Lower Bounds for Subgraph Detection in the CONGEST Model

In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to de- termine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ? 4, and constructing a graph H ? from Ck by replacing each edge {i, (i + 1) mod k} of the cycle with a connected graph Hi, subject to some constraints on the graphs H_{0}, . . .H_{k?1}. In this case we obtain a polynomial lower bound for the new graph H ?, depending on the size of the shortest cycle in H ? passing through the vertices of the original k-cycle

Binding effects in multivalent Gibbs-Donnan equilibrium

The classical Gibbs-Donnan equilibrium describes excess osmotic pressure associated with confined colloidal charges embedded in an electrolyte solution. In this work, we extend this approach to describe the influence of multivalent ion binding on the equilibrium force acting on a charged rod translocating between two compartments, thereby mimicking ionic effects on force balance during in vitro DNA ejection from bacteriophage. The subtle interplay between Gibbs-Donnan equilibrium and adsorption equilibrium leads to a non-monotonic variation of the ejection force as multivalent salt concentration is increased, in qualitative agreement with experimental observations

Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs

In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we obtain a constant-time algorithm for additive +1 approximation in Congested Clique, and the first parametrized algorithm for exact computation in Congest. In the Congested Clique model, we first develop a technique for learning small neighborhoods, and apply it to obtain an O(1)-round algorithm that computes the girth with only an additive +1 error. Next, we introduce a new technique (the partition tree technique) allowing for efficiently listing all copies of any subgraph, which is deterministic and improves upon the state-of the-art for non-dense graphs. We give two concrete applications of the partition tree technique: First we show that for constant k, it is possible to solve C_{2k}-detection in O(1) rounds in the Congested Clique, improving on prior work, which used fast matrix multiplication and thus had polynomial round complexity. Second, we show that in triangle-free graphs, the girth can be exactly computed in time polynomially faster than the best known bounds for general graphs. We remark that no analogous result is currently known for sequential algorithms. In the Congest model, we describe a new approach for finding cycles, and instantiate it in two ways: first, we show a fast parametrized algorithm for girth with round complexity O?(min{g? n^{1-1/?(g)},n}) for any girth g; and second, we show how to find small even-length cycles C_{2k} for k = 3,4,5 in O(n^{1-1/k}) rounds. This is a polynomial improvement upon the previous running times; for example, our C?-detection algorithm runs in O(n^{2/3}) rounds, compared to O(n^{3/4}) in prior work. Finally, using our improved C?-freeness algorithm, and the barrier on proving lower bounds on triangle-freeness of Eden et al., we show that improving the current ??(?n) lower bound for C?-freeness of Korhonen et al. by any polynomial factor would imply strong circuit complexity lower bounds

The Influence of the Timing of Cyclic Load Application on Cardiac Cell Contraction

Cardiac cells are subjected to mechanical load during each heart-beat. Normal heart load is essential for physiological development and cardiac function. At the same time, excessive load can induce pathologies such as cardiac hypertrophy. While the forces working on the heart as an organ are well-understood, information regarding stretch response at the cellular level is limited. Since cardiac stretch-response depends on the amplitude and pattern of the applied load as well as its timing during the beating cycle, the directionality of load application and its phase relative to action potential generation must be controlled precisely. Here, we design a new experimental setup, which enables high-resolution fluorescence imaging of cultured cardiac cells under cyclic uniaxial mechanical load and electrical stimulation. Cyclic stretch was applied in different phases relative to the electrical stimulus and the effect on cardiac cell beating was monitored. The results show a clear phase-dependent response and provide insight into cardiac response to excessive loading conditions

Quantifying exposure and intra-individual reliability of high-speed and sprint running during sided-games training in soccer players: a systematic review and meta-analysis:High-speed and sprint running exposure in soccer sided-games

BACKGROUND: Sided games (i.e., small sided, medium sided, large sided) involve tactical, technical, physical, and psychological elements and are commonly implemented in soccer training. Although soccer sided-games research is plentiful, a meta-analytical synthesis of external load exposure during sided games is lacking. OBJECTIVE: The objective of this systematic review and meta-analysis was to: (1) synthesize the evidence on high-speed and sprint running exposure induced by sided games in adult soccer players, (2) establish pooled estimates and intra-individual reliability for high-speed and sprint running exposure, and (3) explore the moderating effects of game format and playing constraints. METHODS: A literature search was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses 2020 guidelines. Four databases (PubMed/MEDLINE, Scopus, SPORTDiscus, Web of Science Core Collection) were systematically searched up to 25 January, 2022. Eligibility criteria were adult soccer players (population); training programs incorporating sided games (intervention); game manipulations including number of players, pitch dimension, and game orientation (comparator); and high-speed, very high-speed, and sprint relative (m[Formula: see text] min(−1)) running distances and associated intra-individual reliability (outcome). Eligible study risk of bias was evaluated using RoBANS. Pooled estimates for high-speed and sprint running exposure, and their intra-individual reliability, along with the moderating effect of tracking device running velocity thresholds, pitch dimension (i.e., area per player), and game orientation (i.e. score or possession), were determined via a multi-level mixed-effects meta-analysis. Estimate uncertainty is presented as 95% compatibility intervals (CIs) with the likely range of relative distances in similar future studies determined via 95% prediction intervals. RESULTS: A total of 104 and 7 studies met our eligibility criteria for the main and reliability analyses, respectively. The range of relative distances covered across small-sided games, medium-sided games, and large-sided games was 14.8 m[Formula: see text] min(−1) (95% CI 12.3–17.4) to 17.2 m[Formula: see text] min(−1) (95% CI 13.5–20.8) for high-speed running, 2.7 m[Formula: see text] min(−1) (95% CI 1.8–3.5) to 3.6 m[Formula: see text] min(−1) (95% CI 2.3–4.8) for very high-speed running, and 0.2 m[Formula: see text] min(−1) (95% CI 0.1–0.4) to 0.7 m[Formula: see text] min(−1) (95% CI 0.5–0.9) for sprinting. Across different game formats, 95% prediction intervals showed future exposure for high-speed, very high-speed running, and sprinting to be 0–46.5 m[Formula: see text] min(−1), 0–14.2 m[Formula: see text] min(−1), and 0–2.6 m[Formula: see text] min(−1), respectively. High-speed, very high-speed running, and sprinting showed poor reliability with a pooled coefficient of variation of 22.8% with distances being moderated by device speed thresholds, pitch dimension, and game orientation. CONCLUSIONS: This review is the first to provide a detailed synthesis of exposure and intra-individual reliability of high-speed and sprint running during soccer sided games. Our estimates, along with the moderating influence of common programming variables such as velocity thresholds, area per player, and game orientation should be considered for informed planning of small-sided games, medium-sided games, and large-sided games soccer training. CLINICAL TRIAL REGISTRATION: Open Science Framework available through https://osf.io/a4xr2/