2,970 research outputs found
Rapid online learning and robust recall in a neuromorphic olfactory circuit
We present a neural algorithm for the rapid online learning and
identification of odorant samples under noise, based on the architecture of the
mammalian olfactory bulb and implemented on the Intel Loihi neuromorphic
system. As with biological olfaction, the spike timing-based algorithm utilizes
distributed, event-driven computations and rapid (one-shot) online learning.
Spike timing-dependent plasticity rules operate iteratively over sequential
gamma-frequency packets to construct odor representations from the activity of
chemosensor arrays mounted in a wind tunnel. Learned odorants then are reliably
identified despite strong destructive interference. Noise resistance is further
enhanced by neuromodulation and contextual priming. Lifelong learning
capabilities are enabled by adult neurogenesis. The algorithm is applicable to
any signal identification problem in which high-dimensional signals are
embedded in unknown backgrounds.Comment: 52 text pages; 8 figures. Version 3 includes a new figure and
additional detail
Characterization of Finsler Spaces of Scalar Curvature
The aim of the present paper is to provide an intrinsic investigation of two
special Finsler spaces whose defining properties are related to Berwald
connection, namely, Finsler space of scalar curvature and of constant
curvature. Some characterizations of a Finsler space of scalar curvature are
proved. Necessary and sufficient conditions under which a Finsler space of
scalar curvature reduces to a Finsler space of constant curvature are
investigated.Comment: LaTeX file, 10 page
Some Types of Recurrence in Finsler geometry
The pullback approach to global Finsler geometry is adopted. Three classes of
recurrence in Finsler geometry are introduced and investigated: simple
recurrence, Ricci recurrence and concircular recurrence. Each of these classes
consists of four types of recurrence. The interrelationships between the
different types of recurrence are studied. The generalized concircular
recurrence, as a new concept, is singled out.Comment: LaTex file, 13 pages, Concluding remarks are changed, Last diagram is
modifie
On Horizontal Recurrent Finsler Connections
In this paper we adopt the pullback approach to global Finsler geometry. We
investigate horizontally recurrent Finsler connections. We prove that for each
scalar ()1-form , there exists a unique horizontally recurrent Finsler
connection whose -recurrence form is . This result generalizes the
existence and uniqueness theorem of Cartan connection. We then study some
properties of a special kind of horizontally recurrent Finsler connection,
which we call special HRF-connection.Comment: 10 peges, LaTeX file, Few typos corrected, References adde
L-regular linear connections
The aim of this paper is to generalize the theory of nonlinear connections of
Grifone ([3] and [4]). We adopt the point of view of Anona [1] and continue
developing the approach established by the first author in [10].
The first part of the work is devoted to the problem of associating to each
-regular linear connection on a nonlinear -connection on . The
route we have followed is significantly different from that of Grifone. We
introduce an almost-complex and an almost-product structures on by means of
a given -regular linear connection on . The product of these two
structures defines a nonlinear -connection on , which generalizes
Grifone's nonlinear connection.
The seconed part is devoted to the converse problem: associating to each
nonlinear -connection \G on an -regular linear connection on ;
called the -lift of \G. The existence of this lift is established and the
fundamental tensors associated with it are studied.
In the third part, we investigate the -lift of a homogeneous
-connection \G, called the Berwald -lift of \G. Then we particularize our
study to the -lift of a conservative -connection. This -lift enjoys
some interesting properties. We finally deduce various identities concerning
the curvature tensors of such a lift.
Grifone's theory can be retrieved by letting be the tangent bundle of a
differentiable manifold and be the natural almost-tangent structure on
.Comment: 12 pages, LaTeX file, Minor change (concerning reference No. 10
Two nonrelated Finsler structures on a manifold
In the present paper, we consider two different {\em Finsler} structures
and on the same base manifold , with no relation preassumed between
them. \par Introducing the -tensor field representing the difference
between the Cartan connections associated with and , we investigate
the conditions, to be satisfied by this -tensor field, for the geometric
objects associated with and to have the same properties. Among the
items investigated in the paper, we consider the properties of being a
geodesic, a Jacobi field, a Berwald manifold, a locally Minkowskian manifold
and a Landsberg manifold. \par It should be noticed that our approach is
intrinsic, i.e., it does not make use of local coordinate techniques.Comment: 8 pages, LaTeX fil
On Generalized Randers Manifolds
By a Randers' structure on a manifold we mean a Finsler structure
, where is a Riemannian structure and is a 1-form on
. This structure was first introduced by Randers ~\cite{[8]} from the
standpoint of general relativity. In this paper, we replace by a Finsler
structure, calling the resulting manifold a generalized Randers manifold. On
one hand, we develop in some depth generalized Randers manifolds. On the other
hand, we apply the results obtained in a foregoing paper ~\cite{[12]} to
generalized Randers manifolds to obtain some new results in that domain. Among
many results, we establish a necessary and sufficient condition for a
generalized Randers manifold to be a general Landsberg manifold. It should be
noticed that our approach is in general a global one.Comment: 10 pages, LaTeX fil
Nullity distributions associated to Cartan connection
The Klein-Grifone approach to global Finsler geometry is adopted. The nullity
distributions of the three curvature tensors of Cartan connection are
investigated. Nullity distributions concerning certain relevant special Finsler
spaces are considered. Concrete examples are given whenever the situation
needs.Comment: Forgotten author is added, Some typos correcte
Conformal change of special Finsler spaces
The present paper is a continuation of a foregoing paper [Tensor, N. S., 69
(2008), 155-178]. The main aim is to establish \emph{an intrinsic
investigation} of the conformal change of the most important special Finsler
spaces, namely, -recurrent, -recurrent, -recurrent,
-like, quasi--reducible, -reducible, Berwald space,
-recurrent, -Finsler manifold, -like, -symmetric, Finsler
manifold of -scalar curvature and Finsler manifold of --curvature.
Necessary and sufficient conditions for such special Finsler manifolds to be
invariant under a conformal change are obtained. Moreover, the conformal change
of Chern and Hashiguchi connections, as well as their curvature tensors, are
given.Comment: LaTeX file, 18 page
New Conformal Invariants in Absolute Parallelism Geometry
The aim of the present paper is to investigate conformal changes in absolute
parallelism geometry. We find out some new conformal invariants in terms of the
Weitzenb\"ock connection and the Levi-Civita connection of an absolute
parallelism space.Comment: 9 pages, some typos in the proof of Theorem B are correte
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