•The additive coloring conjecture is proved for split graphs.•Exact formulas for computing the additive chromatic number on several graphs are presented.•A tool is proposed for checking the ...conjecture over all connected graphs up to 10 vertices.
The Additive Coloring Problem is a variation of the Coloring Problem where labels of {1,…,k} are assigned to the vertices of a graph G so that the sum of labels over the neighborhood of each vertex is a proper coloring of G. The least value k for which G admits such labeling is called additive chromatic number of G. This problem was first presented by Czerwiński, Grytczuk and Żelazny who also proposed a conjecture that for every graph G, the additive chromatic number never exceeds the classic chromatic number. Up to date, the conjecture has been proved for complete graphs, trees, non-3-colorable planar graphs with girth at least 13 and non-bipartite planar graphs with girth at least 26. In this work, we show that the conjecture holds for split graphs. We also present exact formulas for computing the additive chromatic number for some subfamilies of split graphs (complete split, headless spiders and complete sun), regular bipartite, complete multipartite, fan, windmill, circuit, wheel, cycle sun and wheel sun.
In this work, we present a branch-and-price algorithm to solve the weighted version of the List Coloring Problem, based on a vertex cover formulation by stable sets. This problem is interesting for ...its applications and also for the many other problems that it generalizes, including the well-known Graph Coloring Problem. With the introduction of the concept of indistinguishable colors, some theoretical results are presented which are later incorporated into the algorithm. We propose two branching strategies based on others for the Graph Coloring Problem, the first is an adaptation of the one used by Mehrotra and Trick in their pioneering branch-and-price algorithm and the other is inspired by the one used by Méndez-Díaz and Zabala in their branch-and-cut algorithm. The rich structure of this problem makes both branching strategies robust. Extensive computation experimentation on a wide variety of instances shows the effectiveness of this approach and evidences the different behaviors that the algorithm can have according to the structure of each type of instance.
•Branch-and-price algorithm for weighted list coloring problem; exact resolution.•List coloring problem generalizes many graph coloring and set covering problems.•List coloring solves graph vertex coloring, mu-coloring, precoloring extension.•Indistinguishable colors cut symmetric solutions in the ILP formulation.•Experimentation with branching strategies on random and benchmark instances.
Light exerts a range of powerful biological effects beyond image vision, including mood and learning regulation. While the source of photic information affecting mood and cognitive functions is well ...established, viz. intrinsically photosensitive retinal ganglion cells (ipRGCs), the central mediators are unknown. Here, we reveal that the direct effects of light on learning and mood utilize distinct ipRGC output streams. ipRGCs that project to the suprachiasmatic nucleus (SCN) mediate the effects of light on learning, independently of the SCN’s pacemaker function. Mood regulation by light, on the other hand, requires an SCN-independent pathway linking ipRGCs to a previously unrecognized thalamic region, termed perihabenular nucleus (PHb). The PHb is integrated in a distinctive circuitry with mood-regulating centers and is both necessary and sufficient for driving the effects of light on affective behavior. Together, these results provide new insights into the neural basis required for light to influence mood and learning.
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•Distinct ipRGC subpopulations drive the effects of light on learning and mood•SCN-projecting ipRGCs affect learning without disrupting the central pacemaker•The ipRGC-PHb pathway drives the light-mediated mood alterations•Thalamic PHb is integrated in a distinctive circuitry with mood-regulating centers
The effects of light on learning and mood via intrinsically photosensitive retinal ganglion cells involve a pacemaker-independent role for the suprachiasmatic nucleus as well as distinct circuitry in a region of the thalamus called the perihabenular nucleus.
A legal dominating sequence of a graph is an ordered dominating set of vertices where each element dominates at least another one not dominated by its predecessors in the sequence. The length of a ...largest legal dominating sequence is called Grundy domination number. In this work, we introduce a generalized version of the Grundy domination problem. We explicitly calculate the corresponding parameter for paths and web graphs. We propose integer programming formulations for the new problem, find families of valid inequalities and perform extensive computational experiments to compare the formulations as well as to test these inequalities as cuts in a branch-and-cut framework. We also design and evaluate the performance of a heuristic for finding good initial lower and upper bounds and a tabu search that improves the initial lower bound. The test instances include randomly generated graphs, structured graphs, classical benchmark instances and two instances from a real application. Our approach is exact for graphs with 20–50 vertices and provides good solutions for graphs up to 10000 vertices.
A balance between synaptic excitation and inhibition (E/I balance) maintained within a narrow window is widely regarded to be crucial for cortical processing. In line with this idea, the E/I balance ...is reportedly comparable across neighboring neurons, behavioral states, and developmental stages and altered in many neurological disorders. Motivated by these ideas, we examined whether synaptic inhibition changes over the 24-h day to compensate for the well-documented sleep-dependent changes in synaptic excitation. We found that, in pyramidal cells of visual and prefrontal cortices and hippocampal CA1, synaptic inhibition also changes over the 24-h light/dark cycle but, surprisingly, in the opposite direction of synaptic excitation. Inhibition is upregulated in the visual cortex during the light phase in a sleep-dependent manner. In the visual cortex, these changes in the E/I balance occurred in feedback, but not feedforward, circuits. These observations open new and interesting questions on the function and regulation of the E/I balance.
•The excitation/inhibition (E/I) ratio is dynamic across the 24-h day•Fluctuations in the E/I ratio depend on sleep/wake history•E/I ratio changes are circuit specific, not uniform across all synapses
Bridi et al. investigate whether inhibition tracks known changes in excitation over the 24-h day to maintain a stable excitation/inhibition ratio. Surprisingly, the excitation/inhibition ratio is dynamic over the day in feedback, but not feedforward, visual cortical circuits.
A simultaneous vehicle routing and crew scheduling problem (SVRCSP) consists of planning routes for a fleet of vehicles and scheduling their crews, with the particularity that the vehicle–crew ...correspondence is not fixed through time. This allows a greater planning flexibility and a more efficient use of the fleet, but in counterpart it requires high synchronization. In this work, an SVRCSP is presented, where long‐distance pickup‐and‐delivery requests must be fulfilled over a multiday planning horizon, subject to several constraints such as multiple time windows, hour of services regulation, among others. Crews can be composed of one or two drivers and any of them can be relieved in a given set of locations. Also, they are allowed to travel between locations with noncompany shuttles. The objective is to minimize the cost of travel in company and noncompany vehicles, which depends on the distance, and the penalization for completing requests with delay. A two‐stage sequential approach is applied: a set of truck routes is computed in the first stage and a set of driver routes consistent with the previous routes is obtained in the second stage. An algorithm based on the GRASP × ILS metaheuristic, embedded with a repair heuristic to facilitate the construction of initial solutions, is proposed and evaluated for the latter stage. High‐quality solutions were found for instances generated with up to 3000 requests and a planning horizon of one to four weeks spread over 15 Argentine cities in less than an hour. Additionally, the possibility of carrying an additional driver reduced the cost of external shuttles by 2.25 times on average compared to individual crews and, in some cases, removed this cost completely.
In this work a balanced
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-way partitioning problem with weight constraints is defined to model the sports team realignment. Sports teams must be partitioned into a fixed number of groups according ...to some regulations, where the total distance of the road trips that all teams must travel to play a double round robin tournament in each group is minimized. Two integer programming formulations for this problem are introduced, and the validity of three families of inequalities associated to the polytope of these formulations is proved. The performance of a tabu search procedure and a branch and cut algorithm, which uses the valid inequalities as cuts, is evaluated over simulated and real-world instances. In particular, an optimal solution for the realignment of the Ecuadorian football league is reported and the methodology can be suitable adapted for the realignment of other sports leagues.
Neuromodulatory systems are essential for remodeling glutamatergic connectivity during experience-dependent cortical plasticity. This permissive/enabling function of neuromodulators has been ...associated with their capacity to facilitate the induction of Hebbian forms of long-term potentiation (LTP) and depression (LTD) by affecting cellular and network excitability. In vitro studies indicate that neuromodulators also affect the expression of Hebbian plasticity in a pull-push manner: receptors coupled to the G-protein Gs promote the expression of LTP at the expense of LTD, and Gq-coupled receptors promote LTD at the expense of LTP. Here we show that pull-push mechanisms can be recruited in vivo by pairing brief monocular stimulation with pharmacological or chemogenetical activation of Gs- or Gq-coupled receptors to respectively enhance or reduce neuronal responses in primary visual cortex. These changes were stable, inducible in adults after the termination of the critical period for ocular dominance plasticity, and can rescue deficits induced by prolonged monocular deprivation.
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