Minimum Weight Flat Antichains of Subsets

Building on classical theorems of Sperner and Kruskal-Katona, we investigate antichains $\mathcal F$ in the Boolean lattice $B_n$ of all subsets of $[n]:=\{1,2,\dots,n\}$, where $\mathcal F$ is flat, meaning that it contains sets of at most two consecutive sizes, say $\mathcal F=\mathcal{A}\cup\mathcal{B}$, where $\mathcal{A}$ contains only $k$-subsets, while $\mathcal{B}$ contains only $(k-1)$-subsets. Moreover, we assume $\mathcal{A}$ consists of the first $m$ $k$-subsets in squashed (colexicographic) order, while $\mathcal{B}$ consists of all $(k-1)$-subsets not contained in the subsets in $\mathcal{A}$. Given reals $\alpha,\beta>0$, we say the weight of $\mathcal F$ is $\alpha\cdot|\mathcal{A}|+\beta\cdot|\mathcal{B}|$. We characterize the minimum weight antichains $\mathcal F$ for any given $n,k,\alpha,\beta$, and we do the same when in addition $\mathcal F$ is a maximal antichain. We can then derive asymptotic results on both the minimum size and the minimum Lubell function

Sizes of flat maximal antichains of subsets

This is the second of two papers investigating for which positive integers $m$ there exists a maximal antichain of size $m$ in the Boolean lattice $B_n$ (the power set of $[n]:=\{1,2,\dots,n\}$, ordered by inclusion). In the first part, the sizes of maximal antichains have been characterized. Here we provide an alternative construction with the benefit of showing that almost all sizes of maximal antichains can be obtained using antichains containing only $l$-sets and $(l+1)$-sets for some $l$

The saturation spectrum for antichains of subsets

Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a maximal antichain of size $m$ in the Boolean lattice $B_n$, that is, the power set of $[n]:=\{1,2,\dots,n\}$, ordered by inclusion. As an important ingredient in the proof, we initiate the study of an extension of the Kruskal-Katona theorem which is of independent interest. For given positive integers $t$ and $k$, we ask which integers $s$ have the property that there exists a family $\mathcal F$ of $k$-sets with $\lvert\mathcal F\rvert=t$ such that the shadow of $\mathcal F$ has size $s$, where the shadow of $\mathcal F$ is the collection of $(k-1)$-sets that are contained in at least one member of $\mathcal F$. We provide a complete answer for $t\leqslant k+1$. Moreover, we prove that the largest integer which is not the shadow size of any family of $k$-sets is $\sqrt 2k^{3/2}+\sqrt[4]{8}k^{5/4}+O(k)$.Comment: This is a merger of arXiv:2106.02226v2 with arXiv:2106.0223

Irrigated Alfalfa Vaariety Performance, 1999-2002; Kaysville, Utah

This report summarizes alfalfa yields from four harvest years of an irrigated trial at the Utah Agricultural Experiment station research farm at Kaysville, Cavis Co

Combinatorial control of temporal gene expression in the Drosophila wing by enhancers and core promoters

Abstract Background The transformation of a developing epithelium into an adult structure is a complex process, which often involves coordinated changes in cell proliferation, metabolism, adhesion, and shape. To identify genetic mechanisms that control epithelial differentiation, we analyzed the temporal patterns of gene expression during metamorphosis of the Drosophila wing. Results We found that a striking number of genes, approximately 50% of the Drosophila transcriptome, exhibited changes in expression during a time course of wing development. While cis-acting enhancer sequences clearly correlated with these changes, a stronger correlation was discovered between core-promoter types and the dynamic patterns of gene expression within this differentiating tissue. In support of the hypothesis that core-promoter type influences the dynamics of expression, expression levels of several TATA-box binding protein associated factors (TAFs) and other core promoter-associated components changed during this developmental time course, and a testes-specific TAF (tTAF) played a critical role in timing cellular differentiation within the wing. Conclusions Our results suggest that the combinatorial control of gene expression via cis-acting enhancer sequences and core-promoter types, determine the complex changes in gene expression that drive morphogenesis and terminal differentiation of the Drosophila wing epithelium.http://deepblue.lib.umich.edu/bitstream/2027.42/112935/1/12864_2012_Article_4965.pd

Combretastatin-A4 disrupts neovascular development in non-neoplastic tissue

Combretastatin-A4 phosphate (cis -CA-4) is a tubulin-binding agent currently undergoing clinical trials as an anti-tumour drug. We have investigated whether CA-4 functions as a tumour-specific anti-vascular agent using the hyperplastic thyroid as a novel in vivo model of neovascularization. CA-4 elicited pathological changes in normal tissue, manifested as the induction of multiple, discrete intravascular thrombi. These vascular-damaging effects indicate that CA-4P does not function as a tumour-specific agent but targets neovasculature irrespective of the primary angiogenic stimulus. © 2001 Cancer Research Campaign http://www.bjcancer.co

Cardiovascular effects in patrol officers are associated with fine particulate matter from brake wear and engine emissions

BACKGROUND: Exposure to fine particulate matter air pollutants (PM(2.5)) affects heart rate variability parameters, and levels of serum proteins associated with inflammation, hemostasis and thrombosis. This study investigated sources potentially responsible for cardiovascular and hematological effects in highway patrol troopers. RESULTS: Nine healthy young non-smoking male troopers working from 3 PM to midnight were studied on four consecutive days during their shift and the following night. Sources of in-vehicle PM(2.5 )were identified with variance-maximizing rotational principal factor analysis of PM(2.5)-components and associated pollutants. Two source models were calculated. Sources of in-vehicle PM(2.5 )identified were 1) crustal material, 2) wear of steel automotive components, 3) gasoline combustion, 4) speed-changing traffic with engine emissions and brake wear. In one model, sources 1 and 2 collapsed to a single source. Source factors scores were compared to cardiac and blood parameters measured ten and fifteen hours, respectively, after each shift. The "speed-change" factor was significantly associated with mean heart cycle length (MCL, +7% per standard deviation increase in the factor score), heart rate variability (+16%), supraventricular ectopic beats (+39%), % neutrophils (+7%), % lymphocytes (-10%), red blood cell volume MCV (+1%), von Willebrand Factor (+9%), blood urea nitrogen (+7%), and protein C (-11%). The "crustal" factor (but not the "collapsed" source) was associated with MCL (+3%) and serum uric acid concentrations (+5%). Controlling for potential confounders had little influence on the effect estimates. CONCLUSION: PM(2.5 )originating from speed-changing traffic modulates the autonomic control of the heart rhythm, increases the frequency of premature supraventricular beats and elicits pro-inflammatory and pro-thrombotic responses in healthy young men

Types of directed triple systems

We introduce three types of directed triple systems. Two of these, Mendelsohn directed triple systems and Latin directed triple systems, have previously appeared in the literature but we prove further results about them. The third type, which we call skewed directed triple systems, is new and we determine the existence spectrum to be v ≡ 1 (mod 3), v ≠ 7, except possibly for v = 22, as well as giving enumeration results for small orders

Particulate Matter Exposure in Cars Is Associated with Cardiovascular Effects in Healthy Young Men

Exposure to fine airborne particulate matter (PM(2.5)) is associated with cardiovascular events and mortality in older and cardiac patients. Potential physiologic effects of in-vehicle, roadside, and ambient PM(2.5) were investigated in young, healthy, nonsmoking, male North Carolina Highway Patrol troopers. Nine troopers (age 23 to 30) were monitored on 4 successive days while working a 3 P.M. to midnight shift. Each patrol car was equipped with air-quality monitors. Blood was drawn 14 hours after each shift, and ambulatory monitors recorded the electrocardiogram throughout the shift and until the next morning. Data were analyzed using mixed models. In-vehicle PM(2.5) (average of 24 microg/m(3)) was associated with decreased lymphocytes (-11% per 10 microg/m(3)) and increased red blood cell indices (1% mean corpuscular volume), neutrophils (6%), C-reactive protein (32%), von Willebrand factor (12%), next-morning heart beat cycle length (6%), next-morning heart rate variability parameters, and ectopic beats throughout the recording (20%). Controlling for potential confounders had little impact on the effect estimates. The associations of these health endpoints with ambient and roadside PM(2.5) were smaller and less significant. The observations in these healthy young men suggest that in-vehicle exposure to PM(2.5) may cause pathophysiologic changes that involve inflammation, coagulation, and cardiac rhythm

Porcine and Canine von Willebrand Factor and von Willebrand Disease: Hemostasis, Thrombosis, and Atherosclerosis Studies

Use of animal models of inherited and induced von Willebrand factor (VWF) deficiency continues to advance the knowledge of VWF-related diseases: von Willebrand disease (VWD), thrombotic thrombocytopenic purpura (TTP), and coronary artery thrombosis. First, in humans, pigs, and dogs, VWF is essential for normal hemostasis; without VWF bleeding events are severe and can be fatal. Second, the ADAMTS13 cleavage site is preserved in all three species suggesting all use this mechanism for normal VWF multimer processing and that all are susceptible to TTP when ADAMTS13 function is reduced. Third, while the role of VWF in atherogenesis is debated, arterial thrombosis complicating atherosclerosis appears to be VWF-dependent. The differences in the VWF gene and protein between humans, pigs, and dogs are relatively few but important to consider in the design of VWF-focused experiments. These homologies and differences are reviewed in detail and their implications for research projects are discussed. The current status of porcine and canine VWD are also reviewed as well as their potential role in future studies of VWF-related disorders of hemostasis and thrombosis