Log-concavity of the Alexander polynomial

The central question of knot theory is that of distinguishing links up to isotopy. The first polynomial invariant of links devised to help answer this question was the Alexander polynomial (1928). Almost a century after its introduction, it still presents us with tantalizing questions such as Fox's conjecture (1962) that the absolute values of the coefficients of the Alexander polynomial $\Delta_L(t)$ of an alternating link $L$ are unimodal. Fox's conjecture remains open in general, with special cases settled by Hartley (1979) for two-bridged knots, by Murasugi (1985) for a family of alternating algebraic links, and by Ozsv\'ath and Szab\'o (2003) for the case of genus $2$ alternating knots, among others. We settle Fox's conjecture for special alternating links. We do so by proving that a certain multivariate generalization of the Alexander polynomial of special alternating links is Lorentzian. As a consequence, we obtain that the absolute values of the coefficients of $\Delta_L(t)$, where $L$ is a special alternating link, form a log-concave sequence with no internal zeros. In particular, they are unimodal.Comment: V.3 Corrected the setup of Crowell's model, changing oriented spanning trees to arborescences. This change does not affect the proofs. Updated the notation G(L_G) to \mathcal{G}(L_G) to eliminate the notational clash. 10 page

The co-chaperone Fkbp5 shapes the acute stress response in the paraventricular nucleus of the hypothalamus of male mice

Disturbed activation or regulation of the stress response through the hypothalamic-pituitary-adrenal (HPA) axis is a fundamental component of multiple stress-related diseases, including psychiatric, metabolic, and immune disorders. The FK506 binding protein 51 (FKBP5) is a negative regulator of the glucocorticoid receptor (GR), the main driver of HPA axis regulation, and FKBP5 polymorphisms have been repeatedly linked to stress-related disorders in humans. However, the specific role of Fkbp5 in the paraventricular nucleus of the hypothalamus (PVN) in shaping HPA axis (re)activity remains to be elucidated. We here demonstrate that the deletion of Fkbp5 in Sim1(+) neurons dampens the acute stress response and increases GR sensitivity. In contrast, Fkbp5 overexpression in the PVN results in a chronic HPA axis over-activation, and a PVN-specific rescue of Fkbp5 expression in full Fkbp5 KO mice normalizes the HPA axis phenotype. Single-cell RNA sequencing revealed the cell-type-specific expression pattern of Fkbp5 in the PVN and showed that Fkbp5 expression is specifically upregulated in Crh(+) neurons after stress. Finally, Crh-specific Fkbp5 overexpression alters Crh neuron activity, but only partially recapitulates the PVN-specific Fkbp5 overexpression phenotype. Together, the data establish the central and cell-type-specific importance of Fkbp5 in the PVN in shaping HPA axis regulation and the acute stress response

Daily volume, intraday and overnight returns for volatility prediction: profitability or accuracy?

This article presents a comprehensive analysis of the relative ability of three information sets—daily trading volume, intraday returns and overnight returns—to predict equity volatility. We investigate the extent to which statistical accuracy of one-day-ahead forecasts translates into economic gains for technical traders. Various profitability criteria and utility-based switching fees indicate that the largest gains stem from combining historical daily returns with volume information. Using common statistical loss functions, the largest degree of predictive power is found instead in intraday returns. Our analysis thus reinforces the view that statistical significance does not have a direct mapping onto economic value. As a byproduct, we show that buying the stock when the forecasted volatility is extremely high appears largely profitable, suggesting a strong return-risk relationship in turbulent conditions

The Lsm1-7/Pat1 complex binds to stress-activated mRNAs and modulates the response to hyperosmotic shock

RNA-binding proteins (RBPs) establish the cellular fate of a transcript, but an understanding of these processes has been limited by a lack of identified specific interactions between RNA and protein molecules. Using MS2 RNA tagging, we have purified proteins associated with individual mRNA species induced by osmotic stress, STL1 and GPD1. We found members of the Lsm1-7/Pat1 RBP complex to preferentially bind these mRNAs, relative to the non-stress induced mRNAs, HYP2 and ASH1. To assess the functional importance, we mutated components of the Lsm1-7/Pat1 RBP complex and analyzed the impact on expression of osmostress gene products. We observed a defect in global translation inhibition under osmotic stress in pat1 and lsm1 mutants, which correlated with an abnormally high association of both non-stress and stress-induced mRNAs to translationally active polysomes. Additionally, for stress-induced proteins normally triggered only by moderate or high osmostress, in the mutants the protein levels rose high already at weak hyperosmosis. Analysis of ribosome passage on mRNAs through co-translational decay from the 5' end (5P-Seq) showed increased ribosome accumulation in lsm1 and pat1 mutants upstream of the start codon. This effect was particularly strong for mRNAs induced under osmostress. Thus, our results indicate that, in addition to its role in degradation, the Lsm1-7/Pat1 complex acts as a selective translational repressor, having stronger effect over the translation initiation of heavily expressed mRNAs. Binding of the Lsm1-7/Pat1p complex to osmostress-induced mRNAs mitigates their translation, suppressing it in conditions of weak or no stress, and avoiding a hyperresponse when triggered

Community Partners’ Satisfaction with Community-Based Learning Collaborations

Community-university partnerships offer the potential for a number of mutual benefits, yet working with institutions of higher education can pose unique challenges for community participants. To better understand the community perspective, this paper explores community partners’ satisfaction with their involvement in various forms of community-based learning (e.g., service-learning, internships, community-based research). Drawn from a larger, mixed-methods study of community partners across 13 states, the current analysis assesses community agency representatives’ (N = 201) satisfaction with their community-university partnerships in general as well their satisfaction with specific elements of these collaborations. While the findings reflect generally positive levels of satisfaction overall, several areas of concern are identified, including communication with and presence of faculty, commitment and efficacy of students, and partnership equality and recognition of agency contributions. These findings provide a starting point for improving the community partner experience

The Role of Natural Gas in the EU Decarbonisation Path

Over the last decade decarbonisation has become a key priority for the EU. However, on the contrary of renewable energy or energy efficiency, the role of gas in this process has never been clearly defined. This uncertainty opens a wide debate on the future role of gas in the EU energy system, particularly vis-à-vis the progressively stronger role of renewables in the EU energy mix. This paper tackles this issue with the aim to explore what role gas might play in making the EU decarbonisation path more balanced and secure up to 2030 and beyond