arXiv research

Sum-of-norms clustering recovers mixtures of Gaussians even with infinite samples.

With this work we try to analyse the agglomeration process in the Portuguese regions, using the New Economic Geography models. In these models the base idea is that where has increasing returns to scale in the manufactured industry and low transport costs, there is agglomeration. Of referring, as summary conclusion, th…

The aim of this paper is to analyze the processes of polarization and agglomeration, to explain the mechanisms and causes of these phenomena in order to identify similarities and differences. As the main implication of this study should be noted that both process pretend to explain the concentration of economic activit…

The aim of this paper is to analyze the relationship between inter-industry, intra-industry and inter-regional clustering and demand for labor by companies in Portugal. Is expected at the outset that there is more demand for work where the agglomeration is greater. It should be noted, as a summary conclusion, the resul…

DEFRAG accelerates extreme classification by reducing feature dimensions.

This work aims to study the Portuguese regional agglomeration process, using the linear form the New Economic Geography models that emphasize the importance of spatial factors (distance, costs of transport and communication) in explaining of the concentration of economic activity in certain locations. In a theoretical …

Newly available data on the spatial distribution of retail activities in cities makes it possible to build models formalized at the level of the single retailer. Current models tackle consumer location choices at an aggregate level and the opportunity new data offers for modeling at the retail unit level lacks a theore…

ANN clusters multi-view data by agglomerating subviews and avoiding postprocessing.

A new text clustering method using NMF and LSA improves stability and performance.

The paper explores various forms of calibration scores and their implications for fairness.

Efficiently clusters data with weak assumptions, robust to contamination.

New bounds improve linkage methods for clustering, distinguishing complete-link from single-link.

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure…

Using open source data, we observe the fascinating dynamics of nighttime light. Following a global economic regime shift, the planetary center of light can be seen moving eastwards at a pace of about 60 km per year. Introducing spatial light Gini coefficients, we find a universal pattern of human settlements across dif…

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we…

Study a simplified model of multiverse structure with synchronized timelines.

Unified method for simultaneous denoising and clustering.

Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with city size. We study scaling of per capita incomes for separate census defined incom…

With this study we want to test the validity of the well known "Verdoorn's Law" which considers the relationship between the growth of productivity and output in the case of the Portuguese economy at a regional and sectoral levels (NUTs II) for the period 1995-1999. The importance of some additional variables in the or…

It has always been a great challenge for clustering algorithms to automatically determine the cluster numbers according to the distribution of datasets. Several approaches have been proposed to address this issue, including the recent promising work which incorporate Bayesian Nonparametrics into the $k$-means clusterin…

Inverse inference, or "brain reading", is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data, based on pattern recognition and statistical learning. By predicting some cognitive variables related to brain activation maps, this approach aims at decoding brain activity. Inverse inference ta…

Spatial orderness metric improves CNN performance for non-spatial data.

With the large-scale penetration of the internet, for the first time, humanity has become linked by a single, open, communications platform. Harnessing this fact, we report insights arising from a unified internet activity and location dataset of an unparalleled scope and accuracy drawn from over a trillion (1.5$\times…

Polyhedra volume conjecture supports Stoker conjecture weakly.

Survey on two non-Kähler geometry conjectures.

Numerical study confirms Brennan's conjecture for a counterexample to Thurston's $K=2$ conjecture.

The non-vanishing conjecture implies the abundance conjecture in certain cases.

Proves Gromov's conjecture and answers Stoker's polyhedron conjecture.

This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincare Conjecture. The paper also gives two other algebraic conjectures; one is equi…

Paper discusses conjectures and proves some related inequalities.

Symmetry-breaking in three differential geometry conjectures.

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particula…

Study proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.

New proof shows most thin knots satisfy Cabling Conjecture.

We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which tog…

Metric SYZ conjecture proved using non-archimedean geometry.

Paper confirms Chen's biharmonic conjecture for hypersurfaces in 5D.

Proved Farrell-Jones conjecture for free-by-cyclic groups.

Counterexample disproves recent Penrose conjecture variant.

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

Proof outlined for 4D smooth Poincaré conjecture.

CAF-HFCM automatically forms a cluster hierarchy and optimizes the number of clusters without trial-and-validation.

This study predicts stock prices using various machine and deep learning models.

In this paper, we generalize the Cosmetic Surgery Conjecture to an $n$-cusped hyperbolic $3$-manifold and prove it under the assumption of another well-known conjecture in number theory, so called the Zilber-Pink Conjecture. For $n=1$ and $2$, we show them without the assumption.

Survey on Novikov conjecture and its applications.

Paper connects AJ conjecture and colored Jones polynomial potential function.

Akbulut and Kirby conjectured that two knots with the same $0$-surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.

Counterexample disproves conjectures about log canonical thresholds.