Edge- and Node-Disjoint Paths in P Systems

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, but our approach is totally distributed, when initially no structural information is available and each P system cell has to even learn its immediate neighbors. For the node-disjoint version, our P system rules are designed to enforce node weight capacities (of one), in addition to edge capacities (of one), which are not readily available in the standard network flow algorithms.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Electric Field-Tuned Topological Phase Transition in Ultra-Thin Na3Bi - Towards a Topological Transistor

The electric field induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor [1-4]. In this scheme an electric field can switch 'on' the ballistic flow of charge and spin along dissipationless edges of the two-dimensional (2D) quantum spin Hall insulator [5-9], and when 'off' is a conventional insulator with no conductive channels. Such as topological transistor is promising for low-energy logic circuits [4], which would necessitate electric field-switched materials with conventional and topological bandgaps much greater than room temperature, significantly greater than proposed to date [6-8]. Topological Dirac semimetals(TDS) are promising systems in which to look for topological field-effect switching, as they lie at the boundary between conventional and topological phases [3,10-16]. Here we use scanning probe microscopy/spectroscopy (STM/STS) and angle-resolved photoelectron spectroscopy (ARPES) to show that mono- and bilayer films of TDS Na3Bi [3,17] are 2D topological insulators with bulk bandgaps >400 meV in the absence of electric field. Upon application of electric field by doping with potassium or by close approach of the STM tip, the bandgap can be completely closed then re-opened with conventional gap greater than 100 meV. The large bandgaps in both the conventional and quantum spin Hall phases, much greater than the thermal energy kT = 25 meV at room temperature, suggest that ultrathin Na3Bi is suitable for room temperature topological transistor operation

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Subcortical amyloid load is associated with shape and volume in cognitively normal individuals

Amyloid-beta (Aβ) deposition is one of the main hallmarks of Alzheimer’s disease. The study assessed the associations between cortical and subcortical 11C-Pittsburgh Compound B retention, namely in the hippocampus, amygdala, putamen, caudate, pallidum, and thalamus, and subcortical morphology in cognitively normal individuals. We recruited 104 cognitive normal individuals who underwent extensive neuropsychological assessment, PiB-positron emission tomography (PET) scan and 3-tesla magnetic resonance imaging (MRI) acquisition of T1-weighted images. Global, cortical, and subcortical regional PiB retention values were derived from each scan and subcortical morphology analyses were performed to investigate vertex-wise local surface and global volumes, including the hippocampal subfields volumes. We found that subcortical regional Aβ was associated with the surface of the hippocampus, thalamus, and pallidum, with changes being due to volume and shape. Hippocampal Aβ was marginally associated with volume of the whole hippocampus as well as with the CA1 subfield, subiculum, and molecular layer. Participants showing higher subcortical Aβ also showed worse cognitive performance and smaller hippocampal volumes. In contrast, global and cortical PiB uptake did not associate with any subcortical metrics. This study shows that subcortical Aβ is associated with subcortical surface morphology in cognitively normal individuals. This study highlights the importance of quantifying subcortical regional PiB retention values in these individuals

Prevalence of abnormal Alzheimer’s disease biomarkers in patients with subjective cognitive decline: cross-sectional comparison of three European memory clinic samples

Introduction: Subjective cognitive decline (SCD) in cognitively unimpaired older individuals has been recognized as an early clinical at-risk state for Alzheimer's disease (AD) dementia and as a target population for future dementia prevention trials. Currently, however, SCD is heterogeneously defined across studies, potentially leading to variations in the prevalence of AD pathology. Here, we compared the prevalence and identified common determinants of abnormal AD biomarkers in SCD across three European memory clinics participating in the European initiative on harmonization of SCD in preclinical AD (Euro-SCD). Methods: We included three memory clinic SCD samples with available cerebrospinal fluid (CSF) biomaterial (IDIBAPS, Barcelona, Spain, n = 44; Amsterdam Dementia Cohort (ADC), The Netherlands, n = 50; DELCODE multicenter study, Germany, n = 42). CSF biomarkers (amyloid beta (Aβ)42, tau, and phosphorylated tau (ptau181)) were centrally analyzed in Amsterdam using prespecified cutoffs to define prevalence of pathological biomarker concentrations. We used logistic regression analysis in the combined sample across the three centers to investigate center effects with regard to likelihood of biomarker abnormality while taking potential common predictors (e.g., age, sex, apolipoprotein E (APOE) status, subtle cognitive deficits, depressive symptoms) into account. Results: The prevalence of abnormal Aβ42, but not tau or ptau181, levels was different across centers (64% DELCODE, 57% IDIBAPS, 22% ADC; p < 0.001). Logistic regression analysis revealed that the likelihood of abnormal Aβ42 (and also abnormal tau or ptau181) levels was predicted by age and APOE status. For Aβ42 abnormality, we additionally observed a center effect, indicating between-center heterogeneity not explained by age, APOE, or the other included covariates. Conclusions: While heterogeneous frequency of abnormal Aβ42 was partly explained by between-sample differences in age range and APOE status, the additional observation of center effects indicates between-center heterogeneity that may be attributed to different recruitment procedures. These findings highlight the need for the development of harmonized recruitment protocols for SCD case definition in multinational studies to achieve similar enrichment rates of preclinical AD

The Clever Shopper Problem

15 pages, 3 figures, to appear at the 13th International Computer Science Symposium in Russia (CSR 2018)International audienceWe investigate a variant of the so-called "Internet Shopping Problem" introduced by Blazewicz et al. (2010), where a customer wants to buy a list of products at the lowest possible total cost from shops which offer discounts when purchases exceed a certain threshold. Although the problem is NP-hard, we provide exact algorithms for several cases, e.g. when each shop sells only two items, and an FPT algorithm for the number of items, or for the number of shops when all prices are equal. We complement each result with hardness proofs in order to draw a tight boundary between tractable and intractable cases. Finally, we give an approximation algorithm and hardness results for the problem of maximising the sum of discounts