Improving the smoothed complexity of FLIP for max cut problems

Finding locally optimal solutions for max-cut and max-$k$-cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and R\"{o}glin showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei showed that the smoothed complexity of FLIP for max-cut in complete graphs is $O(\phi^5n^{15.1})$, where $\phi$ is an upper bound on the random edge-weight density and $n$ is the number of vertices in the input graph. While Angel et al.'s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress towards improving the run-time bound. We prove that the smoothed complexity of FLIP in complete graphs is $O(\phi n^{7.83})$. Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for max-$3$-cut in complete graphs is polynomial and for max-$k$-cut in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest towards addressing the smoothed complexity of FLIP for max-$k$-cut in complete graphs for larger constants $k$.Comment: 36 page

Remarks on Stable Formulas in Intuitionistic Logic

ONNILLI-formulas were introduced in [2] and were shown to be the set of formulas that are preserved under monotonic images of descriptive or Kripke frames. As a result, ONNILLI is a syntactically defined set of formulas that axiomatize all stable logics. In this paper, among other things, by proving the uniform interpolation property for ONNILLI we show that ONNILLI is exactly the set of formulas that are preserved in monotonic bijections of descriptive or (finite) Kripke models. This resolves an open problem in [2]

Marine macro-algae as a bio-indicator of heavy metal pollution in the marine environments, Persian Gulf

357-363The northern parts of the Persian Gulf are more affected by pollutants because of their low depth, limited rotation, salinity, and high temperature. The anthropogenic and non-anthropogenic contaminations caused by organic and inorganic pollutants in aquatic ecosystems will eventually lead to increase pollution in water, sediments, and aquatic organisms. It seems that, algae are the most suitable indicator for soluble heavy metals (HMs) in both active and passive states. Samplings were carried out on a monthly basis in four different stations in Bushehr Province, northwest of the Persian Gulf from March 2016 to March 2017. ICP-mass spectrometry was used to determine Pb, Cu, Cd, As, Cr, Zn, Al, Mn, Co, V, Ni, Mg, S, Fe, and Ca concentrations in some macroalgae. In this study Padina gymnospora (brown algae) and Hypnea hamulosa (red algae) had the highest absorption, while the Cladophoropsis membranacea (green algae) showed the least absorption in all the sampling areas

Assessing some heavy metals pollutions in sediments of the northern Persian Gulf (Bushehr province)

Background: Land and water pollution by heavy metals is a universal issue. Although the pollution affects all countries, but its range and severity vary hugely. The pollution of the marine environment by heavy metals is a worldwide problem. Marine sediments can be sensitive indicators for monitoring contaminants in aquatic environments. Methods: The concentration of 10 elements (As, Cd, Cr, Cu, Al, Fe, Ni, Pb, Sb, and Zn) was determined in the sediments of four shoreline stations including Imam Hassan port, Ameri port, Bushehr port, and Nayband Bay at the west Persian Gulf from March to December 2017. The elements were measured by inductively coupled plasma mass spectrometry (ICP-MS). Data were analyzed using SPSS version 16. Results: The contamination of the sediments was assessed based on the geoaccumulation index (Igeo) and enrichment factor (EF). Spearman correlation matrix was calculated between all the trace metals and major elements as well as corresponding sampling regions. Statistically significant inter-elemental correlations (e.g., Cr-Fe, Cr-Al, Cr-Ni, Cr-Zn, and Cr-Cu) were found between some metals. High EF levels for Fe, Al, and Pb suggest that metals in the sediments of the northern Persian Gulf could have originated from anthropogenic sources. Conclusion: The contamination pattern of sediments is affected by factors such as sedimentation patterns, physical and chemical properties of the sediments. For example, sediments with fine-grained and high surface area-to-volume ratio can act as good absorbents for many pollutants. Keywords: Heavy metals, Geologic sediment, Persian Gulf, Busheh

Assessing some heavy metals pollutions in sediments of the northern Persian Gulf (Bushehr province)

Background: Land and water pollution by heavy metals is a universal issue. Although the pollution affects all countries, but its range and severity vary hugely. The pollution of the marine environment by heavy metals is a worldwide problem. Marine sediments can be sensitive indicators for monitoring contaminants in aquatic environments. Methods: The concentration of 10 elements (As, Cd, Cr, Cu, Al, Fe, Ni, Pb, Sb, and Zn) was determined in the sediments of four shoreline stations including Imam Hassan port, Ameri port, Bushehr port, and Nayband Bay at the west Persian Gulf from March to December 2017. The elements were measured by inductively coupled plasma mass spectrometry (ICP-MS). Data were analyzed using SPSS version 16. Results: The contamination of the sediments was assessed based on the geoaccumulation index (Igeo) and enrichment factor (EF). Spearman correlation matrix was calculated between all the trace metals and major elements as well as corresponding sampling regions. Statistically significant inter-elemental correlations (e.g., Cr-Fe, Cr-Al, Cr-Ni, Cr-Zn, and Cr-Cu) were found between some metals. High EF levels for Fe, Al, and Pb suggest that metals in the sediments of the northern Persian Gulf could have originated from anthropogenic sources. Conclusion: The contamination pattern of sediments is affected by factors such as sedimentation patterns, physical and chemical properties of the sediments. For example, sediments with fine-grained and high surface area-to-volume ratio can act as good absorbents for many pollutants

تاثير تمريناتTabata باستخدام المقاومات في بعض مكونات اللياقة الصحية والحركية لدى المتدربات باعمار 30 – 39 سنة

تكمن اهمية البحث في اعداد تمرينات Tabata باستخدام المقاومات في بعض المتغيرات الوظيفية والمورفولوجية واللياقة البدنية لدى المتدربات في مراكز اللياقة البدنية لغرض الارتقاء بمستوى عناصر اللياقة البدنية وحرق السعرات الحرارية لدى المتدربات، هدف البحث الى إعداد تمرينات Tabata باستخدام المقاومات لعينة البحث، التعرف على الفروق بين الاختبارات القبلية والبعدية في المتغيرات المبحوثة لدى المجموعتين الضابطة والتجريبية، التعرف على الفروق بين الاختبارات البعدية في المتغيرات المبحوثة لدى مجموعتي البحث الضابطة والتجريبية، استخدام الباحثون المنهج التجريبي كونه يلائم طبيعة مشكلة البحث المراد حلها، تم تحديد مجتمع البحث بالطريقة العمدية من المتدربات المشتركات في الصالة الرياضية (كيك بوكسينك باوه نور) بأعمار( 30- 39 سنة)، والبالغ عددهن ( 30 ) متدربا، وتم اختيار (14) منهن كعينة للبحث، وبنسبة (46%) من المجتمع الكلي، وتم تقسيمهم عشوائيا الى مجموعتين، تجريبية وضابطة، وكل مجموعة تتكون من (7) متدربات، تكون المنهاج التدريبي من دورتين متوسـطتين ، كل دورة متوســطة تحتوي على ( 3 ) دورات تدريبية صغرى (اسبوعية)، وعدد الوحدات التدريبية الاسبوعية (3) وحدات ولمدة (6) اسابيع اي ( 18 ) وحدة تدريبية، تموج الحمل لكل اسبوع كانت (2-1) اي ان التغير كانت بالحجم مع ثبات الشدة والراحة، عدد التمرينات في البرنامج التدريبي تكونت من (42) تمرين، وكل وحدة تدريبية تضمنت (8) تمارين، ، وقد توصل الباحثون الى الاستنتاجات الاتية: ان التمرينات باسلوب Tabata لها تاثير ايجابي في الارتقاء بمستوى بعض المتغيرات الوظيفية والمورفولوجية واللياقة البدنية لدى المجموعة التجريبية، لم تظهر تاثير معنوي لبعض المتغيرات المبحوثة (قياس محيط البطن بمستوى السرة، قياس محيط الفخذ، قياس وزن الجسم) في الاختبارات البعدية بين المجموعتين الضابطة والتجريبي