961 research outputs found
On Colorful Bin Packing Games
We consider colorful bin packing games in which selfish players control a set
of items which are to be packed into a minimum number of unit capacity bins.
Each item has one of colors and cannot be packed next to an item of
the same color. All bins have the same unitary cost which is shared among the
items it contains, so that players are interested in selecting a bin of minimum
shared cost. We adopt two standard cost sharing functions: the egalitarian cost
function which equally shares the cost of a bin among the items it contains,
and the proportional cost function which shares the cost of a bin among the
items it contains proportionally to their sizes. Although, under both cost
functions, colorful bin packing games do not converge in general to a (pure)
Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we
design an algorithm for computing a Nash equilibrium whose running time is
polynomial under the egalitarian cost function and pseudo-polynomial for a
constant number of colors under the proportional one. We also provide a
complete characterization of the efficiency of Nash equilibria under both cost
functions for general games, by showing that the prices of anarchy and
stability are unbounded when while they are equal to 3 for black and
white games, where . We finally focus on games with uniform sizes (i.e.,
all items have the same size) for which the two cost functions coincide. We
show again a tight characterization of the efficiency of Nash equilibria and
design an algorithm which returns Nash equilibria with best achievable
performance
Assessing the resilience of a river management regime: Informal learning in a shadow network in the Tisza River Basin
Global sources of change offer unprecedented challenges to conventional river management strategies, which no longer appear capable of credibly addressing a trap: the failure of conventional river defense engineering to manage rising trends of disordering extreme events, including frequency and intensity of floods, droughts, and water stagnation in the Hungarian reaches of the Tisza River Basin. Extreme events punctuate trends of stagnation or decline in the ecosystems, economies, and societies of this river basin that extend back decades, and perhaps, centuries. These trends may be the long-term results of defensive strategies of the historical river management regime that reflect a paradigm dating back to the Industrial Revolution: "Protect the Landscape from the River." Since then all policies have defaulted to the imperatives of this paradigm such that it became the convention underlying the current river management regime. As an exponent of this convention the current river management regimes' methods, concepts, infrastructure, and paradigms that reinforce one another in setting the basin's development trajectory, have proven resilient to change from wars, political, and social upheaval for centuries. Failure to address the trap makes the current river management regimes resilience appear detrimental to the regions future development prospects and prompts demand for transformation to a more adaptive river management regime. Starting before transition to democracy, a shadow network has generated multiple dialogues in Hungary, informally exploring the roots of this trap as part of a search for ideas and methods to revitalize the region. We report on how international scientists joined one dialogue, applying system dynamics modeling tools to explore barriers and bridges to transformation of the current river management regime and develop the capacity for participatory science to expand the range of perspectives that inform, monitor, and revise learning, policy, and the practice of river management
Научная инициатива иностранных студентов и аспирантов. Т. 1
Сборник представляет интерес для специалистов и исследователей в области математики, механики, электротехники, информатики и вычислительных систем, физики, химии, геологии, гуманитарных наук и экономики
Bounding sup-norms of cusp forms of large level
Let f be an -normalized weight zero Hecke-Maass cusp form of square-free
level N, character and Laplacian eigenvalue . It is
shown that , from which the hybrid
bound (for some
) is derived. The first bound holds also for where F
is a holomorphic cusp form of weight k with the implied constant now depending
on k.Comment: version 3: substantially revised versio
The Collins-Roscoe mechanism and D-spaces
We prove that if a space X is well ordered , or linearly
semi-stratifiable, or elastic then X is a D-space
Filtered multiplicative bases of restricted enveloping algebras
We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie
algebra over a field of positive characteristic p
Individual and collective stock dynamics: intra-day seasonalities
We establish several new stylised facts concerning the intra-day
seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the
volatility, we find that the average correlation between stocks increases
throughout the day, leading to a smaller relative dispersion between stocks.
Somewhat paradoxically, the kurtosis (a measure of volatility surprises)
reaches a minimum at the open of the market, when the volatility is at its
peak. We confirm that the dispersion kurtosis is a markedly decreasing function
of the index return. This means that during large market swings, the
idiosyncratic component of the stock dynamics becomes sub-dominant. In a
nutshell, early hours of trading are dominated by idiosyncratic or sector
specific effects with little surprises, whereas the influence of the market
factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure
The critical window for the classical Ramsey-Tur\'an problem
The first application of Szemer\'edi's powerful regularity method was the
following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any
K_4-free graph on N vertices with independence number o(N) has at most (1/8 +
o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising
geometric construction, utilizing the isoperimetric inequality for the high
dimensional sphere, of a K_4-free graph on N vertices with independence number
o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in
1976, several problems have been asked on estimating the minimum possible
independence number in the critical window, when the number of edges is about
N^2 / 8. These problems have received considerable attention and remained one
of the main open problems in this area. In this paper, we give nearly
best-possible bounds, solving the various open problems concerning this
critical window.Comment: 34 page
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