Binomial Ideals and Congruences on Nn

Producción CientíficaA congruence on Nn is an equivalence relation on Nn that is compatible with the additive structure. If k is a field, and I is a binomial ideal in k[X1,…,Xn] (that is, an ideal generated by polynomials with at most two terms), then I induces a congruence on Nn by declaring u and v to be equivalent if there is a linear combination with nonzero coefficients of Xu and Xv that belongs to I. While every congruence on Nn arises this way, this is not a one-to-one correspondence, as many binomial ideals may induce the same congruence. Nevertheless, the link between a binomial ideal and its corresponding congruence is strong, and one may think of congruences as the underlying combinatorial structures of binomial ideals. In the current literature, the theories of binomial ideals and congruences on Nn are developed separately. The aim of this survey paper is to provide a detailed parallel exposition, that provides algebraic intuition for the combinatorial analysis of congruences. For the elaboration of this survey paper, we followed mainly (Kahle and Miller Algebra Number Theory 8(6):1297–1364, 2014) with an eye on Eisenbud and Sturmfels (Duke Math J 84(1):1–45, 1996) and Ojeda and Piedra Sánchez (J Symbolic Comput 30(4):383–400, 2000).National Science Foundation (grant DMS-1500832)Ministerio de Economía, Industria y Competitividad (project MTM2015-65764-C3-1)Junta de Extremadura (grupo de investigación FQM-024

Strategies to promote translational research within the European Organisation for Research and Treatment of Cancer (EORTC) Head and Neck Cancer Group: a report from the Translational Research Subcommittee

Head and neck squamous cell cancer (HNSCC) is the sixth leading cause of cancer-related deaths worldwide. These tumors are commonly diagnosed at advanced stages and mortality rates remain high. Even cured patients suffer the consequences of aggressive treatment that includes surgery, chemotherapy, and radiotherapy. In the past, in clinical trials, HNSCC was considered as a single disease entity. Advances in molecular biology with the development of genomic and proteomic approaches have demonstrated distinct prognostic HNSCC patient subsets beyond those defined by traditional clinical-pathological factors such as tumor subsite and stage [Cho W (ed). An Omics Perspective on Cancer Research. New York/Berlin: Springer 2010]. Validation of these biomarkers in large prospective clinical trials is required before their clinical implementation. To promote this research, the European Organisation for Research and Treatment of Cancer (EORTC) Head and Neck Cancer Program will develop the following strategies—(i) biobanking: prospective tissue collection from uniformly treated patients in the setting of clinical trials; (ii) a group of physicians, physician—scientists, and EORTC Headquarters staff devoted to patient-oriented head and neck cancer research; (iii) a collaboration between the basic scientists of the Translational Research Division interested in head and neck cancer research and the physicians of the Head and Neck Cancer Group; and (iv) funding through the EORTC Grant Program and the Network Core Institutions Consortium. In the present report, we summarize our strategic plans to promote head and neck cancer research within the EORTC framewor

Magnetic resonance thermometry: methodology, pitfalls and practical solutions

Clinically established thermal therapies such as thermoablative approaches or adjuvant hyperthermia treatment rely on accurate thermal dose information for the evaluation and adaptation of the thermal therapy. Intratumoural temperature measurements have been correlated successfully with clinical end points. Magnetic resonance imaging is the most suitable technique for non-invasive thermometry avoiding complications related to invasive temperature measurements. Since the advent of MR thermometry two decades ago, numerous MR thermometry techniques have been developed, continuously increasing accuracy and robustness for in vivo applications. While this progress was primarily focused on relative temperature mapping, current and future efforts will likely close the gap towards quantitative temperature readings. These efforts are essential to benchmark thermal therapy efficiency, to understand temperature-related biophysical and physiological processes and to use these insights to set new landmarks for diagnostic and therapeutic applications. With that in mind, this review summarises and discusses advances in MR thermometry, providing practical considerations, pitfalls and technical obstacles constraining temperature measurement accuracy, spatial and temporal resolution in vivo. Established approaches and current trends in thermal therapy hardware are surveyed with respect to potential benefits for MR thermometry

Thermal magnetic resonance: physics considerations and electromagnetic field simulations up to 23.5 Tesla (1GHz)

Background: Glioblastoma multiforme is the most common and most aggressive malign brain tumor. The 5-year survival rate after tumor resection and adjuvant chemoradiation is only 10 %, with almost all recurrences occurring in the initially treated site. Attempts to improve local control using a higher radiation dose were not successful so that alternative additive treatments are urgently needed. Given the strong rationale for hyperthermia as part of a multimodal treatment for patients with glioblastoma, non-invasive radio frequency (RF) hyperthermia might significantly improve treatment results. Methods: A non-invasive applicator was constructed utilizing the magnetic resonance (MR) spin excitation frequency for controlled RF hyperthermia and MR imaging in an integrated system, which we refer to as thermal MR. Applicator designs at RF frequencies 300 MHz, 500 MHz and 1GHz were investigated and examined for absolute applicable thermal dose and temperature hotspot size. Electromagnetic field (EMF) and temperature simulations were performed in human voxel models. RF heating experiments were conducted at 300 MHz and 500 MHz to characterize the applicator performance and validate the simulations. Results: The feasibility of thermal MR was demonstrated at 7.0 T. The temperature could be increased by ~11 °C in 3 min in the center of a head sized phantom. Modification of the RF phases allowed steering of a temperature hotspot to a deliberately selected location. RF heating was monitored using the integrated system for MR thermometry and high spatial resolution MRI. EMF and thermal simulations demonstrated that local RF hyperthermia using the integrated system is feasible to reach a maximum temperature in the center of the human brain of 46.8 °C after 3 min of RF heating while surface temperatures stayed below 41 °C. Using higher RF frequencies reduces the size of the temperature hotspot significantly. Conclusion: The opportunities and capabilities of thermal magnetic resonance for RF hyperthermia interventions of intracranial lesions are intriguing. Employing such systems as an alternative additive treatment for glioblastoma multiforme might be able to improve local control by "fighting fire with fire". Interventions are not limited to the human brain and might include temperature driven targeted drug and MR contrast agent delivery and help to understand temperature dependent bio- and physiological processes in-vivo

More efficient periodic traversal in anonymous undirected graphs

We consider the problem of periodic graph exploration in which a mobile entity with constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is, nodes are unlabeled. However, while visiting a node, the robot has to distinguish between edges incident to it. For each node v the endpoints of the edges incident to v are uniquely identified by different integer labels called port numbers. We are interested in minimisation of the length of the exploration period. This problem is unsolvable if the local port numbers are set arbitrarily. However, surprisingly small periods can be achieved when assigning carefully the local port numbers. Dobrev et al. described an algorithm for assigning port numbers, and an oblivious agent (i.e. agent with no memory) using it, such that the agent explores all graphs of size n within period 10n. Providing the agent with a constant number of memory bits, the optimal length of the period was previously proved to be no more than 3.75n (using a different assignment of the port numbers). In this paper, we improve both these bounds. More precisely, we show a period of length at most 4 1/3 n for oblivious agents, and a period of length at most 3.5n for agents with constant memory. Moreover, we give the first non-trivial lower bound, 2.8n, on the period length for the oblivious case

Integration of radiation oncology teaching in medical studies by German medical faculties due to the new licensing regulations: an overview and recommendations of the consortium academic radiation oncology of the German Society for Radiation Oncology (DEGRO)

The new Medical Licensing Regulations 2025 (Ärztliche Approbationsordnung, ÄApprO) will soon be passed by the Federal Council (Bundesrat) and will be implemented step by step by the individual faculties in the coming months. The further development of medical studies essentially involves an orientation from fact-based to competence-based learning and focuses on practical, longitudinal and interdisciplinary training. Radiation oncology and radiation therapy are important components of therapeutic oncology and are of great importance for public health, both clinically and epidemiologically, and therefore should be given appropriate attention in medical education. This report is based on a recent survey on the current state of radiation therapy teaching at university hospitals in Germany as well as the contents of the National Competence Based Learning Objectives Catalogue for Medicine 2.0 (Nationaler Kompetenzbasierter Lernzielkatalog Medizin 2.0, NKLM) and the closely related Subject Catalogue (Gegenstandskatalog, GK) of the Institute for Medical and Pharmaceutical Examination Questions (Institut für Medizinische und Pharmazeutische Prüfungsfragen, IMPP). The current recommendations of the German Society for Radiation Oncology (Deutsche Gesellschaft für Radioonkologie, DEGRO) regarding topics, scope and rationale for the establishment of radiation oncology teaching at the respective faculties are also included

Definitive radiotherapy and Single-Agent radiosensitizing Ifosfamide in Patients with localized, irresectable Soft Tissue Sarcoma: A retrospective analysis

<p>Abstract</p> <p>Background and Purpose</p> <p>Standard therapy for soft-tissue sarcomas remains complete resection. For primary radiotherapy local control rates of 30-45% have been reported. We analyzed retrospectively 11 cases of radiochemotherapy with single-agent ifosfamide in patients with macroscopic soft-tissue sarcomas.</p> <p>Patients and Methods</p> <p>The patients were treated in irresectable high risk situations. Radiation therapy was performed with median 60 Gy. During the first and fifth week the concomitant chemotherapy with ifosfamide was added. Two patients received trimodal therapy with additional regional hyperthermia.</p> <p>Results</p> <p>The therapy was completed in 73% of the patients. Average local control time was 91 months, median disease-free-survival/overall-survival was 8/26 months. Five-year rates for local control/disease free survival/overall survival were 70%/34%/34%. The limited prognosis is mainly caused by systemic treatment failure.</p> <p>Conclusions</p> <p>The data strongly suggest a better outcome of radiochemotherapy with ifosfamide compared to radiotherapy alone and radiotherapy in combination with other radiosensitizers.</p