Mesoscopic scales in hierarchical configuration models

To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. Connections between communities are formed as in a configuration model. We study the component sizes of HCM at criticality, and we study critical bond percolation. We find the conditions on the community sizes such that the critical component sizes of HCM behave similarly as in the configuration model. We show that the ordered components of a critical HCM on $N$ vertices are $O\left(N^{2∕3}\right)$. More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.     

A generalized Turán problem in random graphs

We study a generalization of the Turán problem in random graphs. Given graphs T and H, let ex(G(n,p),T,H) be the largest number of copies of T in an H‐free subgraph of G(n,p). We study the threshold phenomena arising in the evolution of the typical value of this random variable, for every H and every 2‐balanced T. Our results in the case when m₂(H) > m₂(T) are a natural generalization of the Erd?s‐Stone theorem for G(n,p), proved several years ago by Conlon‐Gowers and Schacht; the case T = K_m was previously resolved by Alon, Kostochka, and Shikhelman. The case when m₂(H) ≤ m₂(T) exhibits a more complex behavior. Here, the location(s) of the (possibly multiple) threshold(s) are determined by densities of various coverings of H with copies of T and the typical value(s) of ex(G(n,p),T,H) are given by solutions to deterministic hypergraph Turán‐type problems that we are unable to solve in full generality.     

Increased Entropic Brain Dynamics during DeepDream-Induced Altered Perceptual Phenomenology

In recent years, the use of psychedelic drugs to study brain dynamics has flourished due to the unique opportunity they offer to investigate the neural mechanisms of conscious perception. Unfortunately, there are many difficulties to conduct experiments on pharmacologically-induced hallucinations, especially regarding ethical and legal issues. In addition, it is difficult to isolate the neural effects of psychedelic states from other physiological effects elicited by the drug ingestion. Here, we used the DeepDream algorithm to create visual stimuli that mimic the perception of hallucinatory states. Participants were first exposed to a regular video, followed by its modified version, while recording electroencephalography (EEG). Results showed that the frontal region’s activity was characterized by a higher entropy and lower complexity during the modified video, with respect to the regular one, at different time scales. Moreover, we found an increased undirected connectivity and a greater level of entropy in functional connectivity networks elicited by the modified video. These findings suggest that DeepDream and psychedelic drugs induced similar altered brain patterns and demonstrate the potential of adopting this method to study altered perceptual phenomenology in neuroimaging research.     

A pointwise constrained version of the Liapunov convexity theorem for single integrals

Given any AC solution ${\overline{x} : [a,b] \rightarrow \mathbb{R}^{n}}$ to the convex ordinary differential inclusion $$x^{\prime} ( t) \in co\{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e. on [ a,b], \qquad \qquad (^{*})$$ we aim at solving the associated nonconvex inclusion $$x^{\prime} ( t) \in \{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e.,x( a) = \overline{x} ( a), x( b) = \overline{x} ( b), \qquad \qquad (^{**})$$ under an extra pointwise constraint (e.g. on the first coordinate): $$x_{1} ( t) \leq \overline{x}_{1} ( t) \qquad \forall t \in [ a,b]. \qquad \qquad \qquad (^{***})$$ While the unconstrained inclusion (**) had been solved already in 1940 by Liapunov, its constrained version, with (***), was solved in 1994 by Amar and Cellina in the scalar n = 1 case. In this paper we add an extra geometrical hypothesis which is necessary and sufficient, in the vector n > 1 case, for it existence of solution to the constrained inclusion (**) and (***). We also present many examples and counterexamples to the 2 × 2 case.     

Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this article is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps $(M,g)$ and a metric $h$ on the surface that is a conformal transformation of the initial metric $g$ . We prove the existence of the relative determinant of the pair $(\Delta _{h},\Delta _{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips, and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov’s formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.     

Courtship and agonistic sounds by the cichlid fish Pseudotropheus zebra

Courtship and agonistic interactions in an African cichlid species present a richer diversity of acoustic stimuli than previously reported. Male cichlids, including those from the genus Pseudotropheus (P.), produce low frequency short pulsed sounds during courtship. Sounds emitted by P. zebra males in the early stages of courtship (during quiver) were found to be significantly longer and with a higher number of pulses than sounds produced in later stages. During agonistic intrasexual quiver displays, males produced significantly longer sounds with more pulses than females. Also, male sounds had a shorter duration and pulse period in courtship than in male-male interactions. Taken together, these results show that the acoustic repertoire of this species is larger than what was previously known and emphasize the importance of further research exploiting the role of acoustic stimuli in intra- and interspecific communication in African cichlids.     

Biomedical application of VIMP: screening of malignant cells in the prostate

An electrochemical method for discriminating healthy and malignant tissues in prostate biopsies using the voltammetry of immobilized particles methodology is described. The method involves the sampling with graphite bars 0.5 mm in diameter on paraffin-impregnated cross sections of prostate tissues used in ordinary cytological evaluation after local staining with methylene blue (MB). The subsequent record of the voltammetric response of sample-modified graphite electrodes displays clearly different MB-centered features for healthy and malignant regions due to the different association of the dye to the respective cells.