Counting Basic-Irreducible Factors Mod p^k in Deterministic Poly-Time and p-Adic Applications

Finding an irreducible factor, of a polynomial f(x) modulo a prime p, is not known to be in deterministic polynomial time. Though there is such a classical algorithm that counts the number of irreducible factors of f mod p. We can ask the same question modulo prime-powers p^k. The irreducible factors of f mod p^k blow up exponentially in number; making it hard to describe them. Can we count those irreducible factors mod p^k that remain irreducible mod p? These are called basic-irreducible. A simple example is in f=x^2+px mod p^2; it has p many basic-irreducible factors. Also note that, x^2+p mod p^2 is irreducible but not basic-irreducible! We give an algorithm to count the number of basic-irreducible factors of f mod p^k in deterministic poly(deg(f),k log p)-time. This solves the open questions posed in (Cheng et al, ANTS\u2718 & Kopp et al, Math.Comp.\u2719). In particular, we are counting roots mod p^k; which gives the first deterministic poly-time algorithm to compute Igusa zeta function of f. Also, our algorithm efficiently partitions the set of all basic-irreducible factors (possibly exponential) into merely deg(f)-many disjoint sets, using a compact tree data structure and split ideals

Heart Smart Diabetes Care

The world is growing smarter day by day, and so is health care. In spite of innumerable inventions and tech-tools, however, we struggle to contain chronic illnesses like diabetes and heart disease. We need to work together and design a rational, scientific and socially sustainable Heart Smart diabetes care ecosystem, with Heart Smart management strategies, to ensure happiness and harmony in persons who live with diabetes

Heart Smart Diabetes Care

The world is growing smarter day by day, and so is health care. In spite of innumerable inventions and tech-tools, however, we struggle to contain chronic illnesses like diabetes and heart disease. We need to work together and design a rational, scientific and socially sustainable Heart Smart diabetes care ecosystem, with Heart Smart management strategies, to ensure happiness and harmony in persons who live with diabetes

Stationary axisymmetric solutions of five dimensional gravity

We consider stationary axisymmetric solutions of general relativity that asymptote to five dimensional Minkowski space. It is known that this system has a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers-Perry black hole starting from the Schwarzschild solution in five dimensions.Comment: 31 pages, LaTeX; references adde

Systems And Methods For Performing Geo-User Content Provision Experiments

Systems, methods, and computer-readable storage media that may be used to conduct geo-user advertising experiments. One method includes determining a set of content items and filtering an activity log based on one or more characteristics of the set of content items to determine a subset of users. The method further includes retrieving geo-based data from the subset of users over a first timeframe. The method further includes designating one or more geographic regions associated with the subset of users as a treatment group and one or more geographic regions associated with the subset of users as a control group. The method further includes modifying a spend level associated with the treatment group and retrieving geo-based data over a second timeframe. The method further includes calculating an impact of the modification of the spend level and generating graphical interface data for presentation to a device of a content provider

Miniaturized fracture experiments on pearlitic steel: Challenges and solutions

Pearlitic steels with their lamellar microstructure of thin Fe3C lamellae embedded in the α-Fe matrix finds multiple applications from railway steels to thin wires. During service as railway steels or during wire drawing a refinement and modification of the microstructure occurs due to the exposure to severe plastic deformation. The Fe3C lamellae are thinning and the α-Fe matrix becomes supersaturated with C turning it in body centered tetragonal structure which corresponds to martensite as we recently resolved by combining atom probe tomography and synchrotron experiments [1]. Severe wire drawing also reduces the wire diameter down to ca. 20 µm which prevents conventional mechanical fracture testing, thus requiring miniaturized fracture approaches. Similarly, at the surface of railway steels the lamellar microstructure decomposes and martensite formation together with Fe3C dissolution is observed leading to a so called white etching layer. Please click Additional Files below to see the full abstract

Assessing the Burden of Unnecessary Central Venous Catheters in Patients on Medical-Surgical Floors

Project goals: Our project goals are to: a) assess the burden of unnecessary PICCs and other non-tunneled central lines on med-surg units at TJUH and b) understand the underlying reasons behind the problem. In the first phase of our project we conducted an audit of med-surg unit PICCs and other non-tunneled central lines with the goal of obtaining a rough estimate of the number of line days that are unnecessary. SMART AIM By December 31, 2017, the TJUH medical-surgical floors will reduce the number of unnecessary PICC lines by 30%.https://jdc.jefferson.edu/patientsafetyposters/1024/thumbnail.jp

QUANTIFICATION OF URAPIDIL IN HUMAN PLASMA USING ULTRA PERFORMANCE LIQUID CHROMATOGRAPHY-ELECTROSPRAY IONIZATION MASS SPECTROMETRY (UPLC-MS/MS) FOR PHARMACOKINETIC STUDY IN HEALTHY INDIAN VOLUNTEERS

Objective: A rapid and selective quantitative method was developed and validated in human plasma for urapidil pharmacokinetic study in healthy Indian volunteers. Methods: The ultra-performance liquid chromatography–tandem mass spectrometry (UPLC-MS/MS) method with solid-phase extraction technique utilized Strata X 33µ polymeric reversed phase (30 mg/mL), extraction cartridge. Simple gradient chromatographic conditions and selective reaction monitoring in mass spectrometric detection enabled accurate and precise measurement of urapidil at nanogram levels in 0.1 mL of human plasma. The method used a deuterium labeled internal standard. Results: The method was validated for a linear range of 5–500 ng/mL for urapidil with a correlation coefficient ³ 0.99 The intra-run and inter-run precision and accuracy were within 10%. The overall recoveries for urapidil and urapidil D4 were more than 90%. The urapidil was found to be stable in plasma matrix and aqueous media. Conclusion: The developed and validated method was specific, sensitive and reproducible in the analysis of clinical samples interspersed with quality control samples under freshly prepared calibration standards. The method was applied for the determination of the pharmacokinetic parameters of urapidil following a single oral administration of urapidil 60 mg capsules in nineteen healthy Indian male volunteers for fasting and fed study