K-MACE Clustering. (arXiv:1911.11890v1 [math.ST])

Determining the correct number of clusters (CNC) is an important task in data clustering and has a critical effect on finalizing the partitioning results. K-means is one of the popular methods of clustering that requires CNC. Validity index methods use an additional optimization procedure to estimate the CNC for K-means. We propose an alternative validity…

### Singular solutions for the constant $Q-$curvature problem. (arXiv:1911.11891v1 [math.AP])

This paper is devoted to the construction of weak solutions to the singular constant $Q-$curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) $Q-$curvature.

### Smooth homotopy 4-sphere. (arXiv:1911.11904v1 [math.GT])

Every smooth homotopy 4-sphere is diffeomorphic to the 4-sphere.

### An Efficient Machine Learning-based Elderly Fall Detection Algorithm. (arXiv:1911.11976v1 [cs.LG])

Falling is a commonly occurring mishap with elderly people, which may cause serious injuries. Thus, rapid fall detection is very important in order to mitigate the severe effects of fall among the elderly people. Many fall monitoring systems based on the accelerometer have been proposed for the fall detection. However, many of them mistakenly identify…

### Benefits of Jointly Training Autoencoders: An Improved Neural Tangent Kernel Analysis. (arXiv:1911.11983v1 [cs.LG])

A remarkable recent discovery in machine learning has been that deep neural networks can achieve impressive performance (in terms of both lower training error and higher generalization capacity) in the regime where they are massively over-parameterized. Consequently, over the last several months, the community has devoted growing interest in analyzing optimization and generalization properties of…

### SAG-VAE: End-to-end Joint Inference of Data Representations and Feature Relations. (arXiv:1911.11984v1 [cs.LG])

Variational Autoencoders (VAEs) are powerful in data representation inference, but it cannot learn relations between features with its vanilla form and common variations. The ability to capture relations within data can provide the much needed inductive bias necessary for building more robust Machine Learning algorithms with more interpretable results. In this paper, inspired by recent…

### GRIm-RePR: Prioritising Generating Important Features for Pseudo-Rehearsal. (arXiv:1911.11988v1 [cs.LG])

Pseudo-rehearsal allows neural networks to learn a sequence of tasks without forgetting how to perform in earlier tasks. Preventing forgetting is achieved by introducing a generative network which can produce data from previously seen tasks so that it can be rehearsed along side learning the new task. This has been found to be effective in…

### Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions. (arXiv:1911.11992v1 [math.FA])

Composition operators have been extensively studied in complex analysis, and recently, they have been utilized in engineering and machine learning. Here, we focus on composition operators associated with maps in Euclidean spaces that are on reproducing kernel Hilbert spaces with respect to analytic positive definite functions, and prove the maps are affine if the composition…

### A race-DC in Big Data. (arXiv:1911.11993v1 [stat.ME])

The strategy of divide-and-combine (DC) has been widely used in the area of big data. Bias-correction is crucial in the DC procedure for validly aggregating the locally biased estimators, especial for the case when the number of batches of data is large. This paper establishes a race-DC through a residual-adjustment composition estimate (race). The race-DC…