The Effect of Planarization on Width

We study the effects of planarization (the construction of a planar diagram $D$ from a non-planar graph $G$ by replacing each crossing by a new vertex) on graph width parameters. We show that for treewidth, pathwidth, branchwidth, clique-width, and tree-depth there exists a family of $n$-vertex graphs with bounded parameter value, all of whose planarizations have parameter value $\Omega(n)$. However, for bandwidth, cutwidth, and carving width, every graph with bounded parameter value has a planarization of linear size whose parameter value remains bounded. The same is true for the treewidth, pathwidth, and branchwidth of graphs of bounded degree.Comment: 15 pages, 6 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Recent results in topological graph theory

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41775/1/10474_2005_Article_BF01897149.pd

High-risk HPV test in cervical cancer prevention - present and future

Introduction. Cervical cancer is the fourth most common cancer among women. It is related to persistent HPV infection. In order to improve diagnostic methods, a lot of research has been focused on detecting HPV DNA. A test known as a high- risk HPV test or HPV primary screening provides very encouraging results. Objective.The aim of this review is to present the actual knowledge about the possibilities of cervical cancer screening methods. Particular attention is paid to the question concerning the effectiveness of detecting viral DNA as a screening programme, compared to pap smear. State of knowledge. The HPV primary screening has higher sensitivity than the cervical smear test and it is able to detect lower-stage lesions, which are considered clinically irrelevant. Nonetheless, many HPV infections recede naturally. Therefore, relying only on the results of this test may expose women to unnecessary colposcopies and stress. Due to this fact, women under 30 years should not be screened with the hrHPV test. In view of its limitations, the HPV primary screening strategy is still tested worldwide as a pilot project. In Poland in 2019, a pilot project with the hrHPV test started at the National Institute of Oncology. Conclusions. Detecting viral DNA has its advantages and disadvantages. Further research is still required, but the hrHPV test has a great opportunity to become one of the main screening programmes worldwide, or at least, a valuable addition to cervical smear test

Occurrence of depression in patients with psoriasis - the role of inflammation, stress and mechanism of the vicious circle

Introduction. Psoriasis is a chronic skin disease which can have a detrimental impact on the patient’s life. The correlation between depression, psoriasis and inflammation is a subject of many publications. The depressive and psoriatic symptoms, unhealthy coping strategies and stigmatization might be presented in the mechanism of the vicious circle. The appropriate understanding of this phenomenon might be extremely useful for specialists to improve their bedside manner. Objective. The aim of this review is to analyze the current data about the worldwide presence of the major depressive disorder – psoriasis, and the occurrence of depression in patients suffering from psoriasis. Research and analysis were based on searching sources such as PubMed, UpToDate and World Health Organization pages for the integrative publications collected mainly from last 10 years. The data about the origin of the psoriasis disease was taken from as 1979 publication. State of knowledge. The study demonstrated that the link between psoriasis and depression is bi-directional. The pro- inflammatory cytokine, such as IL-6, TNF-α, CRP and IL-17, are elevated in both cases, which provokes the exacerbation of sickness symptoms. The inflammation dangerously disturbs the functioning of neuronal system and human homeostasis. Summary. According to the cited research, the prevalence of depressive disorders in psoriatic patients is higher in comparison to people without psoriasis. Inflammation plays an essential role by being a peculiar connector between psoriasis and depression. Stress and inflammation are crucial factors in pathogenesis of those two disorders and triggers the pathological mechanisms

HER2-positive breast cancer -a vailable anti-HER2 therapies and new agents under investigation

Introduction and objectives. Breast cancer (BC) is the most common malignancy and the leading cause of cancer death among women. About 15–20% of all BCs are HER2-positive. Proper assessment of HER2 status is crucial to choose appropriate treatment. The review summarizes data on anti-HER2 drugs used to treat HER2-positive BC and provides basic information on new agents under investigation. Brief description of the state of knowledge. Specific HER2-targeting drugs are available or are being evaluated in clinical trials. Anti-HER2 agents include: monoclonal antibodies, tyrosine kinase inhibitors, antibody-drug conjugates, bispecific antibodies, PI3K/AKT/mTOR inhibitors and heat shock protein 90 inhibitors, HER2-targeting vaccines and CDK4/6 inhibitors. The advent of anti-HER2 therapies increased the time of progression free survival and overall survival in BC patients. Results. Final analysis of the CLEOPATRA trial shows that the combination of trastuzumab, pertuzumab and taxane significantly improved outcomes in metastatic HER2-positive BC and it is currently preferred first-line treatment. The recommended second-line treatment is based on trastuzumab emtansine or on the combination of lapatinib and capecitabine. Some promising agents such as margetuximab or trastuzumab deruxtecan are still under investigation. Conclusions. Anti-HER2 directed treatment undoubtedly improves outcomes among patients with HER2-positive BC. Access to drugs such as trastuzumab, pertuzumab, lapatinib and T-DM1 improves prognosis even in patients with advanced disease. Further studies and clinical trials on novel anti-HER2 therapies are required. Nevertheless, BC treatment is becoming more effective and, hopefully, one day it may be possible to cure patients even with metastases