Real-valued functions of a real variable which are continuous with respect to the density topology on both the domain and the range are called density continuous. A typical continuous function is nowhere density continuous. The same is true of a typical homeomorphism of the real line. A subset of the real line is the set of points of discontinuity of a density continuous function if and only if...

In this paper, we propose a sentence ordering algorithm using a semi-supervised sentence classification and historical ordering strategy. The classification is based on the manifold structure underlying sentences, addressing the problem of limited labeled data. The historical ordering helps to ensure topic continuity and avoid topic bias. Experiments demonstrate that the method is effective.

Summarization is the process of condensing a source text into a shorter version preserving its information content ([2]). This paper presents some original methods for text summarization by extraction of a single source document based on a particular intuition which is not explored till now: the logical structure of a text. The summarization relies on an original linear segmentation algorithm w...

We establish an integration by parts formula for the random functionals of a continuous-time Markov chain, based on partial differentiation with respect to jump times. In comparison with existing methods, our approach does not rely on the Girsanov theorem and it imposes less restrictions on the choice of directions of differentiation, while assuming additional continuity conditions on the consi...

The prediction of ground level ozone for air quality monitoring and assessment is simulated through an integrated system of gridded models (meteorological, photochemical), where the atmosphere is represented with a three-dimensional grid that may include thousands of grid cells. The continuity equation solved by the Photochemical Air Quality Model (PAQM) reproduces the atmospheric processes (dy...

This paper discusses details related to the automatic control of effects parameters. Specifically, it examines control of audio effects when synchronized with a musical piece’s rhythm. Synchronization is achieved by having control data that is periodic with the bar-length. The need for continuity in the control data is also discussed. This concept is introduced in terms of modulation techniques...

We show that the closure of compactly supported mapping class group an infinite type surface is not perfect and its abelianization contains a direct summand isomorphic to uncountable sum rationals. also extend this Torelli in case surfaces with genus indivisible copy free abelian as well. Finally we give application question automatic continuity by exhibiting discontinuous homomorphisms