Distinct Lengths Modular Zero-sum Subsequences: A Proof of Graham's Conjecture

Let $n$ be a positive integer and let $S$ be a sequence of $n$ integers in the interval $[0,n-1]$. If there is an $r$ such that any nonempty subsequence with sum $\equiv 0$ $\pmod n$ has length $=r,$ then $S$ has at most two distinct values. This proves a conjecture of R. L. Graham. A previous result of P. Erd\H{o}s and E. Szemer\'edi shows the validity of this conjecture if $n$ is a large prime number

Observation of orbital ordering and origin of the nematic order in FeSe

To elucidate the origin of nematic order in FeSe, we performed field-dependent 77Se-NMR measurements on single crystals of FeSe. We observed orbital ordering from the splitting of the NMR spectra and Knight shift and a suppression of it with magnetic field B0 up to 16 T applied parallel to the Fe-planes. There is a significant change in the distribution and magnitude of the internal magnetic field across the orbital ordering temperature Torb while stripe-type antiferromagnetism is absent. Giant antiferromagnetic (AFM) spin fluctuations measured by the NMR spin-lattice relaxation are gradually developed starting at ~ 40 K, which is far below the nematic ordering temperature Tnem. These results demonstrate that orbital ordering is the origin of the nematic order, and the AFM spin fluctuation is the driving mechanism of superconductivity in FeSe under the presence of the nematic order.Comment: 6 pages, 4 figure

Interrogating Bromodomain Inhibitor Resistance in KMT2A-Rearranged Leukemia Through Combinatorial CRISPR Screens

Bromo- and extra-terminal domain inhibitors (BETi) have exhibited therapeutic activities in many cancers. However, the mechanisms controlling BETi response and resistance are not well understood. We conducted genome-wide loss-of-function CRISPR screens using BETi-treated KMT2A-rearranged (KMT2A-r) cell lines. We revealed that Speckle-type POZ protein (SPOP) gene (Speckle Type BTB/POZ Protein) deficiency caused significant BETi resistance, which was further validated in cell lines and xenograft models. Proteomics analysis and a kinase-vulnerability CRISPR screen indicated that cells treated with BETi are sensitive to GSK3 perturbation. Pharmaceutical inhibition of GSK3 reversed the BETi-resistance phenotype. Based on this observation, a combination therapy regimen inhibiting both BET and GSK3 was developed to impede KMT2A-r leukemia progression in patient-derived xenografts in vivo. Our results revealed molecular mechanisms underlying BETi resistance and a promising combination treatment regimen of ABBV-744 and CHIR-98014 by utilizing unique ex vivo and in vivo KMT2A-r PDX models

Variation of Tensor Force due to Nuclear Medium Effect

The enhancement of $J^{\pi}(T)$=3$^{+}$(0) state with isospin $T=0$ excited by the tensor force in the free $^{6}$Li nucleus has been observed, for the first time, relative to a shrinkable excitation in the $^{6}$Li cluster component inside its host nucleus. Comparatively, the excitation of $J^{\pi}(T)$=0$^{+}$(1) state with isospin $T=1$ for these two $^{6}$Li formations take on an approximately equal excitation strength. The mechanism of such tensor force effect was proposed due to the intensive nuclear medium role on isospin $T$=0 state.Comment: 6 pages, 4 figure

Aspect of Clusters Correlation at Light Nuclei Excited State

The correlation of $\alpha\alpha$ was probed via measuring the transverse momentum $p_{T}$ and width $\delta p_{T}$ of one $\alpha$, for the first time, which represents the spatial and dynamical essentialities of the initial coupling state in $^{8}$Be nucleus. The weighted interaction vertex of 3$\alpha$ reflected by the magnitudes of their relative momentums and relative emission angles proves the isosceles triangle configuration for 3$\alpha$ at the high excited energy analogous Hoyle states.Comment: 8 pages, 9 figure

Variation in WNT7A is unlikely to be a cause of familial Congenital Talipes Equinovarus

<p>Abstract</p> <p>Background</p> <p>Genetic factors make an important contribution to the aetiology of congenital talipes equinovarus (CTEV), the most common developmental disorder of the lower limb. WNT7A was suggested as a candidate gene for CTEV on the basis of a genome-wide scan for linkage in a large multi-case family. WNT7A is a plausible candidate gene for CTEV as it provides a signal for pattern formation during limb development, and mutation in WNT7A has been reported in a number of limb malformation syndromes.</p> <p>Methods</p> <p>We investigated the role of WNT7A using a family-based linkage approach in our large series of European multi-case CTEV families. Three microsatellite markers were used, of which one (D3S2385) is intragenic, and the other two (D3S2403, D3S1252) are 700 kb 5' to the start and 20 kb from the 3' end of the gene, respectively. Ninety-one CTEV families, comprising 476 individuals of whom 211 were affected, were genotyped. LOD scores using recessive and incomplete-dominant inheritance models, and non-parametric linkage scores, excluded linkage.</p> <p>Results</p> <p>No significant evidence for linkage was observed using either parametric or non-parametric models. LOD scores for the parametric models remained strongly negative in the regions between the markers, and in the 0.5 cM intervals outside the marker map. No significant lod scores were obtained when the data were analysed allowing for heterogeneity.</p> <p>Conclusion</p> <p>Our evidence suggests that the WNT7A gene is unlikely to be a major contributor to the aetiology of familial CTEV.</p

Multi-alpha Boson Gas state in Fusion Evaporation Reaction and Three-body Force

The experimental evidence for the $\alpha$ Boson gas state in the $^{11}$C+$^{12}$C$\rightarrow$$^{23}$Mg$^{\ast}$ fusion evaporation reaction is presented. By measuring the $\alpha$ emission spectrum with multiplicity 2 and 3, we provide insight into the existence of a three-body force among $\alpha$ particles. The observed spectrum exhibited distinct tails corresponding to $\alpha$ particles emitted in pairs and triplets consistent well with the model-calculations of AV18-UX and chiral effective field theory of NV2-3-la*, indicating the formation of $\alpha$ clusters with three-body force in the Boson gas state.Comment: 7 pages, 6 figure

Gene-Expression Signatures Can Distinguish Gastric Cancer Grades and Stages

Microarray gene-expression data of 54 paired gastric cancer and adjacent noncancerous gastric tissues were analyzed, with the aim to establish gene signatures for cancer grades (well-, moderately-, poorly- or un-differentiated) and stages (I, II, III and IV), which have been determined by pathologists. Our statistical analysis led to the identification of a number of gene combinations whose expression patterns serve well as signatures of different grades and different stages of gastric cancer. A 19-gene signature was found to have discerning power between high- and low-grade gastric cancers in general, with overall classification accuracy at 79.6%. An expanded 198-gene panel allows the stratification of cancers into four grades and control, giving rise to an overall classification agreement of 74.2% between each grade designated by the pathologists and our prediction. Two signatures for cancer staging, consisting of 10 genes and 9 genes, respectively, provide high classification accuracies at 90.0% and 84.0%, among early-, advanced-stage cancer and control. Functional and pathway analyses on these signature genes reveal the significant relevance of the derived signatures to cancer grades and progression. To the best of our knowledge, this represents the first study on identification of genes whose expression patterns can serve as markers for cancer grades and stages