The Complexity of Election Problems with Group-Separable Preferences

We analyze the complexity of several NP-hard election-related problems under the assumptions that the voters have group-separable preferences. We show that under this assumption our problems typically remain NP-hard, but we provide more efficient algorithms if additionally the clone decomposition tree is of moderate height.

Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition

Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes.By building on the work of Gioan and Paul (2012) and Chauve et al.(2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding induced subgraphs in the original graph.We thus provide the grammars and full enumeration for a wide set of graph classes: ptolemaic, block, and variants of cactus graphs (2,3-cacti, 3-cacti and 4-cacti). In certain cases, no enumeration was known (ptolemaic, 4-cacti); in other cases, although the enumerations were known, an abundant potential is unlocked by the grammars we provide (in terms of asymptotic analysis, random generation, and parameter analyses, etc.).We believe this methodology here shows its potential; the natural next step to develop its reach would be to study split-decomposition trees which contain certain prime nodes. This will be the object of future work.

On Two-Sided Gamma-Positivity for Simple Permutations

Gessel conjectured that the two-sided Eulerian polynomial, recording the common distribution of the descent number of a permutation and that of its inverse, has non-negative integer coefficients when expanded in terms of the gamma basis. This conjecture has been proved recently by Lin.We conjecture that an analogous statement holds for simple permutations, and use the substitution decomposition tree of a permutation (by repeated inflation) to show that this would imply the Gessel-Lin result. We provide supporting evidence for this stronger conjecture.

MIST: A multi-resolution parcellation of functional brain networks

Functional brain connectomics investigates functional connectivity between distinct brain parcels. There is an increasing interest to investigate connectivity across several levels of spatial resolution, from networks down to localized areas. Here we present the Multiresolution Intrinsic Segmentation Template (MIST), a multi-resolution parcellation of the cortical, subcortical and cerebellar gray matter. We provide annotated functional parcellations at nine resolutions from 7 to 444 functional parcels. The MIST parcellations compare well with prior work in terms of homogeneity and generalizability. We found that parcels at higher resolutions largely fell within the boundaries of larger parcels at lower resolutions. This allowed us to provide an overlap based pseudo-hierarchical decomposition tree that relates parcels across resolutions in a meaningful way. We provide an interactive web interface to explore the MIST parcellations and also made it accessible in the neuroimaging library nilearn. We believe that the MIST parcellation will facilitate future investigations of the multiresolution basis of brain function.

The Simulation of the Psychological Impact of Computer Vision De-Noising Technology

The paper mainly discusses the analysis method for the psychological impact of computer vision noising technology. Actually, people's psychological acceptance and corresponding memory capacity of computer vision images with lots of noise are relatively poor. The de-noising process to computer vision images can improve the clarity, thus generating passive psychological impact. Therefore, the paper proposes a spatial domain filtering algorithm-based de-noising method for computer vision. It establishes wavelet packet decomposition tree for computer vision images and de-noises accordance with the decomposing results. The experiment results show that the proposed de-noising method has passive psychological influence and improves the memory capacity of computer vision images.