9,719 research outputs found
Extending Feynman's Formalisms for Modelling Human Joint Action Coordination
The recently developed Life-Space-Foam approach to goal-directed human action
deals with individual actor dynamics. This paper applies the model to
characterize the dynamics of co-action by two or more actors. This dynamics is
modelled by: (i) a two-term joint action (including cognitive/motivatonal
potential and kinetic energy), and (ii) its associated adaptive path integral,
representing an infinite--dimensional neural network. Its feedback adaptation
loop has been derived from Bernstein's concepts of sensory corrections loop in
human motor control and Brooks' subsumption architectures in robotics.
Potential applications of the proposed model in human--robot interaction
research are discussed.
Keywords: Psycho--physics, human joint action, path integralsComment: 6 pages, Late
On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory
Given a particular solution of a one-dimensional stationary Schroedinger
equation (SE) this equation of second order can be reduced to a first order
linear differential equation. This is done with the aid of an auxiliary Riccati
equation. We show that a similar fact is true in a multidimensional situation
also. We consider the case of two or three independent variables. One
particular solution of (SE) allows us to reduce this second order equation to a
linear first order quaternionic differential equation. As in one-dimensional
case this is done with the aid of an auxiliary Riccati equation. The resulting
first order quaternionic equation is equivalent to the static Maxwell system.
In the case of two independent variables it is the Vekua equation from theory
of generalized analytic functions. We show that even in this case it is
necessary to consider not complex valued functions only, solutions of the Vekua
equation but complete quaternionic functions. Then the first order quaternionic
equation represents two separate Vekua equations, one of which gives us
solutions of (SE) and the other can be considered as an auxiliary equation of a
simpler structure. For the auxiliary equation we always have the corresponding
Bers generating pair, the base of the Bers theory of pseudoanalytic functions,
and what is very important, the Bers derivatives of solutions of the auxiliary
equation give us solutions of the main Vekua equation and as a consequence of
(SE). We obtain an analogue of the Cauchy integral theorem for solutions of
(SE). For an ample class of potentials (which includes for instance all radial
potentials), this new approach gives us a simple procedure allowing to obtain
an infinite sequence of solutions of (SE) from one known particular solution
A note on compactly generated co-t-structures
The idea of a co-t-structure is almost "dual" to that of a t-structure, but
with some important differences. This note establishes co-t-structure analogues
of Beligiannis and Reiten's corresponding results on compactly generated
t-structures.Comment: 10 pages; details added to proofs, small correction in the main
resul
On a factorization of second order elliptic operators and applications
We show that given a nonvanishing particular solution of the equation
(divpgrad+q)u=0 (1) the corresponding differential operator can be factorized
into a product of two first order operators. The factorization allows us to
reduce the equation (1) to a first order equation which in a two-dimensional
case is the Vekua equation of a special form. Under quite general conditions on
the coefficients p and q we obtain an algorithm which allows us to construct in
explicit form the positive formal powers (solutions of the Vekua equation
generalizing the usual powers of the variable z). This result means that under
quite general conditions one can construct an infinite system of exact
solutions of (1) explicitly, and moreover, at least when p and q are real
valued this system will be complete in ker(divpgrad+q) in the sense that any
solution of (1) in a simply connected domain can be represented as an infinite
series of obtained exact solutions which converges uniformly on any compact
subset of . Finally we give a similar factorization of the operator
(divpgrad+q) in a multidimensional case and obtain a natural generalization of
the Vekua equation which is related to second order operators in a similar way
as its two-dimensional prototype does
High resolution spectroscopy of single NV defects coupled with nearby C nuclear spins in diamond
We report a systematic study of the hyperfine interaction between the
electron spin of a single nitrogen-vacancy (NV) defect in diamond and nearby
C nuclear spins, by using pulsed electron spin resonance spectroscopy.
We isolate a set of discrete values of the hyperfine coupling strength ranging
from 14 MHz to 400 kHz and corresponding to C nuclear spins placed at
different lattice sites of the diamond matrix. For each lattice site, the
hyperfine interaction is further investigated through nuclear spin polarization
measurements and by studying the magnetic field dependence of the hyperfine
splitting. This work provides informations that are relevant for the
development of nuclear-spin based quantum register in diamond.Comment: 8 pages, 5 figure
The Shapovalov determinant for the Poisson superalgebras
Among simple Z-graded Lie superalgebras of polynomial growth, there are
several which have no Cartan matrix but, nevertheless, have a quadratic even
Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields
on the (1|6)-dimensional supercircle preserving the contact form, and the
series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian
fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using
C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for
the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov
described irreducible finite dimensional representations of po(0|n) and
sh(0|n); we generalize his result for Verma modules: give criteria for
irreducibility of the Verma modules over po(0|2k) and sh(0|2k)
Efficient Discrete Approximations of Quantum Gates
Quantum compiling addresses the problem of approximating an arbitrary quantum
gate with a string of gates drawn from a particular finite set. It has been
shown that this is possible for almost all choices of base sets and furthermore
that the number of gates required for precision epsilon is only polynomial in
log 1/epsilon. Here we prove that using certain sets of base gates quantum
compiling requires a string length that is linear in log 1/epsilon, a result
which matches the lower bound from counting volume up to constant factor.Comment: 7 pages, no figures, v3 revised to correct major error in previous
version
Multiobjective parsimony enforcement for superior generalisation performance
Program Bloat - phenomenon of ever-increasing program size during a GP run - is a recognised and widespread problem. Traditional techniques to combat program bloat are program size limitations of parsimony pressure (penalty functions). These techniques suffer from a number of problems, in particular their reliance on parameters whose optimal values it is difficult to a priori determine. In this paper, we introduce POPE-GP, a system that makes use of the NSGA-II multiobjective evolutionary algorithm as an alternative, parameter-free technique for eliminating program bloat. We test it on a classification problem and find that while vastly reducing program size, it does improve generalisation performance
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