Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Phase I study of bortezomib and cetuximab in patients with solid tumours expressing epidermal growth factor receptor

Bortezomib inhibits nuclear factor-κB (NF-κB). Cetuximab is a chimeric mouse–human antibody targeted against epidermal growth factor receptor (EGFR). We hypothesised that concomitant blockade of NF-κB and EGFR signalling would overcome EGFR-mediated resistance to single-agent bortezomib and induce apoptosis through two molecular pathways. The aim of this phase I trial was to establish the maximum tolerated dose (MTD) for bortezomib plus cetuximab in patients with EGFR-expressing epithelial tumours. The 21-day treatment cycle consisted of bortezomib administered on days 1 and 8 through dose escalation (1.3–2 mg m−2). Cetuximab was delivered at a dose of 250 mg m−2 on days 1, 8 and 15 (400 mg m−2 day 1 cycle 1). A total of 37 patients were enroled and given a total 91 cycles. No grade ⩾3 haematological toxicity was noted. Non-hematological grade ⩾3 toxicities included fatigue (22% of patients), dyspnoea (16%) and infection (11%). The MTD was not reached at the highest tested bortezomib dose (2.0 mg m−2). Efficacy outcomes included disease progression in 21 patients (56.7%) and stable disease (SD) at 6 weeks in 16 patients (43.3%). Five of the six patients with SD at 12 weeks were diagnosed with cancers of the lungs or head and neck. This combination therapy was moderately effective in extensively pretreated patients with non-small cell lung or head and neck cancers and warrants further investigation

NUCLEAR MERCHANT SHIP REACTOR PROJECT. EXTENDED ZERO POWER TESTS NS SAVANNAH CORE I. Final Report

Experiments were performed on the NS Savannah Service Core I to supply irformation on future shipboard operation of the Nuclear Merchant Ship Reactor. Testing of instrumentation equipment was satisfactory. Correction factors for shipboard use were determined. Fast neutron flux, neutron fiux distribution, and stuck control rod studies were carried out successfully, as was a three- dimesional calculation to match two critical rod patterns. (auth

Light interception principally drives the understory response to boxelder invasion in riparian forests

Since several decades, American boxelder (Acer negundo) is replacing white willow (Salix alba) riparian forests along southern European rivers. This study aims to evaluate the consequences of boxelder invasion on understory community in riparian areas. We determined the understory species richness, composition and biomass in boxelder and white willow stands located in three riparian forests, representative of three rivers with distinct hydrological regimes. We investigated correlation of these variables to soil moisture and particle size, main soil nutrient stocks, potential nitrification and denitrification, tree canopy cover and photosynthetic active radiation (PAR) at the ground level. A greenhouse experiment was then conducted to identify the causal factors responsible for changes in the understory. The effect of soil type, PAR level and water level on the growth and the biomass production of Urtica dioica were examined. A lower plant species richness and biomass, and a modification of community composition were observed for boxelder understory in all sites, regardless of their environmental characteristics. The strongest modification that follows boxelder invasion was the decline in U. dioica, the dominant species of the white willow forest understory. These differences were mainly correlated with a lower incident PAR under boxelder canopy. The greenhouse experiment identified PAR level as the main factor responsible for the changes in U. dioica stem number and biomass. Our results indicate that adult boxelder acts as an ecosystem engineer that decreases light availability. The opportunistic invasion by boxelder leads to important understory changes, which could alter riparian ecosystem functioning

The proteasome inhibitor MG-132 sensitizes PC-3 prostate cancer cells to ionizing radiation by a DNA-PK-independent mechanism

BACKGROUND: By modulating the expression levels of specific signal transduction molecules, the 26S proteasome plays a central role in determining cell cycle progression or arrest and cell survival or death in response to stress stimuli, including ionizing radiation. Inhibition of proteasome function by specific drugs results in cell cycle arrest, apoptosis and radiosensitization of many cancer cell lines. This study investigates whether there is also a concomitant increase in cellular radiosensitivity if proteasome inhibition occurs only transiently before radiation. Further, since proteasome inhibition has been shown to activate caspase-3, which is involved in apoptosis, and caspase-3 can cleave DNA-PKcs, which is involved in DNA-double strand repair, the hypothesis was tested that caspase-3 activation was essential for both apoptosis and radiosensitization following proteasome inhibition. METHODS: Prostate carcinoma PC-3 cells were treated with the reversible proteasome inhibitor MG-132. Cell cycle distribution, apoptosis, caspase-3 activity, DNA-PKcs protein levels and DNA-PK activity were monitored. Radiosensitivity was assessed using a clonogenic assay. RESULTS: Inhibition of proteasome function caused cell cycle arrest and apoptosis but this did not involve early activation of caspase-3. Short-time inhibition of proteasome function also caused radiosensitization but this did not involve a decrease in DNA-PKcs protein levels or DNA-PK activity. CONCLUSION: We conclude that caspase-dependent cleavage of DNA-PKcs during apoptosis does not contribute to the radiosensitizing effects of MG-132

CAD modeling, multibody system formalisms and visualization : an integrated approach

In this paper an integrated approach of CAD (Computer Aided Design) modeling, generation of equations of motion, simulation and visualization of multibody systems is described. An object-oriented data model for different multibody formalisms is integrated in a commercially available CAD-3D-system. With respect to existing CAD-interfaces, different solid model design methods and various visualization demands the datamodel allow, multi body modeling with a direct interface to a data base. Different software tools like an integrated Newton-Euler formalism are able to use immediately the parametrized multi body system data base. For multibody systems with closed kinematic loops a set of ordinary differential equations and decoupled algebraic equations is formulated automatically which can be solved with explicit multistep integration algorithms. This is achieved by a minimal set of generalized coordinates being specified during the numerical integration. A additional interface provides data for visualization from the simulation tool

The genomic landscape of balanced cytogenetic abnormalities associated with human congenital anomalies

Despite the clinical significance of balanced chromosomal abnormalities (BCAs), their characterization has largely been restricted to cytogenetic resolution. We explored the landscape of BCAs at nucleotide resolution in 273 subjects with a spectrum of congenital anomalies. Whole-genome sequencing revised 93% of karyotypes and demonstrated complexity that was cryptic to karyotyping in 21% of BCAs, highlighting the limitations of conventional cytogenetic approaches. At least 33.9% of BCAs resulted in gene disruption that likely contributed to the developmental phenotype, 5.2% were associated with pathogenic genomic imbalances, and 7.3% disrupted topologically associated domains (TADs) encompassing known syndromic loci. Remarkably, BCA breakpoints in eight subjects altered a single TAD encompassing MEF2C, a known driver of 5q14.3 microdeletion syndrome, resulting in decreased MEF2C expression. We propose that sequence-level resolution dramatically improves prediction of clinical outcomes for balanced rearrangements and provides insight into new pathogenic mechanisms, such as altered regulation due to changes in chromosome topology