63,295 research outputs found
Polynomial Fermionic Forms for the Branching Functions of the Rational Coset Conformal Field Theories }
General fermionic expressions for the branching functions of the rational
coset conformal field theories are given. The equality of the bosonic
and fermionic representations for the branching functions is proven by
introducing polynomial truncations of these branching functions which are the
configuration sums of the RSOS models in regime III. The path space
interpretation of the RSOS models provides recursion relations for the
configuration sums. The proof of the recursion relations for the fermionic
expressions is given by using telescopic expansion techniques. The
configuration sums of the RSOS model in regime II which correspond to the
branching functions of the -parafermion conformal field theory are
obtained by the duality transformation .Comment: 40 pages, LATEX, no figures; revised version to appear in Nuclear
Physics
Plural Slot Theory
Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism
User Activity Detection in Massive Random Access: Compressed Sensing vs. Coded Slotted ALOHA
Machine-type communication services in mobile cel- lular systems are
currently evolving with an aim to efficiently address a massive-scale user
access to the system. One of the key problems in this respect is to efficiently
identify active users in order to allocate them resources for the subsequent
transmissions. In this paper, we examine two recently suggested approaches for
user activity detection: compressed-sensing (CS) and coded slotted ALOHA (CSA),
and provide their comparison in terms of performance vs resource utilization.
Our preliminary results show that CS-based approach is able to provide the
target user activity detection performance with less overall system resource
utilization. However, this comes at a price of lower energy- efficiency per
user, as compared to CSA-based approach.Comment: Accepted for presentation at IEEE SPAWC 201
Optimal Collision/Conflict-free Distance-2 Coloring in Synchronous Broadcast/Receive Tree Networks
This article is on message-passing systems where communication is (a)
synchronous and (b) based on the "broadcast/receive" pair of communication
operations. "Synchronous" means that time is discrete and appears as a sequence
of time slots (or rounds) such that each message is received in the very same
round in which it is sent. "Broadcast/receive" means that during a round a
process can either broadcast a message to its neighbors or receive a message
from one of them. In such a communication model, no two neighbors of the same
process, nor a process and any of its neighbors, must be allowed to broadcast
during the same time slot (thereby preventing message collisions in the first
case, and message conflicts in the second case). From a graph theory point of
view, the allocation of slots to processes is know as the distance-2 coloring
problem: a color must be associated with each process (defining the time slots
in which it will be allowed to broadcast) in such a way that any two processes
at distance at most 2 obtain different colors, while the total number of colors
is "as small as possible". The paper presents a parallel message-passing
distance-2 coloring algorithm suited to trees, whose roots are dynamically
defined. This algorithm, which is itself collision-free and conflict-free, uses
colors where is the maximal degree of the graph (hence
the algorithm is color-optimal). It does not require all processes to have
different initial identities, and its time complexity is , where d
is the depth of the tree. As far as we know, this is the first distributed
distance-2 coloring algorithm designed for the broadcast/receive round-based
communication model, which owns all the previous properties.Comment: 19 pages including one appendix. One Figur
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