3,618 research outputs found
The Role of NMDA Currents in State Transitions of the Nucleus Accumbens Medium Spiny Neuron
The nucleus accumbens (NAcb) integrates information from a wide range of glutamatergic afferent inputs, including the prefrontal cortex, hippocampus and amygdala. One of the glutamatergic receptors, the NMDA channel, has been implicated in the non-linearity of the current–voltage relationship in these cells under certain input conditions. In order to examine the relationship of the different glutamatergic receptors to the membrane response, we modeled the AMPA, GABAA and NMDA receptors in the medium spiny (MSP) cells and their afferent input. The model demonstrates that the NMDA current is capable of sustaining certain membrane states and contributes to the non-linearity of the membrane response to input
Quantum and random walks as universal generators of probability distributions
Quantum walks and random walks bear similarities and divergences. One of the
most remarkable disparities affects the probability of finding the particle at
a given location: typically, almost a flat function in the first case and a
bell-shaped one in the second case. Here I show how one can impose any desired
stochastic behavior (compatible with the continuity equation for the
probability function) on both systems by the appropriate choice of time- and
site-dependent coins. This implies, in particular, that one can devise quantum
walks that show diffusive spreading without loosing coherence, as well as
random walks that exhibit the characteristic fast propagation of a quantum
particle driven by a Hadamard coin.Comment: 8 pages, 2 figures; revised and enlarged versio
Quasi-Exact Solvability and the direct approach to invariant subspaces
We propose a more direct approach to constructing differential operators that
preserve polynomial subspaces than the one based on considering elements of the
enveloping algebra of sl(2). This approach is used here to construct new
exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line
which are not Lie-algebraic. It is also applied to generate potentials with
multiple algebraic sectors. We discuss two illustrative examples of these two
applications: an interesting generalization of the Lam\'e potential which
posses four algebraic sectors, and a quasi-exactly solvable deformation of the
Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure
Bounded Determinization of Timed Automata with Silent Transitions
Deterministic timed automata are strictly less expressive than their
non-deterministic counterparts, which are again less expressive than those with
silent transitions. As a consequence, timed automata are in general
non-determinizable. This is unfortunate since deterministic automata play a
major role in model-based testing, observability and implementability. However,
by bounding the length of the traces in the automaton, effective
determinization becomes possible. We propose a novel procedure for bounded
determinization of timed automata. The procedure unfolds the automata to
bounded trees, removes all silent transitions and determinizes via disjunction
of guards. The proposed algorithms are optimized to the bounded setting and
thus are more efficient and can handle a larger class of timed automata than
the general algorithms. The approach is implemented in a prototype tool and
evaluated on several examples. To our best knowledge, this is the first
implementation of this type of procedure for timed automata.Comment: 25 page
Kleene Algebras and Semimodules for Energy Problems
With the purpose of unifying a number of approaches to energy problems found
in the literature, we introduce generalized energy automata. These are finite
automata whose edges are labeled with energy functions that define how energy
levels evolve during transitions. Uncovering a close connection between energy
problems and reachability and B\"uchi acceptance for semiring-weighted
automata, we show that these generalized energy problems are decidable. We also
provide complexity results for important special cases
On the families of orthogonal polynomials associated to the Razavy potential
We show that there are two different families of (weakly) orthogonal
polynomials associated to the quasi-exactly solvable Razavy potential V(x)=(\z
\cosh 2x-M)^2 (\z>0, ). One of these families encompasses the
four sets of orthogonal polynomials recently found by Khare and Mandal, while
the other one is new. These results are extended to the related periodic
potential U(x)=-(\z \cos 2x -M)^2, for which we also construct two different
families of weakly orthogonal polynomials. We prove that either of these two
families yields the ground state (when is odd) and the lowest lying gaps in
the energy spectrum of the latter periodic potential up to and including the
gap and having the same parity as . Moreover, we show
that the algebraic eigenfunctions obtained in this way are the well-known
finite solutions of the Whittaker--Hill (or Hill's three-term) periodic
differential equation. Thus, the foregoing results provide a Lie-algebraic
justification of the fact that the Whittaker--Hill equation (unlike, for
instance, Mathieu's equation) admits finite solutions.Comment: Typeset in LaTeX2e using amsmath, amssymb, epic, epsfig, float (24
pages, 1 figure
Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
Inozemtsev models are classically integrable multi-particle dynamical systems
related to Calogero-Moser models. Because of the additional q^6 (rational
models) or sin^2(2q) (trigonometric models) potentials, their quantum versions
are not exactly solvable in contrast with Calogero-Moser models. We show that
quantum Inozemtsev models can be deformed to be a widest class of partly
solvable (or quasi-exactly solvable) multi-particle dynamical systems. They
posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A
new method for identifying and solving quasi-exactly solvable systems, the
method of pre-superpotential, is presented.Comment: LaTeX2e 28 pages, no figure
Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations
In a recent paper, the canonical forms of a new multi-parameter class of Abel
differential equations, so-called AIR, all of whose members can be mapped into
Riccati equations, were shown to be related to the differential equations for
the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection
between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and
Biconfluent (BHE) equations is presented. This connection fixes the value of
one of the Heun parameters, expresses another one in terms of those remaining,
and provides closed form solutions in terms of pFq functions for the resulting
GHE, CHE and BHE, respectively depending on four, three and two irreducible
parameters. This connection also turns evident what is the relation between the
Heun parameters such that the solutions admit Liouvillian form, and suggests a
mechanism for relating linear equations with N and N-1 singularities through
the canonical forms of a non-linear equation of one order less.Comment: Original version submitted to Journal of Physics A: 16 pages, related
to math.GM/0002059 and math-ph/0402040. Revised version according to
referee's comments: 23 pages. Sign corrected (June/17) in formula (79).
Second revised version (July/25): 25 pages. See also
http://lie.uwaterloo.ca/odetools.ht
Inflaton Fragmentation and Oscillon Formation in Three Dimensions
Analytical arguments suggest that a large class of scalar field potentials
permit the existence of oscillons -- pseudo-stable, non-topological solitons --
in three spatial dimensions. In this paper we numerically explore oscillon
solutions in three dimensions. We confirm the existence of these field
configurations as solutions to the Klein-Gorden equation in an expanding
background, and verify the predictions of Amin and Shirokoff for the
characteristics of individual oscillons for their model. Further, we
demonstrate that significant numbers of oscillons can be generated via
fragmentation of the inflaton condensate, consistent with the analysis of Amin.
These emergent oscillons can easily dominate the post-inflationary universe.
Finally, both analytic and numerical results suggest that oscillons are stable
on timescales longer than the post-inflationary Hubble time. Consequently, the
post-inflationary universe can contain an effective matter-dominated phase,
during which it is dominated by localized concentrations of scalar field
matter.Comment: See http://easther.physics.yale.edu/downloads.html for numerical
codes. Visualizations available at http://www.mit.edu/~mamin/oscillons.html
and http://easther.physics.yale.edu/fields.html V2 Minor fixes to reference
lis
Parameterized Verification of Safety Properties in Ad Hoc Network Protocols
We summarize the main results proved in recent work on the parameterized
verification of safety properties for ad hoc network protocols. We consider a
model in which the communication topology of a network is represented as a
graph. Nodes represent states of individual processes. Adjacent nodes represent
single-hop neighbors. Processes are finite state automata that communicate via
selective broadcast messages. Reception of a broadcast is restricted to
single-hop neighbors. For this model we consider a decision problem that can be
expressed as the verification of the existence of an initial topology in which
the execution of the protocol can lead to a configuration with at least one
node in a certain state. The decision problem is parametric both on the size
and on the form of the communication topology of the initial configurations. We
draw a complete picture of the decidability and complexity boundaries of this
problem according to various assumptions on the possible topologies.Comment: In Proceedings PACO 2011, arXiv:1108.145
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