Conditional Lower Bounds for Space/Time Tradeoffs

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on well-studied hardness assumptions such as 3SUM, APSP, SETH, etc. This line of research helps to obtain a better understanding of the complexity inside P. A related question asks to prove conditional space lower bounds on data structures that are constructed to solve certain algorithmic tasks after an initial preprocessing stage. This question received little attention in previous research even though it has potential strong impact. In this paper we address this question and show that surprisingly many of the well-studied hard problems that are known to have conditional polynomial time lower bounds are also hard when concerning space. This hardness is shown as a tradeoff between the space consumed by the data structure and the time needed to answer queries. The tradeoff may be either smooth or admit one or more singularity points. We reveal interesting connections between different space hardness conjectures and present matching upper bounds. We also apply these hardness conjectures to both static and dynamic problems and prove their conditional space hardness. We believe that this novel framework of polynomial space conjectures can play an important role in expressing polynomial space lower bounds of many important algorithmic problems. Moreover, it seems that it can also help in achieving a better understanding of the hardness of their corresponding problems in terms of time

Sunlight exposure is just one of the factors which influence Vitamin D status

© The Royal Society of Chemistry and Owner Societies. Studies on the determinants of vitamin D status have tended to concentrate on input-exposure to ultraviolet B radiation and the limited sources in food. Yet, vitamin D status, determined by circulating concentrations of 25-hydroxyvitamin D (25(OH)D), can vary quite markedly in groups of people with apparently similar inputs of vitamin D. There are small effects of polymorphisms in the genes for key proteins involved in vitamin D production and metabolism, including 7-dehydrocholesterol reductase, which converts 7-dehydrocholesterol, the precursor of vitamin D, to cholesterol, CYP2R1, the main 25-hydroxylase of vitamin D, GC, coding for the vitamin D binding protein which transports 25(OH)D and other metabolites in blood and CYP24A1, which 24-hydroxylates both 25(OH)D and the hormone, 1,25-dihydroxyvitamin D. 25(OH)D has a highly variable half-life in blood. There is evidence that the half-life of 25(OH)D is affected by calcium intake and some therapeutic agents. Fat tissue seems to serve as a sink for the parent vitamin D, which is released mainly when there are reductions in adiposity. Some evidence is presented to support the proposal that skeletal muscle provides a substantial site of sequestration of 25(OH)D, protecting this metabolite from degradation by the liver, which may help to explain why exercise, not just outdoors, is usually associated with better vitamin D status

Antibiotic Spacers in Shoulder Arthroplasty: Comparison of Stemmed and Stemless Implants.

Background: Antibiotic spacers in shoulder periprosthetic joint infection deliver antibiotics locally and provide temporary stability. The purpose of this study was to evaluate differences between stemmed and stemless spacers. Methods: All spacers placed from 2011 to 2013 were identified. Stemless spacers were made by creating a spherical ball of cement placed in the joint space. Stemmed spacers had some portion in the humeral canal. Operative time, complications, reimplantation, reinfection, and range of motion were analyzed. Results: There were 37 spacers placed: 22 were stemless and 15 were stemmed. The stemless spacer population was older (70.9 ± 7.8 years vs. 62.8 ± 8.4 years, p = 0.006). The groups had a similar percentage of each gender (stemless group, 45% male vs. stemmed group, 40% male; p = 0.742), body mass index (stemless group, 29.1 ± 6.4 kg/m2 vs. stemmed group, 31.5 ± 8.3 kg/m2; p = 0.354) and Charlson Comorbidity Index (stemless group, 4.2 ± 1.2 vs. stemmed group, 4.2 ± 1.7; p = 0.958). Operative time was similar (stemless group, 127.5 ± 37.1 minutes vs. stemmed group, 130.5 ± 39.4 minutes). Two stemless group patients had self-resolving radial nerve palsies. Within the stemless group, 15 of 22 (68.2%) underwent reimplantation with 14 of 15 having forward elevation of 109° ± 23°. Within the stemmed group, 12 of 15 (80.0%, p = 0.427) underwent reimplantation with 8 of 12 having forward elevation of 94° ± 43° (range, 30° to 150°; p = 0.300). Two stemmed group patients had axillary nerve palsies, one of which self-resolved but the other did not. One patient sustained dislocation of reverse shoulder arthroplasty after reimplantation. One stemless group patient required an open reduction and glenosphere exchange of dislocated reverse shoulder arthroplasty at 6 weeks after reimplantation. Conclusions: Stemmed and stemless spacers had similar clinical outcomes. When analyzing all antibiotic spacers, over 70% were converted to revision arthroplasties. The results of this study do not suggest superiority of either stemmed or stemless antibiotic spacers

A study to guide breeding of new cultivars of organic cherry tomato following a consumer-driven approach.

Agricultural studies focusing on the development and/or improvement of new varieties of fruits and vegetables usually prioritize the productivity, disease resistance, response to fertilization, and higher nutrient content. However, new product development needs to take into account not only flavour preference, but also consumer preference for appearance since without tasting products, consumers have to make decisions based on the way a product looks. The present study evaluated the sensory characteristics and consumer preference of ten promising accessions of organic cherry tomato for fresh consumption aiming at identifying the sensory attributes related to appearance that contributed to consumer liking/disliking the fruit. More specifically, the objective of the study was to guide producers regarding the target appearance attributes that play a role on consumer acceptance of cherry tomatoes. Ten accessions of organic cherry tomatoes were evaluated by a trained panel using the QDA methodology, and also by 80 tomato consumers for the acceptance of appearance and intention to purchase. The results achieved after integrating these two data sets (from the trained panel and consumers) in a multidimensional map allowed the elucidation of consumer liking of tomatoes in relation to the appearance, i.e. drivers of liking/disliking were identified. Results revealed that tomatoes with round shape and red colour (reddish) (cultivar ENAS 1031, ENAS 1010, ?Perinha Agua Branca?, Super Sweet, and ?Joana?) were the most liked cherry tomatoes. Those genotypes were also liked by the smallest segment (17.5% of participants) but for them unusual shapes (oblong and pear), orange-yellow colour, and bigger size were also liked. Despite the small number of participants in this study (80 consumers), new shapes and colours for the organic cherry tomatoes could be considered promising alternatives in the Brazilian market, and can be an opportunity for the producers of the state of Rio de Janeiro

Distributed Edge Connectivity in Sublinear Time

We present the first sublinear-time algorithm for a distributed message-passing network sto compute its edge connectivity $\lambda$ exactly in the CONGEST model, as long as there are no parallel edges. Our algorithm takes $\tilde O(n^{1-1/353}D^{1/353}+n^{1-1/706})$ time to compute $\lambda$ and a cut of cardinality $\lambda$ with high probability, where $n$ and $D$ are the number of nodes and the diameter of the network, respectively, and $\tilde O$ hides polylogarithmic factors. This running time is sublinear in $n$ (i.e. $\tilde O(n^{1-\epsilon})$) whenever $D$ is. Previous sublinear-time distributed algorithms can solve this problem either (i) exactly only when $\lambda=O(n^{1/8-\epsilon})$ [Thurimella PODC'95; Pritchard, Thurimella, ACM Trans. Algorithms'11; Nanongkai, Su, DISC'14] or (ii) approximately [Ghaffari, Kuhn, DISC'13; Nanongkai, Su, DISC'14]. To achieve this we develop and combine several new techniques. First, we design the first distributed algorithm that can compute a $k$-edge connectivity certificate for any $k=O(n^{1-\epsilon})$ in time $\tilde O(\sqrt{nk}+D)$. Second, we show that by combining the recent distributed expander decomposition technique of [Chang, Pettie, Zhang, SODA'19] with techniques from the sequential deterministic edge connectivity algorithm of [Kawarabayashi, Thorup, STOC'15], we can decompose the network into a sublinear number of clusters with small average diameter and without any mincut separating a cluster (except the `trivial' ones). Finally, by extending the tree packing technique from [Karger STOC'96], we can find the minimum cut in time proportional to the number of components. As a byproduct of this technique, we obtain an $\tilde O(n)$-time algorithm for computing exact minimum cut for weighted graphs.Comment: Accepted at 51st ACM Symposium on Theory of Computing (STOC 2019

1,25-Dihydroxycholecalciferol (calcitriol) modifies uptake and release of 25-hydroxycholecalciferol in skeletal muscle cells in culture

© 2017 Elsevier Ltd The major circulating metabolite of vitamin D 3 , 25-hydroxycholecalciferol [25(OH)D], has a remarkably long half-life in blood for a (seco)steroid. Data from our studies and others are consistent with the hypothesis that there is a role for skeletal muscle in the maintenance of vitamin D status. Muscle cells internalise vitamin D-binding protein (DBP) from the circulation by means of a megalin/cubilin plasma membrane transport mechanism. The internalised DBP molecules then bind to actin and thus provide an intracellular array of high affinity binding sites for its specific ligand, 25(OH)D. There is evidence that the residence time for DBP in muscle cells is short and that it undergoes proteolytic degradation, releasing bound 25(OH)D. The processes of internalisation of DBP and its intracellular residence time, bound to actin, appear to be regulated. To explore whether 1,25-dihydroxycholecalciferol (calcitriol) has any effect on this process, cell cultures of myotubes and primary skeletal muscle fibers were incubated in a medium containing 10 −10 M calcitriol but with no added DBP. After 3 h pre-incubation with calcitriol, the net uptake of 25(OH)D by these calcitriol-treated cells over a further 4 h was significantly greater than that in vehicle-treated control cells. This was accompanied by a significant increase in intracellular DBP protein. However, after 16 h of pre-incubation with calcitriol, the muscle cells showed a significantly depressed ability to accumulate 25(OH)D compared to control cells over a further 4 or 16 hours. These effects of pre-incubation with calcitriol were abolished in fibers from VDR-knockout mice. The effect was also abolished by the addition of 4,4\u27-diisothiocyano-2,2\u27-stilbenedisulfonic acid (DIDS), which inhibits chloride channel opening. Incubation of C2 myotubes with calcitriol also significantly reduced retention of previously accumulated 25(OH)D after 4 or 8 h. It is concluded from these in vitro studies that calcitriol can modify the DBP-dependent uptake and release of 25(OH)D by skeletal muscle cells in a manner that suggests some inducible change in the function of these cells