455 research outputs found

### An Etude on Recursion Relations and Triangulations

Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by
applying a one-parameter deformation of kinematic variables for tree-level
scattering amplitudes in bi-adjoint $\phi^3$ theory. The recursion relies on
properties of the amplitude that can be made manifest in the underlying
kinematic associahedron, and it provides triangulations for the latter.
Furthermore, we solve the recursion relation and present all-multiplicity
results for the amplitude: by reformulating the associahedron in terms of its
vertices, it is given explicitly as a sum of "volume" of simplicies for any
triangulation, which is an analogy of BCFW representation/triangulation of
amplituhedron for ${\cal N}=4$ SYM.Comment: 26 pages, 3 figure

### An Etude on Recursion Relations and Triangulations

Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by
applying a one-parameter deformation of kinematic variables for tree-level
scattering amplitudes in bi-adjoint $\phi^3$ theory. The recursion relies on
properties of the amplitude that can be made manifest in the underlying
kinematic associahedron, and it provides triangulations for the latter.
Furthermore, we solve the recursion relation and present all-multiplicity
results for the amplitude: by reformulating the associahedron in terms of its
vertices, it is given explicitly as a sum of "volume" of simplicies for any
triangulation, which is an analogy of BCFW representation/triangulation of
amplituhedron for ${\cal N}=4$ SYM.Comment: 26 pages, 3 figure

### Algorithm and Architecture for Path Metric Aided Bit-Flipping Decoding of Polar Codes

Polar codes attract more and more attention of researchers in recent years,
since its capacity achieving property. However, their error-correction
performance under successive cancellation (SC) decoding is inferior to other
modern channel codes at short or moderate blocklengths. SC-Flip (SCF) decoding
algorithm shows higher performance than SC decoding by identifying possibly
erroneous decisions made in initial SC decoding and flipping them in the
sequential decoding attempts. However, it performs not well when there are more
than one erroneous decisions in a codeword. In this paper, we propose a path
metric aided bit-flipping decoding algorithm to identify and correct more
errors efficiently. In this algorithm, the bit-flipping list is generated based
on both log likelihood ratio (LLR) based path metric and bit-flipping metric.
The path metric is used to verify the effectiveness of bit-flipping. In order
to reduce the decoding latency and computational complexity, its corresponding
pipeline architecture is designed. By applying these decoding algorithms and
pipeline architecture, an improvement on error-correction performance can be
got up to 0.25dB compared with SCF decoding at the frame error rate of
$10^{-4}$, with low average decoding latency.Comment: 6 pages, 6 figures, IEEE Wireless Communications and Networking
Conference (2019 WCNC

### Notes on cluster algebras and some all-loop Feynman integrals

We study cluster algebras for some all-loop Feynman integrals, including
box-ladder, penta-box-ladder, and (seven-point) double-penta-ladder integrals.
In addition to the well-known box ladder whose symbol alphabet is $D_2\simeq
A_1^2$, we show that penta-box ladder has an alphabet of $D_3\simeq A_3$ and
provide strong evidence that the alphabet of double-penta ladder can be
identified with a $D_4$ cluster algebra. We relate the symbol letters to the
${\bf u}$ variables of cluster configuration space, which provide a
gauge-invariant description of the cluster algebra, and we find various
sub-algebras associated with limits of the integrals. We comment on constraints
similar to extended-Steinmann relations or cluster adjacency conditions on
cluster function spaces. Our study of the symbol and alphabet is based on the
recently proposed Wilson-loop ${\rm d}\log$ representation, which allows us to
predict higher-loop alphabet recursively; by applying such recursions to
six-dimensional hexagon integrals, we also find $D_5$ and $D_6$ cluster
functions for the two-mass-easy and three-mass-easy case, respectively.Comment: 28 pages, several figures; v2: typos corrected, functions of ladder
integrals computed to higher loops; v3: more examples of double-penta-ladder
integrals and discussions about their alphabet adde

### High Capacity Silicon Electrodes with Nafion as Binders for Lithium-Ion Batteries

Silicon is capable of delivering a high theoretical specific capacity of 3579 mAh g−1 which is about 10 times higher than that of the state-of-the-art graphite based negative electrodes for lithium-ion batteries. However, the poor cycle life of silicon electrodes, caused by the large volumetric strain during cycling, limits the commercialization of silicon electrodes. As one of the essential components, the polymeric binder is critical to the performance and durability of lithium-ion batteries as it keeps the integrity of electrodes, maintains conductive path and must be stable in the electrolyte. In this work, we demonstrate that electrodes consisting of silicon nanoparticles mixed with commercially available Nafion and ion-exchanged Nafion can maintain a high specific capacity over 2000 mAh g−1 cycled between 1.0 V and 0.01 V. For comparison, the capacity of electrodes made of the same silicon nanoparticles mixed with a traditional binder, polyvinylidene fluoride (PVDF), fades rapidly. In addition, stable cycling at 1C rate for more than 500 cycles is achieved by limiting the lithiation capacity to 1200 mAh g−1

### Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras

Multi-loop scattering amplitudes/null polygonal Wilson loops in ${\mathcal
N}=4$ super-Yang-Mills are known to simplify significantly in reduced
kinematics, where external legs/edges lie in an $1+1$ dimensional subspace of
Minkowski spacetime (or boundary of the $\rm AdS_3$ subspace). Since the edges
of a $2n$-gon with even and odd labels go along two different null directions,
the kinematics is reduced to two copies of $G(2,n)/T \sim A_{n{-}3}$. In the
simplest octagon case, we conjecture that all loop amplitudes and Feynman
integrals are given in terms of two overlapping $A_2$ functions (a special case
of two-dimensional harmonic polylogarithms): in addition to the letters $v,
1+v, w, 1+w$ of $A_1 \times A_1$, there are two letters $v-w, 1- v w$ mixing
the two sectors but they never appear together in the same term; these are the
reduced version of four-mass-box algebraic letters. Evidence supporting our
conjecture includes all known octagon amplitudes as well as new computations of
multi-loop integrals in reduced kinematics. By leveraging this alphabet and
conditions on first and last entries, we initiate a bootstrap program in
reduced kinematics: within the remarkably simple space of overlapping $A_2$
functions, we easily obtain octagon amplitudes up to two-loop NMHV and
three-loop MHV. We also briefly comment on the generalization to $2n$-gons in
terms of $A_2$ functions and beyond.Comment: 26 pages, several figures and tables, an ancilary fil

### Feynman Integrals and Scattering Amplitudes from Wilson Loops

We study Feynman integrals and scattering amplitudes in ${\cal N}=4$
super-Yang-Mills by exploiting the duality with null polygonal Wilson loops.
Certain Feynman integrals, including one-loop and two-loop chiral pentagons,
are given by Feynman diagrams of a supersymmetric Wilson loop, where one can
perform loop integrations and be left with simple integrals along edges. As the
main application, we compute analytically for the first time, the symbol of the
generic ($n\geq 12$) double pentagon, which gives two-loop MHV amplitudes and
components of NMHV amplitudes to all multiplicities. We represent the double
pentagon as a two-fold $\mathrm{d} \log$ integral of a one-loop hexagon, and
the non-trivial part of the integration lies at rationalizing square roots
contained in the latter. We obtain a remarkably compact "algebraic words" which
contain $6$ algebraic letters for each of the $16$ square roots, and they all
nicely cancel in combinations for MHV amplitudes and NMHV components which are
free of square roots. In addition to $96$ algebraic letters, the alphabet
consists of $152$ dual conformal invariant combinations of rational letters.Comment: 8 pages, 4 figures, 1 ancillary file; v3: important updates, a
compact form for the symbol of double pentagon integral added; typos
correcte

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