3,582 research outputs found
Adiabatic connection at negative coupling strengths
The adiabatic connection of density functional theory (DFT) for electronic
systems is generalized here to negative values of the coupling strength
(with {\em attractive} electrons). In the extreme limit
a simple physical solution is presented and its implications
for DFT (as well as its limitations) are discussed. For two-electron systems (a
case in which the present solution can be calculated exactly), we find that an
interpolation between the limit and the opposite limit of
infinitely strong repulsion () yields a rather accurate
estimate of the second-order correlation energy E\cor\glt[\rho] for several
different densities , without using virtual orbitals. The same procedure
is also applied to the Be isoelectronic series, analyzing the effects of
near-degeneracy.Comment: 9 pages, submitted to PR
Novel properties of the Kohn-Sham exchange potential for open systems: application to the two-dimensional electron gas
The properties of the Kohn-Sham (KS) exchange potential for open systems in
thermodynamical equilibrium, where the number of particles is non-conserved,
are analyzed with the Optimized Effective Potential (OEP) method of Density
Functional Theory (DFT) at zero temperature. The quasi two-dimensional electron
gas (2DEG) is used as an illustrative example. The main findings are that the
KS exchange potential builds a significant barrier-like structure under slight
population of the second subband, and that both the asymptotic value of the KS
exchange potential and the inter-subband energy jump discontinuously at the
one-subband (1S) -> two-subband (2S) transition. The results obtained in this
system offer new insights on open problems of semiconductors, such as the
band-gap underestimation and the band-gap renormalization by photo-excited
carriers.Comment: 7 pages, 3 figures, uses epl.cls(included), accepted for publication
in Europhysics Letter
An Active Inference Approach to Modeling Structure Learning: Concept Learning as an Example Case
Within computational neuroscience, the algorithmic and neural basis of structure learning
remains poorly understood. Concept learning is one primary example, which requires
both a type of internal model expansion process (adding novel hidden states that explain
new observations), and a model reduction process (merging different states into one
underlying cause and thus reducing model complexity via meta-learning). Although
various algorithmic models of concept learning have been proposed within machine
learning and cognitive science, many are limited to various degrees by an inability
to generalize, the need for very large amounts of training data, and/or insufficiently
established biological plausibility. Using concept learning as an example case, we
introduce a novel approach for modeling structure learningâand specifically state-space
expansion and reductionâwithin the active inference framework and its accompanying
neural process theory. Our aim is to demonstrate its potential to facilitate a novel line
of active inference research in this area. The approach we lay out is based on the idea
that a generative model can be equipped with extra (hidden state or cause) âslotsâ that
can be engaged when an agent learns about novel concepts. This can be combined
with a Bayesian model reduction process, in which any concept learningâassociated
with these slotsâcan be reset in favor of a simpler model with higher model evidence.
We use simulations to illustrate this modelâs ability to add new concepts to its state
space (with relatively few observations) and increase the granularity of the concepts it
currently possesses. We also simulate the predicted neural basis of these processes.
We further show that it can accomplish a simple form of âone-shotâ generalization to
new stimuli. Although deliberately simple, these simulation results highlight ways in which
active inference could offer useful resources in developing neurocomputational models of
structure learning. They provide a template for how future active inference research could
apply this approach to real-world structure learning problems and assess the added utility
it may offer
Linear Parsing Expression Grammars
PEGs were formalized by Ford in 2004, and have several pragmatic operators
(such as ordered choice and unlimited lookahead) for better expressing modern
programming language syntax. Since these operators are not explicitly defined
in the classic formal language theory, it is significant and still challenging
to argue PEGs' expressiveness in the context of formal language theory.Since
PEGs are relatively new, there are several unsolved problems.One of the
problems is revealing a subclass of PEGs that is equivalent to DFAs. This
allows application of some techniques from the theory of regular grammar to
PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is
equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some
patterns of recursive nonterminal in PEGs, and include the full set of ordered
choice, unlimited lookahead, and greedy repetition, which are characteristic of
PEGs. Although the conversion judgement of parsing expressions into DFAs is
undecidable in general, the formalism of LPEGs allows for a syntactical
judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin
Particle-Number Restoration within the Energy Density Functional Formalism
We give a detailed analysis of the origin of spurious divergences and finite
steps that have been recently identified in particle-number restoration
calculations within the nuclear energy density functional framework. We isolate
two distinct levels of spurious contributions to the energy. The first one is
encoded in the definition of the basic energy density functional itself whereas
the second one relates to the canonical procedure followed to extend the use of
the energy density functional to multi-reference calculations. The first level
of spuriosity relates to the long-known self-interaction problem and to the
newly discussed self-pairing interaction process which might appear when
describing paired systems with energy functional methods using auxiliary
reference states of Bogoliubov or BCS type. A minimal correction to the second
level of spuriosity to the multi-reference nuclear energy density functional
proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to
remove completely the anomalies encountered in particle-number restored
calculations. In particular, it restores sum-rules over (positive) particle
numbers that are to be fulfilled by the particle-number-restored formalism. The
correction is found to be on the order of several hundreds of keVs up to about
1 MeV in realistic calculations, which is small compared to the total binding
energy, but often accounts for a substantial percentage of the energy gain from
particle-number restoration and is on the same energy scale as the excitations
one addresses with multi-reference energy density functional methods.Comment: 37 pages, 14 figures, accepted for publication in PR
A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations
The Hartree-Fock equations are modified to directly yield Wannier functions
following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)].
This approach circumvents the a posteriori application of the Wannier
transformation to Bloch functions. I give a novel and rigorous derivation of
the relevant equations by introducing an orthogonalizing potential to ensure
the orthogonality among the resulting functions. The properties of these,
so-called a priori Wannier functions, are analyzed and the relation of the
modified Hartree-Fock equations to the conventional, Bloch-function-based
equations is elucidated. It is pointed out that the modified equations offer a
different route to maximally localized Wannier functions. Their computational
solution is found to involve an effort that is comparable to the effort for the
solution of the conventional equations. Above all, I show how a priori Wannier
functions can be obtained by a modification of the Kohn-Sham equations of
density-functional theory.Comment: 7 pages, RevTeX4, revise
Dynamic causal modelling of immune heterogeneity
An interesting inference drawn by some COVID-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection-even at the start of the current pandemic. This paper introduces a model of the immune response to a virus. This is based upon the same sort of mean-field dynamics as used in epidemiology. However, in place of the location, clinical status, and other attributes of people in an epidemiological model, we consider the state of a virus, B and T-lymphocytes, and the antibodies they generate. Our aim is to formalise some key hypotheses as to the mechanism of resistance. We present a series of simple simulations illustrating changes to the dynamics of the immune response under these hypotheses. These include attenuated viral cell entry, pre-existing cross-reactive humoral (antibody-mediated) immunity, and enhanced T-cell dependent immunity. Finally, we illustrate the potential application of this sort of model by illustrating variational inversion (using simulated data) of this model to illustrate its use in testing hypotheses. In principle, this furnishes a fast and efficient immunological assay-based on sequential serology-that provides a (1) quantitative measure of latent immunological responses and (2) a Bayes optimal classification of the different kinds of immunological response (c.f., glucose tolerance tests used to test for insulin resistance). This may be especially useful in assessing SARS-CoV-2 vaccines
Dynamical coherent-potential approximation approach to excitation spectra in 3d transition metals
First-principles dynamical CPA (Coherent-Potential Approximation) for
electron correlations has been developed further by taking into account
higher-order dynamical corrections with use of the asymptotic approximation.
The theory is applied to the investigations of a systematic change of
excitation spectra in transition metals from Sc to Cu at finite
temperatures. It is shown that the dynamical effects damp main peaks in the
densities of states (DOS) obtained by the local density approximation to the
density functional theory, reduce the band broadening due to thermal spin
fluctuations, create the Mott-Hubbard type bands in the case of fcc Mn and fcc
Fe, and create a small hump corresponding to the `6 eV' satellite in the case
of Co, Ni, and Cu. Calculated DOS explain the X-ray photoelectron spectroscopy
data as well as the bremsstrahlung isochromat spectroscopy data. Moreover, it
is found that screening effects on the exchange energy parameters are
significant for understanding the spectra in magnetic transition metals.Comment: To be published in Phys. Rev.
Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability
We recently presented a constructive solution to the N-representability
problem of the two-electron reduced density matrix (2-RDM)---a systematic
approach to constructing complete conditions to ensure that the 2-RDM
represents a realistic N-electron quantum system [D. A. Mazziotti, Phys. Rev.
Lett. 108, 263002 (2012)]. In this paper we provide additional details and
derive further N-representability conditions on the 2-RDM that follow from the
constructive solution. The resulting conditions can be classified into a
hierarchy of constraints, known as the (2,q)-positivity conditions where the q
indicates their derivation from the nonnegativity of q-body operators. In
addition to the known T1 and T2 conditions, we derive a new class of
(2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity
conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of
(2,6)-positivity conditions. The constraints obtained can be divided into two
general types: (i) lifting conditions, that is conditions which arise from
lifting lower (2,q)-positivity conditions to higher (2,q+1)-positivity
conditions and (ii) pure conditions, that is conditions which cannot be derived
from a simple lifting of the lower conditions. All of the lifting conditions
and the pure (2,q)-positivity conditions for q>3 require tensor decompositions
of the coefficients in the model Hamiltonians. Subsets of the new
N-representability conditions can be employed with the previously known
conditions to achieve polynomially scaling calculations of ground-state
energies and 2-RDMs of many-electron quantum systems even in the presence of
strong electron correlation
Inter-cluster reactivity of Metallo-aromatic and anti-aromatic Compounds and Their Applications in Molecular Electronics: A Theoretical Investigation
Local reactivity descriptors such as the condensed local softness and Fukui
function have been employed to investigate the inter-cluster reactivity of the
metallo-aromatic (Al4Li- and Al4Na-) and anti-aromatic (Al4Li4 and Al4Na4)
compounds. We use the concept of group softness and group Fukui function to
study the strength of the nucleophilicity of the Al4 unit in these compounds.
Our analysis shows that the trend of nucleophilicity of the Al4 unit in the
above clusters is as follows;
Al4Li- > Al4Na- > Al4Li4 > Al4Na 4
For the first time we have used the reactivity descriptors to show that these
clusters can act as electron donating systems and thus can be used as a
molecular cathode.Comment: 23 pages, 1 figure and 1 table of conten
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