Factorization of Joint Probability Mass Functions into Parity Check Interactions

We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors an d factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity chec k equation. In other words, marginalization of a joint PMF is equivalent to a soft decoding task as long as a finite field can be constructed over the alphabet of the PMF. In factor graph terminology this claim means that a factor graph representing such a joint PMF always has an equivalent Tanner graph. We provide a systematic method based on the Hilbert space of PMF s and orthogonal projections for obtaining this factorization

Evaluation of the effect of multi-dose Methotrexate therapy on ovarian reserve in ectopic pregnancies: Is polycystic ovarian morphology a protective condition for ovarian reserve?

Objectives: The study aims to evaluate the effects of multi-dose methotrexate (MTX) or subsequent salpingectomy on ovarian reserve and explain the conditions that cause the change in serum anti-Müllerian hormone (AMH) levels. Material and methods: Our department had 58 tubal EP patients treated with a multiple-dose MTX protocol or subsequent salpingectomy between 2017–2020. Serum AMH level was measured in each patient before the medication and 3–6 months after therapy. Patients' details were recorded and analyzed later. Results: The mean AMH value decreased in 32 patients (−17.8%), increased in 26 patients (+31.5%) (p < 0.0001). In the group with an increase, there was a rather high number of patients with a polycystic ovary (PCO) condition compared to the other group (p = 0.0001). AMH values increased in patients with PCO and decreased in patients having no PCO (p < 0.001). Conclusions: Multiple-dose MTX or subsequent salpingectomy treatment in tubal ectopic pregnancy (EP) patients might not refer to significant differences in patients' AMH levels. Remarkably, post-treatment AMH levels were significantly increased in EP patients with PCO and decreased in those without this condition. PCO may be a protective condition for ovarian reserve

Autologous microsurgical breast reconstruction and coronary artery bypass grafting: an anatomical study and clinical implications

OBJECTIVE: To identify possible avenues of sparing the internal mammary artery (IMA) for coronary artery bypass grafting (CABG) in women undergoing autologous breast reconstruction with deep inferior epigastric artery perforator (DIEP) flaps. BACKGROUND: Optimal autologous reconstruction of the breast and coronary artery bypass grafting (CABG) are often mutually exclusive as they both require utilisation of the IMA as the preferred arterial conduit. Given the prevalence of both breast cancer and coronary artery disease, this is an important issue for women's health as women with DIEP flap reconstructions and women at increased risk of developing coronary artery disease are potentially restricted from receiving this reconstructive option should the other condition arise. METHODS: The largest clinical and cadaveric anatomical study (n=315) to date was performed, investigating four solutions to this predicament by correlating the precise requirements of breast reconstruction and CABG against the anatomical features of the in situ IMAs. This information was supplemented by a thorough literature review. RESULTS: Minimum lengths of the left and right IMA needed for grafting to the left-anterior descending artery are 160.08 and 177.80 mm, respectively. Based on anatomical findings, the suitable options for anastomosis to each intercostals space are offered. In addition, 87-91% of patients have IMA perforator vessels to which DIEP flaps can be anastomosed in the first- and second-intercostal spaces. CONCLUSION: We outline five methods of preserving the IMA for future CABG: (1) lowering the level of DIEP flaps to the fourth- and fifth-intercostals spaces, (2) using the DIEP pedicle as an intermediary for CABG, (3) using IMA perforators to spare the IMA proper, (4) using and end-to-side anastomosis between the DIEP pedicle and IMA and (5) anastomosis of DIEP flaps using retrograde flow from the distal IMA. With careful patient selection, we hypothesize using the IMA for autologous breast reconstruction need not be an absolute contraindication for future CABG

Kinetic, Isotherm and Thermodynamic Analysis on Adsorption of Cr(VI) Ions from Aqueous Solutions by Synthesis and Characterization of Magnetic-Poly(divinylbenzene-vinylimidazole) Microbeads

The magnetic-poly(divinylbenzene-1-vinylimidazole) [m-poly(DVB-VIM)] microbeads (average diameter 53–212 μm) were synthesized and characterized; their use as adsorbent in removal of Cr(VI) ions from aqueous solutions was investigated. The m-poly(DVB-VIM) microbeads were prepared by copolymerizing of divinylbenzene (DVB) with 1-vinylimidazole (VIM). The m-poly(DVB-VIM) microbeads were characterized by N2 adsorption/desorption isotherms, ESR, elemental analysis, scanning electron microscope (SEM) and swelling studies. At fixed solid/solution ratio the various factors affecting adsorption of Cr(VI) ions from aqueous solutions such as pH, initial concentration, contact time and temperature were analyzed. Langmuir, Freundlich and Dubinin–Radushkvich isotherms were used as the model adsorption equilibrium data. Langmuir isotherm model was the most adequate. The pseudo-first-order, pseudo-second-order, Ritch-second-order and intraparticle diffusion models were used to describe the adsorption kinetics. The apparent activation energy was found to be 5.024 kJ mol−1, which is characteristic of a chemically controlled reaction. The experimental data fitted to pseudo-second-order kinetic. The study of temperature effect was quantified by calculating various thermodynamic parameters such as Gibbs free energy, enthalpy and entropy changes. The thermodynamic parameters obtained indicated the endothermic nature of adsorption of Cr(VI) ions. Morever, after the use in adsorption, the m-poly(DVB-VIM) microbeads with paramagnetic property were separeted via the applied magnetic force. The magnetic beads could be desorbed up to about 97% by treating with 1.0 M NaOH. These features make the m-poly(DVB-VIM) microbeads a potential candidate for support of Cr(VI) ions removal under magnetic field

A Hilbert Space of Probability Mass Functions and Applications on the Sum-Product Algorithm

In this paper a Hilbert space structure of probability mass functions (PMF) will be presented. The tools provided by the Hilbert space, specifically the norm and the inner product, may be useful while analyzing and improving the sum-product algorithm in many aspects. Our approach provides a metric distance between PMFs and a new point of a view of the log-likelihood ratio (LLR) such that the LLR representation is nothing but a Hilbert space representation