Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Development of Device Identity using WIFI Layer 2 Management Frames for Combating Rogue APs

The susceptibility of WiFi networks to Rogue Access Point attacks derives from the lack of identity for 802.11 devices. The most common means of detecting these attacks in current research is through tracking the credentials or the location of unauthorised and possibly malicious APs. In this paper, the authors outline a method of distinguishing WiFi Access Points using 802.11 MAC layer management frame traffic profiles. This system does not require location estimation or credential tracking techniques as used in current research techniques, which are known to be inaccurate. These characteristic management traffic profiles are shown to be unique for each device, tantamount to a MAC identity. The application of this technique to solving Rogue AP attacks under the constraints of an open access, public WiFi environment is discussed with the conclusion that the identity is practically very difficult to forge

Evaluation of Microcollimated Pars Plana External Beam Radiation in the Porcine Eye

Purpose: To evaluate the clinical and histological side effects of a prototype stereotactic radiotherapy system delivering microcollimated external beam radiation through pars plana in porcine eyes.

Methods: Five Yucatan mini-swine (10 eyes) were randomized to five treatment groups. Eight eyes were dosed with X-ray radiation on Day 1, and two eyes served as untreated controls. Treated eyes received doses up to 60 Gy to the retina and up to 130 Gy to the sclera using single or overlapping beams. The treatment beams were highly collimated such that the diameter was approximately 2.5 mm on the sclera and 3 mm on the retinal surface. Fundus photography, fluorescein angiography (FA), and spectral domain optical coherence tomography (SD-OCT) were obtained on days 7, 30, 60, and 110. Images were examined by a masked grader and evaluated for abnormalities. Animals were sacrificed on day 111 and gross and histopathological analysis was conducted.

Results: Histological and gross changes to eye structures including conjunctiva and lens were minimal at all doses. Fundus, FA, and SD-OCT of the targeted region failed to disclose any abnormality in the control or 21 Gy treated animals. In the 42 and 60 Gy animals, hypopigmented spots were noted after treatment on clinical exam, and corresponding hyperfluorescent staining was seen in late frames. No evidence of choroidal hypoperfusion was seen. The histological specimens from the 60 Gy animals showed photoreceptor loss and displacement of cone nuclei.

Conclusion: Transcleral stereotactic radiation dosing in porcine eyes can be accomplished with no significant adverse events as doses less than 42 Gy.

Effect of serviceability limits on optimal design of steel portal frames

The design of hot-rolled steel portal frames can be sensitive to serviceability deflection limits. In such cases, in order to reduce frame deflections, practitioners increase the size of the eaves haunch and / or the sizes of the steel sections used for the column and rafter members of the frame. This paper investigates the effect of such deflection limits using a real-coded niching genetic algorithm (RC-NGA) that optimizes frame weight, taking into account both ultimate as well as serviceability limit states. The results show that the proposed GA is efficient and reliable. Two different sets of serviceability deflection limits are then considered: deflection limits recommended by the Steel Construction Institute (SCI), which is based on control of differential deflections, and other deflection limits based on suggestions by industry. Parametric studies are carried out on frames with spans ranging between 15 m to 50 m and column heights between 5 m to 10 m. It is demonstrated that for a 50 m span frame, use of the SCI recommended deflection limits can lead to frame weights that are around twice as heavy as compared to designs without these limits.

Establishing optimal quantitative-polymerase chain reaction assays for routine diagnosis and tracking of minimal residual disease in JAK2-V617F-associated myeloproliferative neoplasms:a joint European LeukemiaNet/MPN&MPNr-EuroNet (COST action BM0902) study

Reliable detection of JAK2-V617F is critical for accurate diagnosis of myeloproliferative neoplasms (MPNs); in addition, sensitive mutation-specific assays can be applied to monitor disease response. However, there has been no consistent approach to JAK2-V617F detection, with assays varying markedly in performance, affecting clinical utility. Therefore, we established a network of 12 laboratories from seven countries to systematically evaluate nine different DNA-based quantitative PCR (qPCR) assays, including those in widespread clinical use. Seven quality control rounds involving over 21,500 qPCR reactions were undertaken using centrally distributed cell line dilutions and plasmid controls. The two best-performing assays were tested on normal blood samples (n=100) to evaluate assay specificity, followed by analysis of serial samples from 28 patients transplanted for JAK2-V617F-positive disease. The most sensitive assay, which performed consistently across a range of qPCR platforms, predicted outcome following transplant, with the mutant allele detected a median of 22 weeks (range 6-85 weeks) before relapse. Four of seven patients achieved molecular remission following donor lymphocyte infusion, indicative of a graft vs MPN effect. This study has established a robust, reliable assay for sensitive JAK2-V617F detection, suitable for assessing response in clinical trials, predicting outcome and guiding management of patients undergoing allogeneic transplant.

Cold-formed steel portal frames in fire: Full-scale testing and finite element analysis

A full-scale, non-uniform natural fire test on a cold-formed steel portal frame building is described. The results of the test are used to validate a non-linear, elasto-plastic, finite element shell idealisation, for the purposes of later forming the basis of a performance-based design approach for cold-formed steel portal frames at elevated temperatures.