Structured Space-Sphere Point Processes and K-Functions

Structured Determinantal Point Processes

We present a novel probabilistic model for distributions over sets of structures— for example, sets of sequences, trees, or graphs. The critical characteristic of our model is a preference for diversity: sets containing dissimilar structures are more likely. Our model is a marriage of structured probabilistic models, like Markov random fields and context free grammars, with determinantal point ...

Random Functions and Point Processes

Tilings of space and superhomogeneous point processes.

We consider the construction of point processes from tilings, with equal-volume tiles, of d -dimensional Euclidean space R;{d} . We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are "superhomogeneous" (or "hyperuniform")-i.e., for which the structure factor S(k) vanishes when the wave vector k tends to zero. The exponent gamm...

Fixed Point Results on $b$-Metric Space via Picard Sequences and $b$-Simulation Functions

In a recent paper, Khojasteh emph{et al.} [F. Khojasteh, S. Shukla, S. Radenovi'c, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), 1189-–1194] presented a new class of simulation functions, say $mathcal{Z}$-contractions, with unifying power over known contractive conditions in the literature. Following this line of research, we extend and ...

k-DPPs: Fixed-Size Determinantal Point Processes

Determinantal point processes (DPPs) have recently been proposed as models for set selection problems where diversity is preferred. For example, they can be used to select diverse sets of sentences to form document summaries, or to find multiple nonoverlapping human poses in an image. However, DPPs conflate the modeling of two distinct characteristics: the size of the set, and its content. For ...