740 research outputs found
On a conjecture by Pierre Cartier about a group of associators
In \cite{cartier2}, Pierre Cartier conjectured that for any non commutative
formal power series on with coefficients in a
\Q-extension, , subjected to some suitable conditions, there exists an
unique algebra homomorphism from the \Q-algebra generated by the
convergent polyz\^etas to such that is computed from
Drinfel'd associator by applying to each coefficient. We prove
exists and it is a free Lie exponential over . Moreover, we give a
complete description of the kernel of polyz\^eta and draw some consequences
about a structure of the algebra of convergent polyz\^etas and about the
arithmetical nature of the Euler constant
Electroweak phase transition in the economical 3-3-1 model
We consider the EWPT in the economical 3-3-1 (E331) model. Our analysis shows
that the EWPT in the model is a sequence of two first-order phase transitions,
at the TeV scale and at the
GeV scale. The EWPT is triggered by the new
bosons and the exotic quarks; its strength is about if the mass ranges
of these new particles are . The
EWPT is strengthened by only the new bosons; its
strength is about if the mass parts of , and
are in the ranges . The
contributions of and to the strengths of both EWPTs may
make them sufficiently strong to provide large deviations from thermal
equilibrium and B violation necessary for baryogenesis.Comment: 17 pages, 9 figure
Combinatorics of -deformed stuffle Hopf algebras
In order to extend the Sch\"utzenberger's factorization to general
perturbations, the combinatorial aspects of the Hopf algebra of the
-deformed stuffle product is developed systematically in a parallel way
with those of the shuffle product
Efficacy of Neural Prediction-Based NAS for Zero-Shot NAS Paradigm
In prediction-based Neural Architecture Search (NAS), performance indicators
derived from graph convolutional networks have shown significant success. These
indicators, achieved by representing feed-forward structures as component
graphs through one-hot encoding, face a limitation: their inability to evaluate
architecture performance across varying search spaces. In contrast, handcrafted
performance indicators (zero-shot NAS), which use the same architecture with
random initialization, can generalize across multiple search spaces. Addressing
this limitation, we propose a novel approach for zero-shot NAS using deep
learning. Our method employs Fourier sum of sines encoding for convolutional
kernels, enabling the construction of a computational feed-forward graph with a
structure similar to the architecture under evaluation. These encodings are
learnable and offer a comprehensive view of the architecture's topological
information. An accompanying multi-layer perceptron (MLP) then ranks these
architectures based on their encodings. Experimental results show that our
approach surpasses previous methods using graph convolutional networks in terms
of correlation on the NAS-Bench-201 dataset and exhibits a higher convergence
rate. Moreover, our extracted feature representation trained on each
NAS-Benchmark is transferable to other NAS-Benchmarks, showing promising
generalizability across multiple search spaces. The code is available at:
https://github.com/minh1409/DFT-NPZS-NASComment: 12 pages, 6 figure
Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization
In this work, an effective construction, via Sch\"utzenberger's monoidal
factorization, of dual bases for the non commutative symmetric and
quasi-symmetric functions is proposed
Independence of hyperlogarithms over function fields via algebraic combinatorics
We obtain a necessary and sufficient condition for the linear independence of
solutions of differential equations for hyperlogarithms. The key fact is that
the multiplier (i.e. the factor in the differential equation ) has
only singularities of first order (Fuchsian-type equations) and this implies
that they freely span a space which contains no primitive. We give direct
applications where we extend the property of linear independence to the largest
known ring of coefficients
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