On the spectrum of hypergraphs

Here we study the spectral properties of an underlying weighted graph of a non-uniform hypergraph by introducing different connectivity matrices, such as adjacency, Laplacian and normalized Laplacian matrices. We show that different structural properties of a hypergrpah, can be well studied using spectral properties of these matrices. Connectivity of a hypergraph is also investigated by the eigenvalues of these operators. Spectral radii of the same are bounded by the degrees of a hypergraph. The diameter of a hypergraph is also bounded by the eigenvalues of its connectivity matrices. We characterize different properties of a regular hypergraph characterized by the spectrum. Strong (vertex) chromatic number of a hypergraph is bounded by the eigenvalues. Cheeger constant on a hypergraph is defined and we show that it can be bounded by the smallest nontrivial eigenvalues of Laplacian matrix and normalized Laplacian matrix, respectively, of a connected hypergraph. We also show an approach to study random walk on a (non-uniform) hypergraph that can be performed by analyzing the spectrum of transition probability operator which is defined on that hypergraph. Ricci curvature on hypergraphs is introduced in two different ways. We show that if the Laplace operator, $\Delta$, on a hypergraph satisfies a curvature-dimension type inequality $CD (\mathbf{m}, \mathbf{K})$ with $\mathbf{m}>1$ and $\mathbf{K}>0$ then any non-zero eigenvalue of $- \Delta$ can be bounded below by $\frac{ \mathbf{m} \mathbf{K}}{ \mathbf{m} -1 }$. Eigenvalues of a normalized Laplacian operator defined on a connected hypergraph can be bounded by the Ollivier's Ricci curvature of the hypergraph

Profiling of pluripotency factors in individual stem cells and early embryos [preprint]

Major cell fate decisions are governed by sequence-specific transcription factors (TFs) that act in small cell populations within developing embryos. To understand how TFs regulate cell fate it is important to identify their genomic binding sites in these populations. However, current methods cannot profile TFs genome-wide at or near the single cell level. Here we adapt the CUT&RUN method to profile chromatin proteins in low cell numbers, mapping TF-DNA interactions in single cells and individual pre-implantation embryos for the first time. Using this method, we demonstrate that the pluripotency TF NANOG is significantly more dependent on the SWI/SNF family ATPase BRG1 for association with its genomic targets in vivo than in cultured cells, a finding that could not have been made using traditional approaches. Ultra-low input CUT&RUN (uliCUT&RUN) enables interrogation of TF binding from low cell numbers, with broad applicability to rare cell populations of importance in development or disease

Synthesis of Cycloheptatriene-Containing Azetidine Lactones

This document is the Accepted Manuscript version of a Published Work that appeared in final form in The Journal of Organic Chemistry, copyright © 2022 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.joc.2c00367.We prepared a collection of complex cycloheptatriene-containing azetidine lactones by applying two key photochemical reactions: “aza-Yang” cyclization and Buchner carbene insertion into aromatic rings. While photolysis of phenacyl amines leads to a rapid charge transfer and elimination, we found that a simple protonation of the amine enables the formation of azetidinols as single diastereomers. We provide evidence, through ultrafast spectroscopy, for the electron transfer from free amines in the excited state. Further, we characterize the aza-Yang reaction by establishing the dependence of the initial reaction rates on the rates of photon absorption. An unanticipated change in reactivity in morpholine analogues is explained through interactions with the tosylate anion. The Buchner reaction proceeds with a slight preference for one diastereomer over the other, and successful reaction requires electron-donating carbene-stabilizing substituents. Overall, 16 compounds were prepared over seven steps. Guided by an increase in structural complexity, efforts such as this one extend the reach of chemists into unexplored chemical space and provide useful quantities of new compounds for studies focused on their properties

Quantum tunneling in a three dimensional network of exchange coupled single-molecule magnets

A Mn4 single-molecule magnet (SMM) is used to show that quantum tunneling of magnetization (QTM) is not suppressed by moderate three dimensional exchange coupling between molecules. Instead, it leads to an exchange bias of the quantum resonances which allows precise measurements of the effective exchange coupling that is mainly due to weak intermolecular hydrogen bounds. The magnetization versus applied field was recorded on single crystals of [Mn4]2 using an array of micro-SQUIDs. The step fine structure was studied via minor hysteresis loops.Comment: 4 pages, 4 figure

A systematic review and meta-analyses of pregnancy and fetal outcomes in women with multiple sclerosis: a contribution from the IMI2 ConcePTION project.

Neurologists managing women with Multiple Sclerosis (MS) need information about the safety of disease modifying drugs (DMDs) during pregnancy. However, this knowledge is limited. The present study aims to summarize previous studies by performing a systematic review and meta-analyses. The terms "multiple sclerosis" combined with DMDs of interest and a broad profile for pregnancy terms were used to search Embase and Medline databases to identify relevant studies published from January 2000 to July 2019.1260 studies were identified and ten studies met our inclusion criteria. Pooled risk ratios (RR) of pregnancy and birth outcomes in pregnancies exposed to DMDs compared to those not exposed were calculated using a random effects model. For spontaneous abortion RR = 1.14, 95% CI 0.99-1.32, for preterm births RR = 0.93, 95% CI 0.72-1.21 and for major congenital malformations RR = 0.86, 95% CI 0.47-1.56. The most common major congenital malformations reported in MS patients exposed to MS drugs were atrial septal defect (ASD) (N = 4), polydactyly (N = 4) and club foot (N = 3), which are among the most prevalent birth defects observed in the general population. In conclusion, interferons, glatiramer acetate or natalizumab, do not appear to increase the risk for spontaneous abortions, pre-term birth or major congenital malformations. There were very few patients included that were exposed to fingolimod, azathioprine and rituximab; therefore, these results cannot be generalized across drugs. Future studies including internal comparators are needed to enable treating physicians and their patients to decide on the best treatment options

Identification of the PS1 Thr147Ile Variant in a Family with Very Early Onset Dementia and Expressive Aphasia

Background: Early onset dementias have variable clinical presentations and are often difficult to diagnose. We established a family pedigree that demonstrated consistent recurrence of very early onset dementia in successive generations. Objective and Method: In order to refine the diagnosis in this family, we sequenced the exomes of two affected family members and relied on discrete filtering to identify disease genes and the corresponding causal variants. Results: Among the 720 nonsynonymous single nucleotide polymorphisms (SNPs) shared by two affected members, we found a C to T transition that gives rise to a Thr147Ile missense substitution in the presenilin 1 (PS1) protein. The presence of this same mutation in a French early-onset Alzheimer’s disease family, other affected members of the family, and the predicted high pathogenicity of the substitution strongly suggest that it is the causal variant. In addition to exceptionally young age of onset, we also observed significant limb spasticity and early loss of speech, concurrent with progression of dementia in affected family members. These findings extend the clinical presentation associated with the Thr147Ile variant. Lastly, one member with the Thr147Ile variant was treated with the PKC epsilon activator, bryostatin, in a compassionate use trial after successful FDA review. Initial improvements with this treatment were unexpectedly clear, including return of some speech, increased attentional focus, ability to swallow, and some apparent decrease in limb spasticity. Conclusions: Our findings confirm the role of the PS1 Thr147Ile substitution in Alzheimer’s disease and expand the clinical phenotype to include expressive aphasia and very early onset of dementia

Spin dynamics in molecular ring nanomagnets: Significant effect of acoustic phonons and magnetic anisotropies

The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magnetic ring clusters by fully diagonalizing their microscopic spin Hamiltonians. Whether the nearest-neighbor exchange interaction J is ferromagnetic or antiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may be peaked at around k_B_T=|J| provided the lifetime broadening of discrete energy levels is in proportion to T^3^. Experimental findings for ferromagnetic and antiferromagnetic Cu^II^ rings are reproduced with crucial contributions of magnetic anisotropies as well as acoustic phonons.Comment: 5 pages with 5 figures embedded, to be published in J. Phys. Soc. Jpn. 75, No. 10 (2006

BCAT1 redox function maintains mitotic fidelity

The metabolic enzyme branched-chain amino acid transaminase 1 (BCAT1) drives cell proliferation in aggressive cancers such as glioblastoma. Here, we show that BCAT1 localizes to mitotic structures and has a non-metabolic function as a mitotic regulator. Furthermore, BCAT1 is required for chromosome segregation in cancer and induced pluripotent stem cells and tumor growth in human cerebral organoid and mouse syngraft models. Applying gene knockout and rescue strategies, we show that the BCAT1 CXXC redox motif is crucial for controlling cysteine sulfenylation specifically in mitotic cells, promoting Aurora kinase B localization to centromeres, and securing accurate chromosome segregation. These findings offer an explanation for the well-established role of BCAT1 in promoting cancer cell proliferation. In summary, our data establish BCAT1 as a component of the mitotic apparatus that safeguards mitotic fidelity through a moonlighting redox functionality

Spin-parity dependent tunneling of magnetization in single-molecule magnets

Single-molecule magnets facilitate the study of quantum tunneling of magnetization at the mesoscopic level. The spin-parity effect is among the fundamental predictions that have yet to be clearly observed. It is predicted that quantum tunneling is suppressed at zero transverse field if the total spin of the magnetic system is half-integer (Kramers degeneracy) but is allowed in integer spin systems. The Landau-Zener method is used to measure the tunnel splitting as a function of transverse field. Spin-parity dependent tunneling is established by comparing the transverse field dependence of the tunnel splitting of integer and half-integer spin systems.Comment: 4 pages, 6 figure