Irredundant Triangular Decomposition

Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds for a single triangular set in terms of intrinsic data of the variety it represents, and powerful randomized algorithms for computing triangular decompositions using Hensel lifting in the zero-dimensional case and for irreducible varieties. However, in the general case, most of the algorithms computing triangular decompositions produce embedded components, which makes it impossible to directly apply the intrinsic degree bounds. This, in turn, is an obstacle for efficiently applying Hensel lifting due to the higher degrees of the output polynomials and the lower probability of success. In this paper, we give an algorithm to compute an irredundant triangular decomposition of an arbitrary algebraic set $W$ defined by a set of polynomials in C[x_1, x_2, ..., x_n]. Using this irredundant triangular decomposition, we were able to give intrinsic degree bounds for the polynomials appearing in the triangular sets and apply Hensel lifting techniques. Our decomposition algorithm is randomized, and we analyze the probability of success

PD-0473: Comparing VMAT with IMRT and 3D-CRT for stereotactic body radiotherapy in early lung cancer

https://digitalcommons.wpi.edu/ourmutualfriend/1001/thumbnail.jp

Iranian-American Relations after 11 September

Following the tragic events of 11 September 2001, Samuel Huntington's theory of a 'clash of civilizations' has been garnering greater currency. Whereas it was roundly condemned in 1993 as a new manifestation of Orientalism, in today's post-11 September world it is hailed as having 'lasting importance'. Such dangerous thinking is now beginning to pervade presentations of Iranian-American relations, distorting the reality that conflict between Iran and the United States is a result of conflicting interests, not cultures

Bone morphogenetic proteins − 7 and − 2 in the treatment of delayed osseous union secondary to bacterial osteitis in a rat model

Background: Bone infections due to trauma and subsequent delayed or impaired fracture healing represent a great challenge in orthopedics and trauma surgery. The prevalence of such bacterial infection-related types of delayed non-union is high in complex fractures, particularly in open fractures with additional extensive soft-tissue damage. The aim of this study was to establish a rat model of delayed osseous union secondary to bacterial osteitis and investigate the impact of rhBMP-7 and rhBMP-2 on fracture healing in the situation of an ongoing infection. Methods: After randomization to four groups 72 Sprague-Dawley rats underwent a transverse fracture of the midshaft tibia stabilized by intramedullary titanium K-wires. Three groups received an intramedullary inoculation with Staphylococcus aureus (103 colony-forming units) before stabilization and the group without bacteria inoculation served as healing control. After 5 weeks, a second surgery was performed with irrigation of the medullary canal and local rhBMP-7 and rhBMP-2 treatment whereas control group and infected control group received sterile saline. After further 5 weeks rats were sacrificed and underwent biomechanical testing to assess the mechanical stability of the fractured bone. Additional micro-CT analysis, histological, and histomorphometric analysis were done to evaluate bone consolidation or delayed union, respectively, and to quantify callus formation and the mineralized area of the callus. Results: Biomechanical testing showed a significantly higher fracture torque in the non-infected control group and the infected rhBMP-7- and rhBMP-2 group compared with the infected control group (p < 0.001). RhBMP-7 and rhBMP-2 groups did not show statistically significant differences (p = 0.57). Histological findings supported improved bone-healing after rhBMP treatment but quantitative micro-CT and histomorphometric results still showed significantly more hypertrophic callus tissue in all three infected groups compared to the non-infected group. Results from a semiquantitative bone-healing-score revealed best bone-healing in the non-infected control group. The expected chronic infection was confirmed in all infected groups. Conclusions: In delayed bone healing secondary to infection rhBMP treatment promotes bone healing with no significant differences in the healing efficacy of rhBMP-2 and rhBMP-7 being noted. Further new therapeutic bone substitutes should be analyzed with the present rat model for delayed osseous union secondary to bacterial osteitis

Formation of a morphine-conditioned place preference does not change the size of evoked potentials in the ventral hippocampus–nucleus accumbens projection

Abstract In opioid addiction, cues and contexts associated with drug reward can be powerful triggers for drug craving and relapse. The synapses linking ventral hippocampal outputs to medium spiny neurons of the accumbens may be key sites for the formation and storage of associations between place or context and reward, both drug-related and natural. To assess this, we implanted rats with electrodes in the accumbens shell to record synaptic potentials evoked by electrical stimulation of the ventral hippocampus, as well as continuous local-field-potential activity. Rats then underwent morphine-induced (10 mg/kg) conditioned-place-preference training, followed by extinction. Morphine caused an acute increase in the slope and amplitude of accumbens evoked responses, but no long-term changes were evident after conditioning or extinction of the place preference, suggesting that the formation of this type of memory does not lead to a net change in synaptic strength in the ventral hippocampal output to the accumbens. However, analysis of the local field potential revealed a marked sensitization of theta- and high-gamma-frequency activity with repeated morphine administration. This phenomenon may be linked to the behavioral changes—such as psychomotor sensitization and the development of drug craving—that are associated with chronic use of addictive drugs

A survey of relationship between anxiety, depression and duration of infertility

BACKGROUND: A cross sectional study was designed to survey the relationship between anxiety/depression and duration/cause of infertility, in Vali-e-Asr Reproductive Health Research Center, Tehran, Iran. METHODS: After obtaining their consents, 370 female patients with different infertility causes participated in, and data gathered by Beck Depression Inventory(BDI) and Cattle questionnaires for surveying anxiety and depression due to the duration of infertility. This was studied in relation to patients' age, educational level, socio-economic status and job (patients and their husbands). RESULTS: Age range was 17–45 years and duration and cause of infertility was 1–20 years. This survey showed that 151 women (40.8%) had depression and 321 women (86.8%) had anxiety. Depression had a significant relation with cause of infertility, duration of infertility, educational level, and job of women. Anxiety had a significant relationship with duration of infertility and educational level, but not with cause of infertility, or job. Findings showed that anxiety and depression were most common after 4–6 years of infertility and especially severe depression could be found in those who had infertility for 7–9 years. CONCLUSIONS: Adequate attention to these patients psychologically and treating them properly, is of great importance for their mental health and will improve quality of their lives

Iranian-American Relations after 11 September

Following the tragic events of 11 September 2001, Samuel Huntington's theory of a 'clash of civilizations' has been garnering greater currency. Whereas it was roundly condemned in 1993 as a new manifestation of Orientalism, in today's post-11 September world it is hailed as having 'lasting importance'. Such dangerous thinking is now beginning to pervade presentations of Iranian-American relations, distorting the reality that conflict between Iran and the United States is a result of conflicting interests, not cultures