Revisiting perfect fluid dark matter: Observational constraints from our galaxy

We revisit certain features of an assumed spherically symmetric perfect fluid dark matter halo in the light of the observed data of our galax

On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness

In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:1208.612

On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

Improving Sequential Determinantal Point Processes for Supervised Video Summarization

It is now much easier than ever before to produce videos. While the ubiquitous video data is a great source for information discovery and extraction, the computational challenges are unparalleled. Automatically summarizing the videos has become a substantial need for browsing, searching, and indexing visual content. This paper is in the vein of supervised video summarization using sequential determinantal point process (SeqDPP), which models diversity by a probabilistic distribution. We improve this model in two folds. In terms of learning, we propose a large-margin algorithm to address the exposure bias problem in SeqDPP. In terms of modeling, we design a new probabilistic distribution such that, when it is integrated into SeqDPP, the resulting model accepts user input about the expected length of the summary. Moreover, we also significantly extend a popular video summarization dataset by 1) more egocentric videos, 2) dense user annotations, and 3) a refined evaluation scheme. We conduct extensive experiments on this dataset (about 60 hours of videos in total) and compare our approach to several competitive baselines