scholarly journals Chvátal Rank in Binary Polynomial Optimization

2021 ◽  
pp. ijoo.2019.0049
Author(s):  
Alberto Del Pia ◽  
Silvia Di Gregorio
Keyword(s):  
Cutting Planes ◽  
Linear Time ◽  
Valid Inequalities ◽  
Polynomial Optimization ◽  
Combinatorial Structure ◽  
First Results ◽  
Rank 2 ◽  
Almost All ◽  
Do So

Recently, several classes of cutting planes have been introduced for binary polynomial optimization. In this paper, we present the first results connecting the combinatorial structure of these inequalities with their Chvátal rank. We determine the Chvátal rank of all known cutting planes and show that almost all of them have Chvátal rank 1. We observe that these inequalities have an associated hypergraph that is β-acyclic. Our second goal is to derive deeper cutting planes; to do so, we consider hypergraphs that admit β-cycles. We introduce a novel class of valid inequalities arising from odd β-cycles, that generally have Chvátal rank 2. These inequalities allow us to obtain the first characterization of the multilinear polytope for hypergraphs that contain β-cycles. Namely, we show that the multilinear polytope for cycle hypergraphs is given by the standard linearization inequalities, flower inequalities, and odd β-cycle inequalities. We also prove that odd β-cycle inequalities can be separated in linear time when the hypergraph is a cycle hypergraph. This shows that instances represented by cycle hypergraphs can be solved in polynomial time. Last, to test the strength of odd β-cycle inequalities, we perform numerical experiments that imply that they close a significant percentage of the integrality gap.

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

Physicochemical and bacteriological characterization of hospital effluents and their impact on the environment

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Human Health ◽  
Fecal Coliforms ◽  
Chemical Pollution ◽  
Hospital Effluents ◽  
Biological Contaminants ◽  
Almost All ◽  
Direct Discharge ◽  
Significant Chemical

Liquid effluents discharged by hospitals may contain chemical and biological contaminants whose main source is the different substances used for the treatment of patients. This type of rejection can present a sanitary potentially dangerous risk for human health and can provoke a strong degradation of diverse environmental compartments mainly water and soils. The present study focuses on the quality of the liquid effluents of Hassani Abdelkader’s hospital of Sidi Bel-Abbes (West of Algeria). The results reveal a significant chemical pollution (COD: 879 mgO2/L, BOD5: 850 mgO2/L, NH4+ : 47.9 mg/l, NO2- : 4.2 mg/l, NO3- : 56.8 mg/l with respect to WHO standard of 90 mgO2/L, 30 mgO2/L, 0.5 mg/l, 1 mg/l and 1 mg/l respectively). However, these effluents are biodegradable since the ratio COD/BOD5 do not exceeded the value of 2 in almost all samples. The presence of pathogen germs is put into evidence such as pseudomonas, the clostridium, the staphylococcus, the fecal coliforms and fecal streptococcus. These results show that the direct discharge of these effluents constitutes a major threat to human health and the environment.

scholarly journals Stoichiometry and compositional plasticity of the yeast nuclear pore complex revealed by quantitative fluorescence microscopy

2018 ◽  
Vol 115 (17) ◽  
pp. E3969-E3977 ◽  
Author(s):  
Sasikumar Rajoo ◽  
Pascal Vallotton ◽  
Evgeny Onischenko ◽  
Karsten Weis
Keyword(s):  
Nuclear Pore Complex ◽  
Yeast Cells ◽  
Nuclear Pore ◽  
Altered Expression ◽  
Copy Numbers ◽  
Quantitative Image ◽  
Multiple Copies ◽  
Almost All ◽  
High Degree

The nuclear pore complex (NPC) is an eightfold symmetrical channel providing selective transport of biomolecules across the nuclear envelope. Each NPC consists of ∼30 different nuclear pore proteins (Nups) all present in multiple copies per NPC. Significant progress has recently been made in the characterization of the vertebrate NPC structure. However, because of the estimated size differences between the vertebrate and yeast NPC, it has been unclear whether the NPC architecture is conserved between species. Here, we have developed a quantitative image analysis pipeline, termed nuclear rim intensity measurement (NuRIM), to precisely determine copy numbers for almost all Nups within native NPCs of budding yeast cells. Our analysis demonstrates that the majority of yeast Nups are present at most in 16 copies per NPC. This reveals a dramatic difference to the stoichiometry determined for the human NPC, suggesting that despite a high degree of individual Nup conservation, the yeast and human NPC architecture is significantly different. Furthermore, using NuRIM, we examined the effects of mutations on NPC stoichiometry. We demonstrate for two paralog pairs of key scaffold Nups, Nup170/Nup157 and Nup192/Nup188, that their altered expression leads to significant changes in the NPC stoichiometry inducing either voids in the NPC structure or substitution of one paralog by the other. Thus, our results not only provide accurate stoichiometry information for the intact yeast NPC but also reveal an intriguing compositional plasticity of the NPC architecture, which may explain how differences in NPC composition could arise in the course of evolution.

scholarly journals Towards Reduced CNNs for De-Noising Phase Images Corrupted with Speckle Noise

Photonics ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 255
Author(s):  
Marie Tahon ◽  
Silvio Montresor ◽  
Pascal Picart
Keyword(s):  
Phase Error ◽  
Speckle Noise ◽  
Experimental Conditions ◽  
Benchmark Data ◽  
Wide Range ◽  
Phase Images ◽  
Different Depths ◽  
Phase Data ◽  
Do So

Digital holography is a very efficient technique for 3D imaging and the characterization of changes at the surfaces of objects. However, during the process of holographic interferometry, the reconstructed phase images suffer from speckle noise. In this paper, de-noising is addressed with phase images corrupted with speckle noise. To do so, DnCNN residual networks with different depths were built and trained with various holographic noisy phase data. The possibility of using a network pre-trained on natural images with Gaussian noise is also investigated. All models are evaluated in terms of phase error with HOLODEEP benchmark data and with three unseen images corresponding to different experimental conditions. The best results are obtained using a network with only four convolutional blocks and trained with a wide range of noisy phase patterns.

Study of Painting Materials and Techniques in the 18th Century St.Athanasius Church in Moschopolis, Albania

2007 ◽  
Vol 1047 ◽  
Author(s):  
Eleni Pavlidou ◽  
N. Civici ◽  
E. Caushi ◽  
L. Anastasiou ◽  
T. Zorba ◽  
...  
Keyword(s):  
18Th Century ◽  
Orthodox Church ◽  
Wall Paintings ◽  
Cultural Center ◽  
Green Earth ◽  
Almost All ◽  
The City ◽  
The Church ◽  
Compositional Characterization

AbstractIn this paper are presented the studies of the paint materials and the technique used in 18th century wall paintings, originated from the orthodox church of St Athanasius, in the city of Maschopolis, a flourishing economical and cultural center, in Albania. The church was painted in 1745 by Konstantinos and Athanasios Zografi, and during the last years, restoration activities are being performed at the church. Samples that included plasters and pigments of different colors were collected from important points of the wall paintings. Additionally, as some parts of the wall-paintings were over-painted, the analysis was extended to the compositional characterization of these areas. The identification of the used materials was done by using complementary analytical methods such as Optical Microscopy, Fourier Transform Infrared spectroscopy (FTIR), Scanning Electron Microscopy (SEM-EDS) and X-ray fluorescence (TXRF).The presence of calcite in almost all the pigments is indicative for the use of the fresco technique at the studied areas, while the detection of gypsum and calcium oxalate, indicates an environmental degradation along with a biodegradation. Common pigments used in this area at 15-16th centuries, such as cinnabar, green earth, manganese oxide, carbon black and calcite were identified.

Experimental Study of Ductile Fracture for Non-Aligned Multiple Flaws in a Plate

2009 ◽  
Author(s):  
Katsumasa Miyazaki ◽  
Kunio Hasegawa ◽  
Koichi Saito ◽  
Bostjan Bezensek
Keyword(s):  
Experimental Study ◽  
Ductile Fracture ◽  
Estimation Procedure ◽  
Maximum Load ◽  
Experimental Results ◽  
Collapse Load ◽  
Plate Specimen ◽  
Fracture Tests ◽  
Almost All

The fitness-for-service code requires the characterization of non-aligned multiple flaws for the flaw evaluation, which is performed using a flaw proximity rule. Worldwide almost all codes provide own proximity rule, often with unclear technical bases of the application of proximity rule to ductile fracture. To clarify the appropriate proximity rule for non-aligned multiple flaws in fully plastic fracture, fracture tests on flat plate specimen with non-aligned multiple through wall flaws were conducted at ambient temperature. The emphasis of this study was put on the flaw alignment rule, which determines whether non-aligned flaws are treated as independent or aligned onto the same plane for the purpose of flaw evaluations. The effects of the flaw separation and flaw size on the maximum load were investigated. The experimental results were compared with the estimations of the collapse load using the alignment rules in the ASME Section XI, BS7910 and API 579-1 codes. A new estimation procedure specific to the fully plastic fracture was proposed and compared with the comparison with the experimental results.

scholarly journals Isolation and Characterization of Bacteriophage ZCSE6 against Salmonella spp.: Phage Application in Milk

Biologics ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 164-176
Author(s):  
Abdallah S. Abdelsattar ◽  
Anan Safwat ◽  
Rana Nofal ◽  
Amera Elsayed ◽  
Salsabil Makky ◽  
...  
Keyword(s):  
Pathogenic Bacteria ◽  
Raw Milk ◽  
Salmonella Spp ◽  
Isolation And Characterization ◽  
Food Borne ◽  
Wide Range ◽  
Almost All ◽  
And Control ◽  
Milk And Dairy Products

Food safety is very important in the food industry as most pathogenic bacteria can cause food-borne diseases and negatively affect public health. In the milk industry, contamination with Salmonella has always been a challenge, but the risks have dramatically increased as almost all bacteria now show resistance to a wide range of commercial antibiotics. This study aimed to isolate a bacteriophage to be used as a bactericidal agent against Salmonella in milk and dairy products. Here, phage ZCSE6 has been isolated from raw milk sample sand molecularly and chemically characterized. At different multiplicities of infection (MOIs) of 0.1, 0.01, and 0.001, the phage–Salmonella interaction was studied for 6 h at 37 °C and 24 h at 8 °C. In addition, ZCSE6 was tested against Salmonella contamination in milk to examine its lytic activity for 3 h at 37 °C. The results showed that ZCSE6 has a small genome size (<48.5 kbp) and belongs to the Siphovirus family. Phage ZCSE6 revealed a high thermal and pH stability at various conditions that mimic milk manufacturing and supply chain conditions. It also demonstrated a significant reduction in Salmonella concentration in media at various MOIs, with higher bacterial eradication at higher MOI. Moreover, it significantly reduced Salmonella growth (MOI 1) in milk, manifesting a 1000-fold decrease in bacteria concentration following 3 h incubation at 37 °C. The results highlighted the strong ability of ZCSE6 to kill Salmonella and control its growth in milk. Thus, ZCSE6 is recommended as a biocontrol agent in milk to limit bacterial growth and increase the milk shelf-life.

Effect of Flaw Dimensions on Ductile Fracture Behavior of Non-Aligned Multiple Flaws in a Plate

2011 ◽  
Author(s):  
Katsumasa Miyazaki ◽  
Kunio Hasegawa ◽  
Koichi Saito
Keyword(s):  
Ductile Fracture ◽  
Flat Plate ◽  
Fracture Behavior ◽  
Maximum Load ◽  
Surface Flaws ◽  
Fracture Tests ◽  
The Difference ◽  
Almost All ◽  
Maximum Minimum

The fitness-for-service codes require the characterization of non-aligned multiple flaws for flaw evaluation, which is performed using a flaw proximity rule. Worldwide, almost all such codes provide their own proximity rule, often with unclear technical bases of the application of proximity rule to ductile or fully plastic fracture. In particular, the effect of flaw dimensions of multiple surface flaws on fully plastic fracture of non-aligned multiple flaws had not been clear. To clarify the effect of the difference of part through-wall and through-wall flaws on the behavior of fully plastic fracture, the fracture tests of flat plate specimens with non-aligned multiple part through-wall flaws were conducted. When the flaw depth a was shallow with 0.4 in ratio of a to thickness t, the maximum load Pmax occurred at penetration of multiple flaws and the effect of vertical distance of non-aligned multiple flaws H on Pmax was not so significant. However, when flaw depth was deep with 0.8 in a/t, Pmax occurred after penetration of flaws and the effect of H on Pmax could be seen clearly. It was judged that the through-wall flaw tests were appropriate for discussion of the effect of H on Pmax and the alignment rule of multiple flaws. In addition, in order to clarify the appropriate length parameter to estimate Pmax of test specimens with dissimilar non-aligned through-wall multiple flaws, the fracture tests of plate specimens were also conducted. The effect of different flaw length on Pmax was discussed with maximum, minimum and averages of dissimilar non-aligned multiple flaw lengths. Experimental results showed that the maximum length lmax would be an appropriate length parameter to estimate Pmax, when the non-aligned multiple through-wall flaws were dissimilar.

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