690 research outputs found
Existence and uniqueness for Mean Field Games with state constraints
In this paper, we study deterministic mean field games for agents who operate
in a bounded domain. In this case, the existence and uniqueness of Nash
equilibria cannot be deduced as for unrestricted state space because, for a
large set of initial conditions, the uniqueness of the solution to the
associated minimization problem is no longer guaranteed. We attack the problem
by interpreting equilibria as measures in a space of arcs. In such a relaxed
environment the existence of solutions follows by set-valued fixed point
arguments. Then, we give a uniqueness result for such equilibria under a
classical monotonicity assumption
The singular continuous diffraction measure of the Thue-Morse chain
The paradigm for singular continuous spectra in symbolic dynamics and in
mathematical diffraction is provided by the Thue-Morse chain, in its
realisation as a binary sequence with values in . We revisit this
example and derive a functional equation together with an explicit form of the
corresponding singular continuous diffraction measure, which is related to the
known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio
Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm
In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on
graphs possessing quantum decomposition (QD graphs) have been calculated by a
new method based on spectral distribution associated to their adjacency matrix.
Here in this paper, it is shown that the continuous-time quantum walk on any
arbitrary graph can be investigated by spectral distribution method, simply by
using Krylov subspace-Lanczos algorithm to generate orthonormal bases of
Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new
type of graphs possessing generalized quantum decomposition have been
introduced, where this is achieved simply by relaxing some of the constrains
imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit
vectors of strata are identical with the orthonormal basis produced by Lanczos
algorithm. Moreover, it is shown that probability amplitude of observing walk
at a given vertex is proportional to its coefficient in the corresponding unit
vector of its stratum, and it can be written in terms of the amplitude of its
stratum. Finally the capability of Lanczos-based algorithm for evaluation of
walk on arbitrary graphs (GQD or non-QD types), has been tested by calculating
the probability amplitudes of quantum walk on some interesting finite
(infinite) graph of GQD type and finite (infinite) path graph of non-GQD type,
where the asymptotic behavior of the probability amplitudes at infinite limit
of number of vertices, are in agreement with those of central limit theorem of
Ref.\cite{nko}.Comment: 29 pages, 4 figure
A symmetry group of a Thue-Morse quasicrystal
We present a method of coding general self-similar structures. In particular,
we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal,
i.e., of a nonperiodic ground state of a certain translation-invariant,
exponentially decaying interaction.Comment: 6 pages, Late
An Arabidopsis jmjC domain protein protects transcribed genes from DNA methylation at CHG sites
Differential cytosine methylation of genes and transposons is important for maintaining integrity of plant genomes. In Arabidopsis, transposons are heavily methylated at both CG and non-CG sites, whereas the non-CG methylation is rarely found in active genes. Our previous genetic analysis suggested that a jmjC domain-containing protein IBM1 (increase in BONSAI methylation 1) prevents ectopic deposition of non-CG methylation, and this process is necessary for normal Arabidopsis development. Here, we directly determined the genomic targets of IBM1 through high-resolution genome-wide analysis of DNA methylation. The ibm1 mutation induced extensive hyper-methylation in thousands of genes. Transposons were unaffected. Notably, long transcribed genes were most severely affected. Methylation of genes is limited to CG sites in wild type, but CHG sites were also methylated in the ibm1 mutant. The ibm1-induced hyper-methylation did not depend on previously characterized components of the RNAi-based DNA methylation machinery. Our results suggest novel transcription-coupled mechanisms to direct genic methylation not only at CG but also at CHG sites. IBM1 prevents the CHG methylation in genes, but not in transposons
Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels
We investigate entanglement transmission over an unknown channel in the
presence of a third party (called the adversary), which is enabled to choose
the channel from a given set of memoryless but non-stationary channels without
informing the legitimate sender and receiver about the particular choice that
he made. This channel model is called arbitrarily varying quantum channel
(AVQC). We derive a quantum version of Ahlswede's dichotomy for classical
arbitrarily varying channels. This includes a regularized formula for the
common randomness-assisted capacity for entanglement transmission of an AVQC.
Quite surprisingly and in contrast to the classical analog of the problem
involving the maximal and average error probability, we find that the capacity
for entanglement transmission of an AVQC always equals its strong subspace
transmission capacity. These results are accompanied by different notions of
symmetrizability (zero-capacity conditions) as well as by conditions for an
AVQC to have a capacity described by a single-letter formula. In he final part
of the paper the capacity of the erasure-AVQC is computed and some light shed
on the connection between AVQCs and zero-error capacities. Additionally, we
show by entirely elementary and operational arguments motivated by the theory
of AVQCs that the quantum, classical, and entanglement-assisted zero-error
capacities of quantum channels are generically zero and are discontinuous at
every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2
and arXiv:1010.0418. Published "Online First" in Communications in
Mathematical Physics, 201
The Administration of Xultophy for Diabetic Patients on Hemodialysis
Background: Recent diabetic treatments include Insulin Degludec/ liraglutide (IDeg/Lira, Xultophy) in clinical practice. Authors have continued clinical research concerning diabetes, chronic renal failure, dialysis, and others.
Subjects and Methods: Ten patients with type 2 diabetes mellitus (T2DM) undergoing hemodialysis were investigated. They showed that ages 74.5 ± 5.9 years, M/F=6/4, BMI 21.1± 3.8kg/m2, hemodialysis duration 8.1 ± 5.7 years. At the beginning, fundamental data were Cre 8.2 ± 1.9 mg/dL, HbA1c 6.5 ± 0.8%. Xultophy was started on 5-12 doses and continued for 6 months with the same or 1-4 increased doses for better glycemic variability.
Results: Out of 10 subjects, the changes in HbA1c showed a decrease in 7, stable in 2, and an increase in 1. HbA1c value was 6.2 ± 0.8% in average at 6 months. There were no remarkable adverse effects by Xultophy for 6 months.
Discussion and Conclusion: Xultophy was started at 5-12 doses, which were remarkably lower doses than usual doses with satisfactory efficacy. One of the reasons may be from the characteristic of the patients, who were diabetic with undergoing hemodialysis. Another factor is possibly from liraglutide, which has hepatic clearance with potential vascular protective effects. These results are expected to become reference data for future research
Conformally Invariant Fractals and Potential Theory
The multifractal (MF) distribution of the electrostatic potential near any
conformally invariant fractal boundary, like a critical O(N) loop or a
-state Potts cluster, is solved in two dimensions. The dimension of the boundary set with local wedge angle is , with the central charge of the
model. As a corollary, the dimensions
of the external perimeter and of the hull of a Potts cluster obey
the duality equation . A related covariant
MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.Comment: 5 pages, 1 figur
Electron-acoustic plasma waves: oblique modulation and envelope solitons
Theoretical and numerical studies are presented of the amplitude modulation
of electron-acoustic waves (EAWs) propagating in space plasmas whose
constituents are inertial cold electrons, Boltzmann distributed hot electrons
and stationary ions. Perturbations oblique to the carrier EAW propagation
direction have been considered. The stability analysis, based on a nonlinear
Schroedinger equation (NLSE), reveals that the EAW may become unstable; the
stability criteria depend on the angle between the modulation and
propagation directions. Different types of localized EA excitations are shown
to exist.Comment: 10 pages, 5 figures; to appear in Phys. Rev.
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