Krissia Zawadzki

Unveiling the Neuromorphological Space

This article proposes the concept of neuromorphological space as the multidimensional space defined by a set of measurements of the morphology of a representative set of almost 6000 biological neurons available from the NeuroMorpho database. For the first time, we analyze such a large database in order to find the general distribution of the geometrical features. We resort to McGhees biological shape space concept in order to formalize our analysis, allowing for comparison between the geometrically possible tree-like shapes, obtained by using a simple reference model, and real neuronal shapes. Two optimal types of projections, namely, principal component analysis and canonical analysis, are used in order to visualize the originally 20-D neuron distribution into 2-D morphological spaces. These projections allow the most important features to be identified. A data density analysis is also performed in the original 20-D feature space in order to corroborate the clustering structure. Several interesting results are reported, including the fact that real neurons occupy only a small region within the geometrically possible space and that two principal variables are enough to account for about half of the overall data variability. Most of the measurements have been found to be important in representing the morphological variability of the real neurons.

Morphological Homogeneity of Neurons: Searching for Outlier Neuronal Cells

We report a morphology-based approach for the automatic identification of outlier neurons, as well as its application to the NeuroMorpho.org database, with more than 5,000xa0neurons. Each neuron in a given analysis is represented by a feature vector composed of 20 measurements, which are then projected into a two-dimensional space by applying principal component analysis. Bivariate kernel density estimation is then used to obtain the probability distribution for the group of cells, so that the cells with highest probabilities are understood as archetypes while those with the smallest probabilities are classified as outliers. The potential of the methodology is illustrated in several cases involving uniform cell types as well as cell types for specific animal species. The results provide insights regarding the distribution of cells, yielding single and multi-variate clusters, and they suggest that outlier cells tend to be more planar and tortuous. The proposed methodology can be used in several situations involving one or more categories of cells, as well as for detection of new categories and possible artifacts.

Symmetries and Boundary Conditions with a Twist

Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2–7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.

How sharply does the Anderson model depict a single-electron transistor?

AbstractnThe single-impurity Anderson model has been the focus of theoretical studies of molecular junctions and the single-electron transistor, a nanostructured device comprising a quantum dot that bridges two otherwise decoupled metallic leads. The low-temperature transport properties of the model are controlled by the ground-state occupation of the quantum dot, a circumstance that recent density-functional approaches have explored. Here we show that the ground-state dot occupation also parametrizes a linear mapping between the thermal dependence of the zero-bias conductance and a universal function of the temperature scaled by the Kondo temperature. Careful measurements by Grobis and co-workers are very accurately fitted by the universal mapping. Nonetheless, the dot occupation and an asymmetry parameter extracted from the same mapping are relatively distant from the expected values. We conclude that mathematical results derived from the model Hamiltonian reproduce accurately the universal physical properties of the device. In contrast, non-universal features cannot be reproduced quantitatively. To circumvent this limitation, ab initio studies of the device at high energies seem necessary, to accurately define the model Hamiltonian. Our conclusion reinforces findings by Gross and coworkers, who applied time-dependent density-functional theory to show that, to describe the low-energy properties of molecular junctions, one must be able to describe the high-energy regime.n

Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics

AbstractnThe competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here, we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn the competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results.n

Entanglement in Finite Quantum Systems Under Twisted Boundary Conditions

In a recent publication, we have discussed the effects of boundary conditions in finite quantum systems and their connection with symmetries. Focusing on the one-dimensional Hubbard Hamiltonian under twisted boundary conditions, we have shown that properties, such as the ground-state and gap energies, converge faster to the thermodynamical limit (L→∞

Scaling of quantum work distribution for interacting many-body systems

L rightarrow infty

Scalability of DFT protocols for calculating quantum work in many-body systems

) if a special torsion Θ∗ is adjusted to ensure particle-hole symmetry. Complementary to the previous research, the present paper extends our analysis to a key quantity for understanding correlations in many-body systems: the entanglement. Specifically, we investigate the average single-site entanglement 〈Sj〉 as a function of the coupling U/t in Hubbard chains with up to L =u20098 sites and further examine the dependence of the per-site ground-state 𝜖0 on the torsion Θ in different coupling regimes. We discuss the scaling of 𝜖0 and 〈Sj〉 under Θ∗ and analyze their convergence to Bethe Ansatz solution of the infinite Hubbard Hamiltonian. Additionally, we describe the exact diagonalization procedure used in our numerical calculations and show analytical calculations for the case study of a trimer.