Compressibility and probabilistic proofs

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.Comment: Invited talk for CiE 2017 (full version

Struggle Against Gender Inequality in Anne with an E (2019)

This study examines gender inequality in Anne with an E (2019) and how it affects the main character. Gender inequality includes women exploitation, victims of sexual harassment, no freedom of the press, women and education, barriers to women's education, unequal right at work, exploring gendered expression and sexuality, and racial segregation and discrimination. This study used Marxist Feminism as a theory. Marx's approach has provided us with the tools and ideas that allow us to think about feminism, class, and anti-capitalism all at once. Marxist feminism and historicism understanding reproduction concerning production may assist people in better comprehending how exploited and abused women are under capitalism. The feminist Netflix series Anne with an E (2019) brings up various still-relevant societal topics from the 1900s, including unequal treatment between men and women. The purpose of this study is to see how the movie Anne with an E Season 3 faced gender inequality in education. Gender inequality issues in the movie matched with Marxist Feminism. The result of this study shows how gender inequality is depicted, such as women's exploitation, including child abuse, unequal right at work, and barriers to girls’ education. Those make the main character react to the inequality and bring out to women's liberation movemen

Widely wavelength-selective Al2O3:Er3+ ring laser

Integrated Al2O3:Er3+ channel waveguide ring lasers were realized on thermally oxidized silicon substrates. High pump power coupling into- and low output power coupling from the ring is achieved in a straightforward design. Wavelength\ud selection in the range 1532 to 1557 nm was demonstrated by\ud varying the length of the output coupler from the ring

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Knockouts, Robustness and Cell Cycles

The response to a knockout of a node is a characteristic feature of a networked dynamical system. Knockout resilience in the dynamics of the remaining nodes is a sign of robustness. Here we study the effect of knockouts for binary state sequences and their implementations in terms of Boolean threshold networks. Beside random sequences with biologically plausible constraints, we analyze the cell cycle sequence of the species Saccharomyces cerevisiae and the Boolean networks implementing it. Comparing with an appropriate null model we do not find evidence that the yeast wildtype network is optimized for high knockout resilience. Our notion of knockout resilience weakly correlates with the size of the basin of attraction, which has also been considered a measure of robustness.Comment: 11 pages, 3 figures, 3 table

PCA and K-Means decipher genome

In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they ``discover'' that the information in the genome is encoded by non-overlapping triplets. Next, they learn how to find gene positions. This exercise on PCA and K-Means clustering enables active study of the basic bioinformatics notions. Appendix 1 contains program listings that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich ones. Animated 3D PCA plots are attached as separate gif files. Topology (cluster structure) and geometry (mutual positions of clusters) of these plots depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes and additional animated 3D PCA plot

Parametric Fokker-Planck equation

We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite dimensional ODE on parameter space. Some analytical example and numerical examples are presented

Bottom-Up versus Top-Down Induction of Sleep by Zolpidem Acting on Histaminergic and Neocortex Neurons

Zolpidem, a GABAA receptor-positive modulator, is the gold-standard drug for treating insomnia. Zolpidem prolongs IPSCs to decrease sleep latency and increase sleep time, effects that depend on α2 and/or α3 subunit-containing receptors. Compared with natural NREM sleep, zolpidem also decreases the EEG power, an effect that depends on α1 subunit-containing receptors, and which may make zolpidem-induced sleep less optimal. In this paper, we investigate whether zolpidem needs to potentiate only particular GABAergic pathways to induce sleep without reducing EEG power. Mice with a knock-in F77I mutation in the GABAA receptor γ2 subunit gene are zolpidem-insensitive. Using these mice, GABAA receptors in the frontal motor neocortex and hypothalamic (tuberomammillary nucleus) histaminergic-neurons of γ2I77 mice were made selectively sensitive to zolpidem by genetically swapping the γ2I77 subunits with γ2F77 subunits. When histamine neurons were made selectively zolpidem-sensitive, systemic administration of zolpidem shortened sleep latency and increased sleep time. But in contrast to the effect of zolpidem on wild-type mice, the power in the EEG spectra of NREM sleep was not decreased, suggesting that these EEG power-reducing effects of zolpidem do not depend on reduced histamine release. Selective potentiation of GABAA receptors in the frontal cortex by systemic zolpidem administration also reduced sleep latency, but less so than for histamine neurons. These results could help with the design of new sedatives that induce a more natural sleep