Locke’s conjecture (L) states that the binary hypercube Qn with k deleted vertices of each parity is Hamiltonian if n ≥ k + 2. In 2003, S. C. Locke and R. Stong published in The American Mathematical Monthly a proof of (L) for the case k = 1. In 2007, in the paper Path coverings with prescribed ends in faulty hypercubes the authors proved (L) for every k ≤ 4 and formulated the following conject...

Brief radiant laser pulses can be used to activate cutaneous Adelta and C nociceptors selectively and elicit a number of transient brain responses in the ongoing EEG (N1, N2 and P2 waves of laser-evoked brain potentials, LEPs). Despite its physiological and clinical relevance, the early-latency N1 wave of LEPs is often difficult to measure reliably, because of its small signal-to-noise ratio (S...

BACKGROUND The amplitude of the auditory evoked N1 component that can be derived from noninvasive electroencephalographic recordings increases as a function of time between subsequent tones. N1 amplitudes in individuals with schizophrenia saturate at a lower asymptote, thus giving rise to a reduced dynamic range. Reduced N1 dynamic range is a putative electrophysiological biomarker of altered s...

OBJECTIVE Complete resection is the therapy of choice in non-small-cell lung cancer (NSCLC). There is no agreement on the type of resection, especially when interlobar N1 disease is present. The present study explored the effect of the type of resection on survival in the presence of N1 disease. METHOD Medical records of 195 patients with NSCLC who underwent resection between 1998 and 2006 an...

Age significantly influences the detection thresholds to noxious heat; such thresholds depend on responses in the cerebral cortex to thermal stimuli and the psychophysical perception of such responses. To understand the influence of age on cerebral responses, we used contact heat-evoked potentials (CHEPs) to investigate the physiology of cerebral responses to thermal stimuli in 70 healthy subje...

Many previous studies have demonstrated that the visual N1 component is larger for attended-location stimuli than for unattended-location stimuli. This difference is observed typically only for tasks involving a discrimination of the attended-location stimuli, suggesting that the N1 wave reflects a discrimination process that is applied to the attended location. The present study tested this hy...

The N1 auditory event-related potential (ERP) is reduced in chronic schizophrenia, as is the P2 to attended tones. N1 reduction may be endophenotypic for schizophrenia, being reduced in twins of schizophrenic patients and showing heritability. Results in family members, however, are equivocal, with abnormally small N1 (consistent with an endophenotype) and abnormally large N1 (inconsistent with...

Let Qn,d denote the random combinatorial matrix whose rows are independent of one another and such that each row is sampled uniformly at from subset vectors in {0,1}n having precisely d entries equal to 1. We present a short proof fact P[det?(Qn,d)=0]=O(n1/2log3/2?nd)=o(1), whenever ?(n1/2log3/2?n)=d?n/2. In particular, our accommodates sparse matrices sense d=o(n) allowed. also consider singul...