28,227 research outputs found
Further Results of the Cryptographic Properties on the Butterfly Structures
Recently, a new structure called butterfly introduced by Perrin et at. is
attractive for that it has very good cryptographic properties: the differential
uniformity is at most equal to 4 and algebraic degree is also very high when
exponent . It is conjecture that the nonlinearity is also optimal for
every odd , which was proposed as a open problem. In this paper, we further
study the butterfly structures and show that these structure with exponent
have also very good cryptographic properties. More importantly, we
prove in theory the nonlinearity is optimal for every odd , which completely
solve the open problem. Finally, we study the butter structures with trivial
coefficient and show these butterflies have also optimal nonlinearity.
Furthermore, we show that the closed butterflies with trivial coefficient are
bijective as well, which also can be used to serve as a cryptographic
primitive.Comment: 20 page
Strategy intervention for the evolution of fairness
Masses of experiments have shown individual preference for fairness which
seems irrational. The reason behind it remains a focus for research. The effect
of spite (individuals are only concerned with their own relative standing) on
the evolution of fairness has attracted increasing attention from experiments,
but only has been implicitly studied in one evolutionary model. The model did
not involve high-offer rejections, which have been found in the form of
non-monotonic rejections (rejecting offers that are too high or too low) in
experiments. Here, we introduce a high offer and a non-monotonic rejection in
structured populations of finite size, and use strategy intervention to
explicitly study how spite influences the evolution of fairness: five
strategies are in sequence added into the competition of a fair strategy and a
selfish strategy. We find that spite promotes fairness, altruism inhibits
fairness, and the non-monotonic rejection can cause fairness to overcome
selfishness, which cannot happen without high-offer rejections. Particularly
for the group-structured population with seven discrete strategies, we
analytically study the effect of population size, mutation, and migration on
fairness, selfishness, altruism, and spite. A larger population size cannot
change the dominance of fairness, but it promotes altruism and inhibits
selfishness and spite. Intermediate mutation maximizes selfishness and
fairness, and minimizes spite; intermediate mutation maximizes altruism for
intermediate migration and minimizes altruism otherwise. The existence of
migration inhibits selfishness and fairness, and promotes altruism; sufficient
migration promotes spite. Our study may provide important insights into the
evolutionary origin of fairness.Comment: 15 pages, 7 figures. Comments welcom
Convergence in Comparable Almost Periodic Reaction-Diffusion Systems with Dirichlet Boundary Condition
The paper is to study the asymptotic dynamics in nonmonotone comparable
almost periodic reaction-diffusion system with Dirichlet boundary condition,
which is comparable with uniformly stable strongly order-preserving system. By
appealing to the theory of skew-product semiflows, we obtain the asymptotic
almost periodicity of uniformly stable solutions to the comparable
reaction-diffusion system
Does the circularization radius exist or not for low angular momentum accretion?
If the specific angular momentum of accretion gas at large radius is small
compared to the local Keplerian value, one usually believes that there exists a
"circularization radius" beyond which the angular momentum of accretion flow is
almost a constant while within which a disk is formed and the angular momentum
roughly follows the Keplerian distribution. In this paper, we perform numerical
simulations to study whether the picture above is correct in the context of hot
accretion flow. We find that for a steady accretion flow, the "circularization
radius" does not exist and the angular momentum profile will be smooth
throughout the flow. However, for transient accretion systems, such as the
tidal disruption of a star by a black hole, a "turning point" should exist in
the radial profile of the angular momentum, which is conceptually similar to
the "circularization radius". At this radius, the viscous timescale equals the
life time of the accretion event. The specific angular momentum is close to
Keplerian within this radius, while beyond this radius the angular momentum is
roughly constant.Comment: 5 pages, 2 figures, accepted by MNRA
Coupled-Channel-Induced mixing of Charmonia and Testing Possible Assignments for and
The mass spectrum and the two-body open-charm decays of the
charmonium states are studied with the coupled-channel effects taken into
account. The coupled-channel-induced mixing effects among the excited vector
charmonia are studied. Based on our calculations of the masses and the decay
widths, we find that the tension between the observed properties of
and their conventional charmonia interpretations could be
softened.Comment: 13 pages, 5 figures, 5 table
Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out
This paper investigates the evolution of strategic play where players drawn
from a finite well-mixed population are offered the opportunity to play in a
public goods game. All players accept the offer. However, due to the
possibility of unforeseen circumstances, each player has a fixed probability of
being unable to participate in the game, unlike similar models which assume
voluntary participation. We first study how prescribed stochastic opting-out
affects cooperation in finite populations. Moreover, in the model, cooperation
is favored by natural selection over both neutral drift and defection if return
on investment exceeds a threshold value defined solely by the population size,
game size, and a player's probability of opting-out. Ultimately, increasing the
probability that each player is unable to fulfill her promise of participating
in the public goods game facilitates natural selection of cooperators. We also
use adaptive dynamics to study the coevolution of cooperation and opting-out
behavior. However, given rare mutations minutely different from the original
population, an analysis based on adaptive dynamics suggests that the over time
the population will tend towards complete defection and non-participation, and
subsequently, from there, participating cooperators will stand a chance to
emerge by neutral drift. Nevertheless, increasing the probability of
non-participation decreases the rate at which the population tends towards
defection when participating. Our work sheds light on understanding how
stochastic opting-out emerges in the first place and its role in the evolution
of cooperation.Comment: 30 pages, 4 figures. This is one of the student project papers arsing
from the Mathematics REU program at Dartmouth 2017 Summer. See
https://math.dartmouth.edu/~reu/ for more info. Comments are always welcom
Fundamental Plane of Black Hole Activity in Quiescent Regime
A correlation among the radio luminosity (), X-ray luminosity
(), and black hole mass () in active galactic nuclei
(AGNs) and black hole binaries is known to exist and is called the "Fundamental
Plane" of black hole activity. Yuan & Cui (2005) predicts that the radio/X-ray
correlation index, , changes from to
when decreases below a
critical value . While many works favor such a change, there are
also several works claiming the opposite. In this paper, we gather from
literature a largest quiescent AGN (defined as ) sample to date, consisting of sources. We find that these
quiescent AGNs follow a radio/X-ray relationship, in
excellent agreement with the Yuan \& Cui prediction. The reason for the
discrepancy between the present result and some previous works is that their
samples contain not only quiescent sources but also "normal" ones (i.e.,
). In this case, the quiescent sources will
mix up with those normal ones in and . The value of
will then be between and , with the exact value
being determined by the sample composition, i.e., the fraction of the quiescent
and normal sources. Based on this result, we propose that a more physical way
to study the Fundamental Plane is to replace and with
and , respectively.Comment: 11 pages, 7 figures, accepted for publication in The Astrophysical
Journa
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