5,372 research outputs found
Modeling error analysis of stationary linear discrete-time filters
The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available
Algorithms for adaptive stochastic control for a class of linear systems
Control of linear, discrete time, stochastic systems with unknown control gain parameters is discussed. Two suboptimal adaptive control schemes are derived: one is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single input, third order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known
Gopakumar-Vafa invariants via vanishing cycles
In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of
Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal
is a modification of a recent approach of Kiem-Li, which is itself based on
earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants
are equivalent to other curve-counting theories such as Gromov-Witten theory
and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces,
our invariants agree with PT invariants for irreducible one-cycles. We also
give a counter-example to the Kiem-Li conjectures, where our invariants match
the predicted answer. Finally, we give examples where our invariant matches the
expected answer in cases where the cycle is non-reduced, non-planar, or
non-primitive.Comment: 63 pages, many improvements of the exposition following referee
comments, final version to appear in Inventione
Toda brackets and cup-one squares for ring spectra
In this paper we prove the laws of Toda brackets on the homotopy groups of a
connective ring spectrum and the laws of the cup-one square in the homotopy
groups of a commutative connective ring spectrum.Comment: 22 page
Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models
A system of first-order differential-difference equations with time lag
describes the formation of density waves, called as quasi-solitons for
dissipative systems in this paper. For co-moving density waves, the system
reduces to some exactly solvable lattice models. We construct a shock-wave
solution as well as one-quasi-soliton solution, and argue that there are
pseudo-conserved quantities which characterize the formation of the co-moving
waves. The simplest non-trivial one is given to discuss the presence of a
cascade phenomena in relaxation process toward the pattern formation.Comment: REVTeX, 4 pages, 1 figur
Poincare duality and Periodicity
We construct periodic families of Poincare complexes, partially solving a
question of Hodgson that was posed in the proceedings of the 1982 Northwestern
homotopy theory conference. We also construct infinite families of Poincare
complexes whose top cell falls off after one suspension but which fail to embed
in a sphere of codimension one. We give a homotopy theoretic description of the
four-fold periodicity in knot cobordism.Comment: A significant revision. In this version we produce infinite families
of examples of Poincare complexes whose top cell falls off after one
suspension, but which do not embed in codimension one. We also rewrote the
knot periodicity section in terms of Seifert surfaces rather than knot
complement
The Effect of Social Distancing on the Reach of an Epidemic in Social Networks
How does social distancing affect the reach of an epidemic in social
networks? We present Monte Carlo simulation results of a capacity constrained
Susceptible-Infected-Removed (SIR) model. The key modelling feature is that
individuals are limited in the number of acquaintances that they can interact
with, thereby constraining disease transmission to an infectious subnetwork of
the original social network. While increased social distancing always reduces
the spread of an infectious disease, the magnitude varies greatly depending on
the topology of the network. Our results also reveal the importance of
coordinating social distancing policies at the global level. In particular, the
public health benefits from social distancing to a group (e.g., a country) may
be completely undone if that group maintains connections with outside groups
that are not following suit
Anomalies, absence of local equilibrium and universality in 1-d particles systems
One dimensional systems are under intense investigation, both from
theoretical and experimental points of view, since they have rather peculiar
characteristics which are of both conceptual and technological interest. We
analyze the dependence of the behaviour of one dimensional, time reversal
invariant, nonequilibrium systems on the parameters defining their microscopic
dynamics. In particular, we consider chains of identical oscillators
interacting via hard core elastic collisions and harmonic potentials, driven by
boundary Nos\'e-Hoover thermostats. Their behaviour mirrors qualitatively that
of stochastically driven systems, showing that anomalous properties are typical
of physics in one dimension. Chaos, by itslef, does not lead to standard
behaviour, since it does not guarantee local thermodynamic equilibrium. A
linear relation is found between density fluctuations and temperature profiles.
This link and the temporal asymmetry of fluctuations of the main observables
are robust against modifications of thermostat parameters and against
perturbations of the dynamics.Comment: 26 pages, 16 figures, revised text, two appendices adde
An integrable generalization of the Toda law to the square lattice
We generalize the Toda lattice (or Toda chain) equation to the square
lattice; i.e., we construct an integrable nonlinear equation, for a scalar
field taking values on the square lattice and depending on a continuous (time)
variable, characterized by an exponential law of interaction in both discrete
directions of the square lattice. We construct the Darboux-Backlund
transformations for such lattice, and the corresponding formulas describing
their superposition. We finally use these Darboux-Backlund transformations to
generate examples of explicit solutions of exponential and rational type. The
exponential solutions describe the evolution of one and two smooth
two-dimensional shock waves on the square lattice.Comment: 14 pages, 4 figures, to appear in Phys. Rev. E http://pre.aps.org
An exactly solvable many-body problem in one dimension
For N impenetrable particles in one dimension where only the nearest and
next-to-nearest neighbours interact, we obtain the complete spectrum both on a
line and on a circle. Further, we establish a mapping between these N-body
problems and the short-range Dyson model introduced recently to model
intermediate spectral statistics in some systems using which we compute the
two-point correlation function and prove the absence of long-range order in the
corresponding many-body theory. Further, we also show the absence of
off-diagonal long-range order in these systems.Comment: LaTeX, 4 pages, 1 figur
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