Optimal Bounds for the k -cut Problem

In the k -cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into k connected components. Algorithms of Karger and Stein can solve this in roughly O ( n 2k ) time. However, lower bounds from conjectures about the k -clique problem imply that Ω ( n (1- o (1)) k ) time is likely needed. Recent results of Gupta, Lee, and Li have given new algorithms for general k -cut in n 1.98k + O(1) time, as well as specialized algorithms with better performance for certain classes of graphs (e.g., for small integer edge weights). In this work, we resolve the problem for general graphs. We show that the Contraction Algorithm of Karger outputs any fixed k -cut of weight α λ k with probability Ω k ( n - α k ), where λ k denotes the minimum k -cut weight. This also gives an extremal bound of O k ( n k ) on the number of minimum k -cuts and an algorithm to compute λ k with roughly n k polylog( n ) runtime. Both are tight up to lower-order factors, with the algorithmic lower bound assuming hardness of max-weight k -clique. The first main ingredient in our result is an extremal bound on the number of cuts of weight less than 2 λ k / k , using the Sunflower lemma. The second ingredient is a fine-grained analysis of how the graph shrinks—and how the average degree evolves—in the Karger process.

Concentration of Pro-Health Compound of Sorghum Grain-Based Foods

More than 35% of the world sorghum seed production is a human food source. The main ingredient of fully ripe sorghum grains is starch. Sorghum does not contain gluten, and it is also a rich source of antioxidant compounds other than vitamins or macro- and microelements, including phenolic acids, flavonoids, and sterols. The aim of this study was to determine the antioxidant activity and the content of selected bioactive compounds, i.e., total phenolic acids, total flavonoids, and total phytosterols, as well as determination of the qualitative and quantitative profile of phenolic acids, flavonoids, and phytosterols in various food products, the basic ingredient of which was sorghum grain. It was found that antioxidant activity is related to the total phenolic compounds content. The ABTS•+ ranged from 319 to 885 µmol TROLOX/kg. However, white sorghum grain flour contained almost two times more polyphenols than red sorghum grain flour. The FPA ranged from 224 in raw pasta to 689 mgGAE/100 g in white sorghum grain. During this study, the quantitative profile of selected polyphenols in grain flour, wafers, pasta, and cookies containing sorghum grain was also investigated, as well as the content of 11 selected phenolic acids. Total content of the latter ranged from 445 to 2850 mg/kg. Phytosterols such as beta-sitosterol, campesterol, and stigmasterol were found in all the analyzed products. Based on this research, it was investigated that the products containing sorghum grains can be classified as functional food.

Comparison of Domestic and International Technical Standards: Study on Improvement of Quality Control of Halogenated Fire Extinguishing Agents

Recently, the National Fire Protection Association (NFPA) announced the revised standards for halogen compound fire extinguishing facilities (NFPA 2001). Characteristically, it is strengthening the quality control standards for halogenated fire extinguishing agents, by presenting specific standards regarding the effects of not only their main ingredient, but also their additional ingredients on the human body. However, in Korea, halogen compound fire extinguishing agents used for firefighting purposes are managed by designating “purity” as the sole criteria for inspection. Considering that halogen compounds utilized for other purposes in Korea are undergoing quality control through various inspections for the safety of humans and the environment, it is evident that a higher level of quality control is required for halogen compounds used for firefighting purposes. Therefore, we would like to suggest a specific improvement plan to enhance safety while using halogenated fire extinguishing agents, through the comparative analysis of inspection criteria, and acceptance standards of corresponding domestic and foreign standards.

Network Pharmacology-Based Strategy and Molecular Docking to Explore the Potential Mechanism of Jintiange Capsule for Treating Osteoporosis

Background. With the advent of ageing population, osteoporosis (OP) has already become a global challenge. Jintiange capsule is extensively applied to treat OP in China. Although recent studies demonstrate that it generates significant effects on strengthening bone, the exact mechanism of the jintiange capsule for treating OP remains unknown. Purpose. To understand the main ingredients of the jintiange capsule, predict the possible targets and the relevant signal transduction pathways, and explore the mechanism of the jintiange capsule for the treatment of OP. Methods. Main ingredients of the jintiange capsule, drug targets, and potential disease targets for OP were obtained from public databases. Molecular biological processes and signaling pathways were determined via bioinformatic analysis, containing protein-protein interaction (PPI), Gene Ontology (GO), and Kyoto Encyclopedia of Genes and Genomes (KEGG). Subsequently, the disease-drug-ingredient-targets-pathways networks were constructed using Cytoscape. According to CytoNCA, core targets were acquired. Finally, the present study conducted molecular docking for better testing the abovementioned results. Results. In the current work, we found that 4 main ingredients of the jintiange capsule, 33 drug targets, 4745 potential disease targets for OP, and 12 overlapping targets were identified. PPI network containing 12 nodes and 25 edges proved that there existed a complex relationship. As revealed by GO functional annotation, the intersected targets were mostly associated with BP, CC, and MF. The targets were enriched to 368 items in BP, 27 items in CC, and 42 items in MF. They mainly included calcium ion homeostasis, calcium channel complex, and calcium channel regulator activity. According to KEGG pathway analysis, the intersected targets were mostly associated with Rap 1, cGMP-PKG, Ras, cAMP, calcium pathways, and so on. Based on the analysis with CytoNCA, we acquired 4 core targets, respectively—CALR, SPARC, CALM1, and CALM2. Besides, 2 core targets, CALR and CALM1, were selected for molecular docking experiments. Molecular docking revealed that the main ingredient, calcium phosphate, had good binding with the CALR protein and CALM1 protein. Conclusion. To conclude, the main ingredient of the jintiange capsule, particularly calcium phosphate, may interact with 2 targets, CALR and CALM1, and regulate multiple signaling pathways to treat OP. Additionally, this also benefits us in further understanding the mechanism of the jintiange capsule for treating OP.

Complex Structures for Klein-Gordon theory on globally hyperbolic spacetimes

We develop a rigorous method to parametrize complex structures for Klein-Gordon theory in globally hyperbolic spacetimes that satisfy a completeness condition. The complex structures are conserved under time-evolution and implement unitary quantizations. They can be interpreted as corresponding to global choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of globally hyperbolic spacetimes. In particular, we consider static, expanding and Friedmann-Robertson-Walker spacetimes. Moreover, for a huge class of spacetimes we prove that the differential equation for the complex structure is given by the Gelfand-Dikki equation.

Karakteristik Fisikokimia dan Sensoris Kopi Arabika Menoreh dengan Teknik Seduhan Cold Brew

<p><em>Coffee is one of the most widely distributed and </em><em>consumed</em><em> </em><em>beverages</em><em> in the world. </em><em>In general, coffee is brewed using hot water, but</em><em> </em><em>a</em><em>s the coffee industry develops, cold water</em><em> also</em><em> </em><em>can be used for </em><em>the coffee brewing process</em><em>. This brewing technique is known as </em><em>cold bre</em><em>w.</em><em> There is</em><em> little</em><em> information </em><em>regarding</em><em> the characteristics of cold brew</em><em> coffee</em><em>. T</em><em>herefore</em><em> it is necessary to study the characteristics of cold brew </em><em>beverage</em><em>s, especially with local Indonesian coffee</em><em> as its main ingredient. This research used</em><em> Menoreh Arabica coffee</em><em> as its main research object</em><em>. Th</em><em>is study aimed</em><em> to determine the physicochemical and sensory characteristics of </em><em>M</em><em>enoreh </em><em>A</em><em>rabica coffee with cold brew brewing techniques.</em><em> This research</em><em> begins with roasting coffee into three types, </em><em>which</em><em> is light (T = 193</em><em> </em><em>^o</em><em>C, t = 5 minute), medium (T = 208</em><em> </em><em>^o</em><em>C, t = 7 minute), and dark (T = 223</em><em> </em><em>^o</em><em>C, t = 13 minute). Furthermore,</em><em> </em><em>the coffee is g</em><em>rinded</em><em> into two types</em><em> grind size</em><em> </em><em>(</em><em>medium and coarse</em><em>)</em><em>. </em><em>Samples</em><em> of cold brew formulation w</em><em>ere</em><em> made with an extraction time of 8 hours. </em><em>The </em><em>sensory analysis</em><em> is conducted</em><em> based on the SCA method. </em><em>Sensory data analysis was done to</em><em> determine the three best formulations</em><em> </em><em>according to roast </em><em>profiles,</em><em> continued with</em><em> the physicochemical analysis. The best cold brew sample obtained from this research was </em><em>medium-coarse</em><em> Arabica Menoreh coffee, </em><em>with the highest </em><em>sensory </em><em>parameters </em><em>values in </em><em>aroma, acidity, aftertaste, and sweetness</em><em>. </em><em>The value of pH, chlorogenic acid, and some organic acids affect acidity. Lactic acid affects</em><em> </em><em>body value,</em><em> and c</em><em>affeine levels were relatively stable in each sample. </em><em>This research result can be used as a reference for product diversification of Arabica Menoreh coffee.</em><em></em></p>

The effect of silanes as integral hydrophobic admixture on the physical properties of cement based materials

The paper explores the possibility of using organosilicon compounds (e.g., poly(dimethylsiloxane) and triethoxyoctylsilane) in commercial admixtures as internal hydrophobization agents for porous cement-based materials. The study involved the cement mortar with five different hydrophobic admixtures. Four of them is based on triethoxyoctylsilane, but with various concentration of the main ingredient, and one of them on poly(dimethylsiloxane). Mechanical properties, capillary water absorption, as well as microstructure were investigated. The organosilicon admixtures efficiently decrease the capillary water absorption even by 81% decreasing mechanical strength of cement mortar at the same time even by 55%. Only one admixture, based on poly(dimethylsiloxane) caused significant changes in microstructure of cement mortar.

Analysis on rhizome shrinkage of two expected kencur (Kaempferia galanga) accessions from east java using MgSO4 fertilizer under shading

Kencur (Kaempferia galanga L.) is one of the plants that mainly can be used as the main ingredient in medicine, food, drinks, and spices with benefits. Environmental conditions are a supporting factor for cultivating kencur. Nutrient needs are important factors for plant cultivation. A good environment is an environment that fulfills macro and micronutrients. It is also an important thing in kencur cultivating plants. We should know in which condition the plant can show the best result so the kencur plant is tested under shade. One of the macro nutrients needed by plants are sulfur (S) and magnesium (Mg). The purpose of this research is to determine if there is an interaction between accessions and Sulfur (MgSO4) at two different shades levels. The design used in this study was a Split Plot Design with the main plot: kencur plant with Blitar and Banyuwangi accessions, sub plots: MgSO4 fertilizer with dose of 0, 60, 90 and 120 kg ha-1, land under shade. The shrinkage of the rhizomes that occurred with a dose of sulfur fertilizer ranged from 13% to 19% and without a dose of sulfur fertilizer decreased 34% with results showing that the treatment with a dose of 90 kg ha-1 of sulfur fertilizer resulted in lower shrinkage.

FORMULASI DAN EVALUASI HAND SANITIZER SPRAY EKSTRAK BUAH BELIMBING WULUH (Averrhoa bilimbi L)

The tendency of society at this time to return to nature (Back to nature) is by using plants as treatment. The use of star fruit as the main ingredient in the manufacture of a hand sanitizer spray on the basis of star fruit has flavonoid compounds that have the potential as antibacterial. Hand sanitizer spray is made into 3 formulas with a concentration ratio of F1 (10%), F2 (12%), and F3 (15%). Each formula was subjected to physical tests in the form of organoleptic tests, pH tests, homogeneity tests and freeze and thaw stability tests for 6 storage cycles at 4°C and 40°C. The organoleptic results showed that the preparation did not change during four weeks of storage. On examination, the pH of the preparation decreased for F1 with a pH of 5.25 to 4.88; F2 with a pH of 5.14 becomes 4.77, and F3 with a pH of 4.87 becomes 4.60 but this value is still included in the specified range. The homogeneity of the preparations F1, F2, and F3 was only homogeneous in the first week and for the stability of the preparations F1, F2 and F3 were only stable in cycle 1 and cycle 2.