Search

In this paper we recast the Serret theorem about a characterization of palindromic continued fractions in the context of polynomial continued fractions. Then, using the relation between symmetric tridiagonal matrices and polynomial continued fractions we give a quick exposition of the mathematical aspect of the perfect quantum state transfer problem., 19 pages

Significance: Time-domain functional near-infrared spectroscopy (TD-fNIRS) has been considered as the gold standard of noninvasive optical brain imaging devices. However, due to the high cost, complexity, and large form factor, it has not been as widely adopted as continuous wave NIRS systems. Aim: Kernel Flow is a TD-fNIRS system that has been designed to break through these limitations by maintaining the performance of a research grade TD-fNIRS system while integrating all of the components into a small modular device. Approach: The Kernel Flow modules are built around miniaturized laser drivers, custom integrated circuits, and specialized detectors. The modules can be assembled into a system with dense channel coverage over the entire head. Results: We show performance similar to benchtop systems with our miniaturized device as characterized by standardized tissue and optical phantom protocols for TD-fNIRS and human neuroscience results. Conclusions: The miniaturized design of the Kernel Flow system allows for broader applications of TD-fNIRS.

Weights of permutations were originally introduced by Dugan, Glennon, Gunnells, and Steingr\'imsson (Journal of Combinatorial Theory, Series A 164:24-49, 2019) in their study of the combinatorics of tiered trees. Given a permutation $\sigma$ viewed as a sequence of integers, computing the weight of $\sigma$ involves recursively counting descents of certain subpermutations of $\sigma$. Using this weight function, one can define a $q$-analog $E_n(x,q)$ of the Eulerian polynomials. We prove two main results regarding weights of permutations and the polynomials $E_n(x,q)$. First, we show that the coefficients of $E_n(x, q)$ stabilize as $n$ goes to infinity, which was conjectured by Dugan, Glennon, Gunnells, and Steingr\'imsson (Journal of Combinatorial Theory, Series A 164:24-49, 2019), and enables the definition of the formal power series $W_d(t)$, which has interesting combinatorial properties. Second, we derive a recurrence relation for $E_n(x, q)$, similar to the known recurrence for the classical Eulerian polynomials $A_n(x)$. Finally, we give a recursive formula for the numbers of certain integer partitions and, from this, conjecture a recursive formula for the stabilized coefficients mentioned above., Comment: 11 pages

Phagocytic monocyte-derived macrophages associate with the nodes of Ranvier and initiate demyelination while microglia clear debris and display a suppressed metabolic gene signature in EAE., In the human disorder multiple sclerosis (MS) and in the model experimental autoimmune encephalomyelitis (EAE), macrophages predominate in demyelinated areas and their numbers correlate to tissue damage. Macrophages may be derived from infiltrating monocytes or resident microglia, yet are indistinguishable by light microscopy and surface phenotype. It is axiomatic that T cell–mediated macrophage activation is critical for inflammatory demyelination in EAE, yet the precise details by which tissue injury takes place remain poorly understood. In the present study, we addressed the cellular basis of autoimmune demyelination by discriminating microglial versus monocyte origins of effector macrophages. Using serial block-face scanning electron microscopy (SBF-SEM), we show that monocyte-derived macrophages associate with nodes of Ranvier and initiate demyelination, whereas microglia appear to clear debris. Gene expression profiles confirm that monocyte-derived macrophages are highly phagocytic and inflammatory, whereas those arising from microglia demonstrate an unexpected signature of globally suppressed cellular metabolism at disease onset. Distinguishing tissue-resident macrophages from infiltrating monocytes will point toward new strategies to treat disease and promote repair in diverse inflammatory pathologies in varied organs.