Science progress in the twentieth century : a quarterly journal of scientific work & thought.

v. 2 (1907-1908)

Science progress in the twentieth century : a quarterly journal of scientific work & thought.

v. 8 (1913-1914)

Science progress.

v. 12 (1917-1918)

Science progress in the twentieth century : a quarterly journal of scientific work & thought.

v. 1 (1907)

Science progress in the twentieth century : a quarterly journal of scientific work & thought.

v. 9 (1914-1915)

Science progress.

v. 13 (1918-1919)

Science progress in the twentieth century : a quarterly journal of scientific work & thought.

v. 6 (1911-1912)

Science progress in the twentieth century : a quarterly journal of scientific work & thought.

v. 7 (1912-1913)

Report on the scientific results of the voyage of H.M.S. Challenger during the years 1873-76 under the command of Captain George S. Nares ... and the late Captain Frank Tourle Thomson, R.N.

Zoology v.32=pt.80-82 (1888-1889)

Report on the scientific results of the voyage of H.M.S. Challenger during the years 1873-76 under the command of Captain George S. Nares ... and the late Captain Frank Tourle Thomson, R.N.

Zoology v.30=pt.51 (1888-1889) [Text]

Report on the scientific results of the voyage of H.M.S. Challenger during the years 1873-76 under the command of Captain George S. Nares ... and the late Captain Frank Tourle Thomson, R.N.

Zoology v.28 [pt.77]

Catalan's intervals and realizers of triangulations

The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice which is an extension of the Kreweras lattice. The Stanley order can be defined on the set of Dyck paths of size n as the relation of being above. Hence, intervals in the Stanley lattice are pairs of non-crossing Dyck paths. In a former article, the second author defined a bijection Φ between pairs of non-crossing Dyck paths and the realizers of triangulations (or Schnyder woods). We give a simpler description of the bijection Φ. Then, we study the restriction of Φ to Tamari’s and Kreweras’ intervals. We prove that Φ induces a bijection between Tamari intervals and minimal realizers. This gives a bijection between Tamari intervals and triangulations. We also prove that Φ induces a bijection between Kreweras intervals and the (unique) realizers of stack triangulations. Thus, Φ induces a bijection between Kreweras intervals and stacktriangulations which are known to be in bijection with ternary trees.

The word problem distinguishes counter languages

Counter automata are more powerful versions of finite state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Zn is accepted by a nondeterministic m-counter automaton if and only if m &= n.

Getting in touch: segregated somatosensory what and where pathways in humans revealed by electrical neuroimaging.

Whether the somatosensory system, like its visual and auditory counterparts, is comprised of parallel functional pathways for processing identity and spatial attributes (so-called what and where pathways, respectively) has hitherto been studied in humans using neuropsychological and hemodynamic methods. Here, electrical neuroimaging of somatosensory evoked potentials (SEPs) identified the spatio-temporal mechanisms subserving vibrotactile processing during two types of blocks of trials. What blocks varied stimuli in their frequency (22.5 Hz vs. 110 Hz) independently of their location (left vs. right hand). Where blocks varied the same stimuli in their location independently of their frequency. In this way, there was a 2x2 within-subjects factorial design, counterbalancing the hand stimulated (left/right) and trial type (what/where). Responses to physically identical somatosensory stimuli differed within 200 ms post-stimulus onset, which is within the same timeframe we previously identified for audition (De Santis, L., Clarke, S., Murray, M.M., 2007. Automatic and intrinsic auditory "what" and "where" processing in humans revealed by electrical neuroimaging. Cereb Cortex 17, 9-17.). Initially (100-147 ms), responses to each hand were stronger to the what than where condition in a statistically indistinguishable network within the hemisphere contralateral to the stimulated hand, arguing against hemispheric specialization as the principal basis for somatosensory what and where pathways. Later (149-189 ms) responses differed topographically, indicative of the engagement of distinct configurations of brain networks. A common topography described responses to the where condition irrespective of the hand stimulated. By contrast, different topographies accounted for the what condition and also as a function of the hand stimulated. Parallel, functionally specialized pathways are observed across sensory systems and may be indicative of a computationally advantageous organization for processing spatial and identity information.