Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions

In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge

Intraoperative blood transfusions in highly alloimmunized patients undergoing orthotopic liver transplantation.

Intraoperative blood requirements were analyzed in patients undergoing primary orthotopic liver transplantation and divided into two groups on the basis of panel reactive antibody of pretransplant serum measured by lymphocytotoxicity testing. One group of highly sensitized patients (n = 25) had PRA values of over 70% and the second group of patients (n = 26) had 0% PRA values and were considered nonsensitized. During the transplant procedure, the 70% PRA group received considerably greater quantities of blood products than the 0% PRA group--namely, red blood cells: 21.1 +/- 3.7 vs. 9.8 +/- 0.8 units (P = 0.002), and platelets: 17.7 +/- 3.2 vs. 7.5 +/- 1.5 units (P = 0.003). Similar differences were observed for fresh frozen plasma and cryoprecipitate. Despite the larger infusion of platelets, the blood platelet counts in the 70% PRA group were lower postoperatively than preoperatively. Twenty patients in the 70% PRA group received platelet transfusions, and their mean platelet count dropped from 95,050 +/- 11,537 preoperatively to 67,750 +/- 8,228 postoperatively (P = 0.028). In contrast, nearly identical preoperative (84,058 +/- 17,297) and postoperative (85,647 +/- 12,445) platelet counts were observed in the 17 0% PRA patients who were transfused intraoperatively with platelets. Prothrombin time, activated partial thromboplastin time, and fibrinogen levels showed no significant differences between both groups. These data demonstrate that lymphocytotoxic antibody screening of liver transplant candidates is useful in identifying patients with increased risk of bleeding problems and who will require large quantities of blood during the transplant operation

Systemic effects of tissue plasminogen activator-associated fibrinolysis and its relation to thrombin generation in orthotopic liver transplantation

Orthotopic liver transplantation is frequently associated with hyperfibrinolysis, the origin and clinical relevance of which is largely unknown. In 20 orthotopic liver transplantations, we studied the occurrence and systemic effects of hyperfibrinolysis. Severe fibrinolysis was defined to be present when the euglobulin-clot lysis time and the whole-blood-clot lysis time, as measured by thrombelastography, were shorter than 60 and 90 min, respectively, at some time during the operation. Based on these criteria, 7 patients had minimal fibrinolysis (group I), and 13 patients had severe fibrinolysis (group II). In group II a gradual increase of tissue-type plasminogen activator (t-PA) activity was seen during the anhepatic stage, followed by an “explosive” increase immediately after graft reperfusion (P=0.0004, compared with group I), and a reduction of plasminogen activator inhibitor (PAI) activity. Plasma degradation products of fibrinogen and fibrin increased parallel to t-PA activity, and levels were significantly higher at 45 min after graft reperfusion in group II compared with group I (P<0.04). Thrombin-antithrombin III complexes showed an identical steady increase in both groups, indicating that increased t-PA activity was not related to thrombin formation. A combination of increased endothelial release and reduced hepatic clearance may have caused the increased t-PA activity. The t-PA—associated destruction of fibrinogen and fibrin after graft reperfusion is consistent with the clinical signs of severe oozing often seen in this period. These observations may have important clinical implications for the treatment of bleeding in patients undergoing orthotopic liver transplantation. © 1989 by The Williams and Wilkins Co

Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free intersection graph. We show that such rectangle arrangements are in bijection with the 4-orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Moreover, we prove that every triangle-free planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.Comment: 15 pages, 13 figures, extended version of a paper to appear at the International Symposium on Graph Drawing and Network Visualization (GD) 201

Intraoperative blood transfusion requirements and deficient hemostasis in highly alloimmunized patients undergoing liver transplantation

During orthopic liver transplantation (OLT) a large transfusion of different blood components is frequently necessary. From 1981 to 1985 at the University Health Center in Pittsburgh, 4,318 units of RBCs and 4,788 units of platelets were administered during 366 OLT performed in adults. This results in a mean of 25 units of RBCs and 30 units of platelets per operation. The majority of adult liver transplant patients receive multiple transfusions of whole blood and/or blood components during their pretransplant course because of complications relating to their original disease. The exposure of these patients to different antigens from random donors facilitates the development of alloimmunization. The heightened alloimmune state can be identified by preoperative values of panel reacting antibodies (PRA). Since platelets possess the HLA antigens of donor specificity, platelets may function as the target of host antibodies, resulting in platelet alteration and subsequent dysfunction. Thus, the effect of alloimmunization on platelet function may be one of the factors responsible for significant blood loss after large transfusions of different blood components. In this retrospective study we compared blood loss and platelet transfusion during OLT with preoperative alloimmunization against random donor antigens, indicated by PRA values

The Complexity of Drawing Graphs on Few Lines and Few Planes

It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the minimum number of lines in $\mathbb{R}^d$ that together can cover all edges of a drawing of $G$. For $d=2$, $G$ must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and algorithmic results. - For $d\in\{2,3\}$, we prove that deciding whether $\rho^1_d(G)\le k$ for a given graph $G$ and integer $k$ is ${\exists\mathbb{R}}$-complete. - Since $\mathrm{NP}\subseteq{\exists\mathbb{R}}$, deciding $\rho^1_d(G)\le k$ is NP-hard for $d\in\{2,3\}$. On the positive side, we show that the problem is fixed-parameter tractable with respect to $k$. - Since ${\exists\mathbb{R}}\subseteq\mathrm{PSPACE}$, both $\rho^1_2(G)$ and $\rho^1_3(G)$ are computable in polynomial space. On the negative side, we show that drawings that are optimal with respect to $\rho^1_2$ or $\rho^1_3$ sometimes require irrational coordinates. - Let $\rho^2_3(G)$ be the minimum number of planes in $\mathbb{R}^3$ needed to cover a straight-line drawing of a graph $G$. We prove that deciding whether $\rho^2_3(G)\le k$ is NP-hard for any fixed $k \ge 2$. Hence, the problem is not fixed-parameter tractable with respect to $k$ unless $\mathrm{P}=\mathrm{NP}$

Mass measurements during lymphocytic leukemia cell polyploidization decouple cell cycle- and cell size-dependent growth

Cell size is believed to influence cell growth and metabolism. Consistently, several studies have revealed that large cells have lower mass accumulation rates per unit mass (i.e., growth efficiency) than intermediate-sized cells in the same population. Sizedependent growth is commonly attributed to transport limitations, such as increased diffusion timescales and decreased surface-to-volume ratio. However, separating cell size- and cell cycle-dependent growth is challenging. To address this, we monitored growth efficiency of pseudodiploid mouse lymphocytic leukemia cells during normal proliferation and polyploidization. This was enabled by the development of large-channel suspended microchannel resonators that allow us to monitor buoyant mass of single cells ranging from 40 pg (small pseudodiploid cell) to over 4,000 pg, with a resolution ranging from ∼1% to ∼0.05%. We find that cell growth efficiency increases, plateaus, and then decreases as cell cycle proceeds. This growth behavior repeats with every endomitotic cycle as cells grow into polyploidy. Overall, growth efficiency changes 33% throughout the cell cycle. In contrast, increasing cell mass by over 100-fold during polyploidization did not change growth efficiency, indicating exponential growth. Consistently, growth efficiency remained constant when cell cycle was arrested in G2. Thus, cell cycle is a primary determinant of growth efficiency. As growth remains exponential over large size scales, our work finds no evidence for transport limitations that would decrease growth efficiency

Conjugated polyelectrolyte nano field emission adlayers.

Here we report on a straightforward and rapid means of enhancing the field electron emission performance of nascent vertically aligned multi-walled carbon nanotubes by introducing a polar zwitterionic conjugated polyelectrolyte adlayer at the vacuum-emitter interface. We attribute the observed 66% decrease in turn-on electric field to the augmented emitter micro-morphology and shifted surface band structure. The composite emitters can be optically modulated by exploiting the absorption cross-section of the solution cast adlayer, which increases the local carrier concentration which broadens the effective electrostatic shape of the emitter during optical excitation. Assessment via scanning anode field emission microscopy reveals a 25% improvement in DC time stability, a significant reduction in long-term hysteresis shift, and a threefold increase in bandwidth during pulsed mode operation.Oppenheimer TrustThis is the final version of the article. It first appeared from the Royal Society of Chemistry via http://dx.doi.org/10.1039/c6nh00071