147 research outputs found
2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties
The solution to a Nash or a nonsymmetric bargaining game is obtained by
maximizing a concave function over a convex set, i.e., it is the solution to a
convex program. We show that each 2-player game whose convex program has linear
constraints, admits a rational solution and such a solution can be found in
polynomial time using only an LP solver. If in addition, the game is succinct,
i.e., the coefficients in its convex program are ``small'', then its solution
can be found in strongly polynomial time. We also give a non-succinct linear
game whose solution can be found in strongly polynomial time
A semantical approach to equilibria and rationality
Game theoretic equilibria are mathematical expressions of rationality.
Rational agents are used to model not only humans and their software
representatives, but also organisms, populations, species and genes,
interacting with each other and with the environment. Rational behaviors are
achieved not only through conscious reasoning, but also through spontaneous
stabilization at equilibrium points.
Formal theories of rationality are usually guided by informal intuitions,
which are acquired by observing some concrete economic, biological, or network
processes. Treating such processes as instances of computation, we reconstruct
and refine some basic notions of equilibrium and rationality from the some
basic structures of computation.
It is, of course, well known that equilibria arise as fixed points; the point
is that semantics of computation of fixed points seems to be providing novel
methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200
Self-similar shear-thickening behavior in CTAB/NaSal surfactant solutions
The effect of salt concentration Cs on the critical shear rate required for
the onset of shear thickening and apparent relaxation time of the
shear-thickened phase, has been investigated systematically for dilute
CTAB/NaSal solutions. Experimental data suggest a self-similar behavior of the
critical shear rate and relaxation time as functions of Cs. Specifically, the
former ~ Cs^(-6) whereas the latter ~ Cs^(6) such that an effective Weissenberg
number for the onset of the shear thickened phase is only weakly dependent on
Cs. A procedure has been developed to collapse the apparent shear viscosity
versus shear rate data obtained for various values of Cs into a single master
curve. The effect of Cs on the elastic modulus and mesh size of the
shear-induced gel phase for different surfactant concentrations is discussed.
Experiments performed using different flow cells (Couette and cone-and-plate)
show that the critical shear rate, relaxation time and the maximum viscosity
attained are geometry-independent. The elastic modulus of the gel phase
inferred indirectly by employing simplified hydrodynamic instability analysis
of a sheared gel-fluid interface is in qualitative agreement with that
predicted for an entangled phase of living polymers. A qualitative mechanism
that combines the effect of Cs on average micelle length and Debye parameter
with shear-induced configurational changes of rod-like micelles is proposed to
rationalize the self-similarity of SIS formation.Comment: 27 pages, 17 figure
Random Sequential Adsorption: From Continuum to Lattice and Pre-Patterned Substrates
The random sequential adsorption (RSA) model has served as a paradigm for
diverse phenomena in physical chemistry, as well as in other areas such as
biology, ecology, and sociology. In the present work, we survey aspects of the
RSA model with emphasis on the approach to and properties of jammed states
obtained for large times in continuum deposition versus that on lattice
substrates, and on pre-patterned surfaces. The latter model has been of recent
interest in the context of efforts to use pre-patterning as a tool to improve
selfassembly in micro- and nanoscale surface structure engineering
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
Delta-matroids as subsystems of sequences of Higgs Lifts
In [30], Tardos studied special delta-matroids obtained from sequences of
Higgs lifts; these are the full Higgs lift delta-matroids that we treat and around which
all of our results revolve. We give an excluded-minor characterization of the class of
full Higgs lift delta-matroids within the class of all delta-matroids, and we give similar
characterizations of two other minor-closed classes of delta-matroids that we define using
Higgs lifts. We introduce a minor-closed, dual-closed class of Higgs lift delta-matroids
that arise from lattice paths. It follows from results of Bouchet that all delta-matroids can
be obtained from full Higgs lift delta-matroids by removing certain feasible sets; to address
which feasible sets can be removed, we give an excluded-minor characterization of deltamatroids
within the more general structure of set systems. Many of these excluded minors
occur again when we characterize the delta-matroids in which the collection of feasible
sets is the union of the collections of bases of matroids of different ranks, and yet again
when we require those matroids to have special properties, such as being paving
Granular Flow in Silo Discharge: Discrete Element Method Simulations and Model Assessment
Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle–wall friction coefficient and particle coefficient of restitution) and system parameters (orifice width) on the discharge rate is quantified. The spatial extent of different regimes (quasi-static, intermediate and inertial) of granular rheology are quantified using a regime map previously established from DEM data of homogeneously sheared granular flow. It is shown that all three regimes of granular rheology coexist during silo discharge, and the intermediate regime plays a significant role in discharge dynamics. A quantitative comparison between results of continuum and DEM simulations is performed by computing discharge rates, solid velocities, and solid stresses for a three-dimensional (3D) flat-bottomed silo. It is found that the three constitutive models investigated in this study overpredict the discharge rate when compared to DEM data. Contour plots of the error in solid stress prediction are compared with the spatial extent of different regimes of granular rheology to deduce that it is inaccurate modeling of the intermediate regime that is responsible for overprediction of the discharge rate
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