Geolocation with FDOA Measurements via Polynomial Systems and RANSAC

The problem of geolocation of a transmitter via time difference of arrival (TDOA) and frequency difference of arrival (FDOA) is given as a system of polynomial equations. This allows for the use of homotopy continuation-based methods from numerical algebraic geometry. A novel geolocation algorithm employs numerical algebraic geometry techniques in conjunction with the random sample consensus (RANSAC) method. This is all developed and demonstrated in the setting of only FDOA measurements, without loss of generality. Additionally, the problem formulation as polynomial systems immediately provides lower bounds on the number of receivers or measurements required for the solution set to consist of only isolated points.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Bounds on the number of real solutions to polynomial equations

We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the number of non-zero real solutions to a system of n polynomials in n variables having n+k+1 monomials whose exponent vectors generate a subgroup of Z^n of odd index. This bound exceeds the bound for positive solutions only by the constant factor (e^4+3)/(e^2+3) and it is asymptotically sharp for k fixed and n large.Comment: 5 page

Physicians' Practice of Dispensing Medicines: A Qualitative Study

Objectives: The physical act of giving medication to patients to administer away from a health care setting, dispensing, is normally performed by pharmacists. Dispensing of medication by physicians is a neglected patient safety issue, and having observed considerable variation in practice, the lead author sought to explore this issue further. A literature review yielded zero articles pertaining to this, so an exploratory study was commenced. The qualitative arm, relating to junior physicians' experience of, and training in, dispensing, is reported here. Methods: Focus groups were conducted to explore the beliefs, ideas, and experiences of physicians-in-training pertaining to dispensing of medication. These were recorded and transcribed. The transcriptions were thematically analyzed using the grounded theory. Results: The emergency department was the most common site of dispensing. No formal training in dispensing had been received. Informal training was variable in content and utility. The physicians felt that dispensing was part of their role. Conclusions: Despite being expected to dispense, and the patient safety issues involved in giving drugs to patients to use at home, physicians do not feel that they have been trained to undertake this task. These findings from 1 hospital raise questions about thewider quality and safety of this practic