4,549 research outputs found
Descartes' Rule of Signs for Polynomial Systems supported on Circuits
We give a multivariate version of Descartes' rule of signs to bound the
number of positive real roots of a system of polynomial equations in n
variables with n+2 monomials, in terms of the sign variation of a sequence
associated both to the exponent vectors and the given coefficients. We show
that our bound is sharp and is related to the signature of the circuit.Comment: 25 pages, 3 figure
A linearized stabilizer formalism for systems of finite dimension
The stabilizer formalism is a scheme, generalizing well-known techniques
developed by Gottesman [quant-ph/9705052] in the case of qubits, to efficiently
simulate a class of transformations ("stabilizer circuits", which include the
quantum Fourier transform and highly entangling operations) on standard basis
states of d-dimensional qudits. To determine the state of a simulated system,
existing treatments involve the computation of cumulative phase factors which
involve quadratic dependencies. We present a simple formalism in which Pauli
operators are represented using displacement operators in discrete phase space,
expressing the evolution of the state via linear transformations modulo D <=
2d. We thus obtain a simple proof that simulating stabilizer circuits on n
qudits, involving any constant number of measurement rounds, is complete for
the complexity class coMod_{d}L and may be simulated by O(log(n)^2)-depth
boolean circuits for any constant d >= 2.Comment: 25 pages, 3 figures. Reorganized to collect complexity results; some
corrections and elaborations of technical results. Differs slightly from the
version to be published (fixed typos, changes of wording to accommodate page
breaks for a different article format). To appear as QIC vol 13 (2013),
pp.73--11
Optimal control of ankle joint moment: Toward unsupported standing in paraplegia
This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations
Voltage Multistability and Pulse Emergency Control for Distribution System with Power Flow Reversal
High levels of penetration of distributed generation and aggressive reactive
power compensation may result in the reversal of power flows in future
distribution grids. The voltage stability of these operating conditions may be
very different from the more traditional power consumption regime. This paper
focused on demonstration of multistability phenomenon in radial distribution
systems with reversed power flow, where multiple stable equilibria co-exist at
the given set of parameters. The system may experience transitions between
different equilibria after being subjected to disturbances such as short-term
losses of distributed generation or transient faults. Convergence to an
undesirable equilibrium places the system in an emergency or \textit{in
extremis} state. Traditional emergency control schemes are not capable of
restoring the system if it gets entrapped in one of the low voltage equilibria.
Moreover, undervoltage load shedding may have a reverse action on the system
and can induce voltage collapse. We propose a novel pulse emergency control
strategy that restores the system to the normal state without any interruption
of power delivery. The results are validated with dynamic simulations of IEEE
-bus feeder performed with SystemModeler software. The dynamic models can
be also used for characterization of the solution branches via a novel approach
so-called the admittance homotopy power flow method.Comment: 13 pages, 22 figures. IEEE Transactions on Smart Grid 2015, in pres
Circuit theory in projective space and homogeneous circuit models
This paper presents a general framework for linear circuit analysis based on
elementary aspects of projective geometry. We use a flexible approach in which
no a priori assignment of an electrical nature to the circuit branches is
necessary. Such an assignment is eventually done just by setting certain model
parameters, in a way which avoids the need for a distinction between voltage
and current sources and, additionally, makes it possible to get rid of voltage-
or current-control assumptions on the impedances. This paves the way for a
completely general -dimensional reduction of any circuit defined by
two-terminal, uncoupled linear elements, contrary to most classical methods
which at one step or another impose certain restrictions on the allowed
devices. The reduction has the form Here, and capture
the graph topology, whereas , , comprise homogeneous
descriptions of all the circuit elements; the unknown is an -dimensional
vector of (say) ``seed'' variables from which currents and voltages are
obtained as , . Computational implementations
are straightforward. These models allow for a general characterization of
non-degenerate configurations in terms of the multihomogeneous Kirchhoff
polynomial, and in this direction we present some results of independent
interest involving the matrix-tree theorem. Our approach can be easily combined
with classical methods by using homogeneous descriptions only for certain
branches, yielding partially homogeneous models. We also indicate how to
accommodate controlled sources and coupled devices in the homogeneous
framework. Several examples illustrate the results.Comment: Updated versio
Chemical reaction systems with toric steady states
Mass-action chemical reaction systems are frequently used in Computational
Biology. The corresponding polynomial dynamical systems are often large
(consisting of tens or even hundreds of ordinary differential equations) and
poorly parametrized (due to noisy measurement data and a small number of data
points and repetitions). Therefore, it is often difficult to establish the
existence of (positive) steady states or to determine whether more complicated
phenomena such as multistationarity exist. If, however, the steady state ideal
of the system is a binomial ideal, then we show that these questions can be
answered easily. The focus of this work is on systems with this property, and
we say that such systems have toric steady states. Our main result gives
sufficient conditions for a chemical reaction system to have toric steady
states. Furthermore, we analyze the capacity of such a system to exhibit
positive steady states and multistationarity. Examples of systems with toric
steady states include weakly-reversible zero-deficiency chemical reaction
systems. An important application of our work concerns the networks that
describe the multisite phosphorylation of a protein by a kinase/phosphatase
pair in a sequential and distributive mechanism
Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses
We investigate the effect of electric synapses (gap junctions) on collective
neuronal dynamics and spike statistics in a conductance-based
Integrate-and-Fire neural network, driven by a Brownian noise, where
conductances depend upon spike history. We compute explicitly the time
evolution operator and show that, given the spike-history of the network and
the membrane potentials at a given time, the further dynamical evolution can be
written in a closed form. We show that spike train statistics is described by a
Gibbs distribution whose potential can be approximated with an explicit
formula, when the noise is weak. This potential form encompasses existing
models for spike trains statistics analysis such as maximum entropy models or
Generalized Linear Models (GLM). We also discuss the different types of
correlations: those induced by a shared stimulus and those induced by neurons
interactions.Comment: 42 pages, 1 figure, submitte
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