New Classes of Distributed Time Complexity

A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental questions in theory of distributed computing: what are the possible time complexity classes of LCL problems in the LOCAL model? In essence, we have a graph problem $\Pi$ in which a solution can be verified by checking all radius-$O(1)$ neighbourhoods, and the question is what is the smallest $T$ such that a solution can be computed so that each node chooses its own output based on its radius-$T$ neighbourhood. Here $T$ is the distributed time complexity of $\Pi$. The time complexity classes for deterministic algorithms in bounded-degree graphs that are known to exist by prior work are $\Theta(1)$, $\Theta(\log^* n)$, $\Theta(\log n)$, $\Theta(n^{1/k})$, and $\Theta(n)$. It is also known that there are two gaps: one between $\omega(1)$ and $o(\log \log^* n)$, and another between $\omega(\log^* n)$ and $o(\log n)$. It has been conjectured that many more gaps exist, and that the overall time hierarchy is relatively simple -- indeed, this is known to be the case in restricted graph families such as cycles and grids. We show that the picture is much more diverse than previously expected. We present a general technique for engineering LCL problems with numerous different deterministic time complexities, including $\Theta(\log^{\alpha}n)$ for any $\alpha\ge1$, $2^{\Theta(\log^{\alpha}n)}$ for any $\alpha\le 1$, and $\Theta(n^{\alpha})$ for any $\alpha <1/2$ in the high end of the complexity spectrum, and $\Theta(\log^{\alpha}\log^* n)$ for any $\alpha\ge 1$, $\smash{2^{\Theta(\log^{\alpha}\log^* n)}}$ for any $\alpha\le 1$, and $\Theta((\log^* n)^{\alpha})$ for any $\alpha \le 1$ in the low end; here $\alpha$ is a positive rational number

Synchronous Counting and Computational Algorithm Design

Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates $f$ Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states. This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of $f = 1$. While no algorithm exists for $n < 4$, we show that as few as 3 states per node are sufficient for all values $n \ge 4$. Moreover, the problem cannot be solved with only 2 states per node for $n = 4$, but there is a 2-state solution for all values $n \ge 6$. In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SAT-solvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.Comment: 35 pages, extended and revised versio

Current Issues in Comparative Pragmatics : Insights into Linguistic and Cultural Encounters

Non peer reviewe

Effects of microwave vs. convection oven heating on the formation of oxidation products in canola (Brassica rapa subsp. oleifera) oil

Research on the effects of microwave vs. "conventional" heating of dietary oils on lipid oxidation has been very limited. In this study, canola oil (Brassica rapa subsp. oleifera) was heated in either convection or microwave oven to compare the effects of heating methods on triacylglycerol (TAG) oxidation. Peroxide and p-anisidine values (PV and p-AV, respectively) were determined and liquid chromatography-mass spectrometric (LC-MS) analysis of non-oxidized and oxidized TAG molecular species was performed. Neither of the heat treatments caused any considerable changes in PV of the oil samples. However, increase in p-AV was observed. The change was higher in the oil heated in microwave oven, demonstrating a higher increase in the amount of secondary oxidation products. The changes were accompanied by a decrease in the polyunsaturated TAG molecular species ACN:DB (acyl carbon number: number of double bonds) 54: 7 and 54: 6, this change also being higher in the oil heated in microwave oven

How Many Cooks Spoil the Soup?

In this work, we study the following basic question: "How much parallelism does a distributed task permit?" Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. We initiate this study in population protocols, a very simple model that not only allows for a straightforward definition of what a role is, but also encloses the challenge of isolating the properties that are due to the protocol from those that are due to the adversary scheduler, who controls the interactions between the processes. We (i) give a partial characterization of the set of predicates on input assignments that can be stably computed with maximum symmetry, i.e., $\Theta(N_{min})$, where $N_{min}$ is the minimum multiplicity of a state in the initial configuration, and (ii) we turn our attention to the remaining predicates and prove a strong impossibility result for the parity predicate: the inherent symmetry of any protocol that stably computes it is upper bounded by a constant that depends on the size of the protocol.Comment: 19 page

Different berries and berry fractions have various but slightly positive effects on the associated variables of metabolic diseases on overweight and obese women

v2011o

Intracellular signalling pathways and cytoskeletal functions converge on the psoriasis candidate gene CCHCR1 expressed at P-bodies and centrosomes

Background: CCHCR1 (Coiled Coil alpha-Helical Rod protein 1) is a putative psoriasis candidate gene with the risk alleles CCHCR1*WWCC and *Iso3, the latter inhibiting the translation of isoform 1. CCHCR1 was recently shown to be a centiosomal piotein, as well as a component of cytoplasmic piocessmg bodies (P-bodies) that regulate mRNA turnovel. The function of CCHCR1 has remained unsettled, partly because of the inconsistent findings, it has been shown to play a wide variety of roles in divergent processes, e.g., cell proliferation and steroidogenesis. Here we utilized RNA sequencing (RNAseq) using HEK293 cells overexpressing isoforms 1 or 3 (Iso1, Iso3 cells), in combination with the coding non-risk or risk (*WWCC haplotype of CCHCR1. Our aim was to study the overall role of CCHCR1 and the effects of its variants. Results: The overexpression of CCHCR1 variants in HEK293 cells resulted in cell line-specific expression profiles though seveial similarities were observable. Overall the Iso1 and Iso3 cells showed a clear isoform-specific clustering as two separate groups, and the Non-risk and Risk cells often exhibited opposite effects. The RNAseq supported a role for CCHCR1 in the centrosomes and P-bodies; the most highlighted pathways included regulation of cytoskeleton, adherens and tight junctions, mRNA surveillance and RNA transport. Interestingly, both the RNAseq and immunofluorescent localization revealed variant-specific differences for CCHCR1 within the P-bodies. Conclusions: CCHCR1 influenced a wide variety of signaling pathways, which could reflect its active role in the P-bodies and centrosomes that both are linked to the cytoskeleton; as a centrosomal P-body protein CCHCR1 may regulate diverse cytoskeleton-mediated functions, such as cell adhesion and division. The piesent findings may explain the previous inconsistent obseivations about the functions of CCHCR1.Peer reviewe