A Note on Knights, Knaves, and Truth Tables

Student and teacher (in the order above) have taken on a project of trying to understand something about Boolean algebra, logic circuits, and applications with the aid of Mathematica. We quickly recognized that the logical puzzles popularized by Raymond Smullyan that involve Knights (truth tellers) and Knaves (liars) are ideally suited for analysis by Boolean methods and truth tables. with a big boost from Mathematica. Not only is there a lot of mathematics to be learned, there is a great deal of fun to be had. The topic seems to us to be an ideal vehicle for exposing young high school and undergraduate college students to wonderful mathematics outside of the standard Advanced Placement Calculus stream

Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems

We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations. We can compute branches of solutions with limit points, bifurcation points, etc. Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations

Role of N-methyl-D-aspartate receptors in action-based predictive coding deficits in schizophrenia

Published in final edited form as:Biol Psychiatry. 2017 March 15; 81(6): 514–524. doi:10.1016/j.biopsych.2016.06.019.BACKGROUND: Recent theoretical models of schizophrenia posit that dysfunction of the neural mechanisms subserving predictive coding contributes to symptoms and cognitive deficits, and this dysfunction is further posited to result from N-methyl-D-aspartate glutamate receptor (NMDAR) hypofunction. Previously, by examining auditory cortical responses to self-generated speech sounds, we demonstrated that predictive coding during vocalization is disrupted in schizophrenia. To test the hypothesized contribution of NMDAR hypofunction to this disruption, we examined the effects of the NMDAR antagonist, ketamine, on predictive coding during vocalization in healthy volunteers and compared them with the effects of schizophrenia. METHODS: In two separate studies, the N1 component of the event-related potential elicited by speech sounds during vocalization (talk) and passive playback (listen) were compared to assess the degree of N1 suppression during vocalization, a putative measure of auditory predictive coding. In the crossover study, 31 healthy volunteers completed two randomly ordered test days, a saline day and a ketamine day. Event-related potentials during the talk/listen task were obtained before infusion and during infusion on both days, and N1 amplitudes were compared across days. In the case-control study, N1 amplitudes from 34 schizophrenia patients and 33 healthy control volunteers were compared. RESULTS: N1 suppression to self-produced vocalizations was significantly and similarly diminished by ketamine (Cohen’s d = 1.14) and schizophrenia (Cohen’s d = .85). CONCLUSIONS: Disruption of NMDARs causes dysfunction in predictive coding during vocalization in a manner similar to the dysfunction observed in schizophrenia patients, consistent with the theorized contribution of NMDAR hypofunction to predictive coding deficits in schizophrenia.This work was supported by AstraZeneca for an investigator-initiated study (DHM) and the National Institute of Mental Health Grant Nos. R01 MH-58262 (to JMF) and T32 MH089920 (to NSK). JHK was supported by the Yale Center for Clinical Investigation Grant No. UL1RR024139 and the US National Institute on Alcohol Abuse and Alcoholism Grant No. P50AA012879. (AstraZeneca for an investigator-initiated study (DHM); R01 MH-58262 - National Institute of Mental Health; T32 MH089920 - National Institute of Mental Health; UL1RR024139 - Yale Center for Clinical Investigation; P50AA012879 - US National Institute on Alcohol Abuse and Alcoholism)Accepted manuscrip

Ректор ТПИ А. А. Воробьев - изобретатель электроимпульсного способа разрушения горных пород

Представлена история создания электроимпульсного способа разрушения горных пород ректором ТПИ А. А. Воробьевым

Structural and functional investigation of ABC transporter STE6-2p from Pichia pastoris reveals unexpected interaction with sterol molecules

Adenosine triphosphate (ATP)-binding cassette (ABC) transporters are multidomain transmembrane proteins, which facilitate the transport of various substances across cell membranes using energy derived from ATP hydrolysis. They are important drug targets since they mediate decreased drug susceptibility during pharmacological treatments. For the methylotrophic yeast Pichia pastoris, a model organism that is a widely used host for protein expression, the role and function of its ABC transporters is unexplored. In this work, we investigated the Pichia ABC-B transporter STE6-2p. Functional investigations revealed that STE6-2p is capable of transporting rhodamines in vivo and is active in the presence of verapamil and triazoles in vitro. A phylogenetic analysis displays homology among multidrug resistance (MDR) transporters from pathogenic fungi to human ABC-B transporters. Further, we present high-resolution single-particle electron cryomicroscopy structures of an ABC transporter from P. pastoris in the apo conformation (3.1 Å) and in complex with verapamil and adenylyl imidodiphosphate (AMP-PNP) (3.2 Å). An unknown density between transmembrane helices 4, 5, and 6 in both structures suggests the presence of a sterol-binding site of unknown function

Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.Comment: 25 pages, 6 figures, accepted for publication in PLoS Computational Biolog

Influence of feeding hematocrit and perfusion pressure on hematocrit reduction (Fåhræus effect) in an artificial microvascular network

Objective Hct in narrow vessels is reduced due to concentration of fast?flowing RBCs in the center, and of slower flowing plasma along the wall of the vessel, which in combination with plasma skimming at bifurcations leads to the striking heterogeneity of local Hct in branching capillary networks known as the network Fåhræus effect. We analyzed the influence of feeding Hct and perfusion pressure on the Fåhræus effect in an AMVN. Methods RBC suspensions in plasma with Hcts between 20% and 70% were perfused at pressures of 5?60 cm H2O through the AMVN. A microscope and high?speed camera were used to measure RBC velocity and Hct in microchannels of height of 5 ?m and widths of 5?19 ?m. Results Channel Hcts were reduced compared with Hctfeeding in 5 and 7 ?m microchannels, but not in larger microchannels. The magnitude of Hct reduction increased with decreasing Hctfeeding and decreasing ?P (flow velocity), showing an about sevenfold higher effect for 40% Hctfeeding and low pressure/flow velocity than for 60% Hctfeeding and high pressure/flow velocity. Conclusions The magnitude of the network Fåhræus effect in an AMVN is inversely related to Hctfeeding and ?P

Influence of red blood cell aggregation on perfusion of an artificial microvascular network

Red blood cells (RBCs) suspended in plasma form multicellular aggregates under low flow conditions, increasing apparent blood viscosity at low shear rates. It has previously been unclear, however, if RBC aggregation affects microvascular perfusion. Here we analyzed the impact of RBC aggregation on perfusion and ‘capillary’ hematocrit in an artificial microvascular network (AMVN) at driving pressures ranging from 5 to 60 cmH2O to determine if aggregation could improve tissue oxygenation. RBCs were suspended at 30% hematocrit in either 46.5 g/L dextran 40 (D40, non-aggregating medium) or 35 g/L dextran 70 (D70, aggregating medium) solutions with equal viscosity. Aggregation was readily observed in the AMVN for RBCs suspended in D70 at driving pressures ? 40 cmH2O. The AMVN perfusion rate was the same for RBCs suspended in aggregating and non-aggregating medium, at both ‘venular’ and ‘capillary’ level. Estimated ‘capillary’ hematocrit was higher for D70 suspensions than for D40 suspensions at intermediate driving pressures (5 – 40 cm H2O). We conclude that although RBC aggregation did not affect the AMVN perfusion rate independently of the driving pressure, a higher hematocrit in the ‘capillaries’ of the network for D70 suspensions suggested a better oxygen transport capacity in the presence of RBC aggregation

Increased plasma viscosity as a reason for inappropriate erythropoietin formation

The aim of this study was to examine whether altered plasma viscosity could contribute to the inappropriately low production rate of erythropoietin (EPO) observed in patients suffering from hypergammaglobulinemias associated with multiple myeloma or Waldenström's disease. We found that the EPO formation in response to anemia in these patients was inversely related to plasma viscosity. A similar inverse relationship between plasma viscosity and EPO production was seen in rats in which EPO formation had been stimulated by exchange transfusion and the plasma viscosity of which was thereby altered by using exchange solutions of different composition to alter plasma viscosity and thus whole blood viscosity independently from hematocrit. Raising the gammaglobulin concentration to approximately 40 mg/ml plasma in the rats almost totally blunted the rise in serum EPO levels despite a fall of the hematocrit to 20%. Determination of renal EPO mRNA levels by RNase protection revealed that the reductions in serum EPO levels at higher plasma viscosities were paralleled by reductions in renal EPO mRNA levels. Taken together, our findings suggest that plasma viscosity may be a significant inhibitory modulator of anemia-induced EPO formation. The increased plasma viscosity in patients with hypergammaglobulinemias may therefore contribute to the inappropriate EPO production, which is a major reason for the anemia developing in these patients

Shape matters: the effect of red blood cell shape on perfusion of an artificial microvascular network

BACKGROUND The shape of human red blood cells (RBCs) deteriorates progressively throughout hypothermic storage, with echinocytosis being the most prevalent pathway of this morphological lesion. As a result, each unit of stored blood contains a heterogeneous mixture of cells in various stages of echinocytosis and normal discocytes. Here we studied how the change in shape of RBCs following along the path of the echinocytic transformation affects perfusion of an artificial microvascular network (AMVN). STUDY DESIGN AND METHODS Blood samples were obtained from healthy consenting volunteers. RBCs were leukocyte-reduced, re-suspended in saline, and treated with various concentrations of sodium salicylate to induce shape changes approximating the stages of echinocytosis experienced by RBCs during hypothermic storage (e.g. discocyte, echinocyte I, echinocyte II, echinocyte III, sphero-echinocyte and spherocyte). The AMVN perfusion rate was measured for 40% hematocrit suspensions of RBCs with different shapes. RESULTS The AMVN perfusion rates for RBCs with discocyte and echinocyte I shapes were similar, but there was a statistically significant decline in the AMVN perfusion rate between RBCs with shapes approximating each subsequent stage of echinocytosis. The difference in AMVN perfusion between discocytes and spherocytes (the last stage of the echinocytic transformation) was 34%. CONCLUSION The change in shape of RBCs from normal discocytes progressively through various stages of echinocytosis to spherocytes produced a substantial decline in the ability of these cells to perfuse an artificial microvascular network. Echinocytosis induced by hypothermic storage could therefore be responsible for a similarly substantial impairment of deformability previously observed for stored RBCs