The Erdös-Ko-Rado theorem for vector spaces

AbstractLet V be an n-dimensional vector space over GF(q) and for integers k⩾t>0 let mq(n, k, t) denote the maximum possible number of subspaces in a t-intersecting family F of k-dimensional subspaces of V, i.e., dim F ∩ F′ ⩾ t holds for all F, F′ ϵ F. It is shown that mq(n,k,t)=maxn−tk−t, 2k−tk for n⩾2k−t while for n⩽2k−t trivially mq(n,k,t)=nk holds

A general 2-part Erdős-Ko-Rado theorem

A two-part extension of the famous Erdo{combining double acute accent}s-Ko-Rado Theorem is proved. The underlying set is partitioned into X1 and X2. Some positive integers ki, ℓi (1 ≤ i ≤ m) are given. We prove that if ℱ is an intersecting family containing members F such that |F ∩ X1| = ki, |F ∩ X2| = ℓi holds for one of the values i (1 ≤ i ≤ m) then |ℱ| cannot exceed the size of the largest subfamily containing one element. © Wydawnictwa AGH, 2017

A list of common expressions featuring the postposition ko.

The principal use of ko is to mark an object. In mE# ram ko btaËÅga “I’ll tell Ram”, ram is said to be the DIRECT object because the action of telling is done to him directly. In mE# yh toh¿Pa ram ko dUÅga “I’ll give this present to Ram”, ko means “to” and is used to mark the INDIRECT object ram; the direct object is yh toh¿Pa and does not take ko. Another use of ko is to pinpoint days of the week or times of day: gu<var ko “on Thursday”, subh ko “in the morning”, xam ko “in the evening”, rat ko “at night” (but idn me# “in the daytime”). So much for the primary uses of ko. The purpose of this handout is to list some of the very numerous constructions and expressions in which ko has a different function. While expressions such as “I have a cold” or “I like bananas” have “I” as subject in English, in Hindi this “logical subject” takes ko (muJko) and the cold or the banana becomes the grammatical subject, with which the verb agrees (¿jukam hE): muJko ¿jkam hE “I have a cold”, muJko kele psMd hE# “I like bananas”. Each of these expressions can refer to either a male or a female, because the pronoun has no gender. And muJko can of course be replaced by its synonym muJe. Familiarise yourself with this list by reading it aloud, and try some substitution exercises by changing the “I” to other pronouns and tenses — “She has a cold, they had a cold”, etc. Then read the note at the end.Asian Studie

Loss of Connective Tissue Growth Factor Expression Promotes Remodeling of the Extracellular Matrix and Epithelial-to-Mesenchymal Transition in Ovarian Cancer

Background: Ovarian Cancer (OC) is the leading cause of death from gynecologic malignancies in the United States largely due to the advanced stage at the time of diagnosis. Epithelial-to-mesenchymal transition (EMT) is a key biological process implicated in the pathophysiology of the metastatic spread of OC. Discovering the “trigger/s,” its downstream targets, and therapeutic targeting are essential to substantively improve the survival of women with OC. The objective of our study is to evaluate the role of Connective Tissue Growth Factor (CTGF) in EMT in OC. Methods: R182 and R2615 are well-described epithelial OC cell and MR182 and MR2615 are the mesenchymal counterparts. R182/R2615 CTGF knock outs (KO) were derived utilizing a Cas9/CRISPR-Cas9 lentivirus plasmid vector and verified by indel sequencing. Invasion, anoikis resistance, and chemosensitivity assays were performed in wild-type (WT) and KO cells. RNA sequence analysis was performed and analyzed using iPathway guide. Top five upregulated and downregulated genes involved in ECM organization pathway were validated by quantitative PCR (qPCR). Immunofluorescence was performed for F-actin. Results: CTGF was expressed in the epithelial and not in the mesenchymal OC cell lines. Loss of CTGF was associated with anoikis resistance, where KO and WT cells displayed 75% and 10% viability, respectively. KO cells were significantly more invasive than WT cells. Administration of exogeneous CTGF in KO cells decreased invasion in a dose dependent manner. No change was seen in chemosensitivity to Cisplatin in KO cells. RNA seq analysis identified ECM organization as the biologic process most affected by loss of CTGF. Upregulated (FREM2, LAMC2, ITGB4) and downregulated (SPP1, SV2A, RELN, COL6A3, COL4A6) extracellular matrix genes were validated by qPCR. Immunofluorescence staining of F-actin demonstrated increased cytoskeleton expression of F-actin in CTGF KO cells. Conclusion: Our data suggests that CTGF expression maintains the epithelial phenotype in OC. Loss of CTGF may be one of the early triggers of EMT in OC through extracellular matrix remodeling affecting anoikis and adhesion characteristics, thus acquiring a more migratory and invasive phenotype

PO-040 Characterisation of cdk12 knocked out ovarian cancer cell lines

Introduction While cyclin-dependent kinases (CDKs) have a key role in promoting/controlling transition between the different phases of the cell cycle, transcriptional kinases, like CDK12, are mainly involved in gene transcription. CDK12 has been shown to regulate the expression of genes involved in DNA damage and to maintain genomic stability. Impairment of CDK12 activity is synergic with PARP inhibitor and cisplatin treatments in different cellular systems. We here aimed to generate ovarian cancer cell lines knocked out (KO) for CDK12 to understand its role in ovarian cancer and in response to chemotherapy. Material and methods A2780 and SKOV3 CDK12 KO clones were generated with CRISPR/Cas9 technology. Cell cycle analysis was evaluated by standard flow cytometric methods and DNA repair genes levels by Real Time PCR. Caspase 3 activity was measured to detect apoptosis with a luminescence-based assay. Cytotoxicity experiments were performed treating cells with different drug concentrations and evaluating cell survival after 72 hours by MTS assay. For in vivo studies 7.5 millions of cells were transplanted subcutaneously in nude mice and animals were monitored for tumour appearance and growth. Results and discussions We obtained 2 CDK12 KO ovarian cancer clones, A2780 KO and SKOV3 KO, out of more than 300 clones screened. The cell growth of both A2780 KO and SKOV3 KO cells is slower than the wild type (WT) cells, they have a less clonogenic ability and a tetraploid DNA content. Both CDK12 KO clones have a higher basal caspase activity than the WT cell lines, indicative of higher basal induction of apoptosis, while no increase in autophagy or senescence is observed. Both CDK12 KO clones show a decreased expression in BRCA1 and FANCD2 DNA repair genes than the WT cells. Cytotoxic experiments with anticancer agents with different mechanism of action show that both KO clones are less sensitive to ATM, CHK1 and WEE1 inhibitors treatment as compared to WT cells, while platinum and PARP inhibitors show similar cytotoxic activity in KO and WT cells. Interestingly enough, when KO clones were transplanted in nude mice, no tumour take was observed. Conclusion We were able to obtain CDK12 KO cells. We think that these models could help in disclosing new roles of CDK12 in ovarian carcinoma and may represent a useful tool to study new combination therapies for tumours with CDK12 mutations