On the Tree Conjecture for the Network Creation Game

Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.[PODC\u2703] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of alpha per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all alpha and that for alpha >= n all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price alpha and employ it to improve on the best known bounds for both conjectures. In particular we show that for alpha > 4n-13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of alpha. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees

Õlavarreluu proksimaalse osa murdude operatiivne ravi

Analüüsitud on õlavarreluu proksimaalse osa murdude ravi tulemusi, kus osteosünteesiks on kasutatud uut Targon-tüüpi lukustuvat naela. Jälgimisel oli 21 opereeritud haiget vanuses 52–87 aastat. Murde liigitasime AO/ASIF klassifi katsiooni järgi. Ravitulemust hindasime röntgenoloogiliselt (2, 4 ja 12 kuud pärast operatsiooni) ning spetsiaalse küsimustiku – constant shoulder score – abil. Meie kogemuse põhjal on proksimaalse õlavarreluu naela kasutamine näidustatud õla varreluu A2–C1 tüüpi murdude raviks. Operatsioonil kasutatud miniinvasiivne juurdepääs võimaldab täielikult säästa õlavarreluu pea verevarustust ja innervatsiooni, mis soodustab kiiret paranemist ja funktsiooni taastumist. Eriti on vajalik märkida, et osteopeenia ja osteoporoos ei ole vastunäidustuseks naela kasutamisel, kuna see meetod võimaldab nurkstabiilse murru fikseerimist ning jäse ei vaja lisaimmobilisatsiooni, mistõttu võib kohe alustada taastusravi. Eesti Arst 2009; 88(Lisa3):16−2

Network Creation Games: Think Global - Act Local

We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bil\`o et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy-changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the price of anarchy.Comment: An extended abstract of this paper has been accepted for publication in the proceedings of the 40th International Conference on Mathematical Foundations on Computer Scienc

Strategic Network Formation with Attack and Immunization

Strategic network formation arises where agents receive benefit from connections to other agents, but also incur costs for forming links. We consider a new network formation game that incorporates an adversarial attack, as well as immunization against attack. An agent's benefit is the expected size of her connected component post-attack, and agents may also choose to immunize themselves from attack at some additional cost. Our framework is a stylized model of settings where reachability rather than centrality is the primary concern and vertices vulnerable to attacks may reduce risk via costly measures. In the reachability benefit model without attack or immunization, the set of equilibria is the empty graph and any tree. The introduction of attack and immunization changes the game dramatically; new equilibrium topologies emerge, some more sparse and some more dense than trees. We show that, under a mild assumption on the adversary, every equilibrium network with $n$ agents contains at most $2n-4$ edges for $n\geq 4$. So despite permitting topologies denser than trees, the amount of overbuilding is limited. We also show that attack and immunization don't significantly erode social welfare: every non-trivial equilibrium with respect to several adversaries has welfare at least as that of any equilibrium in the attack-free model. We complement our theory with simulations demonstrating fast convergence of a new bounded rationality dynamic which generalizes linkstable best response but is considerably more powerful in our game. The simulations further elucidate the wide variety of asymmetric equilibria and demonstrate topological consequences of the dynamics e.g. heavy-tailed degree distributions. Finally, we report on a behavioral experiment on our game with over 100 participants, where despite the complexity of the game, the resulting network was surprisingly close to equilibrium.Comment: The short version of this paper appears in the proceedings of WINE-1

On the Structure of Equilibria in Basic Network Formation

We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by Alon et al. (2010), in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest $k$-vicinity (defined as the the set of vertices within distance $k$ from a vertex), for any $k \geq 1$ and in terms of the number of edges, thus settling positively a conjecture of Alon et al. in the cases of graphs of large $k$-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough. Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.Comment: 11 pages, 4 figure

Range of motion and pain intensity of the first metatarsophalangeal joint in women with hallux valgus deformation after two-month home exercise programme

Hallux Valgus (HV) (also Hallux abducto valgus) is a common deformity of the foot, which causes pain, inflammation and decreased joint mobility in the big toe. There are no universally accepted protocols for treating advanced phase HV, corrective surgery seems to be the most common direction of curing advanced HV deformation. The purpose of this study was to assess the effects of two-month home exercise programme (HEP) on joint mobility and pain of the first metatarsophalangeal joint (MTP-joint) in women with advanced phase HV deformation. Seven women with mean age 55.6±2.9 years with advanced phase HV deformation (first MTP-joint angle more than 20 degrees) participated in the study. Foot pain in different conditions was assessed with modified Foot Function Index's (FFI) pain subscale before and after HEP. Passive range of motion (PROM) of flexion and extension of the first MTP-joint was measured before and after HEP using a standard mechanical goniometer. A significant increase (p<0.001) in the passive extension of the first MTP-joint was noted after HEP compared with the joint mobility before HEP, also passive flexion increased considerably but no significant difference was noted (p>0.05). Foot pain score decreased significantly (p<0.05) after HEP. In conclusion, in advanced phase HV two-month HEP was an effective therapeutic approach for increasing first MTP-joint mobility and reducing foot pain

Selfish Network Creation with Non-Uniform Edge Cost

Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.Comment: To appear at SAGT'1

Time-dependent energy absorption changes during ultrafast lattice deformation

The ultrafast time-dependence of the energy absorption of covalent solids upon excitation with femtosecond laser pulses is theoretically analyzed. We use a microscopic theory to describe laser induced structural changes and their influence on the electronic properties. We show that from the time evolution of the energy absorbed by the system important information on the electronic and atomic structure during ultrafast phase transitions can be gained. Our results reflect how structural changes affect the capability of the system to absorb external energy.Comment: 7 pages RevTeX, 8 ps figures, submitted to Journal of Appl. Physic