Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

Let $F_q$ be a finite field of characteristic $p=2,3$. We give the number of irreducible polynomials x^m+a_{m-1}x^{m-1}+...+a_0\in\F_q[x] with $a_{m-1}$ and $a_{m-3}$ prescribed for any given $m$ if $p=2$, and with $a_{m-1}$ and $a_1$ prescribed for $m=1,...,10$ if $p=2,3$.Comment: 17 pages, Part of the results was presented at the Polynomials over Finite Fields and Applications workshop at Banff International Research Station, Canad

Dynamics of polymer ejection from capsid

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which a viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the escape times scale with polymer length, $\tau \sim N^\alpha$. We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) $\rho$ inside the capsid. For very low densities $\rho \le 0.002$ the polymer is only weakly confined by the capsid, and we measure $\alpha = 1.33$, which is close to $\alpha = 1.4$ obtained for polymer translocation. At intermediate densities the scaling exponents $\alpha = 1.25$ and $1.21$ for $\rho = 0.01$ and $0.02$, respectively. These scalings are in accord with a crude derivation for the lower limit $\alpha = 1.2$. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, $\rho \gtrapprox 0.25$. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.Comment: 10 pages, 6 figure

Structural and psychological empowerment of students obtaining continuing leadership education in Finland-a national survey

Background: In nursing, empowerment may be deemed one's potential to gain power, achieve goals and promote one's skills to advance positive changes in the working environment, or decentralization of authority. Empowerment is associated with nurses' and nurse leaders' satisfaction, performance and organizational commitment, as well as burnout, emotional exhaustion and intentions to leave the profession. Research on nurse empowerment in relation to continuing education is sparse.Objectives: This study describes the structural and psychological empowerment levels of students beginning a collaboratively implemented continuing leadership education program.Design: Cross-sectional electronic survey.Settings: National, continuing nursing leadership education program (37 ECT) organized by five universities that provide masters level education to nurse leaders in Finland.Participants: Students (N = 85) working at nine healthcare organizations across the service system as current or prospective nurse leaders and enrolled in the continuing leadership education program.Methods: The Conditions of Work Effectiveness Questionnaire and the Work Empowerment Questionnaire were each used to measure structural and psychological empowerment, respectively. The data were collected between October 2019 and February 2020.Results: A total of 69 students participated (response rate 81 %). Moderate levels of both structural and psychological empowerment were observed. In structural empowerment, the strongest dimension was access to opportunity (4.1, SD 0.7), whereas access to support was the weakest (2.7, SD 0.7). The strongest psychological empowerment dimension was verbal empowerment (8.5, SD 1.9) and the weakest was outcome empowerment (7.0, SD 1.6).Conclusions: Nurses and nurse leaders seem to lack the status and power required to impact their organizations, possibly causing them to apply for nursing leadership education. Nurse leaders should be given opportunities for continuing leadership education to improve empowerment and, as a result, staff outcomes.</p