5,596 research outputs found
Applications of degree estimate for subalgebras
Let be a field of positive characteristic and be the free
algebra of rank two over . Based on the degree estimate done by Y.-C. Li and
J.-T. Yu, we extend the results of S.J. Gong and J.T. Yu's results: (1) An
element is a test element if and only if does not
belong to any proper retract of ; (2) Every endomorphism preserving the
automorphic orbit of a nonconstant element of is an automorphism; (3)
If there exists some injective endomorphism of such that
where , then is a coordinate. And
we reprove that all the automorphisms of are tame. Moreover, we also
give counterexamples for two conjectures established by Leonid Makar-Limanov,
V. Drensky and J.-T. Yu in the positive characteristic case.Comment: 12 page
A reversal coarse-grained analysis with application to an altered functional circuit in depression
Introduction:
When studying brain function using functional magnetic resonance imaging (fMRI) data containing tens of thousands of voxels, a coarse-grained approach – dividing the whole brain into regions of interest – is applied frequently to investigate the organization of the functional network on a relatively coarse scale. However, a coarse-grained scheme may average out the fine details over small spatial scales, thus rendering it difficult to identify the exact locations of functional abnormalities.
Methods:
A novel and general approach to reverse the coarse-grained approach by locating the exact sources of the functional abnormalities is proposed.
Results:
Thirty-nine patients with major depressive disorder (MDD) and 37 matched healthy controls are studied. A circuit comprising the left superior frontal gyrus (SFGdor), right insula (INS), and right putamen (PUT) exhibit the greatest changes between the patients with MDD and controls. A reversal coarse-grained analysis is applied to this circuit to determine the exact location of functional abnormalities.
Conclusions:
The voxel-wise time series extracted from the reversal coarse-grained analysis (source) had several advantages over the original coarse-grained approach: (1) presence of a larger and detectable amplitude of fluctuations, which indicates that neuronal activities in the source are more synchronized; (2) identification of more significant differences between patients and controls in terms of the functional connectivity associated with the sources; and (3) marked improvement in performing discrimination tasks. A software package for pattern classification between controls and patients is available in Supporting Information
Canonical Gauge Coupling Unification in the Standard Model with High-Scale Supersymmetry Breaking
Inspired by the string landscape and the unified gauge coupling relation in
the F-theory Grand Unified Theories (GUTs) and GUTs with suitable
high-dimensional operators, we study the canonical gauge coupling unification
and Higgs boson mass in the Standard Model (SM) with high-scale supersymmetry
breaking. In the SM with GUT-scale supersymmetry breaking, we achieve the gauge
coupling unification at about 5.3 x 10^{13} GeV, and the Higgs boson mass is
predicted to range from 130 GeV to 147 GeV. In the SM with supersymmetry
breaking scale from 10^4 GeV to 5.3 x 10^{13} GeV, gauge coupling unification
can always be realized and the corresponding GUT scale M_U is from 10^{16} GeV
to 5.3 x 10^{13} GeV, respectively. Also, we obtain the Higgs boson mass from
114.4 GeV to 147 GeV. Moreover, the discrepancies among the SM gauge couplings
at the GUT scale are less than about 4-6%. Furthermore, we present the SU(5)
and SO(10) models from the F-theory model building and orbifold constructions,
and show that we do not have the dimension-five and dimension-six proton decay
problems even if M_U \le 5 x 10^{15} GeV.Comment: RevTex4, 16 pages, 5 figures, version to appear in JHE
Cavity-based architecture to preserve quantum coherence and entanglement
Quantum technology relies on the utilization of resources, like quantum
coherence and entanglement, which allow quantum information and computation
processing. This achievement is however jeopardized by the detrimental effects
of the environment surrounding any quantum system, so that finding strategies
to protect quantum resources is essential. Non-Markovian and structured
environments are useful tools to this aim. Here we show how a simple
environmental architecture made of two coupled lossy cavities enables a switch
between Markovian and non-Markovian regimes for the dynamics of a qubit
embedded in one of the cavity. Furthermore, qubit coherence can be indefinitely
preserved if the cavity without qubit is perfect. We then focus on entanglement
control of two independent qubits locally subject to such an engineered
environment and discuss its feasibility in the framework of circuit quantum
electrodynamics. With up-to-date experimental parameters, we show that our
architecture allows entanglement lifetimes orders of magnitude longer than the
spontaneous lifetime without local cavity couplings. This cavity-based
architecture is straightforwardly extendable to many qubits for scalability.Comment: 12 pages, 9 figures, 1 table. To appear on Nature Scientific Report
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