Solving Large-Scale Optimization Problems Related to Bell's Theorem

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with a matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve problems which are orders of magnitude larger. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is intended for all audiences, no quantum-mechanical background is necessary.Comment: 19 pages, 7 tables, 1 figur

Multipartite nonlocality and random measurements

We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness of genuine multipartite entanglement.Comment: 8 pages, 2 figures, 3 tables, journal versio

Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios

In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to 7 qubits. As a result, in the first part of this manuscript we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements is investigated. We also introduce the concept of typicality of quantum correlations for pure states as the probability to generate a nonlocal behaviour with both random state and measurement. Although this typicality is slightly above 5.3\% for the CHSH scenario, for a modest increase in the number of involved qubits it quickly surpasses 99.99\%.Comment: 5 pages, 5 figure

Nonclassicality of pure two-qutrit entangled states

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.Comment: 6 pages, journal versio

Obesity and obstructive sleep apnea during pregnancy — implications for fetal and maternal health — a case report

W pracy przeanalizowano przypadek skrajnie otyłej ciężarnej z nadciśnieniem tętniczymi zaburzeniami oddychania podczas snu. Nadciśnienie tętnicze zostało rozpoznane czterylata wcześniej. Została przyjęta do szpitala z powodu przedwczesnego pęknięcia błon płodowych,nadciśnienia tętniczego, hipotrofii płodu oraz podejr zenia zespołu Cushinga. Badaniahormonalne wykluczyły zespół Cushinga. R ozpoznano niedoczynność tarczycy i cukr zycęciążową. Pozostałe badania laborator yjne ujawniły białkomocz oraz zmniejszenie stężeniabiałka całkowitego w surowicy krwi. Rozpoznano stan przedrzucawkowy nałożony na nadciśnienietętnicze przewlekłe. W badaniu ultrasonograficznym rozpoznano hipotrofię asymetrycznąpłodu. Z uwagi na zaobser wowaną nasiloną senność dzienną, głośne chrapanie i pr zerwyw oddychaniu podczas snu wykonano u pacjentki badanie polisomnograficzne, w którym obserwowanoliczne epizody bezdechów obturacyjnych i spłyconego oddychania podczas snu.Wartość wskaźnika AHI 77,5 i liczne epizody desaturacji osiągające najniższą wartość 30%.Rozpoznano ciężką postać obturacyjnego bezdechu sennego i włączono leczenie za pomocąprotezy powietrznej (CPAP) . Zastosowanie CPAP pozwoliło na zmniejszenie wskaźnika AHIdo 3,4 oraz lepszą kontrolę ciśnienia tętniczego. Po dwóch tygodniach pacjentka zaprzestałastosowania CPAP. Obserwowano wzrost wartości ciśnienia tętniczego do najwyższej wartości180/120 mm Hg, które było oporne na stosowane dotychczas leki. Pacjentka nie przestrzegałazaleceń żywieniowych. Nastąpił dalszy przyrost masy ciała — BMI > 60. Indukowano poród.W 40. tygodniu ciąży pacjentka urodziła samoistnie hipotroficznego noworodka (masa ciała< 10 centyla) Ap 6,9, gazometria krwi z naczyń pępowinowych w normie. Pacjentka w stanieogólnym dobrym w 4. dobie połogu została zwolniona do domu.Podsumowując, należy stwierdzić że, zaburzenia snu wywierają niekorzystny wpływ na zdrowiematki i płodu, na nastrój i jakość życia ciężarnej. Zaburzenia snu wraz z zaburzeniami oddychaniapodczas snu pr zyczyniają się do rozwoju wielu różnych chorób, bądź też pogarszają ich przebieg. A choroby te z drugiej strony negatywnie wpływają na jakość snu. Podstawoweznaczenie ma leczenie schorzenia podstawowego, lecz towarzyszące mu zaburzenia snu takżewymagają terapii.The paper presents the case of an extremely obese pregnant woman with hypertension andsevere breathing disorders during sleep. Hypertension was diagnosed four years earlier. Thepatient was admitted to the hospital because of premature rupture of membranes, hypertension,fetal hypotrophy, and suspicion of Cushing’s syndrome. Hormonal tests excluded Cushing’ssyndrome. The patient was diagnosed with hypothyroidism and gestational diabetes. Otherlaboratory studies revealed proteinuria and reduced serum concentration of total protein. Thediagnosis of pre-eclampsia superimposed on chronic hypertension was established. The ultrasoundrevealed asymmetric hypotrophy of the fetus. Due to th e observed severe daytimesleepiness of the patient, loud snoring, and pauses in breathing during sleep, the polysomnographicexamination was performed. Polysomnography revealed a high number of episodesof obstructive apnea and hypopnea during sleep. Apnea/hypopnea index was 77.5. Numerousepisodes of desaturation reaching the lowest level of 30% were observed. The patient wasdiagnosed with severe obstructive sleep apnea. The introduced CPAP treatment reduced theAHI to 3.4. Blood pressure values became normalized. After two weeks of treatment the patientdiscontinued the use of CPAP, which caused the increase in blood pressure up to 180/120 mmHg. The used antihypertensive drugs become ineffective. Additionally, the patient did not followthe recommended diet. It resulted soon in a further increase in body weight — BMI > 60.The labour was induced in the 40th week of gestation and the patient spontaneously gave birthto a hypotrophic newborn (body weight < 10th percentile). Ap score of the baby was 6 pointsin first minute and 9 points in fifth minute. Blood gas analysis of the umbilical cord was withinnormal ranges. The patient was discharged from hospital in a good general condition on the4th day postpartum.The conclusion drawn from the case is sleep disorders may adversely affect the health of themother and the fetus. It has been proved that there is a strong relationship between sleep andhealth. Sleep disorders and disorders of breathing during sleep contribute to the developmentof various diseases or they may degrade their course. Therefore, it is essential to treat not onlythe primary disease, but also the accompanying sleep disorders

Is there a relationship between pregnancy induced hypertension and obstructive sleep apnea? Case report

W pracy przeanalizowano przypadek kobiety w ciąży bliźniaczej powikłanej stanem przedrzucawkowym i zaburzeniami oddychania podczas snu. Pacjentka została przyjęta do szpitala z powodu nadciśnienia tętniczego, białkomoczu oraz narastających obrzęków. Wyniki badań laboratoryjnych ujawniły białkomocz oraz zmniejszenie stężenia białka całkowitego w surowicy krwi. Rozpoznano łagodną postać stanu przedrzucawkowego. Z uwagi na zaobserwowaną nasiloną senność dzienną, głośne chrapanie i przerwy w oddychaniu podczas snu wykonano u pacjentki badanie polisomnograficzne, podczas którego obserwowano liczne epizody bezdechów obturacyjnych i spłyconego oddychania podczas snu. Wartość wskaźnika AHI (apnea-hypopnea index) wynosiła 82,1 z licznymi epizodami desaturacji osiągającymi najniższą wartość 82%. Rozpoznano ciężką postać obturacyjnego bezdechu sennego i włączono leczenie za pomocą protezy powietrznej (CPAP). Zastosowanie CPAP pozwoliło na zmniejszenie wskaźnika AHI do 1,2 oraz lepszą kontrolę ciśnienia tętniczego. Między 33. a 35. tygodniem ciąży pacjentka stosowała CPAP. W 35. tygodniu ciąży z uwagi na wystąpienie objawów zagrożenia życia pierwszego bliźniaka w zapisie kardiotokograficznym ukończono ciążę cięciem cesarskim. Urodziły się dwa noworodki płci męskiej w stanie dobrym. W okresie połogu pacjentka zaprzestała stosowania CPAP. Obserwowano wzrost wskaźnika AHI do 45,3 oraz wzrost wartości ciśnienia tętniczego do najwyższej wartości 180/100 mm Hg. Pacjentka w stanie ogólnym dobrym w 7. dobie połogu została zwolniona do domu z zaleceniami dalszej diagnostyki i leczenia w poradni zaburzeń snu. Podsumowując, należy stwierdzić że, zaburzenia snu wywierają niekorzystny wpływ na zdrowie matki i płodu, na nastrój i jakość życia ciężarnej. Udowodniono, że istnieje wiele zależności między snem a zdrowiem. Zaburzenia snu wraz z zaburzeniami oddychania podczas snu przyczyniają się do rozwoju wielu różnych chorób ogólnych bądź też pogarszają ich przebieg. A choroby te z drugiej strony negatywnie wpływają na jakość snu. Podstawowe znaczenie ma leczenie schorzenia podstawowego, lecz towarzyszące mu zaburzenia snu także wymagają terapii.The paper examines the case of a pregnant woman in a twin pregnancy complicated by pre-eclampsia and sleep disordered breathing. The patient was admitted to hospital with high blood pressure, proteinuria and increasing oedema. Laboratory tests revealed proteinuria and reduced total protein concentration in serum. The patient was diagnosed with mild pre-eclampsia. Due to the observed severe daytime sleepiness of the patient, loud snoring and pauses in breathing during sleep, polysomnography was performed. The test revealed a number of episodes of obstructive apnea and hypopnea. The AHI (apnea-hypopnea index) value was 82.1. A number of episodes of desaturation were observed. The lowest saturation had a value of 82%. When the patient was diagnosed with severe obstructive sleep apnea, treatment with CPAP (continuous positive airway pressure) was introduced. The use of CPAP allowed a reduction of the AHI to 1.2, and the blood pressure value normalised. The patient used CPAP between the 33rd and 35th weeks of gestation. At the 35th week of gestation, caesarean section was performed due to life-threatening symptoms of the first foetus in the CTG-recording. Two male infants were delivered in good condition. During the postpartum period, the patient discontinued the use of CPAP. Following this, an increase in AHI to 45.3 and an increase in blood pressure to a maximum of 180/100mmHg were observed. The patient was discharged from hospital in good general condition on the 7th day postpartum with recommendation for further diagnostic and therapy. The conclusion that may be drawn from the case is that sleep disorders adversely affect the health of the mother and the foetus. Also, the mood and quality of life of the pregnant woman deteriorate. It has been proven that there are many relationships between sleep and health. Sleep disorders and disorders of breathing during sleep contribute to the development of various diseases or they degrade the overall phenomena. A disease, on the other hand, additionally negatively affects the quality of sleep. Therefore, it is essential to treat not only the primary disease, but also the accompanying sleep disorders

The correlation of protein peroxidation with morphological changes in experimental oestradiol-induced carcinogenesis

Oestradiol-induced male Syrian hamster carcinogenesis is a well-known experimental model of human cancer of the breast, ovary and uterus. The pathomechanism postulated in this model is 4-hydroxylation of oestradiol and further free radical formation. The same process is suspected in human breast cancer. Dynamic changes in protein peroxidation were reported during the tumour induction. In this paper we try to correlate the protein peroxidation markers with the histopathological progression of the changes. The biochemical and histopathological evaluations were performed after 1, 3, 6 and 9 months of the hormone exposition. Significant protein peroxidation was observed as soon as after 1 month and increased further until the 6th month. After 9 months however, it was not significantly different from the control. The discrete histopathological changes after 1 month, progressed into tubular and interstitial hyperplasias after 3 and 6 months. After 9 months several dysplastic areas, sometimes with features of carcinoma in situ, were observed. The severe 9-month histopathological changes did not correlate with the protein peroxidation

Use of Brassica Plants in the Phytoremediation and Biofumigation Processes

In recent decades, serious contamination of soils by heavy metals has been reported. It is therefore a matter of urgency to develop a new and efficient technology for removing contaminants from soil. Another aspect to this problem is that environmental pollution decreases the biological quality of soil, which is why pesticides and fertilizers are being used in ever-larger quantities. The environmentally friendly solutions to these problems are phytoremediation, which is a technology that cleanses the soil of heavy metals, and biofumigation, a process that helps to protect crops using natural plant compounds. So far, these methods have only been used separately; however, research on a technology that combines them both using white cabbage has been carried out

Interior Point Methods 25 Years Later

Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their low-degree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations which depends very little, if at all, on the problem dimension. Interior point methods are competitive when dealing with small problems of dimensions below one million constraints and variables and are beyond competition when applied to large problems of dimensions going into millions of constraints and variables. In this survey we will discuss several issues related to interior point methods including the proof of the worst-case complexity result, the reasons for their amazingly fast practi-cal convergence and the features responsible for their ability to solve very large problems. The ever-growing sizes of optimization problems impose new requirements on optimizatio