Searcharxiv⌕ Search

arXiv subjects

Nan Gao

Publications and source records attributed to Nan Gao.

62 records · Page 4Linked to original sources

Cutting the Unnecessary Long Tail: Cost-Effective Big Data Clustering in the Cloud

Clustering big data often requires tremendous computational resources where cloud computing is undoubtedly one of the promising solutions. However, the computation cost in the cloud can be unexpectedly high if it cannot be managed properly. The long tail phenomenon has been observed widely in the big data clustering area, which indicates that the majority of time is often consumed in the middle to late stages in the clustering process. In this research, we try to cut the unnecessary long tail in the clustering process to achieve a sufficiently satisfactory accuracy at the lowest possible computation cost. A novel approach is proposed to achieve cost-effective big data clustering in the cloud. By training the regression model with the sampling data, we can make widely used k-means and EM (Expectation-Maximization) algorithms stop automatically at an early point when the desired accuracy is obtained. Experiments are conducted on four popular data sets and the results demonstrate that both k-means and EM algorithms can achieve high cost-effectiveness in the cloud with our proposed approach. For example, in the case studies with the much more efficient k-means algorithm, we find that achieving a 99% accuracy needs only 47.71%-71.14% of the computation cost required for achieving a 100% accuracy while the less efficient EM algorithm needs 16.69%-32.04% of the computation cost. To put that into perspective, in the United States land use classification example, our approach can save up to $94,687.49 for the government in each use.

cs.DC↗

Predicting Personality Traits from Physical Activity Intensity

Call and messaging logs from mobile devices have been used to predict human personality traits successfully in recent years. However, the widely available accelerometer data is not yet utilized for this purpose. In this research, we explored some important features describing human physical activity intensity, used for the very first time to predict human personality traits through raw accelerometer data. Using a set of newly introduced metrics, we combined physical activity intensity features with traditional phone activity features for personality prediction. The experiment results show that the predicted personality scores are closer to the ground truth, with observable reduction of errors in predicting the Big-5 personality traits across male and female.

cs.HC↗

Recollements of abelian categories and ideals in heredity chains - a recursive approach to quasi-hereditary algebras

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity chains, which in turn characterises quasi-hereditary algebras recursively. Further applications are given to hereditary algebras and to Morita context rings.

math.RT↗

Ladders of compactly generated triangulated categories and preprojective algebras

In this paper we characterize when a recollement of compactly generated triangulated categories admits a ladder of some height going either upwards or downwards. As an application, we show that the derived category of the preprojective algebra of Dynkin type $\mathbb{A}_n$ admits a periodic infinite ladder, where the one outer term in the recollement is the derived category of a differential graded algebra.

math.RT↗

Ladders of recollements, categories of monomorphisms and singularity categories

In this paper we show that the (un)bounded derived categories$\colon$(i) of the monomorphism category, (ii) of the morphism category and (iii) of the double morphism category, admit a periodic infinite ladder of recollements. These results are based on a characterization that we provide for a recollement of (compactly generated) triangulated categories to admit a ladder of some height going either upwards or downwards. Moreover, we introduce and study the singularity category of the monomorphism category over an Artin algebra $Λ$ and show that there is a periodic infinite ladder that connects this triangulated category with the standard singularity category of $Λ$. We also provide sufficient conditions for the monomorphism categories of two algebras to be singularly equivalent. The last aim of this paper is to study monomorphisms where the domain has finite projective dimension. We show that the latter category is a Gorenstein subcategory of the monomorphism category when $Λ$ is a Gorenstein Artin algebra. Finally, we consider the category of coherent functors over the stable category of this Gorenstein subcategory, and show that it carries a structure of a Gorenstein abelian category.

math.RT↗

Gorenstein homological aspects of monomorphism categories via Morita rings

For any ring R the category of monomorphisms is a full subcategory of the morphsim category over R, where the latter is equivalent to the module category of the triangular matrix ring with entries the ring R. In this work, we consider the monomorphism category as a full subcategory of the module category over the Morita ring with all entries the ring R and zero bimodule homomorphisms. This approach provides an interesting link between Morita rings and monomorphism categories. The aim of this paper is two-fold. First, we construct Gorenstein-projective modules over Morita rings with zero bimodule homomorphisms and we provide sufficient conditions for such rings to be Gorenstein Artin algebras. This is the first part of our work which is strongly connected with monomorphism categories. In the second part, we investigate monomorphisms where the domain has finite projective dimension. In particular, we show that the latter category is a Gorenstein subcategory of the monomorphism category over a Gorenstein algebra. Finally, we consider the category of coherent functors over the stable category of this Gorenstein subcategory and show that it carries a structure of a Gorenstein abelian category.

math.RT↗

Gorensteinness, homological invariants and Gorenstein derived categories

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra $A$ and invariants with respect to recollements of the bounded Gorenstein derived category $D^{b}_{gp}(A\mbox{-}{\rm mod})$ of $A$ are investigated. Specifically, the Gorensteinness of $A$ is characterized in three ways: the existence of Auslander-Reiten triangles in $D^{b}_{gp}(A\mbox{-}{\rm mod})$; recollements of $D^{b}_{gp}(A\mbox{-}{\rm mod})$; and also Gorenstein derived equivalences. It is shown that the finiteness of Cohen-Macaulay type and of finitistic dimension are invariant with respect to the recollements of $D^{b}_{gp}(A\mbox{-}{\rm mod})$.

math.RT↗

On homotopy categories of Gorenstein modules: compact generation and dimensions

Let $A$ be a virtually Gorenstein algebra of finite CM-type. We establish a duality between the subcategory of compact objects in the homotopy category of Gorenstein projective left $A$-modules and the bounded Gorenstein derived category of finitely generated right $A$-modules. Let $R$ be a two-sided noetherian ring such that the subcategory of Gorenstein flat modules $R\mbox{-}\mathcal{GF}$ is closed under direct products. We show that the inclusion $K(R\mbox{-}\mathcal{GF})\to K(R\mbox{-}{\rm Mod})$ of homotopy categories admits a right adjoint. We introduce the notion of Gorenstein representation dimension for an algebra of finite CM-type, and establish relations among the dimension of its relative Auslander algebra, Gorenstein representation dimension, the dimension of the bounded Gorenstein derived category, and the dimension of the bounded homotopy category of its Gorenstein projective modules.

math.RT↗