arXiv subjects
Publications and source records attributed to J. Petkovic.
We present a review of known models and a new simple mathematical modelling for border completion in the visual cortex V1 highlighting the striking analogies with bicycle rear wheel motions in the plane.
We present a simple mathematical model for the mammalian low visual pathway, taking into account its key elements: retina, lateral geniculate nucleus (LGN), primary visual cortex (V1). The analogies between the cortical level of the visual system and the structure of popular CNNs, used in image classification tasks, suggests the introduction of an additional preliminary convolutional module inspired to precortical neuronal circuits to improve robustness with respect to global light intensity and contrast variations in the input images. We validate our hypothesis on the popular databases MNIST, FashionMNIST and SVHN, obtaining significantly more robust CNNs with respect to these variations, once such extra module is added.
Two tetraquark candidates $Z_b(10610)$ and $Z_b(10650)$ with flavor structure $\bar bb\bar du$ were discovered by Belle experiment in 2011. We present a preliminary $N_f=2$ lattice study of the $\bar bb\bar du$ system in the approximation of static $b$ quarks, where the total spin of heavy quarks is fixed to one. The ground and the excited eigen-energies are determined as a function of separation $r$ between $b$ and $\bar b$. The lower eigenstates are related to a bottomonium and a pion. One of the higher eigenstates is dominated by $B\bar B^*$: its energy is significantly below $m_B+m_{B*}$ for r=[0.1,0.4] fm, which suggests sizable attraction. The attractive potential $V(r)$ between $B$ and $\bar B^*$ is extracted assuming that this eigenstate is related exclusively to $B\bar B^*$. Assuming a certain form of the potential and solving non-relativistic Schrodinger equation, we find a bound state pole below $B\bar B^*$ threshold. For certain parametrizations, the bound state is very close to the $B\bar B^*$ threshold - this feature could be related to $Z_b(10610)$ in the experiment.
Two $Z_b$ hadrons with exotic quark structure $\bar bb\bar du$ were discovered by Belle experiment. We present a lattice QCD study of the $\bar bb\bar du$ system in the approximation of static $b$ quarks, where the total spin of heavy quarks is fixed to one. The energies of eigenstates are determined as a function of the separation $r$ between $b$ and $\bar b$. The lower eigenstates are related to a bottomonium and a pion. The eigenstate dominated by $B\bar B^*$ has energy significantly below $m_B+m_{B^*}$, which points to a sizable attraction for small $r$. The attractive potential $V(r)$ between $B$ and $\bar B^*$ is extracted assuming that this eigenstate is related exclusively to $B\bar B^*$. The Schrödinger equation for $B\bar B^*$ within the extracted potential leads to one bound state below $B\bar B^*$ threshold, whose mass depends on the parametrization of the lattice potential. For certain parametrizations, the bound state is very close to the $B\bar B^*$ threshold and renders a narrow peak in the $B\bar B^*$ rate above threshold - these features could be related to $Z_b(10610)$ in the experiment.