An official website of the United States government
Random values from discrete distributions are typically generated from uniformly-random samples. A common technique is to use a cumulative distribution table (CDT) lookup for inversion sampling, but it is also possible to use Boolean functions to map a uniformly-random bit sequence into a value from a discrete distribution. This work presents a methodology for deriving such functions for any discrete distribution, encoding them in VHDL for implementation in combinational hardware, and (for moderate precision and sample space size) confirming the correctness of the produced distribution. The process is demonstrated using a discrete Gaussian distribution with a small sample space, but it is applicable to any discrete distribution with fixed parameters. Results are presented for sampling schemes from several submissions to the NIST PQC standardization process, comparing this method to CDT lookups on a Xilinx Artix-7 FPGA. The process produces compact solutions for distributions up to moderate size and precision.
more »
« less
Hydrodynamic effective field theories with discrete rotational symmetry
A bstract We develop a hydrodynamic effective field theory on the Schwinger-Keldysh contour for fluids with charge, energy, and momentum conservation, but only discrete rotational symmetry. The consequences of anisotropy on thermodynamics and first-order dissipative hydrodynamics are detailed in some simple examples in two spatial dimensions, but our construction extends to any spatial dimension and any rotation group (discrete or continuous). We find many possible terms in the equations of motion which are compatible with the existence of an entropy current, but not with the ability to couple the fluid to background gauge fields and vielbein.
more »
« less
- Award ID(s):
- 2145544
- PAR ID:
- 10431406
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 3
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract In this article, we obtain an optimal best-approximation-type result for fully discrete approximations of the transient Stokes problem. For the time discretization, we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete inf-sup condition. The analysis uses the technique of discrete maximal parabolic regularity. The results require only natural assumptions on the data and do not assume any additional smoothness of the solutions.more » « less
-
The use of mobile actuators for the control of spatially distributed systems governed by PDEs results in both implementational and computational challenges. First it requires the backward-in-time solution to the actuator guidance and the backward-in-time solution to the control operator Riccati equation. A way to address this computational challenge is to consider a continuous-discrete alternative whereby the mobile actuator is repositioned at discrete instances and resides in a specific spatial location for a certain time interval. In order to find optimal paths for a given time interval, a set of feasible locations is derived using the reachability set. These reachability sets are further constrained to take into account the time it takes to travel to any spatial position with a prescribed maximum velocity. The proposed hybrid continuous-discrete control and actuator guidance is demonstrated for a 2D diffusion PDE that uses no constraints and angular constraints on the actuator motion.more » « less
-
We study the radiative transfer of a spatially modulated plane wave incident on a half-space composed of a uniformly scattering and absorbing medium. For spatial frequencies that are large compared to the scattering coefficient, we find that first-order scattering governs the leading behavior of the radiance backscattered by the medium. The first-order scattering approximation reveals a specific curve on the backscattered hemisphere where the radiance is concentrated. Along this curve, the radiance assumes a particularly simple expression that is directly proportional to the phase function. These results are inherent to the radiative transfer equation at large spatial frequency and do not have a strong dependence on any particular optical property. Consequently, these results provide the means by which spatial frequency domain imaging technologies can directly measure the phase function of a sample. Numerical simulations using the discrete ordinate method along with the source integration interpolation method validate these theoretical findings.more » « less
-
Procedural functionality enables visual creators to rapidly edit, explore alternatives, and fine-tune artwork in many domains including illustration, motion graphics, and interactive animation. Symbolic procedural tools, such as textual programming languages, are highly expressive but often limit directly manipulating concrete artwork; whereas direct manipulation tools support some procedural expression but limit creators to pre-defined behaviors and inputs. Inspired by visions of using geometric input to create procedural relationships, we identify an opportunity to use vector geometry from artwork to specify expressive user-defined procedural functions. We present Drawing Transforms (DTs), a technique that enables the use of any drawing to procedurally transform the stylistic, spatial, and temporal properties of target artwork. We apply DTs in a prototype motion graphics system to author continuous and discrete transformations, modify multiple elements in a composition simultaneously, create animations, and control fine-grained procedural instantiation. We discuss how DTs can unify procedural authoring through direct manipulation across visual media domains.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP03(2022)082
