New results on metric-locating-dominating sets of graphs

A dominating set $S$ of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of $S$, and the minimum cardinality of such a set is called the metric-location-domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominating sets to other special sets: resolving sets, dominating sets, locating-dominating sets and doubly resolving sets. We first characterize classes of trees according to certain relationships between their metric-location-domination number and their metric dimension and domination number. Then, we show different methods to transform metric-locating-dominating sets into locating-dominating sets and doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them involving parameters that have not been related so far.Comment: 13 pages, 3 figure

Antimagic Labelings of Caterpillars

A $k$-antimagic labeling of a graph $G$ is an injection from $E(G)$ to $\{1,2,\dots,|E(G)|+k\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $u$ is the sum of the labels assigned to edges incident to $u$. We call a graph $k$-antimagic when it has a $k$-antimagic labeling, and antimagic when it is 0-antimagic. Hartsfield and Ringel conjectured that every simple connected graph other than $K_2$ is antimagic, but the conjecture is still open even for trees. Here we study $k$-antimagic labelings of caterpillars, which are defined as trees the removal of whose leaves produces a path, called its spine. As a general result, we use constructive techniques to prove that any caterpillar of order $n$ is $(\lfloor (n-1)/2 \rfloor - 2)$-antimagic. Furthermore, if $C$ is a caterpillar with a spine of order $s$, we prove that when $C$ has at least $\lfloor (3s+1)/2 \rfloor$ leaves or $\lfloor (s-1)/2 \rfloor$ consecutive vertices of degree at most 2 at one end of a longest path, then $C$ is antimagic. As a consequence of a result by Wong and Zhu, we also prove that if $p$ is a prime number, any caterpillar with a spine of order $p$, $p-1$ or $p-2$ is $1$-antimagic.Comment: 13 pages, 4 figure

Valoració de la nicotina intraseptal en rates alcohòliques abstinents i no-abstinents, en aprenentatge excitatori i inhibitori

Consultable des del TDXTítol obtingut de la portada digitalitzadaEls coneixements actuals sobre els efectes crònics de l'alcohol en el SNC són encara força limitats. Malgrat haver identificat en part els canvis que subjauen a fenòmens com la tolerància o la dependència, el mecanisme responsable de l'addicció encara és desconegut. Diversos estudis s'han centrat en la neurotransmissió GABAèrgica, glutamatèrgica, dopaminèrgica i serotoninèrgica, aquests sistemes quan son afectats crònicament per l'alcohol, responen amb adaptacions que o bé són reversibles, o es compensen i neutralitzen després d'un període d'abstinència, no poden per tan ésser el suport d'un fenomen permanent com l'addicció. Estudis fets en animals consumidors voluntaris de dosis tòxiques d'alcohol, han mostrat diferències significatives respecte als controls en diversos processos d'aprenentatge tant excitatori com inhibitori, i han estat identificants canvis tan fisiològics com moleculars en la transmissió colinèrgica de tipus nicotínic. Aquests canvis, sensibilització i regulació a l'alça del receptor nicotínic, són presumiblement irreversibles, no obstant, desconeixem si els processos d'aprenentatge, i els substrats neurals subjacents, es troben alterats en aquests animals alcohòlics durant l'abstinència. En aquesta tesi ens hem plantejat estudiar l'estat funcional de la funció colinèrgica de tipus nicotínic del feix septohipocàmpic durant l'abstinència, avaluant l'efecte d'una injecció intraseptal de nicotina en la capacitat de l'animal alcohòlic per aprendre la resposta a la palanca durant l'abstinència d'alcohol (Experiment I). D'altra banda, s'ha estudiat la capacitat d'aprenentatge inhibitòri per tal de conèixer l'estat funcional i la implicació d'aquest circuit en el control de la conducta. Amb aquest objectiu, hem avaluat mitjançant aprenentatge de discriminació (amb estímuls excitatori i inhibitori), l'efecte d'una injecció intraseptal de nicotina en la capacitat d'inhibir una resposta en la Prova de Dos Estímuls de Pavlov i en l'extinció simple, en situació d'abstinència (Experiment II). Els resultats obtinguts en l'Experiment I mostren que l'abstinència d'alcohol modifica dràsticament, en sentit negatiu, la capacitat d'aprenentatge simple en els animals alcohòlics. D'altra banda, la nicotina té efectes oposats en els subjectes alcohòlics Abstinents i No-Abstinents, en aquests empitjora l'adquisició triplicant el temps necessari per assolir l'aprenentatge a la dosi de 10nM, mentre que en el cas dels Abstinents, neutralitza l'efecte disruptor de l'abstinència, en l'aprenentatge d'aquesta resposta, a la dosi de 20nM. Els subjectes alcohòlics No-Abstinents respecte dels controls mostren una sensibilització funcional a la nicotina administrada intraseptalment, que es fa palesa amb el desplaçament de la corba dosi-resposta cap a l'esquerre i amb un increment considerable de l'efecte màxim. Els resultats obtinguts en l'Experiment II mostren que l'abstinència té un efecte disruptor sobre el control inhibitori que és més pronunciat en els animals alcohòlics (sensibilització). Pel que fa a l'efecte de la nicotina en la Prova de Dos Estímuls de Pavlov, s'observa un efecte disruptor dosi-depenent en els alcohòlics No-Abstinents mentre que els Abstinents té l'efecte contrari, millorant el seu control inhibitori. Així doncs, la corba dosi-resposta per a la nicotina intraseptal pels animals alcohòlics Abstinents, respecte a la mateixa corba dels No-Abstinents, mostra la inversió del perfil de la nicotina i un desplaçament a l'esquerre (sensibilització) de l'efecte màxim. Els resultats obtinguts permeten concloure que els subjectes alcohòlics mostren una reactivitat exacerbada a l'administració de nicotina intraseptal, en comparació amb els controls. En l'abstinència d'alcohol, la resposta dels subjectes és molt diferent a la dels alcohòlics No-Abstinents, l'administració de nicotina «normalitza» la resposta dels Abstinents, equiparant-los als No-Abstinents injectats amb salí. Tot plegat és congruent amb una sensibilització funcional de la resposta colinèrgica de tipus nicotínic a l'acció concurrent de l'alcohol i la nicotina, en l'abstinència la nicotina pot substituir l'alcohol i neutralitzar-ne l'abstinència, aquestes propietats caracteritzen el cervell alcohòlic i el distingueixen del cervell control.The current knowledge about chronic alcohol consumption effect on the CNS is still limited. Despite to have identificated some of the changes that underlie phenomenons as tolerance and dependence, we still unknown the main mechanism responsible of addiction. Several studies have focused on GABAergic, glutamatergic, dopaminergic or serotoninergic transmission. These systems, whereas they become adapted by chronic alcohol, after an abstinence period their adaptation is reverted or compensed, for this reason, they could not be the main support of a permanent fenomenon as addiction. Previous studies, done with chronic alcohol drinking animals, have shown significant differences between alcohol and control groups in several excitatory and inhibitory learning processes. On the other hand, it has been identificated several physiologic and molecular changes in the nicotinic cholinergic transmission of these alcoholic animals. These changes, sensitization by up-regulation of the nicotinic receptor, are supposed to be irreversible. However, we unknow if these learning processes, and the underlying neural substratum, are also modificated during abstinence in these alcoholic animals. One of the main objectives of this thesis is to study the functional state of the nicotinic cholinergic function of the septo-hippocampal pathway during abstinence. For this purpose, we have evaluated the effect of an intraseptal injection of nicotine upon the acquisition and extinction of lever-press response during the alcohol abstinence (Experiment I). Furthermore, we have studied the acquisition of an inhibitory learning in order to know the implication and functional state of that pathway over behaviour control during withdrawal. For this purpose, after the acquisition of a discriminative learning (with excitatory and inhibitory stimulus), we have evaluated the effect of an intraseptal injection of nicotine on the capacity of the animal to inhibit a response, in the Pavlov's Two Stimuli Test and extinction session, during alcohol abstinence (Experiment II). Results obtained in Experiment I show that alcohol abstinence drastically impaired in the alcoholic animal the acquisition of a simple learning. On the other hand, nicotine has opposed effects in Abstinent and Non-Abstinent alcoholic animals. In Non-Abstinent subgroup, subjects that received nicotine 10nM show the worst acquisition, taking threefold more time to attain the criterion compared with saline subgroup, while in the case of the Abstinent, nicotine neutralizes the disruptive effect of abstinence at the dose of 20nM. The alcoholic Non-Abstinent animals compared with those of the control group show a functional sensitization to the intraseptal nicotine with an inverted U-shaped dose-response curve that appears shifted leftwards and with a significative increase of the maximum effect. Results obtained in Experiment II show that abstinence has a disruptive effect over the inhibitory control that is more pronounced in alcoholic animals (sensitization). Regarding nicotine effect in Pavlov's Two Stimuli Test, we observe a dose-dependent disruptive effect in Non-Abstinent subgroup while in the case of Abstinent it has the opposite effect improving their inhibitory control. The dose-response curve for the intraseptal nicotine injection in the Abstinent alcoholic animals compared to the same curve for the Non-Abstinent, shows an inverted U-shaped dose-response curve that appears shifted leftwards (sensitization). Overall results show that alcoholic subjects have an exacerbated reactivity to the intraseptal nicotine when compared to the control group. During alcohol abstinence, the response of that subjects is significantly different of that one of the Non-Abstinent, while the nicotine administration «normalizes» the Abstinent animals response equaling them to the Non-Abstinent injected with saline. All these results are congruent with a functional sensitization of the nicotinic cholinergic response to the concurrent action of alcohol and nicotine. During abstinence nicotine seems to substitute the alcohol and to neutralize the abstinence caused by that drug. Those properties would characterize the alcoholic brain and would distinguish it from the control one, implications for pharmacological therapies are discussed

Algoritmos de previsión a corto plazo en base a radar meteorológico

Las consecuencias de las inundaciones suelen ser devastadoras. Los sistemas de protección tradicionales se complementan cada vez más con sistemas de prevención y alerta de inundaciones. En este sentido, el radar meteorológico y los algoritmos de previsión adquieren una importancia clave. El objetivo de la tesina es la mejora de los algoritmos de previsión en base a radar meteorológico a partir del estudio de distintos factores que intervienen

Independent [1,2]-number versus independent domination number

A [1, 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every graph. In this paper we provide local conditions, depending on the degree of vertices, for the existence of independent [1, 2]-sets in caterpillars. We also study the relationship between independent [1, 2]-sets and independent dominating sets in this graph class, that allows us to obtain an upper bound for the associated parameter, the independent [1, 2]-number, in terms of the independent domination number.Peer ReviewedPostprint (published version

New results on metric-locating-dominating sets of graphs

A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominatin g sets to other special sets: resolving sets, dominating sets, locating-dominating set s and doubly resolving sets. We first characterize classes of trees according to cer tain relationships between their metric-location-domination number and thei r metric dimension and domination number. Then, we show different methods to tran sform metric- locating-dominating sets into locating-dominating sets a nd doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them involving parameters that have not been related so farPostprint (published version