On the Complexity of Quantum ACC

For any $q > 1$, let \MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by $q$. We show that for any $q,t > 1$, \MOD_q is equivalent to \MOD_t (up to constant depth). Based on the case $q=2$, Moore \cite{moore99} has shown that quantum analogs of AC$^{(0)}$, ACC$[q]$, and ACC, denoted QAC$^{(0)}_{wf}$, QACC$[2]$, QACC respectively, define the same class of operators, leaving $q > 2$ as an open question. Our result resolves this question, proving that QAC$^{(0)}_{wf} =$ QACC$[q] =$ QACC for all $q$. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC and BQACC_{\rats}. We define a notion $\log$-planar QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in P/poly. We also define a notion of $\log$-gate restricted QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in TC$^{(0)}$. To do this last proof, we show that TC$^{(0)}$ can perform iterated addition and multiplication in certain field extensions. We also introduce the notion of a polynomial-size tensor graph and show that families of such graphs can encode the amplitudes resulting from apply an arbitrary QACC operator to an initial state.Comment: 22 pages, 4 figures This version will appear in the July 2000 Computational Complexity conference. Section 4 has been significantly revised and many typos correcte

A metapopulation model with Markovian landscape dynamics

We study a variant of Hanski's incidence function model that allows habitat patch characteristics to vary over time following a Markov process. The widely studied case where patches are classified as either suitable or unsuitable is included as a special case. For large metapopulations, we determine a recursion for the probability that a given habitat patch is occupied. This recursion enables us to clarify the role of landscape dynamics in the survival of a metapopulation. In particular, we show that landscape dynamics affects the persistence and equilibrium level of the metapopulation primarily through its effect on the distribution of a local population's life span.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

A Note on Universal Measures for Weak Implicit Computational Complexity

Abstract. This note is a case study for finding universal measures for weak implicit computational complexity. We will instantiate “univer-sal measures ” by “dynamic ordinals”, and “weak implicit computational complexity ” by “bounded arithmetic”. Concretely, we will describe the connection between dynamic ordinals and witness oracle Turing ma-chines for bounded arithmetic theories

Promoter methylation of Wnt5a is associated with microsatellite instability and BRAF V600E mutation in two large populations of colorectal cancer patients

BACKGROUND: In colorectal cancer (CRC), tumour microsatellite instability (MSI) status and CpG island methylator phenotype (CIMP) status are indicators of patient outcome, but the molecular events that give rise to these outcomes remain largely unknown. Wnt5a is a critical regulator of non-canonical Wnt activity and promoter hypermethylation of this gene has emerging prognostic roles in CRC; however the frequency and prognostic significance of this epigenetic event have not been explored in the context of colorectal tumour subtype. Consequently, we investigated the frequency and prognostic significance of Wnt5a methylation in a large cohort of MSI-stratified CRCs. METHODS: Methylation was quantified in a large cohort of 1232 colorectal carcinomas from two clinically distinct populations from Canada. Associations were examined between methylation status and clinicopathlogical features, including tumour MSI status, BRAF V600E mutation, and patient survival. RESULTS: In Ontario, Wnt5a methylation was strongly associated with MSI tumours after adjustment for age, sex, and tumour location (odds ratio (OR)=4.2, 95% confidence interval (CI)=2.4-7.4, P<10(-6)) and with BRAF V600E mutation, a marker of CIMP (OR=12.3, 95% CI=6.9-21.7, P<10(-17)), but was not associated with patient survival. Concordant results were obtained in Newfoundland. CONCLUSION: Methylation of Wnt5a is associated with distinct tumour subtypes, strengthening the evidence of an epigenetic-mediated Wnt bias in CRC

Association of Distinct Mutational Signatures With Correlates of Increased Immune Activity in Pancreatic Ductal Adenocarcinoma.

Outcomes for patients with pancreatic ductal adenocarcinoma (PDAC) remain poor. Advances in next-generation sequencing provide a route to therapeutic approaches, and integrating DNA and RNA analysis with clinicopathologic data may be a crucial step toward personalized treatment strategies for this disease.To classify PDAC according to distinct mutational processes, and explore their clinical significance.We performed a retrospective cohort study of resected PDAC, using cases collected between 2008 and 2015 as part of the International Cancer Genome Consortium. The discovery cohort comprised 160 PDAC cases from 154 patients (148 primary; 12 metastases) that underwent tumor enrichment prior to whole-genome and RNA sequencing. The replication cohort comprised 95 primary PDAC cases that underwent whole-genome sequencing and expression microarray on bulk biospecimens.Somatic mutations accumulate from sequence-specific processes creating signatures detectable by DNA sequencing. Using nonnegative matrix factorization, we measured the contribution of each signature to carcinogenesis, and used hierarchical clustering to subtype each cohort. We examined expression of antitumor immunity genes across subtypes to uncover biomarkers predictive of response to systemic therapies.The discovery cohort was 53% male (n = 79) and had a median age of 67 (interquartile range, 58-74) years. The replication cohort was 50% male (n = 48) and had a median age of 68 (interquartile range, 60-75) years. Five predominant mutational subtypes were identified that clustered PDAC into 4 major subtypes: age related, double-strand break repair, mismatch repair, and 1 with unknown etiology (signature 8). These were replicated and validated. Signatures were faithfully propagated from primaries to matched metastases, implying their stability during carcinogenesis. Twelve of 27 (45%) double-strand break repair cases lacked germline or somatic events in canonical homologous recombination genes-BRCA1, BRCA2, or PALB2. Double-strand break repair and mismatch repair subtypes were associated with increased expression of antitumor immunity, including activation of CD8-positive T lymphocytes (GZMA and PRF1) and overexpression of regulatory molecules (cytotoxic T-lymphocyte antigen 4, programmed cell death 1, and indolamine 2,3-dioxygenase 1), corresponding to higher frequency of somatic mutations and tumor-specific neoantigens.Signature-based subtyping may guide personalized therapy of PDAC in the context of biomarker-driven prospective trials

Cholinergic receptor pathways involved in apoptosis, cell proliferation and neuronal differentiation

Acetylcholine (ACh) has been shown to modulate neuronal differentiation during early development. Both muscarinic and nicotinic acetylcholine receptors (AChRs) regulate a wide variety of physiological responses, including apoptosis, cellular proliferation and neuronal differentiation. However, the intracellular mechanisms underlying these effects of AChR signaling are not fully understood. It is known that activation of AChRs increase cellular proliferation and neurogenesis and that regulation of intracellular calcium through AChRs may underlie the many functions of ACh. Intriguingly, activation of diverse signaling molecules such as Ras-mitogen-activated protein kinase, phosphatidylinositol 3-kinase-Akt, protein kinase C and c-Src is modulated by AChRs. Here we discuss the roles of ACh in neuronal differentiation, cell proliferation and apoptosis. We also discuss the pathways involved in these processes, as well as the effects of novel endogenous AChRs agonists and strategies to enhance neuronal-differentiation of stem and neural progenitor cells. Further understanding of the intracellular mechanisms underlying AChR signaling may provide insights for novel therapeutic strategies, as abnormal AChR activity is present in many diseases

Mineral deficiency and the presence of Pinus sylvestris on mires during the mid- to late Holocene: Palaeoecological data from Cadogan's Bog, Mizen Peninsula, Co. Cork, southwest Ireland

Pollen records across parts of Ireland, England and northern Scotland show a dramatic collapse in Pinus pollen percentages at approximately 4000 radiocarbon years BP. This phenomenon has attracted much palaeoecological interest and several hypotheses have been put forward to account for this often synchronous and rapid reduction in pine from mid-Holocene woodland. Explanations for the 'pine decline' include prehistoric human activity, climatic change, in particular a substantial increase in precipitation resulting in increased mire wetness, and airborne pollution associated with the deposition of tephra. Hitherto, one largely untested hypothesis is that mineral deficiency could adversely affect pine growth and regeneration on mire surfaces. The discovery of pine-tree remains (wood pieces, stumps and trunks) within a peat located at Cadogan's Bog on the Mizen Peninsula, southwest Ireland, provided an opportunity to investigate the history of Pinus sylvestris and also to assess the importance of mineral nutrition in maintaining pine growth on mires. Pollen, plant macrofossils, microscopic charcoal and geochemical data are presented from a radiocarbon dated monolith extracted from this peat together with tree ring-width data and radiocarbon dated age estimates from subfossil wood. Analyses of these data suggest that peat accumulation commenced at the site around 6000 years BP when pine was the dominant local tree. Thereafter Pinus pollen percentages diminish in two stages, with the second decline taking place around 4160 ± 50 years BP. Concomitant with this decline in Pinus pollen, there is a noticeable, short-lived increase in wet-loving mire taxa and a decrease in the concentration of phosphorus, potassium, magnesium, calcium, sodium, iron and zinc. These results suggest that increased mire surface wetness, possibly the result of a change in climate, created conditions unsuitable for pine growth c. 4000 years BP. Mire surface wetness, coupled with a period of associated nutrient deficiency, appears to be a possible explanation for a lack of subsequent pine-seedling establishment for most of the later Holocene