Symmetries and reversing symmetries of toral automorphisms

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their connection with unit groups in orders of algebraic number fields. For the question of reversibility, we derive necessary conditions in terms of the characteristic polynomial and the polynomial invariants. We also briefly discuss extensions to (reversing) symmetries within affine transformations, to PGL(n,Z) matrices, and to the more general setting of integer matrices beyond the unimodular ones.Comment: 34 page

Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices

We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodic orbits. Next we study the nature of the symmetries and reversing symmetries of toral automorphisms on a given lattice, which has particular relevance to (quantum) cat maps.Comment: 29 pages, 3 figure

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

Preimplant factors affecting postimplant CT-determined prostate volume and the CT/TRUS volume ratio after transperineal interstitial prostate brachytherapy with 125I free seeds

<p>Abstract</p> <p>Background</p> <p>The aim was to identify preimplant factors affecting postimplant prostate volume and the increase in prostate volume after transperineal interstitial prostate brachytherapy with ¹²⁵I free seeds.</p> <p>Methods</p> <p>We reviewed the records of 180 patients who underwent prostate brachytherapy with ¹²⁵I free seeds for clinical T1/T2 prostate cancer. Eighty-one (45%) of the 180 patients underwent neoadjuvant hormonal therapy. No patient received supplemental external beam radiotherapy. Postimplant computed tomography was undertaken, and postimplant dosimetric analysis was performed. Univariate and multivariate analyses were performed to identify preimplant factors affecting postimplant prostate volume by computed tomography and the increase in prostate volume after implantation.</p> <p>Results</p> <p>Preimplant prostate volume by transrectal ultrasound, serum prostate-specific antigen, number of needles, and number of seeds implanted were significantly correlated with postimplant prostate volume by computed tomography. The increase in prostate volume after implantation was significantly higher in patients with neoadjuvant hormonal therapy than in those without. Preimplant prostate volume by transrectal ultrasound, number of needles, and number of seeds implanted were significantly correlated with the increase in prostate volume after implantation. Stepwise multiple linear regression analysis showed that preimplant prostate volume by transrectal ultrasound and neoadjuvant hormonal therapy were significant independent factors affecting both postimplant prostate volume by computed tomography and the increase in prostate volume after implantation.</p> <p>Conclusions</p> <p>The results of the present study show that preimplant prostate volume by transrectal ultrasound and neoadjuvant hormonal therapy are significant preimplant factors affecting both postimplant prostate volume by computed tomography and the increase in prostate volume after implantation.</p

Narrow safety range of intraoperative rectal irradiation exposure volume for avoiding bleeding after seed implant brachytherapy

<p>Abstract</p> <p>Background & Purpose</p> <p>Rectal toxicity is less common after ¹²⁵I seed implant brachytherapy for prostate cancer, and intraoperative rectal dose-volume constraints (the constraint) is still undetermined in pioneering studies. As our constraint failed to prevent grade 2 or 3 rectal bleeding (bled-pts) in 5.1% of patients, we retrospectively explored another constraint for the prevention of rectal bleeding.</p> <p>Materials and methods</p> <p>The study population consisted of 197 patients treated with the brachytherapy as monotherapy using real-time intraoperative transrectal ultrasound (US)-guided treatment at a prescribed dose of 145 Gy. Post-implant dosimetry was performed on Day 1 and Day 30 after implantation using computed tomography (CT) imaging. Rectal bleeding toxicity was classified by CTC-AE ver. 3.0 during a mean 29-month (range, 12-48 months) period after implantation. The differences in rV100s were compared among intraoperative, Day 1 and Day 30 dosimetry, and between that of patients with grade 2 or 3 rectal bleeding (the bled-pts) and of the others (the spared-pts). All patients were divided into groups based on provisional rV100s that were increased stepwise in 0.1-cc increments from 0 to 1.0 cc. The difference in the ratios of the bled-pts to the spared-pts was tested by chi-square tests, and their odds ratios were calculated (bled-OR). All statistical analyses were performed by <it>t</it>-tests.</p> <p>Results</p> <p>The mean values of rV100us, rV100CT_1, and rV100CT_30 were 0.31 ± 0.43, 0.22 ± 0.36, and 0.59 ± 0.68 cc, respectively. These values temporarily decreased (p = 0.020) on Day 1 and increased (p = 0.000) on Day 30. There was no significant difference in rV100s between the bled-pts and spared-pts at any time of dosimetry. The maximum bled-OR was identified among patients with an rV100us value above 0.1 cc (p = 0.025; OR = 7.8; 95% CI, 1.4-145.8); an rV100CT_1 value above 0.3 cc (p = 0.014; OR = 16.2; 95% CI, 3.9-110.7), and an rV100CT_30 value above 0.5 cc (p = 0.019; OR = 6.3; 95% CI, 1.5-42.3).</p> <p>Conclusion</p> <p>By retrospective analysis exploring rV100 as intraoperative rectal dose-volume thresholds in ¹²⁵I seed implant brachytherapy for prostate cancer, it is proved that rV100 should be less than 0.1 cc for preventing rectal bleeding.</p

Treatment of Small Intracranial Aneurysms Using the SMALLSS Scoring System: A Novel System for Decision Making

BACKGROUND: Treatment of unruptured intracranial aneurysms (UIA) less than 7 mm is controversial. We created a scoring system to guide decision making and validated the system utilizing over 700 cases treated with microsurgery or endovascular procedures. METHODS: The scoring system SMALLSS included Size, (4-7 mm: 1 point, \u3c 3.9 mm: 0 point), Multiple aneurysms (yes: 1, no: 0), Anatomic location (posterior: 1, anterior: 0), Lineage- family history of aneurysm (yes:1, no: 0), Lifetime risk (age \u3c 65: 1, age \u3e 65: 0), Smoking history (yes: 1, no: 0 ), Shape (irregular:1, smooth:0 ). Validation of this system was performed through retrospective review of prospectively maintained data for UIA patients treated between 2014 and 2021. We then performed an external validation of a cohort of 200 small aneurysms \u3c 7 mm treated at a high volume cerebrovascular center. RESULTS: A total of 1152 cases with unruptured intracranial aneurysms were treated over the study interval, of which 771 aneurysms (66.9%) were under 7 mm, with the majority (64.3%) having SMALLSS score more than 2. Serious neurologic complications occurred in 18 out of 771 aneurysms (2.33%) of which 4 were hemorrhagic and 14 were ischemic. The obliteration rate was 98% in microsurgery group, 89.7% in endovascular group. During this same interval, 1126 patients with aneurysms \u3c 7 mm were evaluated and not offered treatment, with 74.7% SMALLSS scores of 2 and under. External validation data showed no significant deviations from our cohort with 150 out of 200 aneurysms (75%) with a SMALLSS score of 2 or greater. CONCLUSION: The SMALLSS scoring system can be a good tool to guide treatment decision making for patients with small UIA. The risk of treatment did not increase with the projected increased risk of rupture and overall high obliteration rates were achieved with endovascular and surgical techniques

Role of Mitochondrial Electron Transport Chain Complexes in Capsaicin Mediated Oxidative Stress Leading to Apoptosis in Pancreatic Cancer Cells

We evaluated the mechanism of capsaicin-mediated ROS generation in pancreatic cancer cells. The generation of ROS was about 4–6 fold more as compared to control and as early as 1 h after capsaicin treatment in BxPC-3 and AsPC-1 cells but not in normal HPDE-6 cells. The generation of ROS was inhibited by catalase and EUK-134. To delineate the mechanism of ROS generation, enzymatic activities of mitochondrial complex-I and complex-III were determined in the pure mitochondria. Our results shows that capsaicin inhibits about 2.5–9% and 5–20% of complex-I activity and 8–75% of complex-III activity in BxPC-3 and AsPC-1 cells respectively, which was attenuable by SOD, catalase and EUK-134. On the other hand, capsaicin treatment failed to inhibit complex-I or complex-III activities in normal HPDE-6 cells. The ATP levels were drastically suppressed by capsaicin treatment in both BxPC-3 and AsPC-1 cells and attenuated by catalase or EUK-134. Oxidation of mitochondria-specific cardiolipin was substantially higher in capsaicin treated cells. BxPC-3 derived ρ0 cells, which lack mitochondrial DNA, were completely resistant to capsaicin mediated ROS generation and apoptosis. Our results reveal that the release of cytochrome c and cleavage of both caspase-9 and caspase-3 due to disruption of mitochondrial membrane potential were significantly blocked by catalase and EUK-134 in BxPC-3 cells. Our results further demonstrate that capsaicin treatment not only inhibit the enzymatic activity and expression of SOD, catalase and glutathione peroxidase but also reduce glutathione level. Over-expression of catalase by transient transfection protected the cells from capsaicin-mediated ROS generation and apoptosis. Furthermore, tumors from mice orally fed with 2.5 mg/kg capsaicin show decreased SOD activity and an increase in GSSG/GSH levels as compared to controls. Taken together, our results suggest the involvement of mitochondrial complex-I and III in capsaicin-mediated ROS generation and decrease in antioxidant levels resulting in severe mitochondrial damage leading to apoptosis in pancreatic cancer cells

Assessment of rubber tree panels under crowns resistant to South American leaf blight

The objective of this work was to assess the performance of panel clones under crowns resistant to South American leaf blight (Microcyclus ulei). The experiment was carried out with 18 panel clones crown-budded with Hevea pauciflora x H. guianensis, in a Xanthic Ferralsol (Oxisol) in Manaus, AM, Brazil. The following parameters were evaluated: dry rubber yield, plant nutritional status, and anatomical and physiological characteristics of the latex vessels. In the first three years of evaluation, the panel clones IAN 2878, IAN 2903, CNS AM 7905, CNS AM 7905 P1, and PB 28/59 showed the highest dry rubber yield potential, while the clones IAN 6158, IAN 6590, and IAN 6515 should not be recommended for crown budding. Higher potassium and copper foliar content in panel clones were associated to an increase in dry rubber yield. The simultaneous evaluation of anatomical and physiological characteristics of latex is fundamental for the selection of panel clones in the Amazon region. Crown budding is an efficient technology for South American leaf blight management in endemic regions

Influence of Ecto-Nucleoside Triphosphate Diphosphohydrolase Activity on Trypanosoma cruzi Infectivity and Virulence

The protozoan Trypanosoma cruzi is the causative agent of Chagas disease, an endemic zoonosis present in some countries of South and Central Americas. The World Health Organization estimates that 100 million people are at risk of acquiring this disease. The infection affects mainly muscle tissues in the heart and digestive tract. There are no vaccines or effective treatment, especially in the chronic phase when most patients are diagnosed, which makes a strong case for the development of new drugs to treat the disease. In this work we evaluate a family of proteins called Ecto-Nucleoside-Triphosphate-Diphosphohydrolase (Ecto-NTPDase) as new chemotherapy target to block T. cruzi infection in mammalian cells and in mice. We have used inhibitors and antibodies against this protein and demonstrated that T. cruzi Ecto-NTPDases act as facilitators of infection in mammalian cells and virulence factors in mice model. Two of the drugs used in this study (Suramin and Gadolinium) are currently used for other diseases in humans, supporting the possibility of their use in the treatment of Chagas disease