691 research outputs found
Learned Belief-Propagation Decoding with Simple Scaling and SNR Adaptation
We consider the weighted belief-propagation (WBP) decoder recently proposed
by Nachmani et al. where different weights are introduced for each Tanner graph
edge and optimized using machine learning techniques. Our focus is on
simple-scaling models that use the same weights across certain edges to reduce
the storage and computational burden. The main contribution is to show that
simple scaling with few parameters often achieves the same gain as the full
parameterization. Moreover, several training improvements for WBP are proposed.
For example, it is shown that minimizing average binary cross-entropy is
suboptimal in general in terms of bit error rate (BER) and a new "soft-BER"
loss is proposed which can lead to better performance. We also investigate
parameter adapter networks (PANs) that learn the relation between the
signal-to-noise ratio and the WBP parameters. As an example, for the (32,16)
Reed-Muller code with a highly redundant parity-check matrix, training a PAN
with soft-BER loss gives near-maximum-likelihood performance assuming simple
scaling with only three parameters.Comment: 5 pages, 5 figures, submitted to ISIT 201
Classification of subsystems for graded-local nets with trivial superselection structure
We classify Haag-dual Poincar\'e covariant subsystems \B\subset \F of a
graded-local net \F on 4D Minkowski spacetime which satisfies standard
assumptions and has trivial superselection structure. The result applies to the
canonical field net \F_\A of a net \A of local observables satisfying
natural assumptions. As a consequence, provided that it has no nontrivial
internal symmetries, such an observable net \A is generated by (the abstract
versions of) the local energy-momentum tensor density and the observable local
gauge currents which appear in the algebraic formulation of the quantum Noether
theorem. Moreover, for a net \A of local observables as above, we also
classify the Poincar\'e covariant local extensions \B \supset \A which
preserve the dynamics.Comment: 38 pages, LaTe
Thermal States in Conformal QFT. II
We continue the analysis of the set of locally normal KMS states w.r.t. the
translation group for a local conformal net A of von Neumann algebras on the
real line. In the first part we have proved the uniqueness of KMS state on
every completely rational net. In this second part, we exhibit several
(non-rational) conformal nets which admit continuously many primary KMS states.
We give a complete classification of the KMS states on the U(1)-current net and
on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro
net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many
primary KMS states. To this end, we provide a variation of the
Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework:
if there is an inclusion of split nets A in B and A is the fixed point of B
w.r.t. a compact gauge group, then any locally normal, primary KMS state on A
extends to a locally normal, primary state on B, KMS w.r.t. a perturbed
translation. Concerning the non-local case, we show that the free Fermi model
admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his
90th birthday. The final version is available under Open Access. This paper
contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a
proof of the same theorem in the book by Bratteli-Robinson). v3: a reference
correcte
Super-KMS functionals for graded-local conformal nets
Motivated by a few preceding papers and a question of R. Longo, we introduce
super-KMS functionals for graded translation-covariant nets over R with
superderivations, roughly speaking as a certain supersymmetric modification of
classical KMS states on translation-covariant nets over R, fundamental objects
in chiral algebraic quantum field theory. Although we are able to make a few
statements concerning their general structure, most properties will be studied
in the setting of specific graded-local (super-) conformal models. In
particular, we provide a constructive existence and partial uniqueness proof of
super-KMS functionals for the supersymmetric free field, for certain subnets,
and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a
separate result, we classify bounded super-KMS functionals for graded-local
conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare
Representations of Conformal Nets, Universal C*-Algebras and K-Theory
We study the representation theory of a conformal net A on the circle from a
K-theoretical point of view using its universal C*-algebra C*(A). We prove that
if A satisfies the split property then, for every representation \pi of A with
finite statistical dimension, \pi(C*(A)) is weakly closed and hence a finite
direct sum of type I_\infty factors. We define the more manageable locally
normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest
ideal vanishing in all locally normal representations and we investigate its
structure. In particular, if A is completely rational with n sectors, then
C*_ln(A) is a direct sum of n type I_\infty factors. Its ideal K_A of compact
operators has nontrivial K-theory, and we prove that the DHR endomorphisms of
C*(A) with finite statistical dimension act on K_A, giving rise to an action of
the fusion semiring of DHR sectors on K_0(K_A)$. Moreover, we show that this
action corresponds to the regular representation of the associated fusion
algebra.Comment: v2: we added some comments in the introduction and new references.
v3: new authors' addresses, minor corrections. To appear in Commun. Math.
Phys. v4: minor corrections, updated reference
Spectral triples and the super-Virasoro algebra
We construct infinite dimensional spectral triples associated with
representations of the super-Virasoro algebra. In particular the irreducible,
unitary positive energy representation of the Ramond algebra with central
charge c and minimal lowest weight h=c/24 is graded and gives rise to a net of
even theta-summable spectral triples with non-zero Fredholm index. The
irreducible unitary positive energy representations of the Neveu-Schwarz
algebra give rise to nets of even theta-summable generalised spectral triples
where there is no Dirac operator but only a superderivation.Comment: 27 pages; v2: a comment concerning the difficulty in defining cyclic
cocycles in the NS case have been adde
Wearable wireless tactile display for virtual interactions with soft bodies.
We describe here a wearable, wireless, compact, and lightweight tactile display, able to mechanically stimulate the fingertip of users, so as to simulate contact with soft bodies in virtual environments. The device was based on dielectric elastomer actuators, as high-performance electromechanically active polymers. The actuator was arranged at the user's fingertip, integrated within a plastic case, which also hosted a compact high-voltage circuitry. A custom-made wireless control unit was arranged on the forearm and connected to the display via low-voltage leads. We present the structure of the device and a characterization of it, in terms of electromechanical response and stress relaxation. Furthermore, we present results of a psychophysical test aimed at assessing the ability of the system to generate different levels of force that can be perceived by users.The authors gratefully acknowledge financial support from COST – European Cooperation in Science and Technology, within the framework of “ESNAM – European Scientific Network for Artificial Muscles” (COST Action MP1003). Gabriele Frediani also acknowledges support from the European Commission, within the framework of the project “CEEDS: The Collective Experience of Empathic Data Systems” (FP7-ICT-2009.8.4, Grant 258749) and “Fondazione Cassa di Risparmio di Pisa,” within the framework of the project “POLOPTEL” (Grant 167/09
Enumeration and Decidable Properties of Automatic Sequences
We show that various aspects of k-automatic sequences -- such as having an
unbordered factor of length n -- are both decidable and effectively enumerable.
As a consequence it follows that many related sequences are either k-automatic
or k-regular. These include many sequences previously studied in the
literature, such as the recurrence function, the appearance function, and the
repetitivity index. We also give some new characterizations of the class of
k-regular sequences. Many results extend to other sequences defined in terms of
Pisot numeration systems
Transition Property for -Power Free Languages with and Letters
In 1985, Restivo and Salemi presented a list of five problems concerning
power free languages. Problem states: Given -power-free words
and , decide whether there is a transition from to . Problem
states: Given -power-free words and , find a transition word
, if it exists.
Let denote an alphabet with letters. Let denote
the -power free language over the alphabet , where
is a rational number or a rational "number with ". If is a "number
with " then suppose and . If is "only" a
number then suppose and or and . We show
that: If is a right extendable word in and
is a left extendable word in then there is a
(transition) word such that . We also show a
construction of the word
An algebraic Haag's theorem
Under natural conditions (such as split property and geometric modular action
of wedge algebras) it is shown that the unitary equivalence class of the net of
local (von Neumann) algebras in the vacuum sector associated to double cones
with bases on a fixed space-like hyperplane completely determines an algebraic
QFT model. More precisely, if for two models there is unitary connecting all of
these algebras, then --- without assuming that this unitary also connects their
respective vacuum states or spacetime symmetry representations --- it follows
that the two models are equivalent. This result might be viewed as an algebraic
version of the celebrated theorem of Rudolf Haag about problems regarding the
so-called "interaction-picture" in QFT.
Original motivation of the author for finding such an algebraic version came
from conformal chiral QFT. Both the chiral case as well as a related conjecture
about standard half-sided modular inclusions will be also discussed
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