•Play-to-earn (P2E) video gaming is a form of digital labor that blurs work and play.•P2E player-workers experience precarity in various platform-mediated ways.•Capital-labor relationships in P2E ...gaming are reconfigured through blockchain.•Blockchain technologies are facilitating the ongoing financialization of labor.
A recent economic phenomenon has emerged where gamers can earn money by playing blockchain-based games and accumulating cryptocurrency rewards. Known as “play-to-earn” (P2E), this gaming model has drawn a large following of economically struggling players during the pandemic, many of whom are in the Global South. This paper positions P2E gaming as an emerging form of digital labor where work and play are blurred. Using the highly popular P2E game Axie Infinity as a case study, this paper traces the everyday realities of players as workers through document analysis of the grey literature and textual analysis of Reddit user comments. The results reveal a form of blockchain-based precarity that is manifested in volatile earnings, insecure contractual “employment” and onerous working conditions among player-workers. Such precarity is driven by P2E’s embeddedness within broader cryptocurrency markets and the platformed blockchain ecosystem, the reworking of capital-labor relationships that are distinguished by ownership of productive virtual assets, and by ongoing code-enabled changes to P2E’s platform governance mechanisms. Examining P2E through a precarity lens reflects the ongoing financialization of labor that is enabled by blockchain.
In this paper we construct a generating function quadratic at infinity for any exact Lagrangian in \(\mathbb R^{2n}\) equal to \(\mathbb R^n\) outside a compact set. This type of Lagrangian is ...equivalent to a Lagrangian filling in \(D^{2n}\) of the standard Legendrian unknot \(S^{n-1}\). Generating functions of the type we construct are related to the space \(\mathcal M_\infty\) considered by Eliashberg and Gromov. We also show that \(\mathcal M_\infty\) is the homotopy fiber of the so-called Hatcher-Waldhausen map. This further relates the understanding of exact Lagrangians (and Legendrians) to algebraic K-theory of spaces. As a result of this and the result by B\"okstedt that the Hatcher-Waldhausen map is a rational homotopy equivalence we prove that the stable Lagrangian Gauss map (relative boundary) of the Lagrangian is homotopy trivial.
We are developing tools for working with arbitrary left-exact localizations of ∞-topoi. We introduce a notion of higher sheaf with respect to an arbitrary set of maps Σ in an ∞-topos E. We show that ...the full subcategory of higher sheaves Sh(E,Σ) is an ∞-topos, and that the sheaf reflection E→Sh(E,Σ) is the left-exact localization generated by Σ. The proof depends on the notion of congruence, which is a substitute for the notion of Grothendieck topology in 1-topos theory.
Let f:Rn→R be a non-constant polynomial function. This paper studies the existence of the following global Łojasiewicz gradient inequality and Łojasiewicz gradient inequality at ...infinity‖∇f(x)‖≥cmin{|f(x)−λ|θ,|f(x)−λ|μ} for x∈Rn and for ‖x‖≫1, where c>0 and θ,μ,λ∈R are constants. We focus our attention on some cases where the exponents are non-negative and belong to 0,1). Moreover, we give some applications in global optimization for the existence of these inequalities with the exponents smaller than 1.
•A Robust perimeter control based on an MFD-based traffic model with partial information feedback is developed.•H∞, observer-based P and PI robust controllers are designed.•Set-point accumulations & ...control values are obtained off-line using an optimization program.•Control parameters are obtained from an LMI problem derived based on the Lyapunov theory.•Control design addresses the correlation between different directions of the perimeter control signals.
Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.
In this note, we investigate the unique continuation property and the sign changing behavior of weak solutions to \(-\Delta u =Vu\) near infinity under certain conditions on the blow-up rate of the ...potential \(V\) near infinity.
TUG-OF-WAR AND THE INFINITY LAPLACIAN PERES, YUVAL; SCHRAMM, ODED; SHEFFIELD, SCOTT ...
Journal of the American Mathematical Society,
01/2009, Letnik:
22, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We prove that every bounded Lipschitz function
F
F
on a subset
Y
Y
of a length space
X
X
admits a
tautest
extension to
X
X
, i.e., a unique Lipschitz extension
u
:
X
→
R
u:X \rightarrow \mathbb {R}
...for which
Lip
U
u
=
Lip
∂
U
u
\operatorname {Lip}_U u =\operatorname {Lip}_{\partial U} u
for all open
U
⊂
X
∖
Y
U \subset X\smallsetminus Y
. This was previously known only for bounded domains in
R
n
\mathbb {R}^n
, in which case
u
u
is
infinity harmonic
; that is, a viscosity solution to
Δ
∞
u
=
0
\Delta _\infty u = 0
, where
\
Δ
∞
u
=
|
∇
u
|
−
2
∑
i
,
j
u
x
i
u
x
i
x
j
u
x
j
.
\Delta _\infty u = |\nabla u|^{-2} \sum _{i,j} u_{x_i} u_{x_ix_j} u_{x_j}.
\
We also prove the first general uniqueness results for
Δ
∞
u
=
g
\Delta _{\infty } u = g
on bounded subsets of
R
n
\mathbb {R}^n
(when
g
g
is uniformly continuous and bounded away from
0
0
) and analogous results for bounded length spaces. The proofs rely on a new game-theoretic description of
u
u
. Let
u
ε
(
x
)
u^\varepsilon (x)
be the value of the following two-player zero-sum game, called
tug-of-war
: fix
x
0
=
x
∈
X
∖
Y
x_0=x\in X \smallsetminus Y
. At the
k
t
h
k^{\mathrm {th}}
turn, the players toss a coin and the winner chooses an
x
k
x_k
with
d
(
x
k
,
x
k
−
1
)
>
ε
d(x_k, x_{k-1})> \varepsilon
. The game ends when
x
k
∈
Y
x_k \in Y
, and player
I
’s payoff is
F
(
x
k
)
−
ε
2
2
∑
i
=
0
k
−
1
g
(
x
i
)
F(x_k) - \frac {\varepsilon ^2}{2}\sum _{i=0}^{k-1} g(x_i)
. We show that
‖
u
ε
−
u
‖
∞
→
0
\|u^\varepsilon - u\|_{\infty } \to 0
. Even for bounded domains in
R
n
\mathbb {R}^n
, the game theoretic description of infinity harmonic functions yields new intuition and estimates; for instance, we prove power law bounds for infinity harmonic functions in the unit disk with boundary values supported in a
δ
\delta
-neighborhood of a Cantor set on the unit circle.
Upper and lower bounds are derived on the capacity of the free-space optical intensity channel. This channel has a nonnegative input (representing the transmitted optical intensity), which is ...corrupted by additive white Gaussian noise. To preserve the battery and for safety reasons, the input is constrained in both its average and its peak power. For a fixed ratio of the allowed average power to the allowed peak power, the difference between the upper and the lower bound tends to zero as the average power tends to infinity and their ratio tends to one as the average power tends to zero. When only an average power constraint is imposed on the input, the difference between the bounds tends to zero as the allowed average power tends to infinity, and their ratio tends to a constant as the allowed average power tends to zero.
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