Linear Time LexDFS on Cocomparability Graphs

Lexicographic depth first search (LexDFS) is a graph search protocol which has already proved to be a powerful tool on cocomparability graphs. Cocomparability graphs have been well studied by investigating their complements (comparability graphs) and their corresponding posets. Recently however LexDFS has led to a number of elegant polynomial and near linear time algorithms on cocomparability graphs when used as a preprocessing step [2, 3, 11]. The nonlinear runtime of some of these results is a consequence of complexity of this preprocessing step. We present the first linear time algorithm to compute a LexDFS cocomparability ordering, therefore answering a problem raised in [2] and helping achieve the first linear time algorithms for the minimum path cover problem, and thus the Hamilton path problem, the maximum independent set problem and the minimum clique cover for this graph family

A Characterization of Mixed Unit Interval Graphs

We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves a problem posed by Dourado, Le, Protti, Rautenbach and Szwarcfiter (Mixed unit interval graphs, Discrete Math. 312, 3357-3363 (2012)).Comment: 17 pages, referees' comments adde

Transcranial magnetic stimulation of the prefrontal cortex in awake nonhuman primates evokes a polysynaptic neck muscle response that reflects oculomotor activity at the time of stimulation.

Transcranial magnetic stimulation (TMS) has emerged as an important technique in cognitive neuroscience, permitting causal inferences about the contribution of a given brain area to behavior. Despite widespread use, exactly how TMS influences neural activity throughout an interconnected network, and how such influences ultimately change behavior, remain unclear. The oculomotor system of nonhuman primates (NHPs) offers a potential animal model to bridge this gap. Here, based on results suggesting that neck muscle activity provides a sensitive indicator of oculomotor activation, we show that single pulses of TMS over the frontal eye fields (FEFs) in awake NHPs evoked rapid (within ∼25 ms) and fairly consistent (∼50-75% of all trials) expression of a contralateral head-turning synergy. This neck muscle response resembled that evoked by subsaccadic electrical microstimulation of the FEF. Systematic variation in TMS location revealed that this response could also be evoked from the dorsolateral prefrontal cortex (dlPFC). Combining TMS with an oculomotor task revealed state dependency, with TMS evoking larger neck muscle responses when the stimulated area was actively engaged. Together, these results advance the suitability of the NHP oculomotor system as an animal model for TMS. The polysynaptic neck muscle response evoked by TMS of the prefrontal cortex is a quantifiable trial-by-trial reflection of oculomotor activation, comparable to the monosynaptic motor-evoked potential evoked by TMS of primary motor cortex. Our results also speak to a role for both the FEF and dlPFC in head orienting, presumably via subcortical connections with the superior colliculus

Overt responses during covert orienting.

A distributed network of cortical and subcortical brain areas controls our oculomotor behavior. This network includes the superior colliculus (SC), which coordinates an ancient visual grasp reflex via outputs that ramify widely within the brainstem and spinal cord, accessing saccadic and other premotor and autonomic circuits. In this Review, we discuss recent results correlating subliminal SC activity in the absence of saccades with diverse components of the visual grasp reflex, including neck and limb muscle recruitment, pupil dilation, and microsaccade propensity. Such subtle manifestations of covert orienting are accessible in the motor periphery and may provide the next generation of oculomotor biomarkers in health and disease

Transient Pupil Dilation after Subsaccadic Microstimulation of Primate Frontal Eye Fields.

UNLABELLED: Pupillometry provides a simple and noninvasive index for a variety of cognitive processes, including perception, attention, task consolidation, learning, and memory. The neural substrates by which such cognitive processes influence pupil diameter remain somewhat unclear, although cortical inputs to the locus coeruleus mediating arousal are likely involved. Changes in pupil diameter also accompany covert orienting; hence the oculomotor system may provide an alternative substrate for cognitive influences on pupil diameter. Here, we show that low-level electrical microstimulation of the primate frontal eye fields (FEFs), a cortical component of the oculomotor system strongly connected to the intermediate layers of the superior colliculus (SCi), evoked robust pupil dilation even in the absence of evoked saccades. The magnitude of such dilation scaled with increases in stimulation parameters, depending strongly on the intensity and number of pulses. Although there are multiple pathways by which FEF stimulation could cause pupil dilation, the timing and profile of dilation closely resembled that evoked by SCi stimulation. Moreover, pupil dilation evoked from the FEFs increased when presumed oculomotor activity was higher at the time of stimulation. Our findings implicate the oculomotor system as a potential substrate for how cognitive processes can influence pupil diameter. We suggest that a pathway from the frontal cortex through the SCi operates in parallel with frontal inputs to arousal circuits to regulate task-dependent modulation of pupil diameter, perhaps indicative of an organization wherein one pathway assumes primacy for a given cognitive process. SIGNIFICANCE STATEMENT: Pupillometry (the measurement of pupil diameter) provides a simple and noninvasive index for a variety of cognitive processes, offering a biomarker that has value in both health and disease. But how do cognitive processes influence pupil diameter? Here, we show that low-level stimulation of the primate frontal eye fields can induce robust pupil dilation without saccades. Pupil dilation scaled with the number and intensity of stimulation pulses and varied with endogenous oculomotor activity at the time of stimulation. The oculomotor system therefore provides a plausible pathway by which cognitive processes may influence pupil diameter, perhaps operating in conjunction with systems regulating arousal

Dorsal Neck Muscle Vibration Induces Upward Shifts in the Endpoints of Memory-Guided Saccades in Monkeys

Producing a movement in response to a sensory stimulus requires knowledge of the body's current configuration, and spindle organs embedded within muscles are a primary source of such kinesthetic information. Here, we sought to develop an animal model of kinesthetic illusions induced by mechanically vibrating muscles as a first step toward a mechanistic understanding of how kinesthesia is integrated into neural plans for action. We elected to examine the effects of mechanical vibration of dorsal neck muscles in head-restrained monkeys performing memory-guided saccades requiring them to look to the remembered location of a flashed target only after an imposed delay. During the delay on one-half of all trials, mechanical vibration (usually 1,500 ms in duration, 200 μm in amplitude, 100 Hz in frequency) was applied to the dorsal aspect on one side of the monkey's neck. We compared the metrics of such vibration saccades to control saccades without vibration during the delay interval. Relative to control saccades, the endpoints of vibration saccades were shifted consistently upward, even though the variability in saccadic endpoints was unaltered. Although the stability of the eye was compromised during the delay interval of vibration trials, as evidenced by an increased incidence of upward drifts and downward microsaccades, vibration saccades displayed different metrics than control saccades, including an upwardly deviated radial direction and increased vertical amplitude. The influence of variations in the duration (500–2,500 ms), amplitude (100–300 μm), or frequency (75–125 Hz) of vibration scaled well with the presumed change in spindle activity entrained by vibration. Comparisons of the profile of these results are made to the human literature. We conclude that neck muscle vibration induces alterations in oculomotor performance in monkeys consistent with a central interpretation of illusory neck flexion and downward gaze deviation due to increased activation in the spindles of neck extensor muscles

On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions

Symbolic ultrametrics define edge-colored complete graphs K_n and yield a simple tree representation of K_n. We discuss, under which conditions this idea can be generalized to find a symbolic ultrametric that, in addition, distinguishes between edges and non-edges of arbitrary graphs G=(V,E) and thus, yielding a simple tree representation of G. We prove that such a symbolic ultrametric can only be defined for G if and only if G is a so-called cograph. A cograph is uniquely determined by a so-called cotree. As not all graphs are cographs, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of G. The latter problem is equivalent to find an optimal cograph edge k-decomposition {E_1,...,E_k} of E so that each subgraph (V,E_i) of G is a cograph. An upper bound for the integer k is derived and it is shown that determining whether a graph has a cograph 2-decomposition, resp., 2-partition is NP-complete

Dynamic and opposing adjustment of movement cancellation and generation in an oculomotor countermanding task.

Adaptive adjustments of strategies help optimize behavior in a dynamic and uncertain world. Previous studies in the countermanding (or stop-signal) paradigm have detailed how reaction times (RTs) change with trial sequence, demonstrating adaptive control of movement generation. Comparatively little is known about the adaptive control of movement cancellation in the countermanding task, mainly because movement cancellation implies the absence of an outcome and estimates of movement cancellation require hundreds of trials. Here, we exploit a within-trial proxy of movement cancellation based on recordings of neck muscle activity while human subjects attempted to cancel large eye-head gaze shifts. On a subset of successfully cancelled trials where gaze remains stable, small head-only movements to the target are actively braked by a pulse of antagonist neck muscle activity. The timing of such antagonist muscle recruitment relative to the stop signal, termed the antagonist latency, tended to decrease or increase after trials with or without a stop-signal, respectively. Over multiple time scales, fluctuations in the antagonist latency tended to be the mirror opposite of those occurring contemporaneously with RTs. These results provide new insights into the adaptive control of movement cancellation at an unprecedented resolution, suggesting it can be as prone to dynamic adjustment as movement generation. Adaptive control in the countermanding task appears to be governed by a dynamic balance between movement cancellation and generation: shifting the balance in favor of movement cancellation slows movement generation, whereas shifting the balance in favor of movement generation slows movement cancellation

Rainbow domination and related problems on some classes of perfect graphs

Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$. The rainbow domination number $\gamma_{kr}(G)$ is the minimum of $\sum_{x \in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs