Tree Nash Equilibria in the Network Creation Game

In the network creation game with n vertices, every vertex (a player) buys a set of adjacent edges, each at a fixed amount {\alpha} > 0. It has been conjectured that for {\alpha} >= n, every Nash equilibrium is a tree, and has been confirmed for every {\alpha} >= 273n. We improve upon this bound and show that this is true for every {\alpha} >= 65n. To show this, we provide new and improved results on the local structure of Nash equilibria. Technically, we show that if there is a cycle in a Nash equilibrium, then {\alpha} < 65n. Proving this, we only consider relatively simple strategy changes of the players involved in the cycle. We further show that this simple approach cannot be used to show the desired upper bound {\alpha} < n (for which a cycle may exist), but conjecture that a slightly worse bound {\alpha} < 1.3n can be achieved with this approach. Towards this conjecture, we show that if a Nash equilibrium has a cycle of length at most 10, then indeed {\alpha} < 1.3n. We further provide experimental evidence suggesting that when the girth of a Nash equilibrium is increasing, the upper bound on {\alpha} obtained by the simple strategy changes is not increasing. To the end, we investigate the approach for a coalitional variant of Nash equilibrium, where coalitions of two players cannot collectively improve, and show that if {\alpha} >= 41n, then every such Nash equilibrium is a tree

Collective fast delivery by energy-efficient agents

We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths) that have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0 with respect to the following: Each agent i has a weight w_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity v_i with which it can move. We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the package arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon*T + (1-epsilon)*E, for a given epsilon, 0<epsilon<1. We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n + k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 3-approximation algorithm for (iii) using a single agent.Comment: In an extended abstract of this paper [MFCS 2018], we erroneously claimed the single agent approach for variant (iii) to have approximation ratio

Potentiometric determination of anionic surfactant using home-made FIA/SIA system

Razvojem znanosti dolazi do sve veće potražnje za bržim i efikasnijim metodama analize tvari. Potreba za korištenjem što manje količine uzorka s velikom preciznošću analize u vrlo kratkom vremenu, dovela je do razvoja mikrofluidike. Analiza injektiranjem u protok (flow injection analysis, FIA) prva je moderna mikrofluidička metoda i definirana je kao analitička metoda za automatsku analizu tekućih uzoraka koja se zasniva na disperziji zone uzorka nastale injektiranjem uzorka u tok otopine nosača. Daljnim razvojem ove metode nastaje sekvencijska injekcijska analiza (sequential injection analysis, SIA ), mikrofluidička metoda čija je glavna karakteristika dvosmjerni neprekinuti tok uzorka. U ovom završnom radu korištena je navedena metoda kako bi se analizirale anionske površinski aktivne tvari pomoću screen-printed mikrosenzora. Površinski aktivne tvari ili tenzidi smanjuju površinsku napetost tekućina i sastoje se od hidrofilnog i hidrofobnog dijela. Koriste se u sredstvima za čišćenje kao i proizvodima za osobnu higijenu. Vrlo je važno kontrolirati njihovu količinu kako u proizvodima u kojima se nalaze tako i u otpadnim vodama zbog naše sigurnosti i sigurnosti okoliša.Rapid development of science demands faster and more efficient methods of matter analysis. The need for using smaller amounts of sample and bigger precision of analysis in shorter periods of time led to development of microfluidics. Flow injection analysis (FIA) is the first modern microfluidic method and it is defined as analytical method for automatic analysis of liquid samples. It is based on dispersion of sample zone that was made by injecting the sample in the carrier flow and detection of the wanted feature. Further development led to sequential injection analysis (sequential injection analysis, SIA), microfluidic method that uses two-way continuous flow. Described method was used in this bachelor thesis to analyze anionic surfactants. Surface active agents or surfactants lower surface tension of liquids. They consist of hydrophobic and hydrophilic end of the molecule. Surfactants are used in cleaning products and products for personal hygiene. It is very important to monitor their amount in products that we use and their presence in waste water for our own safety and the safety of our environment

An Algorithmic View on OVSF Code Assignment

Orthogonal Variable Spreading Factor (OVSF) codes are used in UMTS to share the radio spectrum among several connections of possibly different bandwidth requirements. The combinatorial core of the OVSF code assignment problem is to assign some nodes of a complete binary tree of height h (the code tree) to n simultaneous connections, such that no two assigned nodes (codes) are on the same root-to-leaf path. A connection that uses a 2-d fraction of the total bandwidth requires some code at depth d in the tree, but this code assignment is allowed to change over time. Requests for connections that would exceed the total available bandwidth are rejected. We consider the one-step code assignment problem: Given an assignment, move the minimum number of codes to serve a new request. Minn and Siu propose the so-called DCA algorithm to solve the problem optimally. In contrast, we show that DCA does not always return an optimal solution, and that the problem is NP-hard. We give an exact nO(h)-time algorithm, and a polynomial-time greedy algorithm that achieves approximation ratio Θ(h). A more practically relevant version is the online code assignment problem, where future requests are not known in advance. Our objective is to minimize the overall number of code reassignments. We present a Θ(h)-competitive online algorithm, and show that no deterministic online algorithm can achieve a competitive ratio better than 1.5. We show that the greedy strategy (minimizing the number of reassignments in every step) is not better than Ω(h) competitive. We give a 2-resource augmented online algorithm that achieves an amortized constant number of (re-)assignments. Finally, we show that the problem is fixed-parameter tractabl

Expression of genes for selected plant aminoacyl-tRNA synthetases in the abiotic stress

Plants, as sessile organisms, have evolved intricate mechanisms to adapt to various environmental changes and challenges. Because various types of stress trigger significant decrease in global translation rates we examined the stress-related expression of aminoacyl-tRNA synthetases (aaRSs), enzymes that participate in the first step of protein biosynthesis. We have analyzed promoters of genes encoding cytosolic seryl-tRNA synthetase (SerRS), cytosolic aspartyl-tRNA synthetase (AspRS) and cytosolic cysteinyl-tRNA synthetase (CysRS) in Arabidopsis thaliana L., and examined SerRS, AspRS and CysRS gene expression in seedlings exposed to different abiotic stressors. Although global translation levels are repressed by stress, our results show that plant aaRSs expression is not decreased by osmotic, salt and heavy metal/cadmium stress. Moreover, during exposure to stress conditions we detected increased AspRS and CysRS transcript levels. SerRS gene expression did not change in stress conditions although participation of SerRS in stress response could be regulated at the protein level. Expression of the examined aaRS genes under stress correlated well with the length of their predicted promoters and the number of available binding sites for the stress related transcription factors. It thus appears that during stress it is important to keep steady state levels of aaRSs for translation of specific stress-related mRNAs and furthermore to rapidly continue with translation when stress conditions cease. Importantly, increased levels of plant aaRSs during stress may serve as a pool of aaRS proteins that can participate directly in stress responses through their noncanonical activities

Relaxed Agreement Forests

There are multiple factors which can cause the phylogenetic inference process to produce two or more conflicting hypotheses of the evolutionary history of a set X of biological entities. That is: phylogenetic trees with the same set of leaf labels X but with distinct topologies. This leads naturally to the goal of quantifying the difference between two such trees T_1 and T_2. Here we introduce the problem of computing a 'maximum relaxed agreement forest' (MRAF) and use this as a proxy for the dissimilarity of T_1 and T_2, which in this article we assume to be unrooted binary phylogenetic trees. MRAF asks for a partition of the leaf labels X into a minimum number of blocks S_1, S_2, ... S_k such that for each i, the subtrees induced in T_1 and T_2 by S_i are isomorphic up to suppression of degree-2 nodes and taking the labels X into account. Unlike the earlier introduced maximum agreement forest (MAF) model, the subtrees induced by the S_i are allowed to overlap. We prove that it is NP-hard to compute MRAF, by reducing from the problem of partitioning a permutation into a minimum number of monotonic subsequences (PIMS). Furthermore, we show that MRAF has a polynomial time O(log n)-approximation algorithm where n=|X| and permits exact algorithms with single-exponential running time. When at least one of the two input trees has a caterpillar topology, we prove that testing whether a MRAF has size at most k can be answered in polynomial time when k is fixed. We also note that on two caterpillars the approximability of MRAF is related to that of PIMS. Finally, we establish a number of bounds on MRAF, compare its behaviour to MAF both in theory and in an experimental setting and discuss a number of open problems.Comment: 14 pages plus appendi

Majčina dušica (Thymus serpyllum L.) i njezine komponente protiv okratoksikotvornih vrsta Aspergillusa

The aim of this study was to determine the effects of the essential oil of Thymus serpyllum L. and of its components thymol and total phenols (total phenolic content, TPC) extracted from the plant on the growth and mycotoxin production of Aspergillus ochraceus, A. carbonarius, and A. niger. Minimal inhibitory concentration (MIC) determined for the essential oil and thymol, and selected concentration of the TPC extract inhibited fungal growth and ochratoxin A biosynthesis by more than 60 %, depending on the conditions and duration of incubation with the fungi. Essential oil showed the strongest inhibitory effect which may have been related to the synergistic or cumulative effects of its components.Cilj ovog rada bio je odrediti utjecaj eteričnog ulja majčine dušice (Thymus serpyllum), uljne komponente timola i ukupnih fenola ekstrahiranih iz biljke, na rast plijesni i sintezu mikotoksina. U odabranim uvjetima minimalna inhibitorna koncentracija (MIC) eteričnog ulja i timola, koja je određena u ovom radu, i koncentracija ukupnih fenola (TPC) inhibirale su više od 60 % rasta odabranih plijesni i biosinteze okratoksina A. Njihova inhibitorna učinkovitost ovisila je o uvjetima i trajanju inkubacije s plijesnima. U odnosu na timol i ekstrakt eterično ulje pokazalo je snažniji inhibitorni utjecaj, koji je uvjetovan sinergističkim ili kumulativnim djelovanjem uljnih komponenata

Diff erenze nelle concentrazioni di rame nei prodotti di carne, nel pesce e nei molluschi bivalvi

Koncentracije bakra (Cu) određene su u 65 uzoraka uzorkovanih odnosno kupljenih u Hrvatskoj u ljeto 2012.: meso (goveda, svinja, ovaca), mesne prerađevine (kobasice, pašteta), riba i riblji proizvodi i školjke (dagnje, kamenice). Srednje koncentracije Cu su (mg/kg): svi uzorci mesa 0,77, kobasice 0,69, pašteta 2,24, riba 0,23, riblje prerađevine 1,20, školjke 0,81, kamenice 30,0. Utvrđene su statistički značajne razlike između skupina namirnica. Procijenjene srednje dnevne količine unosa (EDI) Cu u ispitanoj hrani koje doprinose preporučenom unosu hranom (RDA) su (%): 1,54 meso; 1,38 kobasice, 4,48 pašteta, te <1 za ribe, proizvodi od riba i školjke, 10,0 kamenice. Prosječni dnevni unosi Cu izraženi kao % od privremenog maksimalnog dopuštenog dnevnog unosa (PMTDI) su < 0,9 % za meso i mesne proizvode, < 0,085 % za ribu, riblje proizvode i dagnje te 2 % za kamenice. Najviša koncentracija Cu određena je u kamenicama, što ukazuje da ova vrsta može biti uključena u prehranu kao dobar izvor Cu. U zaključku, dobiveni analitički rezultati pokazuju da ne postoje zdravstveni rizici od konzumiranja ispitanih namirnica. Kako bi procijenili onečišćenje mora u Hrvatskoj, treba ispitati sadržaj Cu u kamenicama sa farmi kamenica s različitih lokacija.Copper concentrations were measured in a 65 samples marketed and collected in Croatia in summer 2012: meat samples (bovine, pig, sheep), meat products (sausages, pâté), fi sh and fi sh products and shellfi sh (mussels, oysters). Mean Cu levels were (mg/kg): all meat 0.77, sausages 0.69, pâté 2.24, fi sh 0.23, fi sh products 1.20, mussels 0.81, oysters 30.0. Signifi cant diff erences were found between the foods groups. The estimated mean daily intake (EDI) of Cu in selected food contributing to the recommended dietary allowance (RDA) were (%): meat 1.54; sausages 1.38, pâté 4.48, fi sh, fi sh products and mussels < 1, oysters 10.0. The average daily intake of Cu represented % of the provisional maximum tolerable daily intakes (PMTDI) value were less than 0.9% in meat and meat products, less than 0.085% in fi sh, fi sh products and mussels and 2% for oysters. The highest Cu contents measured in oysters, suggesting that this species may be included in a diet as a good source of Cu. In conclusion, the analytical data obtained indicate there are no health risks from the consumption of the tested food items. In order to estimate sea contamination in Croatia, Cu levels in oyster samples should be investigated for diff erent oyster farm locations.Es wurden Kupferkonzentrationen (Cu) in 65 Mustern in Musterproben bzw. gekauft in Kroatien im Sommer 2012, bestimmt: Fleisch (Rinder, Schweine, Schafe), Fleischerzeugnisse (Würste, Pasteten), Fische und Fischerzeugnisse und Muscheln (Miesmuscheln, Austern). Mittlere Konzentrationen Cu (mg/kg) sind: alle Fleischmuster 0,77, Würste 0,69, Pastete 2,24, Fisch 0,23, Fischerzeugnisse 1,20, Muscheln 0,81, Austern 30,0. Es wurden statistisch bedeutende Unterschiede unter Nahrungsmittelgruppen festgestellt. Bewertete mittlere Tagesmengen der Einnahme (EDI) von Cu in der geprüften Nahrung, die der empfohlenen Einnahmemenge durch die Nahrung (RDA) beitragen, sind (%): 1,54 Fleisch, 1,38 Würste, 4,48 Pasteten, sowie < 1 Fisch, Fischerzeugnisse und Muscheln, 10,0 Austern. Durchschnittliche Tageseinnahmen von Cu ausgedrückt als % von vorläufi g maximaler genehmigter Tageseinnahme (PMTDI) sind < 0,9 % für Fleisch und Fleischerzeugnisse, < 0,085 % für Fisch, Fischerzeugnisse und Miesmuscheln und 2 % für Austern. Die höchste Konzentration von Cu wurde in Austern bestimmt, was darauf hinweist, dass diese Sorte in die Nahrung als gute Quelle von Cu eingeschlossen werden kann. In der Schlussfolgerung zeigen die analytisch erzielten Resultate, dass keine wissenschaftlichen Risiken bestehen, die geprüften Nahrungsmittel zu konsumieren. Um Verunreinigungen des Meeres in Kroatien zu bewerten, soll der Inhalt von Cu in Austern aus verschiedenen Lokalitäten der Austerfarmen geprüft werden.Le concentrazioni di rame (Cu) sono state rilevate in 65 campioni campionati, o meglio acquistati, in Croazia nell\u27estate 2012: carne (bovina, suina, ovina), prodotti a base di carne trasformata (salsicce, pâté), pesce e prodotti a base di pesce trasformato e molluschi bivalvi (cozze, ostriche). Ecco le concentrazioni medie di Cu (mg/kg) rilevate: in tutti i campioni di carne 0,77, nelle salsicce 0,69, nel pâté di carne 2,24, nel pesce 0,23, nei prodotti a base di pesce trasformato 1,20, nei molluschi bivalvi (cozze) 0,81, nelle ostriche 30,0. Sono state accertate diff erenze statisticamente signifi cative tra gruppi di alimenti. L\u27assunzione giornaliera stimata (EDI) di Cu negli alimenti esaminati che contribuiscono alla dose giornaliera consigliata (RDA) sono: 1,54 di carne; 1,38 di salsicce, 4,48 di pâté di carne e <1 per il pesce, i prodotti a base di pesce trasformato e i molluschi bivalvi (cozze), 10,0 di ostriche. I valori di assunzione media giornaliera di Cu, espressi come % della dose giornaliera massima tollerabile provvisoria (PMTDI), sono < 0,9% per la carne e i prodotti a base di carne trasformata, < 0,085 % per il pesce, i prodotti a base di pesce trasformato e le cozze, e il 2% per le ostriche. Nelle ostriche è stata riscontrata la maggior concentrazione di Cu, il che signifi ca che quest\u27alimento potrebbe essere incluso nella dieta equilibrata come una buona fonte di Cu. In conclusione, i risultati analitici ottenuti mostrano che non sussistono rischi per la salute a seguito del consumo degli alimenti campionati e analizzati. Per esaminare il tasso d\u27inquinamento del mare in Croazia, è necessario, quindi, esaminare il contenuto di Cu nelle ostriche provenienti da impianti di acquacoltura ubicati in aree diff erenti

Nicotinic Acetylcholine Receptors Containing α6 Subunits Contribute to Alcohol Reward-Related Behaviors

Evidence is emerging that neuronal nicotinic acetylcholine receptors (nAChRs) in the mesolimbic dopamine (DA) system are involved in mediating the reinforcing effects of alcohol. Midbrain DA neurons express high levels of α6 subunit-containing nAChRs that modulate DA transmission, implicating their involvement in reward-related behaviors. The present study assessed the role of α6-containing nAChRs in modulating alcohol reward using transgenic mice expressing mutant, hypersensitive α6 nAChR subunits (α6L9′S mice). α6L9′S mice and littermate controls were tested in three well-established models of alcohol reward: 24-hr two-bottle choice drinking, drinking in the dark (DID), and conditioned place preference (CPP). Confocal microscopy and patch-clamp electrophysiology were used to demonstrate the localization and function of hypersensitive α6 subunit-containing nAChRs. Results indicate that female α6L9′S mice showed significantly higher alcohol intake at low concentrations of alcohol (3% and 6%) in the two-bottle choice procedure. Both male and female α6L9′S mice drank significantly more in the DID procedure and displayed an alcohol-induced place preference using a low dose of alcohol (0.5 g/kg) that was ineffective in littermate controls. Confocal microscopy showed that α6 subunit-containing nAChRs are selectively expressed on ventral tegmental area (VTA) DAergic, but not GABAergic neurons. Patch-clamp electrophysiology demonstrated that VTA DA neurons of α6L9′S mice are hypersensitive to ACh. Collectively, these results suggest that α6L9′S mice are more sensitive to the rewarding effects of alcohol, and suggest that VTA α6 subunit-containing nAChRs modulate alcohol reward. Thus, α6 subunit-containing nAChRs may be a promising therapeutic target for treatment of alcohol use disorders

Synthetic α-Conotoxin Mutants as Probes for Studying Nicotinic Acetylcholine Receptors and in the Development of Novel Drug Leads

α-Conotoxins are peptide neurotoxins isolated from venomous marine cone snails that are potent and selective antagonists for different subtypes of nicotinic acetylcholine receptors (nAChRs). As such, they are valuable probes for dissecting the role that nAChRs play in nervous system function. In recent years, extensive insight into the binding mechanisms of α-conotoxins with nAChRs at the molecular level has aided in the design of synthetic analogs with improved pharmacological properties. This review examines the structure-activity relationship studies involving α-conotoxins as research tools for studying nAChRs in the central and peripheral nervous systems and their use towards the development of novel therapeutics