8,067 research outputs found
Note on Identities Inspired by New Soft Theorems
The new soft theorems, for both gravity and gauge amplitudes, have inspired a
number of works, including the discovery of new identities related to
amplitudes. In this note, we present the proof and discussion for two sets of
identities. The first set includes an identity involving the half-soft function
which had been used in the soft theorem for one-loop rational gravity
amplitudes, and another simpler identity as its byproduct. The second set
includes two identities involving the KLT momentum kernel, as the consistency
conditions of the KLT relation plus soft theorems for both gravity and gauge
amplitudes. We use the CHY formulation to prove the first identity, and
transform the second one into a convenient form for future discussion.Comment: 17 page
Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction
In order to generalize the integration rules to general CHY integrands which
include higher order poles, algorithms are proposed in two directions. One is
to conjecture new rules, and the other is to use the cross-ratio identity
method. In this paper,we use the cross-ratio identity approach to re-derive the
conjectured integration rules involving higher order poles for several special
cases: the single double pole, single triple pole and duplex-double pole. The
equivalence between the present formulas and the previously conjectured ones is
discussed for the first two situations.Comment: 29 pages, 11 figure
On Multi-step BCFW Recursion Relations
In this paper, we extensively investigate the new algorithm known as the
multi-step BCFW recursion relations. Many interesting mathematical properties
are found and understanding these aspects, one can find a systematic way to
complete the calculation of amplitude after finite, definite steps and get the
correct answer, without recourse to any specific knowledge from field theories,
besides mass dimension and helicities. This process consists of the pole
concentration and inconsistency elimination. Terms that survive inconsistency
elimination cannot be determined by the new algorithm. They include polynomials
and their generalizations, which turn out to be useful objects to be explored.
Afterwards, we apply it to the Standard Model plus gravity to illustrate its
power and limitation. Ensuring its workability, we also tentatively discuss how
to improve its efficiency by reducing the steps.Comment: 38 pages, 13 figures, 3 appendice
Affine embeddings and intersections of Cantor sets
Let be two self-similar sets. Under mild conditions, we
show that can be -embedded into if and only if it can be affinely
embedded into ; furthermore if can not be affinely embedded into ,
then the Hausdorff dimension of the intersection is strictly less
than that of for any -diffeomorphism on . Under certain
circumstances, we prove the logarithmic commensurability between the
contraction ratios of and if can be affinely embedded into . As
an application, we show that when
is any Cantor- set and any Cantor- set, where are two
integers with \log p/\log q\not \in \Q. This is related to a conjecture of
Furtenberg about the intersections of Cantor sets.Comment: The paper will appear in J. Math. Pure. App
RORS: Enhanced Rule-based OWL Reasoning on Spark
The rule-based OWL reasoning is to compute the deductive closure of an
ontology by applying RDF/RDFS and OWL entailment rules. The performance of the
rule-based OWL reasoning is often sensitive to the rule execution order. In
this paper, we present an approach to enhancing the performance of the
rule-based OWL reasoning on Spark based on a locally optimal executable
strategy. Firstly, we divide all rules (27 in total) into four main classes,
namely, SPO rules (5 rules), type rules (7 rules), sameAs rules (7 rules), and
schema rules (8 rules) since, as we investigated, those triples corresponding
to the first three classes of rules are overwhelming (e.g., over 99% in the
LUBM dataset) in our practical world. Secondly, based on the interdependence
among those entailment rules in each class, we pick out an optimal rule
executable order of each class and then combine them into a new rule execution
order of all rules. Finally, we implement the new rule execution order on Spark
in a prototype called RORS. The experimental results show that the running time
of RORS is improved by about 30% as compared to Kim & Park's algorithm (2015)
using the LUBM200 (27.6 million triples).Comment: 12 page
Hysteresis measurement of anomalous microwave surface resistance in superconducting thin films
The anomalous decrease in microwave surface resistance, R_{s}, of
superconducting YBa_{2}Cu_{3}O_{7-d} (YBCO) thin films in the presence of a low
dc magnetic field is studied using a microstrip resonator technique. We have
done a dc field hysteresis measurement of R_{s} to study the effects of vortex
penetration on the anomalous effect. It is shown that the anomaly happens at a
field level far below the low critical field, H_{c1,strip}, of the
superconducting microstrip and vortex (Abrikosov) penetration would eliminate
the anomalous effect observed at low field. This implies that the anomalous
effect is not contributed by vortices.Comment: 2 pages, 1 figure, submitted to Physica C for M2S-HTSC-VI Proceeding
Throughput Optimization in High Speed Downlink Packet Access (HSDPA)
In this paper, we investigate throughput optimization
in High Speed Downlink Packet Access (HSDPA). Specifically,
we propose offline and online algorithms for adjusting
the Channel Quality Indicator (CQI) used by the network to
schedule data transmission. In the offline algorithm, a given
target BLER is achieved by adjusting CQI based on ACK/NAK
history. By sweeping through different target BLERs, we can
find the throughput optimal BLER offline. This algorithm could
be used not only to optimize throughput but also to enable fair
resource allocation among mobile users in HSDPA. In the online
algorithm, the CQI offset is adapted using an estimated short
term throughput gradient without specifying a target BLER. An
adaptive stepsize mechanism is proposed to track temporal variation
of the environment. We investigate convergence behavior
of both algorithms. Simulation results show that the proposed
offline algorithm can achieve the given target BLER with good
accuracy. Both algorithms yield up to 30% HSDPA throughput
improvement over that with 10% target BLER
- …