Computing Optimal Morse Matchings

Morse matchings capture the essential structural information of discrete Morse functions. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present polyhedral results for the corresponding polytope and report on computational results

The human and mammalian cerebrum scale by computational power and information resistance

The cerebrum of mammals spans a vast range of sizes and yet has a very regular structure. The amount of folding of the cortical surface and the proportion of white matter gradually increase with size, but the underlying mechanisms remain elusive. Here, two laws are derived to fully explain these cerebral scaling relations. The first law holds that the long-range information flow in the cerebrum is determined by the total cortical surface (i.e., the number of neurons) and the increasing information resistance of long-range connections. Despite having just one free parameter, the first law fits the mammalian cerebrum better than any existing function, both across species and within humans. According to the second law, the white matter volume scales, with a few minor corrections, to the cortical surface area. It follows from the first law that large cerebrums have much local processing and little global information flow. Moreover, paradoxically, a further increase in long-range connections would decrease the efficiency of information flow.Comment: 15 pages, 2 figures; 3 supplement

The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing

This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several such conditions have been introduced. The most well-known ones are the mutual coherence, the restricted isometry property (RIP), and the nullspace property (NSP). While evaluating the mutual coherence of a given matrix is easy, it has been suspected for some time that evaluating RIP and NSP is computationally intractable in general. We confirm these conjectures by showing that for a given matrix A and positive integer k, computing the best constants for which the RIP or NSP hold is, in general, NP-hard. These results are based on the fact that determining the spark of a matrix is NP-hard, which is also established in this paper. Furthermore, we also give several complexity statements about problems related to the above concepts.Comment: 13 pages; accepted for publication in IEEE Trans. Inf. Theor

The use of drug calendars for the diagnosis of cutaneous drug eruptions in the age of electronic medical records

A morbilliform drug eruption is the most common condition leading to a dermatology consultation for a patient in the hospital. Timing is an important diagnostic tool since the onset of a skin rash usually takes place within days-to-weeks of the start of the implicated drug. A comprehensive, thorough, and reliable drug history by the clinician is essential. Therefore, to assist in the task of determining the causative medication of a new skin rash in a hospitalized patient, the creation of a drug calendar is recommended. The development of an electronic version of the drug calendar offers several benefits over the manual version. As the use of electronic medical records continues to become the standard in medicine, the electronic drug calendar will serve as an invaluable tool for the diagnosis of drug hypersensitivity

Effects of Aprons on Pitfall Trap Catches of Carabid Beetles in Forests and Fields

This study compared the efficacy of three types of pitfall traps in four forest and two field habitats. Two traps had aprons and one did not. The two apron traps were the same except for a gap between the trap and the plywood-apron, allowing captures from above or below. Traps were placed in a split-plot design and had three replicates of the three trap types per habitat. The traps were emptied each week from May to September. ANOVA\u27s were performed on 12 trapped species separately over habitats, weeks, and the in- teractions between them. The nonapron trap captured over 40% more individuals than either apron trap, though apron traps tended to be more effective in fields for species found in both habitats. Habitat-trap interactions were only significant in two species. Trap-week interactions were significant in four species

Higgs couplings in a model with triplets

We study the couplings of a CP-even neutral Higgs boson h in a model containing one scalar SU(2)_L doublet, one real triplet, and one complex triplet with hypercharge 1. Because the two triplets contribute to the rho parameter with opposite signs, the triplet vacuum expectation values can be sizable. We show that (i) the hWW and hZZ couplings can be larger than the corresponding values in the Standard Model, and (ii) the ratio of the WW and ZZ couplings of h can be different than the corresponding ratio in the Standard Model. Neither of these results can occur in models containing only Higgs doublets. We also compute the rates for gg --> h --> WW and gg --> h --> ZZ and find that, for reasonable parameter values and M_h ~ 140-180 GeV, the hadron collider rate for gg --> h --> WW (ZZ) can be up to 20% (5 times) larger than in the Standard Model. We discuss implications for Higgs coupling extraction at the LHC.Comment: 21 pages, 9 figures. v2: typo fixed in Eq. 24, minor improvements to text, accepted by PR

Enhanced visualisation of dance performance from automatically synchronised multimodal recordings

The Huawei/3DLife Grand Challenge Dataset provides multimodal recordings of Salsa dancing, consisting of audiovisual streams along with depth maps and inertial measurements. In this paper, we propose a system for augmented reality-based evaluations of Salsa dancer performances. An essential step for such a system is the automatic temporal synchronisation of the multiple modalities captured from different sensors, for which we propose efficient solutions. Furthermore, we contribute modules for the automatic analysis of dance performances and present an original software application, specifically designed for the evaluation scenario considered, which enables an enhanced dance visualisation experience, through the augmentation of the original media with the results of our automatic analyses