2,886 research outputs found
On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes
We show that if is an infinitesimal elementary supergroup scheme of
height , then the cohomological spectrum of is naturally
homeomorphic to the variety of supergroup homomorphisms
from a certain (non-algebraic) affine
supergroup scheme into . In the case , we further
identify the cohomological support variety of a finite-dimensional
-supermodule as a subset of . We then discuss how our
methods, when combined with recently-announced results by Benson, Iyengar,
Krause, and Pevtsova, can be applied to extend the homeomorphism
to arbitrary infinitesimal unipotent supergroup
schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and
3.3. Simplified the proof of Proposition 3.3.
Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition
Hierarchical uncertainty quantification can reduce the computational cost of
stochastic circuit simulation by employing spectral methods at different
levels. This paper presents an efficient framework to simulate hierarchically
some challenging stochastic circuits/systems that include high-dimensional
subsystems. Due to the high parameter dimensionality, it is challenging to both
extract surrogate models at the low level of the design hierarchy and to handle
them in the high-level simulation. In this paper, we develop an efficient
ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the
surrogate models at the low level. In order to avoid the curse of
dimensionality, we employ tensor-train decomposition at the high level to
construct the basis functions and Gauss quadrature points. As a demonstration,
we verify our algorithm on a stochastic oscillator with four MEMS capacitors
and 184 random parameters. This challenging example is simulated efficiently by
our simulator at the cost of only 10 minutes in MATLAB on a regular personal
computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD
of Integrated Circuits and System
Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques
Process variations are a major concern in today's chip design since they can
significantly degrade chip performance. To predict such degradation, existing
circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically
too slow. Therefore, novel fast stochastic simulators are highly desired. This
paper first reviews our recently developed stochastic testing simulator that
can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we
develop a fast hierarchical stochastic spectral simulator to simulate a complex
circuit or system consisting of several blocks. We further present a fast
simulation approach based on anchored ANOVA (analysis of variance) for some
design problems with many process variations. This approach can reduce the
simulation cost and can identify which variation sources have strong impacts on
the circuit's performance. The simulation results of some circuit and MEMS
examples are reported to show the effectiveness of our simulatorComment: Accepted to IEEE Custom Integrated Circuits Conference in June 2014.
arXiv admin note: text overlap with arXiv:1407.302
Cohomology for infinitesimal unipotent algebraic and quantum groups
In this paper we study the structure of cohomology spaces for the Frobenius
kernels of unipotent and parabolic algebraic group schemes and of their quantum
analogs. Given a simple algebraic group , a parabolic subgroup , and
its unipotent radical , we determine the ring structure of the cohomology
ring . We also obtain new results on computing
as an -module where is a
simple -module with high weight in the closure of the bottom
-alcove. Finally, we provide generalizations of all our results to the
quantum situation.Comment: 18 pages. Some proofs streamlined over previous version. Additional
details added to some proofs in Section
Real-Time Prediction of Gas Flow Dynamics in Diesel Engines using a Deep Neural Operator Framework
We develop a data-driven deep neural operator framework to approximate
multiple output states for a diesel engine and generate real-time predictions
with reasonable accuracy. As emission norms become more stringent, the need for
fast and accurate models that enable analysis of system behavior have become an
essential requirement for system development. The fast transient processes
involved in the operation of a combustion engine make it difficult to develop
accurate physics-based models for such systems. As an alternative to physics
based models, we develop an operator-based regression model (DeepONet) to learn
the relevant output states for a mean-value gas flow engine model using the
engine operating conditions as input variables. We have adopted a mean-value
model as a benchmark for comparison, simulated using Simulink. The developed
approach necessitates using the initial conditions of the output states to
predict the accurate sequence over the temporal domain. To this end, a
sequence-to-sequence approach is embedded into the proposed framework. The
accuracy of the model is evaluated by comparing the prediction output to ground
truth generated from Simulink model. The maximum relative error
observed was approximately . The sensitivity of the DeepONet model is
evaluated under simulated noise conditions and the model shows relatively low
sensitivity to noise. The uncertainty in model prediction is further assessed
by using a mean ensemble approach. The worst-case error at the boundary was found to be . The proposed framework provides the
ability to predict output states in real-time and enables data-driven learning
of complex input-output operator mapping. As a result, this model can be
applied during initial development stages, where accurate models may not be
available.Comment: Updated manuscript title to better reflect this work and field of
stud
RepSeq-A database of amino acid repeats present in lower eukaryotic pathogens
BACKGROUND Amino acid repeat-containing proteins have a broad range of functions and their identification is of relevance to many experimental biologists. In human-infective protozoan parasites (such as the Kinetoplastid and Plasmodium species), they are implicated in immune evasion and have been shown to influence virulence and pathogenicity. RepSeq http://repseq.gugbe.com is a new database of amino acid repeat-containing proteins found in lower eukaryotic pathogens. The RepSeq database is accessed via a web-based application which also provides links to related online tools and databases for further analyses. RESULTS The RepSeq algorithm typically identifies more than 98% of repeat-containing proteins and is capable of identifying both perfect and mismatch repeats. The proportion of proteins that contain repeat elements varies greatly between different families and even species (3 - 35% of the total protein content). The most common motif type is the Sequence Repeat Region (SRR) - a repeated motif containing multiple different amino acid types. Proteins containing Single Amino Acid Repeats (SAARs) and Di-Peptide Repeats (DPRs) typically account for 0.5 - 1.0% of the total protein number. Notable exceptions are P. falciparum and D. discoideum, in which 33.67% and 34.28% respectively of the predicted proteomes consist of repeat-containing proteins. These numbers are due to large insertions of low complexity single and multi-codon repeat regions. CONCLUSION The RepSeq database provides a repository for repeat-containing proteins found in parasitic protozoa. The database allows for both individual and cross-species proteome analyses and also allows users to upload sequences of interest for analysis by the RepSeq algorithm. Identification of repeat-containing proteins provides researchers with a defined subset of proteins which can be analysed by expression profiling and functional characterisation, thereby facilitating study of pathogenicity and virulence factors in the parasitic protozoa. While primarily designed for kinetoplastid work, the RepSeq algorithm and database retain full functionality when used to analyse other species
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