58,954 research outputs found
Impact of membrane bistability on dynamical response of neuronal populations
Neurons in many brain areas can develop pronounced depolarized state of
membrane potential (up state) in addition to the normal hyperpolarized down
state near the resting potential. The influence of the up state on signal
encoding, however, is not well investigated. Here we construct a
one-dimensional bistable neuron model and calculate the linear response to
noisy oscillatory inputs analytically. We find that with the appearance of an
up state, the transmission function is enhanced by the emergence of a local
maximum at some optimal frequency and the phase lag relative to the input
signal is reduced. We characterize the dependence of the enhancement of
frequency response on intrinsic dynamics and on the occupancy of the up state
Jantzen coefficients and simplicity of generalized Verma modules
The main purpose of the paper is to establish new tools in the study of
. We introduce the Jantzen coefficients of
generalized Verma modules. It comes from the Jantzen's simplicity criteria for
generalized Verma modules and has a deep relation with the structure of
. We develop a reduction process to compute those
coefficients. For which we need to consider generalized Verma modules induced
from maximal parabolic subalgebras having maximal nontrivial singularity, so
called basic generalized Verma modules. The classification of such modules is
obtained in this paper. As the first application of our results, we give a
refinement of Jantzen's simplicity criteria.Comment: 43 pages, 4 figure
Authentication of Students and Students’ Work in E-Learning : Report for the Development Bid of Academic Year 2010/11
Global e-learning market is projected to reach $107.3 billion by 2015 according to a new report by The Global Industry Analyst (Analyst 2010). The popularity and growth of the online programmes within the School of Computer Science obviously is in line with this projection. However, also on the rise are students’ dishonesty and cheating in the open and virtual environment of e-learning courses (Shepherd 2008). Institutions offering e-learning programmes are facing the challenges of deterring and detecting these misbehaviours by introducing security mechanisms to the current e-learning platforms. In particular, authenticating that a registered student indeed takes an online assessment, e.g., an exam or a coursework, is essential for the institutions to give the credit to the correct candidate. Authenticating a student is to ensure that a student is indeed who he says he is. Authenticating a student’s work goes one step further to ensure that an authenticated student indeed does the submitted work himself. This report is to investigate and compare current possible techniques and solutions for authenticating distance learning student and/or their work remotely for the elearning programmes. The report also aims to recommend some solutions that fit with UH StudyNet platform.Submitted Versio
An optimal control problem of forward-backward stochastic Volterra integral equations with state constraints
This paper is devoted to the stochastic optimal control problems for systems
governed by forward-backward stochastic Volterra integral equations (FBSVIEs,
for short) with state constraints. Using Ekeland's variational principle, we
obtain one kind of variational inequality. Then, by dual method, we derive a
stochastic maximum principle which gives the necessary conditions for the
optimal controls.Comment: 19 page
Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts
The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is
of an important role for the cosmological applications of the GRBs, which is
however hindered seriously by some selection effects due to redshift
measurements. In order to avoid these selection effects, we suggest to
calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p
relationship. Here, such a relationship is determined by reconciling
the distributions of pseudo- and real redshifts of redshift-known GRBs. The
values of E_p taken from Butler's GRB catalog are estimated with Bayesian
statistics rather than observed. Using the GRB sample with pseudo-redshifts of
a relatively large number, we fit the redshift-resolved luminosity
distributions of the GRBs with a broken-power-law LF. The fitting results
suggest that the LF could evolve with redshift by a redshift-dependent break
luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and
high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is
found that the proportional coefficient between GRB event rate and star
formation rate should correspondingly decrease with increasing redshifts.Comment: 5 pages, 5 figures, accepted for publication in ApJ
Dirac cohomology and Euler-Poincar\'e pairing for weight modules
Let be a reductive Lie algebra over . For any
simple weight module of with finite-dimensional weight spaces,
we show that its Dirac cohomology is vanished unless it is a highest weight
module. This completes the calculation of Dirac cohomology for simple weight
modules since the Dirac cohomology of simple highest weight modules was carried
out in our previous work. We also show that the Dirac index pairing of two
weight modules which have infinitesimal characters agrees with their
Euler-Poincar\'{e} pairing. The analogue of this result for Harish-Chandra
modules is a consequence of the Kazhdan's orthogonality conjecture which was
settled by the first named author and Binyong Sun
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