655 research outputs found
Numerical Verification of Affine Systems with up to a Billion Dimensions
Affine systems reachability is the basis of many verification methods. With
further computation, methods exist to reason about richer models with inputs,
nonlinear differential equations, and hybrid dynamics. As such, the scalability
of affine systems verification is a prerequisite to scalable analysis for more
complex systems. In this paper, we improve the scalability of affine systems
verification, in terms of the number of dimensions (variables) in the system.
The reachable states of affine systems can be written in terms of the matrix
exponential, and safety checking can be performed at specific time steps with
linear programming. Unfortunately, for large systems with many state variables,
this direct approach requires an intractable amount of memory while using an
intractable amount of computation time. We overcome these challenges by
combining several methods that leverage common problem structure. Memory is
reduced by exploiting initial states that are not full-dimensional and safety
properties (outputs) over a few linear projections of the state variables.
Computation time is saved by using numerical simulations to compute only
projections of the matrix exponential relevant for the verification problem.
Since large systems often have sparse dynamics, we use Krylov-subspace
simulation approaches based on the Arnoldi or Lanczos iterations. Our method
produces accurate counter-examples when properties are violated and, in the
extreme case with sufficient problem structure, can analyze a system with one
billion real-valued state variables
From disease incubation to disease receipt:Representing epidemics and race in pre- and post-second world war American cinema (1931–1939 and 1950–1962)
This article analyses continuities and changes in how disease has been instrumentalised in cinema as a way of conceptualizing race—comparing five films depicting epidemics produced before the Second World War and five after. In the 1930s films, non-white populations often passively accept assistance in dealing with epidemic disease—a paternalistic white savior narrative—but not always with “gratitude”, and sometimes direct resistance. Here, epidemics take root in physical sites of economic “underdevelopment”, perpetuated further by perceived “premodern” cultural practices demarcated down the lines of race or ethnicity, and intersect with other gendered and socio-economic categories. After the war, while some cinematic tropes such as the “white knight” continue, other narratives emerge including a shift in emphasis away from the Othered environment as the nexus of disease (the disease’s “incubation”), and towards greater alarm about the appearance of disease within recipient, frequently white, communities
From disease incubation to disease receipt:Representing epidemics and race in pre- and post-second world war American cinema (1931–1939 and 1950–1962)
This article analyses continuities and changes in how disease has been instrumentalised in cinema as a way of conceptualizing race—comparing five films depicting epidemics produced before the Second World War and five after. In the 1930s films, non-white populations often passively accept assistance in dealing with epidemic disease—a paternalistic white savior narrative—but not always with “gratitude”, and sometimes direct resistance. Here, epidemics take root in physical sites of economic “underdevelopment”, perpetuated further by perceived “premodern” cultural practices demarcated down the lines of race or ethnicity, and intersect with other gendered and socio-economic categories. After the war, while some cinematic tropes such as the “white knight” continue, other narratives emerge including a shift in emphasis away from the Othered environment as the nexus of disease (the disease’s “incubation”), and towards greater alarm about the appearance of disease within recipient, frequently white, communities
Staggered Currents in the Vortex Core
We study the electronic structure of the vortex core in the cuprates using
the U(1) slave-boson mean-field wavefunctions and their Gutzwiller projection.
We conclude that there exists local orbital antiferromagnetic order in the core
near optimal doping. We compare the results with that of BCS theory and analyze
the spatial dependence of the local tunneling density of states.Comment: 4 pages, 3 figure
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