Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

Prenatal mechanistic target of rapamycin complex 1 (mTORC1) inhibition by rapamycin treatment of pregnant mice causes intrauterine growth restriction and alters postnatal cardiac growth, morphology, and function

BACKGROUND: Fetal growth impacts cardiovascular health throughout postnatal life in humans. Various animal models of intrauterine growth restriction exhibit reduced heart size at birth, which negatively influences cardiac function in adulthood. The mechanistic target of rapamycin complex 1 (mTORC1) integrates nutrient and growth factor availability with cell growth, thereby regulating organ size. This study aimed at elucidating a possible involvement of mTORC1 in intrauterine growth restriction and prenatal heart growth. METHODS AND RESULTS: We inhibited mTORC1 in fetal mice by rapamycin treatment of pregnant dams in late gestation. Prenatal rapamycin treatment reduces mTORC1 activity in various organs at birth, which is fully restored by postnatal day 3. Rapamycin-treated neonates exhibit a 16% reduction in body weight compared with vehicle-treated controls. Heart weight decreases by 35%, resulting in a significantly reduced heart weight/body weight ratio, smaller left ventricular dimensions, and reduced cardiac output in rapamycin- versus vehicle-treated mice at birth. Although proliferation rates in neonatal rapamycin-treated hearts are unaffected, cardiomyocyte size is reduced, and apoptosis increased compared with vehicle-treated neonates. Rapamycin-treated mice exhibit postnatal catch-up growth, but body weight and left ventricular mass remain reduced in adulthood. Prenatal mTORC1 inhibition causes a reduction in cardiomyocyte number in adult hearts compared with controls, which is partially compensated for by an increased cardiomyocyte volume, resulting in normal cardiac function without maladaptive left ventricular remodeling. CONCLUSIONS: Prenatal rapamycin treatment of pregnant dams represents a new mouse model of intrauterine growth restriction and identifies an important role of mTORC1 in perinatal cardiac growth

Modality-specific tracking of attention and sensory statistics in the human electrophysiological spectral exponent

A hallmark of electrophysiological brain activity is its 1/f-like spectrum – power decreases with increasing frequency. The steepness of this ‘roll-off’ is approximated by the spectral exponent, which in invasively recorded neural populations reflects the balance of excitatory to inhibitory neural activity (E:I balance). Here, we first establish that the spectral exponent of non-invasive electroencephalography (EEG) recordings is highly sensitive to general (i.e., anaesthesia-driven) changes in E:I balance. Building on the EEG spectral exponent as a viable marker of E:I, we then demonstrate its sensitivity to the focus of selective attention in an EEG experiment during which participants detected targets in simultaneous audio-visual noise. In addition to these endogenous changes in E:I balance, EEG spectral exponents over auditory and visual sensory cortices also tracked auditory and visual stimulus spectral exponents, respectively. Individuals’ degree of this selective stimulus–brain coupling in spectral exponents predicted behavioural performance. Our results highlight the rich information contained in 1/f-like neural activity, providing a window into diverse neural processes previously thought to be inaccessible in non-invasive human recordings

Gershgorin disks for multiple eigenvalues of non-negative matrices

Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper

Deterministic Modularity Optimization

We study community structure of networks. We have developed a scheme for maximizing the modularity Q based on mean field methods. Further, we have defined a simple family of random networks with community structure; we understand the behavior of these networks analytically. Using these networks, we show how the mean field methods display better performance than previously known deterministic methods for optimization of Q.Comment: 7 pages, 4 figures, minor change

Line graphs, link partitions, and overlapping communities.

Accepted versio

Analysis of D Pellet Injection Experiments in the W7-AS Stellarator

A centrifugal injector was used to inject deuterium pellets (with 3--5 x 10{sup 19} atoms) at approx. equal 600 m/s into current-less, nearly shear-less plasmas in the Wendelstein 7-AS (W7-AS) stellarator. The D pellet was injected horizontally at a location where the non-circular and non-axisymmetric plasma cross section is nearly triangular. Visible-light TV pictures usually showed the pellet as a single ablating mass in the plasma, although the pellet occasionally broke in two or splintered into a cloud of small particles. The density evolution following pellet injection and the effect of pellet injection on energy confinement and fluctuations are discussed

A lower bound for nodal count on discrete and metric graphs

According to a well-know theorem by Sturm, a vibrating string is divided into exactly N nodal intervals by zeros of its N-th eigenfunction. Courant showed that one half of Sturm's theorem for the strings applies to the theory of membranes: N-th eigenfunction cannot have more than N domains. He also gave an example of a eigenfunction high in the spectrum with a minimal number of nodal domains, thus excluding the existence of a non-trivial lower bound. An analogue of Sturm's result for discretizations of the interval was discussed by Gantmacher and Krein. The discretization of an interval is a graph of a simple form, a chain-graph. But what can be said about more complicated graphs? It has been known since the early 90s that the nodal count for a generic eigenfunction of the Schrodinger operator on quantum trees (where each edge is identified with an interval of the real line and some matching conditions are enforced on the vertices) is exact too: zeros of the N-th eigenfunction divide the tree into exactly N subtrees. We discuss two extensions of this result in two directions. One deals with the same continuous Schrodinger operator but on general graphs (i.e. non-trees) and another deals with discrete Schrodinger operator on combinatorial graphs (both trees and non-trees). The result that we derive applies to both types of graphs: the number of nodal domains of the N-th eigenfunction is bounded below by N-L, where L is the number of links that distinguish the graph from a tree (defined as the dimension of the cycle space or the rank of the fundamental group of the graph). We also show that if it the genericity condition is dropped, the nodal count can fall arbitrarily far below the number of the corresponding eigenfunction.Comment: 15 pages, 4 figures; Minor corrections: added 2 important reference