Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$

Determination of characteristics of plasticity of selected medium and high carbon steel grades in hot torsion test

This study presents results of the examinations aimed at determination of rheological properties of selected grades of medium and high-carbon steel grades ( C45 and C72D). The examinations were carried out for the hot torsion test using STD 812 torsion plastometer. The results of experimental studies were approximated with the function used for determination of yield stress depending on strain, strain rate and temperature. The study allowed for development of mathematical models of rheological properties of steel grades studied in the analysed scope of parameters of strain and temperature

Theoretical and experimental analysis of the backward extrusion process with a rotational die of AZ31 alloy

In this work theoretical and experimental analysis of the backward extrusion with a rotary die of the AZ31 alloy has been performed. The modification of the classical extrusion was based on the use of a rotary die. The results of theoretical research have confirmed that the use of the modified backward extrusion causes the appearance of shear stress in deformed material, which could affects the activation of additional mechanisms of deformation. The numerical modelling of the rotating extrusion of AZ31 alloy has been conducted by using the computer program Forge®. The experimental tests were carried out in the conditions of the STD 810 torsion plastometer using newly designed tools

Clinical Efficacy and Toxicity of Anti-EGFR Therapy in Common Cancers

Epidermal growth factor receptor (EGFR) is a cell surface molecule and member of the ErbB family of receptor tyrosine kinases. Its activation leads to proliferation, antiapoptosis, and metastatic spread, making inhibition of this pathway a compelling target. In recent years, an increasing number of clinical trials in the management of solid malignancies have become available indicating the clinical efficacy of anti-EGFR monoclonal antibodies and oral small molecule tyrosine kinase inhibitors (TKIs). This review addresses frequently used EGFR inhibitors, summarizes clinical efficacy data of these new therapeutic agents, and discusses their associated toxicity and management

Analysis of the temperature change over the continuous ingot length on the parameters of round bar rolling process

The paper presents results of theoretical and experimental studies on the effect of feedstock end overcooling before the first rolling stand on the plastic flow of metal and on the energy and force parameters during bar rolling process. From the obtained investigation results it has been found that the uniform heating of the feedstock in the stepped furnace does not insure the uniform plastic flow of metal over the rolled band length. Therefore, it is necessary to modify the method of feedstock heating in the stepper furnace in order to obtain a uniform temperature over the length of the feedstock before the first rolling stand

11 beta-hydroxysteroid dehydrogenase type 1 regulates glucocorticoid-induced insulin resistance in skeletal muscle

OBJECTIVE: Glucocorticoid excess is characterized by increased adiposity, skeletal myopathy, and insulin resistance, but the precise molecular mechanisms are unknown. Within skeletal muscle, 11beta-hydroxysteroid dehydrogenase type 1 (11beta-HSD1) converts cortisone (11-dehydrocorticosterone in rodents) to active cortisol (corticosterone in rodents). We aimed to determine the mechanisms underpinning glucocorticoid-induced insulin resistance in skeletal muscle and indentify how 11beta-HSD1 inhibitors improve insulin sensitivity. \ud RESEARCH DESIGN AND METHODS: Rodent and human cell cultures, whole-tissue explants, and animal models were used to determine the impact of glucocorticoids and selective 11beta-HSD1 inhibition upon insulin signaling and action. \ud RESULTS: Dexamethasone decreased insulin-stimulated glucose uptake, decreased IRS1 mRNA and protein expression, and increased inactivating pSer$^{307}$ insulin receptor substrate (IRS)-1. 11beta-HSD1 activity and expression were observed in human and rodent myotubes and muscle explants. Activity was predominantly oxo-reductase, generating active glucocorticoid. A1 (selective 11beta-HSD1 inhibitor) abolished enzyme activity and blocked the increase in pSer$^{307}$ IRS1 and reduction in total IRS1 protein after treatment with 11DHC but not corticosterone. In C57Bl6/J mice, the selective 11beta-HSD1 inhibitor, A2, decreased fasting blood glucose levels and improved insulin sensitivity. In KK mice treated with A2, skeletal muscle pSer$^{307}$ IRS1 decreased and pThr$^{308}$ Akt/PKB increased. In addition, A2 decreased both lipogenic and lipolytic gene expression.\ud CONCLUSIONS: Prereceptor facilitation of glucocorticoid action via 11beta-HSD1 increases pSer$^{307}$ IRS1 and may be crucial in mediating insulin resistance in skeletal muscle. Selective 11beta-HSD1 inhibition decreases pSer$^{307}$ IRS1, increases pThr$^{308}$ Akt/PKB, and decreases lipogenic and lipolytic gene expression that may represent an important mechanism underpinning their insulin-sensitizing action