On the inducibility of cycles

In 1975 Pippenger and Golumbic proved that any graph on $n$ vertices admits at most $2e(n/k)^k$ induced $k$-cycles. This bound is larger by a multiplicative factor of $2e$ than the simple lower bound obtained by a blow-up construction. Pippenger and Golumbic conjectured that the latter lower bound is essentially tight. In the present paper we establish a better upper bound of $(128e/81) \cdot (n/k)^k$. This constitutes the first progress towards proving the aforementioned conjecture since it was posed

Differential regulation of different human papilloma virus variants by the POU family transcription factor Brn-3a

The Brn-3a POU family transcription factor is over-expressed in human cervical carcinoma biopsies and is able to activate expression of the human papilloma virus type 16 (HPV-16) upstream regulatory region (URR), which drives the expression of the E6 and E7 oncoproteins. Inhibition of Brn-3a expression in human cervical cancer cells inhibits HPV gene expression and reduces cellular growth and anchorage independence in vitro as well as the ability to form tumours in vivo. Here we show that Brn-3a differentially regulates different HPV-16 variants that have previously been shown to be associated with different risks of progression to cervical carcinoma. In human cervical material Brn-3a levels correlate directly with HPV E6 levels in individuals infected with a high risk variant of HPV-16 whereas this is not the case for a low risk variant. Moreover, the URRs of high and intermediate risk variants are activated by Brn-3a in transfection assays whereas the URR of a low risk variant is not. The change of one or two bases in a low risk variant URR to their equivalent in a higher risk URR can render the URR responsive to Brn-3a and vice versa. These results help explain why the specific interplay between viral and cellular factors necessary for the progression to cervical carcinoma, only occurs in a minority of those infected with HPV-16

Strong Forms of Stability from Flag Algebra Calculations

Given a hereditary family $\mathcal{G}$ of admissible graphs and a function $\lambda(G)$ that linearly depends on the statistics of order-$\kappa$ subgraphs in a graph $G$, we consider the extremal problem of determining $\lambda(n,\mathcal{G})$, the maximum of $\lambda(G)$ over all admissible graphs $G$ of order $n$. We call the problem perfectly $B$-stable for a graph $B$ if there is a constant $C$ such that every admissible graph $G$ of order $n\ge C$ can be made into a blow-up of $B$ by changing at most $C(\lambda(n,\mathcal{G})-\lambda(G)){n\choose2}$ adjacencies. As special cases, this property describes all almost extremal graphs of order $n$ within $o(n^2)$ edges and shows that every extremal graph of order $n\ge n_0$ is a blow-up of $B$. We develop general methods for establishing stability-type results from flag algebra computations and apply them to concrete examples. In fact, one of our sufficient conditions for perfect stability is stated in a way that allows automatic verification by a computer. This gives a unifying way to obtain computer-assisted proofs of many new results.Comment: 44 pages; incorporates reviewers' suggestion

Maximising the number of induced cycles in a graph

We determine the maximum number of induced cycles that can be contained in a graph on $n\ge n_0$ vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Tuza. We also determine the maximum number of odd or even cycles that can be contained in a graph on $n\ge n_0$ vertices and characterise the extremal graphs. This resolves a conjecture of Chv\'atal and Tuza from 1988.Comment: 36 page

Influence of autonomic nervous system in the inducibility of atrial fibrillation.

Cílem této práce je zjištění změn předcházejícím fibrilaci síní. Pozorována je rovnováha mezi sympatikem a parasympatikem. Do experimentu výzkumného ústavu Cleavlendské kliniky bylo zapojeno šest psů různých ras. Signály EKG byly získány Holterovským 24hodinovým monitorováním. Pomocí 40 vysokofrekvenčních impulsů (TI) byla každých 30 minut vyvolávána AF. Z 24hodinového signálu byly extrahovány kratší epizody. Každá z těchto epizod obsahovala 10 minut předcházejících TI a 3 minuty následující po TI. Desetiminutové epizody byly zpracovány automaticky, byly detekovány QRS komplexy a RR intervaly a vypočteny HRV parametry. Přítomnost a délka trvání AF byly zjištěny manuálně z tříminutových intervalů následujících po TI. Byla-li vyvolána AF o délce trvání kratší než 30 sekund došlo ve srovnání s epizodami bez výskytu AF k významným změnám tří HRV parametrů. HF parametr poklesl pro epizody s výskytem AF. LF parametr byl naopak vyšší v epizodách s AF. Pro AF delší než 30 sekund nebyly významné změny pozorovány. Změny v epizodách s krátkou AF mohly být způsobeny změnami vlivu sympatiku a parasympatiku. Ke vzniku dlouhých AF je pravděpodobně zapotřebí i jiného vlivu, který nemusí nutně souviset s nervovým systémem. K dalším analýzám je zapotřebí většího množství signálů.The aim of this study is to investigate changes in sympatho-vagal balance before the initiation of AF. Six mongrel dogs from the Cleveland Clinic foundation were included in this study. ECG was recorded for 24 hours using telemetric Holter monitoring. AF was periodically induced every 30 min. by applying brief bursts of 40 high-frequency atrial train impulses (TI). From the 24 hours signals' traces shorter data episodes were extracted. Each episode consisted of 10 minutes preceding the atrial burst, and 3 minutes following the (TI). The 10 minutes episodes were processed automatically to determine the QRS complexes and RR intervals, and to calculate the HRV parameters. The presence and the duration of AF were determined by manual examination in each of the 3 minutes intervals following the delivery of TI. When the AF was generated, but episodes of AF were shorter than 30 seconds, three HRV parameters were significantly different than when AF was not generated. The HF component was lower in episodes that generated AF. The LF component was higher in episodes that generated AF. No significant differences were found when episodes of AF were longer than 30 seconds. Short episodes of AF could be generated when a certain disorder between sympathetic and parasympathetic tone is present. However in order to be able to generate longer AF episodes it is necessary another component not necessary related to the nervous system. Further analysis with a higher number of dogs should be needed.

Regulation of multiple insulin-like growth factor binding protein genes by 1α,25-dihydroxyvitamin D(3)

Recently, insulin-like growth factor binding proteins (IGFBPs) have been found to be primary mediators of the anti-proliferative actions of the nuclear hormone 1α,25-dihydroxyvitamin D(3) [1α,25(OH)(2)D(3)], but dependent on cellular context IGFBPs can also have a mitogenic effect. In this study, we performed expression profiling of all six human IGFBP genes in prostate and bone cancer cells and demonstrated that IGFBP1, 3 and 5 are primary 1α,25(OH)(2)D(3) target genes. In silico screening of the 174 kb of genomic sequence surrounding all six IGFBP genes identified 15 candidate vitamin D response elements (VDREs) close to or in IGFBP1, 2, 3 and 5 but not in the IGFBP4 and 6 genes. The putative VDREs were evaluated in vitro by gelshift assays and in living cells by reporter gene and chromatin immuno-precipitation (ChIP) assays. Of these 10 VDREs appear to be functional. ChIP assays demonstrated for each of these an individual, stimulation time-dependent association profile not only with the vitamin D receptor, but also with first heterodimeric partner the retinoid X receptor, other regulatory complex components and phosphorylated RNA polymerase II. Some of the VDREs are located distantly from the transcription start sites of IGFBP1, 3 and 5, but all 10 VDREs seem to contribute to the regulation of the genes by 1α,25(OH)(2)D(3). In conclusion, IGFBP1, 3 and 5 are primary 1α,25(OH)(2)D(3) target genes that in intact cells are each under the control of multiple VDREs

Transcriptional and posttranscriptional regulation of human androgen receptor expression by androgen.

Autoregulation is a control mechanism common to several proteins of the steroid/thyroid hormone receptor superfamily. In this work the effect of androgens and antiandrogens on the expression of the human androgen receptor (hAR) in prostate and breast cancer cell lines was studied. Northern blot analysis revealed a decrease in hAR steady state RNA levels in LNCaP cells by 3.3 nht of the synthetic androgen mibolerone. Maximal down-regulation of hAR RNA to 30% of control levels occurred 48 h after hormone addition. T47D breast cancer cells showed a similar effect with mibolerone, while hAR expression in normal skin fibroblasts did not respond to androgen treatment. As shown by nuclease Sl analysis, hAR transcripts initiate at three principal start sites, all of which are equally sensitive to androgen. Steroidal as well as nonsteroidal antiandrogens were capable of partially antagonizing androgen-mediated hAR RNA down-regulation in LNCaP and T47D cells, while not exerting a significant effect when administered alone. While hAR RNA stability was increased by hormone, nuclear run-on analysis revealed a 4-fold reduction of hAR gene transcrip tion 98 h after androgen treatment. Although decreased hAR RNA levels did not coincide with a parallel decrease in AR protein levels, analysis of androgen-inducible reporter constructs demonstrated that prolonged androgen administration to ceils results in a progressively impaired sensitivity of the intracellular androgen response mechanism. These results show that prolonged androgen exposure leads, besides its effect on hAR RNA levels, to functional inactivation of the AR. Thus, in viva, posttranslational control of AR activity appears to be a novel mechanism of negative autoregulation of androgen effects on gene expression