787 research outputs found
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 , we show that penta-box ladder has an alphabet of and
provide strong evidence that the alphabet of double-penta ladder can be
identified with a cluster algebra. We relate the symbol letters to the
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 representation, which allows us to
predict higher-loop alphabet recursively; by applying such recursions to
six-dimensional hexagon integrals, we also find and 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
STUDY OF STABLE MOTION PERCEPTION
The goal of my PhD project was to combine approaches from human psychophysics, Bayesian modeling and animal electrophysiology to study the mechanisms underlying motion perception. The specific goals of the current project are to: i) investigate the relationship between perceptual bias and stabilization with contextual regularity and density in human observers, and develop novel Bayesian models of motion perception that can account for the data; ii) explore motion duration dependence of offset neural activity and its layer specificity in primary visual cortex (V1) of alert monkeys
Modal Analysis of Cylindrical Gears with Arcuate Tooth Trace
In this paper, the forming principle, meshing features and tooth surface equation were introduced. And the modal parameters distribution of cylindrical gears with arcuate tooth trace was researched. The results show: 1. The modulus was the biggest impact factor for modal and natural frequency of cylindrical gears with arcuate tooth trace, then tooth width, and the radius of tooth line have the minimum influence; 2. When the modulus increased, natural frequency of cylindrical gears with arcuate tooth reduced rapidly; 3. When the tooth width increased, natural frequency of cylindrical gears with arcuate tooth has a tendency to rise except for first-order modal; 4. The influence of radius of tooth line can be basic ignored; 5. The second-order modal and third-order modal, fifth-order modal and sixth-order modal was very close. The research on cylindrical gears with arcuate tooth trace in this paper has a certain reference value on gear design and selection
Bootstrapping octagons in reduced kinematics from cluster algebras
Multi-loop scattering amplitudes/null polygonal Wilson loops in super-Yang-Mills are known to simplify significantly in reduced
kinematics, where external legs/edges lie in an dimensional subspace of
Minkowski spacetime (or boundary of the subspace). Since the edges
of a -gon with even and odd labels go along two different null directions,
the kinematics is reduced to two copies of . In the
simplest octagon case, we conjecture that all loop amplitudes and Feynman
integrals are given in terms of two overlapping functions (a special case
of two-dimensional harmonic polylogarithms): in addition to the letters of , there are two letters 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
functions, we easily obtain octagon amplitudes up to two-loop NMHV and
three-loop MHV. We also briefly comment on the generalization to -gons in
terms of functions and beyond.Comment: 26 pages, several figures and tables, an ancilary fil
Neural activity dissociation between thought-based and perception-based response conflict
Based on the idea that intentions have different penetrability to perception and thought (Fodor, 1983), four Stroop-like tasks, AA, AW, WA, and WW are used, where the A represents an arrow and the CPPR (closest processing prior to response) is perception, and the W represents a word and the CPPR is thought. Event-related brain potentials were recorded as participants completed these tasks, and sLORETA (standardized low resolution brain electromagnetic tomography) was used to localize the sources at specific time points. These results showed that there is an interference effect in the AA and WA tasks, but not in the AW or WW tasks. The activated brain areas related to the interference effect in the AA task were the PFC and ACC, and PFC activation took place prior to ACC activation; but only PFC in WA task. Combined with previous results, a new neural mechanism of cognitive control is proposed
Nonlinear vibration modeling and bifurcation characteristic study of a planetary gear train processing device
In this paper, a nonlinear torsional vibration model with meshing errors, time varying meshing stiffness, damping coefficients and gear backlashes was established and dimensionless equations of the system are derived in the planetary gear train processing device. The paper analyzed the nonlinear dynamic behavior of the device which was used to machine the Circular-Arc-Tooth-Trace cylindrical gear. By using the method of numerical integration, the bifurcation diagrams are obtained and the results indicate that the processing device has abundant bifurcation characteristics with the change of the dimensionless speed, and the damping ratios, gear backlashes and meshing errors of meshing pairs could influence the vibration greatly. The bifurcation diagrams reveal that increasing the damping ratios can change the bifurcation and the chaos can be avoid when the damping ratios are bigger enough, reducing the gear backlashes can reduce the dimensionless displacement amplitudes, increasing the meshing errors can make the bifurcation diagrams shift left for a distance, and alternating load torque with large amplitude will cause complex chaos phenomenon. The study can help to avoid the fatigue failure and instabilities caused by chaos and it also contribute to improving the performance of the processing device
Feynman Integrals and Scattering Amplitudes from Wilson Loops
We study Feynman integrals and scattering amplitudes in
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 () 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 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 algebraic letters for each of the square roots, and they all
nicely cancel in combinations for MHV amplitudes and NMHV components which are
free of square roots. In addition to algebraic letters, the alphabet
consists of 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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