Single-cell growth inference of Corynebacterium glutamicum reveals asymptoticallylinear growth

Regulation of growth and cell size is crucial for the optimization of bacterial cellular function. So far, single bacterial cells have been found to grow predominantly exponentially, which implies the need for tight regulation to maintain cell size homeostasis. Here, we characterize the growth behavior of the apically growing bacterium Corynebacterium glutamicum using a novel broadly applicable inference method for single-cell growth dynamics. Using this approach, we find that C. glutamicum exhibits asymptotically linear single-cell growth. To explain this growth mode, we model elongation as being rate-limited by the apical growth mechanism. Our model accurately reproduces the inferred cell growth dynamics and is validated with elongation measurements on a transglycosylase deficient ΔrodA mutant. Finally, with simulations we show that the distribution of cell lengths is narrower for linear than exponential growth, suggesting that this asymptotically linear growth mode can act as a substitute for tight division length and division symmetry regulation.

Black hole entropy sourced by string winding condensate

We calculate the entropy of an asymptotically Schwarzschild black hole, using an effective field theory of winding modes in type II string theory. In Euclidean signature, the geometry of the black hole contains a thermal cycle which shrinks towards the horizon. The light excitations thus include, in addition to the metric and the dilaton, also the winding modes around this cycle. The winding modes condense in the near-horizon region and source the geometry of the thermal cycle. Using the effective field theory action and standard thermodynamic relations, we show that the entropy, which is also sourced by the winding modes condensate, is exactly equal to the Bekenstein-Hawking entropy of the black hole. We then discuss some properties of the winding mode condensate and end with an application of our method to an asymptotically linear-dilaton black hole.

Solvability for a system of Hadamard fractional multi-point boundary value problems

In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.

Periodic solutions for a class of second-order differential delay equations

<p style='text-indent:20px;'>In this paper, we study the existence of periodic solutions of the following differential delay equations</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} z^{\prime\prime}(t) = \sum\limits_{k = 1}^{M-1}(-1)^kf(z(t-k)), \notag \end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ f\in C(\mathbf{R}^N, \mathbf{R}^N) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ M,N\in \mathbf{N} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ M $\end{document}</tex-math></inline-formula> is odd. By making use of <inline-formula><tex-math id="M4">\begin{document}$ S^1 $\end{document}</tex-math></inline-formula>-geometrical index theory, we obtain an estimation about the number of periodic solutions in term of the difference between eigenvalues of asymptotically linear matrices at the origin and at infinity.</p>

Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system

<p style='text-indent:20px;'>This paper study nonstationary homoclinic-type solutions for a fractional reaction-diffusion system with asymptotically linear and local super linear nonlinearity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite, the second lies in verifying the link geometry and showing the boundedness of Cerami sequences when the nonlinearity is not super quadratic at infinity globally. These enable us to develop a direct approach and new tricks to overcome the difficulties. We establish the existence of homoclinic orbit under some weak assumptions on nonlinearity.</p>