5,340 research outputs found
On minimal additive complements of integers
Let . If , then the set is
called an additive complement to in . If no proper subset of
is an additive complement to , then is called a minimal additive
complement. Let . If there exists a positive integer
such that for all sufficiently large integers , then we call
eventually periodic. In this paper, we study the existence of a minimal
complement to when is eventually periodic or not. This partially
answers a problem of Nathanson.Comment: 13 page
Nuclear quantum shape-phase transitions in odd-mass systems
Microscopic signatures of nuclear ground-state shape phase transitions in
odd-mass Eu isotopes are explored starting from excitation spectra and
collective wave functions obtained by diagonalization of a core-quasiparticle
coupling Hamiltonian based on energy density functionals. As functions of the
physical control parameter -- the number of nucleons -- theoretical low-energy
spectra, two-neutron separation energies, charge isotope shifts, spectroscopic
quadrupole moments, and reduced transition matrix elements accurately
reproduce available data, and exhibit more pronounced discontinuities at
neutron number , compared to the adjacent even-even Sm and Gd isotopes.
The enhancement of the first-order quantum phase transition in odd-mass systems
can be attributed to a shape polarization effect of the unpaired proton which,
at the critical neutron number, starts predominantly coupling to Gd core nuclei
that are characterized by larger quadrupole deformation and weaker proton
pairing correlations compared to the corresponding Sm isotopes.Comment: 6 pages, 4 figure
Global analysis of quadrupole shape invariants based on covariant energy density functionals
Coexistence of different geometric shapes at low energies presents a
universal structure phenomenon that occurs over the entire chart of nuclides.
Studies of the shape coexistence are important for understanding the
microscopic origin of collectivity and modifications of shell structure in
exotic nuclei far from stability. The aim of this work is to provide a
systematic analysis of characteristic signatures of coexisting nuclear shapes
in different mass regions, using a global self-consistent theoretical method
based on universal energy density functionals and the quadrupole collective
model. The low-energy excitation spectrum and quadrupole shape invariants of
the two lowest states of even-even nuclei are obtained as solutions of
a five-dimensional collective Hamiltonian (5DCH) model, with parameters
determined by constrained self-consistent mean-field calculations based on the
relativistic energy density functional PC-PK1, and a finite-range pairing
interaction. The theoretical excitation energies of the states: ,
, , , , as well as the
values, are in very good agreement with the corresponding experimental values
for 621 even-even nuclei. Quadrupole shape invariants have been implemented to
investigate shape coexistence, and the distribution of possible
shape-coexisting nuclei is consistent with results obtained in recent
theoretical studies and available data. The present analysis has shown that,
when based on a universal and consistent microscopic framework of nuclear
density functionals, shape invariants provide distinct indicators and reliable
predictions for the occurrence of low-energy coexisting shapes. This method is
particularly useful for studies of shape coexistence in regions far from
stability where few data are available.Comment: 13 pages, 3 figures, accepted for publication in Phys. Rev.
STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting
Multi-step passenger demand forecasting is a crucial task in on-demand
vehicle sharing services. However, predicting passenger demand over multiple
time horizons is generally challenging due to the nonlinear and dynamic
spatial-temporal dependencies. In this work, we propose to model multi-step
citywide passenger demand prediction based on a graph and use a hierarchical
graph convolutional structure to capture both spatial and temporal correlations
simultaneously. Our model consists of three parts: 1) a long-term encoder to
encode historical passenger demands; 2) a short-term encoder to derive the
next-step prediction for generating multi-step prediction; 3) an
attention-based output module to model the dynamic temporal and channel-wise
information. Experiments on three real-world datasets show that our model
consistently outperforms many baseline methods and state-of-the-art models.Comment: 7 page
Multi-Person Brain Activity Recognition via Comprehensive EEG Signal Analysis
An electroencephalography (EEG) based brain activity recognition is a
fundamental field of study for a number of significant applications such as
intention prediction, appliance control, and neurological disease diagnosis in
smart home and smart healthcare domains. Existing techniques mostly focus on
binary brain activity recognition for a single person, which limits their
deployment in wider and complex practical scenarios. Therefore, multi-person
and multi-class brain activity recognition has obtained popularity recently.
Another challenge faced by brain activity recognition is the low recognition
accuracy due to the massive noises and the low signal-to-noise ratio in EEG
signals. Moreover, the feature engineering in EEG processing is time-consuming
and highly re- lies on the expert experience. In this paper, we attempt to
solve the above challenges by proposing an approach which has better EEG
interpretation ability via raw Electroencephalography (EEG) signal analysis for
multi-person and multi-class brain activity recognition. Specifically, we
analyze inter-class and inter-person EEG signal characteristics, based on which
to capture the discrepancy of inter-class EEG data. Then, we adopt an
Autoencoder layer to automatically refine the raw EEG signals by eliminating
various artifacts. We evaluate our approach on both a public and a local EEG
datasets and conduct extensive experiments to explore the effect of several
factors (such as normalization methods, training data size, and Autoencoder
hidden neuron size) on the recognition results. The experimental results show
that our approach achieves a high accuracy comparing to competitive
state-of-the-art methods, indicating its potential in promoting future research
on multi-person EEG recognition.Comment: 10 page
Extreme Equilibria in a General Negotiation Model
We study a bargaining model with a disagreement game between o¤ers and countero¤ers. In order to characterize the set of its subgame perfect equilibrium payo¤s, we provide a recursive technique that relies on the Pareto frontier of equilibrium payo¤s. When players have di¤erent time preferences, reaching an immediate agreement may not be Pareto e ¢ cient. The recursive technique developed in this paper generalizes that of Shaked and Sutton (1984) by incorporating the possibility of making unacceptable proposals into the backward induction analysis. Results from this paper extend all the previous …ndings and resolve some open issues in the current literature
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