785 research outputs found
Quantum Information-Assisted Complete Active Space Optimization (QICAS)
Automated active space selection is arguably one of the most challenging and
essential aspects of multiconfigurational methods. In this work we propose an
effective quantum information-assisted complete active space optimization
(QICAS) scheme. What sets QICAS apart from other correlation-based selection
schemes is (i) the use of unique measures from quantum information that assess
the correlation in electronic structures in an unambiguous and predictive
manner, and (ii) an orbital optimization step that minimizes the correlation
discarded by the active space approximation. Equipped with these features QICAS
yields for smaller correlated molecules sets of optimized orbitals with respect
to which the CASCI energy reaches the corresponding CASSCF energy within
chemical accuracy. For more challenging systems such as the Chromium dimer,
QICAS offers an excellent starting point for CASSCF by greatly reducing the
number of iterations required for numerical convergence. Accordingly, our study
validates a profound empirical conjecture: the energetically optimal non-active
spaces are predominantly those that contain the least entanglement
symQV: Automated Symbolic Verification of Quantum Programs
We present symQV, a symbolic execution framework for writing and verifying
quantum computations in the quantum circuit model. symQV can automatically
verify that a quantum program complies with a first-order specification. We
formally introduce a symbolic quantum program model. This allows to encode the
verification problem in an SMT formula, which can then be checked with a
delta-complete decision procedure. We also propose an abstraction technique to
speed up the verification process. Experimental results show that the
abstraction improves symQV's scalability by an order of magnitude to quantum
programs with 24 qubits (a 2^24-dimensional state space).Comment: This is the extended version of a paper with the same title that
appeared at FM 2023. Tool available at doi.org/10.5281/zenodo.740032
Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0,
1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions
of linear parabolic stochastic partial differential equations on bounded
Lipschitz domains O\subset R^d. The Besov smoothness determines the order of
convergence that can be achieved by nonlinear approximation schemes. The proofs
are based on a combination of weighted Sobolev estimates and characterizations
of Besov spaces by wavelet expansions.Comment: 32 pages, 3 figure
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters
Recently, a stability theory has been developed to study the linear stability
of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory
provides sufficient conditions for a fixed point of an MPRK scheme to be stable
as well as for the convergence of an MPRK scheme towards the steady state of
the corresponding initial value problem, whereas the main assumption is that
the initial value is sufficiently close to the steady state. Initially,
numerical experiments in several publications indicated that these linear
stability properties are not only local, but even global, as is the case for
general linear methods. Recently, however, it was discovered that the linear
stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture
is that this is a result of negative Runge--Kutta (RK) parameters of MPDeC(8)
and that linear stability is indeed global, if the RK parameters are
nonnegative. To support this conjecture, we examine the family of
MPRK22() methods with negative RK parameters and show that even among
these methods there are methods for which the stability properties are only
local. However, this local linear stability is not observed for
MPRK22() schemes with nonnegative Runge-Kutta parameters.Comment: 19 pages, 3 figure
SpecAttack: Specification-Based Adversarial Training for Deep Neural Networks
Safety specification-based adversarial training aims to generate examples
violating a formal safety specification and therefore provides approaches for
repair. The need for maintaining high prediction accuracy while ensuring the
save behavior remains challenging. Thus we present SpecAttack, a
query-efficient counter-example generation and repair method for deep neural
networks. Using SpecAttack allows specifying safety constraints on the model to
find inputs that violate these constraints. These violations are then used to
repair the neural network via re-training such that it becomes provably safe.
We evaluate SpecAttack's performance on the task of counter-example generation
and repair. Our experimental evaluation demonstrates that SpecAttack is in most
cases more query-efficient than comparable attacks, yields counter-examples of
higher quality, with its repair technique being more efficient, maintaining
higher functional correctness, and provably guaranteeing safety specification
compliance
Self-Supervised Learning for Annotation Efficient Biomedical Image Segmentation
The scarcity of high-quality annotated data is omnipresent in machine learning. Especially in biomedical segmentation applications, experts need to spend a lot of their time into annotating due to the complexity. Hence, methods to reduce such efforts are desired. Self-Supervised Learning (SSL) is an emerging field that increases performance when unannotated data is present. However, profound studies regarding segmentation tasks and small datasets are still absent. A comprehensive qualitative and quantitative evaluation is conducted, examining SSL's applicability with a focus on biomedical imaging. We consider various metrics and introduce multiple novel application-specific measures. All metrics and state-of-the-art methods are provided in a directly applicable software package. We show that SSL can lead to performance improvements of up to 10%, which is especially notable for methods designed for segmentation tasks. SSL is a sensible approach to data-efficient learning, especially for biomedical applications, where generating annotations requires much effort. Additionally, our extensive evaluation pipeline is vital since there are significant differences between the various approaches. We provide biomedical practitioners with an overview of innovative data-efficient solutions and a novel toolbox for their own application of new approaches. Our pipeline for analyzing SSL methods is provided as a ready-to-use software package
Lingunite-a high-pressure plagioclase polymorph at mineral interfaces in doleritic rock of the Lockne impact structure (Sweden)
Lingunite nanocrystals and amorphous plagioclase (maskelynite) are identified at the contacts
between augite and labradorite wedge-shaped interfaces in the doleritic rocks of the Lockne impact
structure in Sweden. The occurrence of lingunite suggests that the local pressure was above 19 GPa
and the local temperature overwhelmed 1000 °C. These values are up to 10 times higher than previous
values estimated numerically for bulk pressure and temperature. High shock-induced temperatures
are manifested by maskelynite injections into microfractures in augite located next to the wedges.
We discuss a possible model of shock heterogeneity at mineral interfaces, which may lead to longer
duration of the same shock pressure and a concentration of high temperature thus triggering the
kinetics of labradorite transformation into lingunite and maskelynite
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