Constant-Depth Sorting Networks

In this paper, we address sorting networks that are constructed from comparators of arity k > 2. I.e., in our setting the arity of the comparators - or, in other words, the number of inputs that can be sorted at the unit cost - is a parameter. We study its relationship with two other parameters - n, the number of inputs, and d, the depth. This model received considerable attention. Partly, its motivation is to better understand the structure of sorting networks. In particular, sorting networks with large arity are related to recursive constructions of ordinary sorting networks. Additionally, studies of this model have natural correspondence with a recent line of work on constructing circuits for majority functions from majority gates of lower fan-in. Motivated by these questions, we initiate the studies of lower bounds for constant-depth sorting networks. More precisely, we consider sorting networks of constant depth d and estimate the minimal k for which there is such a network with comparators of arity k. We prove tight lower bounds for d ? 4. More precisely, for depths d = 1,2 we observe that k = n. For d = 3 we show that k = ?n/2?. As our main result, we show that for d = 4 the minimal arity becomes sublinear: k = ?(n^{2/3}). This contrasts with the case of majority circuits, in which k = O(n^{2/3}) is achievable already for depth d = 3. To prove these results, we develop a new combinatorial technique based on the notion of access to cells of a sorting network

Towards Simpler Sorting Networks and Monotone Circuits for Majority

In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of arity $2$ and the generalized setting with operations of arity $k$, where $k$ is a parameter. For both problems and both settings, there are various constructions known, the minimal known depth being logarithmic. However, there is currently no known construction that simultaneously achieves sub-log-squared depth, effective constructability, simplicity, and has a potential to be used in practice. In this paper we make progress towards resolution of this problem. For computing majority by standard monotone circuits (gates of arity 2) we provide an explicit monotone circuit of depth $O(\log_2^{5/3} n)$. The construction is a combination of several known and not too complicated ideas. For arbitrary arity of gates $k$ we provide a new sorting network architecture inspired by representation of inputs as a high-dimensional cube. As a result we provide a simple construction that improves previous upper bound of $4 \log_k^2 n$ to $2 \log_k^2 n$. We prove the similar bound for the depth of the circuit computing majority of $n$ bits consisting of gates computing majority of $k$ bits. Note, that for both problems there is an explicit construction of depth $O(\log_k n)$ known, but the construction is complicated and the constant hidden in $O$-notation is huge

PRIMARY HYPERPARATHYROIDISM AT THE BACKGROUND OF PARATHYROID GLAND HYPERPLASIA. PECULIARITIES AND DIFFICULTIES OF DIAGNOSTICS

The article uses a clinical case of primary hyperparathyroidism in young patient with hyperplastic parathyroid gland localization in tissues of thyroid gland as an example to study the matters of cytological, histological, clinical and laboratory diagnostics of such pathology. It provides a literature reference on the difficulties of establishing a cytological and histological diagnoses, sets out the peculiarities of morphological pattern, discusses the tactical matters of primary hyperparathyroidism management, indications for surgical treatment and case follow-up of patients

Surgical treatment of genital prolapse in combination with endometrial hyperplastic processes in postmenopausal women

Aim. To study the long-term results of surgical treatment of postmenopausal patients with genital prolapse III and IV according to the POP-Q classification in combination with endometrial hyperplastic processes and to assess their quality of life. Materials and methods. Fifty one elderly and senile patients with grade III–IV prolapse according to the POP-Q classification in combination with endometrial hyperplastic processes. 2 groups were formed: 1st – 21 patients after one-stage vaginal extirpation of the uterus with appendages and unilateral sacrospinous fixation of the vaginal stump with a synthetic endoprosthesis-tape in combination with reconstruction of II and III levels of pelvic floor support according to DeLancey; 2nd – 30 patients after one-stage vaginal extirpation of the uterus with appendages and median colporrhaphy using the Lefort and Neugebauer technique. Results. The study was evaluated 1–7 years after surgical treatment. The average age of patients at the time of surgery in group 1 was 63.12±4.32 years, in group 2 – 74.2±3.28 years. The number of women with somatic pathology in the 1st group was 1.7 times less in percentage terms than in the 2nd. The disappearance of symptoms of an overactive bladder after surgery was noted by 4 (50.0%) of 8 patients of the 1st group and 4 (26.7%) of 15 women of the 2nd. Uroflowmetry after surgical treatment showed an increase in the maximum flow rate (Qmax) and a decrease in the volume of residual urine (Vom) in both groups (p0.001). Recurrence of genital prolapse was detected in the apical region in 1 (4.8%) woman, prolapse of the anterior vaginal wall in 1 (4.8%). There were no recurrences of genital prolapse in the 2nd group. A significant improvement in the quality of life after surgery, according to the results of processing the PFDI-20 questionnaire, was noted by 19 (90.5%) women in the 1st group and 29 (96.7%) – in the 2nd. Conclusion. The long-term results of the proposed operational benefits have shown satisfactory results and can be successfully used in the elderly and senile age. The choice of the volume of surgery taking into account age, sexual activity, concomitant gynecological and somatic pathology reduces the number of complications and improves the results of surgical treatment in this category of patients

Obesity and pregnancy: possible ways to overcome complications and improve reproductive outcomes

Introduction. Obesity, due to its high prevalence and relevance, can be considered an epidemic of modern society. Obesity-related microcirculatory vascular disease and chronic inflammation with endothelial dysfunction are associated with adverse effects on reproductive potential. Sulodexide reduces the risk of hemostatic complications in patients planning pregnancy due to its polypotent effect, which is especially important in metabolic disorders and comorbidities. Therefore, it is promising to assess the effectiveness of integrated management of obese patients as part of pregnancy planning. Aim. To modify the complex treatment of obesity in patients planning pregnancy to reduce the risk of reproductive losses and gestational complications. Materials and methods. The prospective analysis included 92 patients with grade 1 obesity. According to the clinical protocols and guidelines of the Reproductive Health Professional Medical Association, 46 patients in the control group (group 1) were prescribed treatment to reduce the body mass index, including lifestyle correction, folic acid, and vitamin D. Patients in the comparison group (Group 2, n=46) also received endotheliotropic agent sulodexide. The treatment efficacy was analyzed based on the frequency of pregnancy, the change of laboratory markers of endothelial dysfunction, the incidence of gestational complications, and reproductive losses. Results. The study showed that in comparison group patients, the frequency of pregnancy (58.7% of cases in Group 1, 71.7% in Group 1), favorable course of the first trimester (39.1% in Group 1, 63.0% in Group 2), and delivery at term (30.4% in Group 1, 56.5% in Group 2) were higher compared to the control group. There was also a more significant decrease in the body mass index and endothelial dysfunction factors (homocysteine level in group 1 before treatment was 172.4 mol/L, and 141.8 mol/L after treatment; 191.7 mol/L before treatment and 91.4 mol/L after treatment in Group 2, respectively) in patients receiving complex treatment with sulodexide. Analysis of the pregnancy course showed a lower risk of gestational diabetes (33.3% in Group 1 and 13.8% in Group 2). Conclusion. Treatment of obesity in patients planning pregnancy requires a complex effect aimed at correcting lifestyle, reducing body weight, restoring the endothelial layer, and reducing the severity of chronic inflammation, thus improving reproductive outcomes and minimizing the risk of gestational complications

Взаимодействие гексагалогеноосматов(IV) с ДМСО

Interaction of К2 [OsX6], where X=Cl, Br ( СOs = n · 10-4 – n · 10-2 mol/l) with DMSO has been studied by electronic absorption spectroscopy at room temperature and heating. It was established that interaction was accompanied by replacement of halide-ions in [OsX6]2- with DMSO molecules and reduction of osmium(IV) to osmium(III), and then to osmium(II). The intermediate forms were defined: [OsIV(dmso-O)Br5]– and [OsIII(dmso-S)2Br4]–. The final product of the interaction in solution in case of heating was cis,fac-[OsII(dmso-S)3(dmso-O)X2], which slowly isomerizes to trans-[OsII(dmso-S)4 Х2 ] at room temperature .Спектрофотометрическим методом изучено взаимодействие К2[ OsX6 ], где X = Cl , Br (СOs = n ·10-4 - n ·10-2 моль/л) с ДМСО при комнатной температуре и нагревании. Установлено, что взаимо-действие носит ступенчатый характер, сопровождается замещением галогенид-ионов на молекулы ДМСО и восстановлением осмия( IV ) до осмия( III ), а затем и до осмия( II ). Определены промежуточные формы: [ OsIV ( dmso - O ) Br5 ]– и [ OsIII ( dmso - S )2 Br4 ]–. При нагревании конечным продуктом взаимодействия в растворе является cis , fac -[ OsII ( dmso - S )3( dmso - O )Х2], который при комнатной температуре медленно изомеризуется в trans -[ OsII ( dmso - S )4Х2]

Was eine Data Governance für das Forschungsdatenmanagement leisten kann

In dem Fraunhofer-internen Projekt „Krisenmanagement und Resilienz – Corona“ (KResCo) wurden Maßnahmen gegen die Covid-19-Pandemie in verschiedenen Ländern sowie deren Wirksamkeit untersucht. Hierbei wurden viele Daten erzeugt und nachgenutzt, deren Management in einem eigenen Arbeitspaket gesteuert wurde. Hierzu wurde ein Data-Governance-Ansatz angewendet, im Rahmen dessen verschiedene strategische, rechtliche und operative Bausteine entwickelt und während des Projektverlaufs erprobt wurden. Der Artikel beschreibt diese Bausteine und und beurteilt deren Umsetzungsgad im Projekt anhand eines Reifegrad-Modells. Im Ergebnis zeigte sich, dass nicht alle Ziele der Data Governance im Projekt erreicht werden konnten, da keine ausreichende Akzeptanz bei den Forschenden aufgebaut werden konnte, so dass diese die Bausteine nicht im erforderlichen Umfang nutzten

Non-surgical management of patients with ectopic pregnancy: A review

An ectopic pregnancy is a medical emergency. Currently, surgery is the main method of therapy, and non-surgical management with methotrexate is considered an acceptable alternative. Methotrexate is a folic acid antagonist and has an inhibitory effect on the proliferation of trophoblast cells. There are various methotrexate regimens; the choice is based on the level of β-subunit of human chorionic gonadotropin, the location of the ectopic pregnancy and the patient's adherence to treatment. Therapy of ectopic tubal pregnancy with methotrexate is an effective and safe alternative to surgical treatment, does not affect the ovarian reserve and preserves the woman's fertility

A Copper-Nitroxide Adduct Exhibiting Separate Single Crystal-to-Single Crystal Polymerization-Depolymerization and Spin Crossover Transitions

© 2016 American Chemical Society.A complex cascade of solid-state processes initiated by variation of temperature was found for the heterospin complex [Cu(hfac)2LMe/Et] formed in the reaction of copper(II) hexafluoroacetylacetonate [Cu(hfac)2] with stable nitronyl nitroxide 2-(1-methyl-3-ethyl-1H-pyrazol-4-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (LMe/Et). The cooling of the compound below 260 K initiated a solid-state chemical reaction, which led to a depolymerization of chains and formation of a pair heterospin complex [Cu(hfac)2LMe/Et2][[Cu(hfac)2]3LMe/Et2]. Further decrease in temperature below 144 K led to a spin transition accompanied by a drastic decrease in the effective magnetic moment from 2.52 to 2.24 μB. When the compound was heated, the order of effects was reversed: at first, the magnetic moment abruptly increased, and then the molecular fragments of the pair cluster united into polymer chains. Two hysteresis loops correspond to this cascade of temperature-induced structural transformations on the experimental dependence μeff(T): one at high (T ' = 283 K and T " = 260 K) and the other at low (T= 161 K, T = 144 K) temperature. The spin transitions were also recorded for the [[Cu(hfac)2]3LBu/Et2] and [[Cu(hfac)2]5LBu/Et4] molecular complexes, which are models of the trinuclear fragment of the {[Cu(hfac)2]3LMe/Et2} pair cluster