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Srimad Bhagavata Book 2-Chapter 6-Worldly life is restricted to the 3 worlds of Bhu (earth), Bhava (the intermediate regions), and Svah (Heaven) There are 4 regions higher than this – these are achieved by the paths of knowledge and God-dedicated correct action Vidya (knowledge of the Supreme) and Avidya (ignorance of ... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 7-Summary of the Narayana's Incarnations and glories told by Brahma to Narada Muni: Cosmic Boar – to rescue the Earth Suyajna – removes the sufferings of all. For this, He is called Hari (the remover of sufferings). | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 7-Kapila Muni – to give the Supreme Knowledge (Sankyha philosophy) Dattatreya – the son of Rishi Atri and Anasuya Sanaka, Sanandana, Sanatana, Sanatakumara – 4 sons of Brahma who are among the greatest of sages Nara and Narayana – 2 great sages Narayana came to help Dhruva after his pray... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 8-Narayana quickly enters the heart of one who thinks of His glories constantly.
This completely purifies the devotee.
Parikshit asks Sri Suka 20 questions whose answers form the Bhagavata: Nature of the Atman Difference between man and God Creation The result of actions Incarnations Dut... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 9-Maya (Narayana's illusory power) causes the Jiva to identify itself with the body Brahma is unsure how to proceed with creation and hears Tapa, Tapa (Meditate! Meditate!) Brahma meditates for many divine years and Vishnu appears Brahma sees Vishnu's Realm (Vaikuntha) where all beings h... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 10-The Viratpurusha (Cosmic Person) created the Cosmic Waters in order to have a place to exist.
Therefore, the Viratpurusha is known as Narayana, the one who rests in the water. | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 10-Description of the Gross Cosmic Form of Narayana Every part of the Cosmic Form was formed with 4 entities: The place (such as the mouth) The organ (such as the tongue) The sense object (such as taste) The Deity (such as Varuna) The first part to develop was the mouth, in order to sati... | milkshake721/2.1M-wiki-STEM |
Design around-Design around-In the field of patents, the phrase "to design around" means to invent an alternative to a patented invention that does not infringe the patent's claims. The phrase can also refer to the invention itself. | milkshake721/2.1M-wiki-STEM |
Design around-Design around-Design-arounds are considered to be one of the benefits of patent law. By providing monopoly rights to inventors in exchange for disclosing how to make and use their inventions, others are given both the information and incentive to invent competitive alternatives that design around the orig... | milkshake721/2.1M-wiki-STEM |
Genu recurvatum-Genu recurvatum-Genu recurvatum is a deformity in the knee joint, so that the knee bends backwards. In this deformity, excessive extension occurs in the tibiofemoral joint. Genu recurvatum is also called knee hyperextension and back knee. This deformity is more common in women and people with familial l... | milkshake721/2.1M-wiki-STEM |
Genu recurvatum-Causes-The following factors may be involved in causing this deformity: Inherent laxity of the knee ligaments Weakness of biceps femoris muscle Instability of the knee joint due to ligaments and joint capsule injuries Inappropriate alignment of the tibia and femur Malunion of the bones around the knee W... | milkshake721/2.1M-wiki-STEM |
Genu recurvatum-Pathophysiology-The most important factors of knee stability include: Ligaments of the knee: The knee joint is stabilized by four main ligaments: Anterior cruciate ligament (ACL). The ACL has an important role in stabilization of knee extension movement by preventing the knee from hyperextending.
Poster... | milkshake721/2.1M-wiki-STEM |
Genu recurvatum-Treatment-Treatment generally includes the following: Sometimes pharmacologic therapy for initial disease treatment Physical therapy: physiotherapy will be beneficial in patient with complaint of pain, discomfort.
Occupational therapy Use of appropriate assistive devices such as orthoses Surgery | milkshake721/2.1M-wiki-STEM |
Genu recurvatum-Incidence-This condition is considered to be rare, with about 1 in 100,000 births being affected by the congenital form of genu recurvatum, although it's a common feature in some disorders, such as in joint hypermobility, which affects 1 in 30 people. | milkshake721/2.1M-wiki-STEM |
Palivizumab-Palivizumab-Palivizumab, sold under the brand name Synagis, is a monoclonal antibody produced by recombinant DNA technology used to prevent severe disease caused by respiratory syncytial virus (RSV) infections. It is recommended for infants at high-risk for RSV due to conditions such as prematurity or other... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Medical use-Palivizumab is indicated for the prevention of serious lower respiratory tract disease requiring hospitalization caused by the respiratory syncytial virus (RSV) in children at high risk for RSV disease: children born at 35 weeks of gestation or less and less than six months of age at the onset o... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Medical use-RSV Prophylaxis All infants younger than one year who were born at <29 weeks (i.e. ≤28 weeks, 6 days) of gestation are recommended to use palivizumab. Infants younger than one year with bronchopulmonary dysplasia (i.e. who were born at <32 weeks gestation and required supplemental oxygen for the... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Medical use-RSV Prophylaxis Target Groups Infants younger than one year of age with hemodynamically significant congenital heart disease.
Infants younger than one year of age with neuromuscular disorders impairing the ability to clear secretions from the upper airways or pulmonary abnormalities.
Children yo... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Medical use-RSV Treatment Because palivizumab is a passive antibody, it is ineffective in the treatment of RSV infection, and its administration is not recommended for this indication. A 2019 Cochrane review found no differences in palivizumab and placebo on outcomes of mortality, length of hospital stay, a... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Mechanism of action-Palivizumab is a monoclonal antibody that targets the fusion (F) glycoprotein on the surface of RSV, and deactivates it. The F protein is a membrane protein responsible for fusing the virus with its target cell and is highly conserved among subgroups of RSV. Deactivating the F protein pr... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Mechanism of action-Pharmacodynamics Palivizumab has demonstrated a significantly higher affinity and potency in neutralizing both A and B subtypes of RSV when compared with RSV-IGIV. Treatment with 2.5 mg/kg of palivizumab led to a serum concentration of 25-30 μg/mL in cotton rats and reduced RSV titers by... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Mechanism of action-Pharmacokinetics Absorption A 2008 meta-analysis found that palivizumab absorption was quicker in the pediatric population compared to adults (ka = 1.01/day vs. ka = 0.373/day). The intramuscular bioavailability of this drug is approximately 70% in healthy young adults. Current recommend... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Mechanism of action-Distribution The volume of distribution is approximately 4.1 liters. | milkshake721/2.1M-wiki-STEM |
Palivizumab-Mechanism of action-Clearance Palivizumab has a drug clearance (CL) of approximately 198 ml/day. The half-life of this drug is approximately 20 days with three doses sustaining body concentrations that will last the entire RSV season (5 to 6 months). A 2008 meta-analysis estimated clearance in the pediatric... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Side effects-Palivizumab use may cause side effects, which include, but are not limited to: Sore throat Runny nose Redness or irritation at the injection site Vomiting DiarrheaSome more serious side effects include: Severe skin rash Itching Hives (urticaria) Difficulty breathing | milkshake721/2.1M-wiki-STEM |
Palivizumab-Contraindications-Contraindications for the use of palivizumab include hypersensitivity reactions upon exposure to palivizumab. Serious cases of anaphylaxis have been reported after exposure to palivizumab. Signs of hypersensitivity include hives, shortness of breath, hypotension, and unresponsiveness. No o... | milkshake721/2.1M-wiki-STEM |
Palivizumab-Cost-Palivizumab is a relatively expensive medication, with a 100-mg vial ranging from $904 to $1866. Multiple studies done by both the manufacturer and independent researchers to determine the cost-effectiveness of palivizumab have found conflicting results. The heterogeneity between these studies makes th... | milkshake721/2.1M-wiki-STEM |
Palivizumab-History-The disease burden of RSV in young infants and its global prevalence have prompted attempts for vaccine development. As of 2019, there was no approved vaccine for RSV prevention. A formalin-inactivated RSV vaccine (FIRSV) was studied in the 1960s. The immunized children who were exposed to the virus... | milkshake721/2.1M-wiki-STEM |
Domestic flight-Domestic flight-A domestic flight is a form of commercial flight within civil aviation where the departure and the arrival take place in the same country.Airports serving domestic flights only are known as domestic airports.
Domestic flights are generally cheaper and shorter than most international flig... | milkshake721/2.1M-wiki-STEM |
Domestic flight-Domestic flight-Domestic flights are the only sector of aviation not exhibiting a global long term growth trend due to many smaller countries increasingly replacing short domestic routes with high speed rail; that said, most of the busiest air routes in the world are domestic flights.Some smaller countr... | milkshake721/2.1M-wiki-STEM |
One-parameter group-One-parameter group-In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism φ:R→G from the real line R (as an additive group) to some other topological group G . If φ is injective then φ(R) , the image, will be a subgroup of G that is isomo... | milkshake721/2.1M-wiki-STEM |
One-parameter group-One-parameter group-The action of a one-parameter group on a set is known as a flow. A smooth vector field on a manifold, at a point, induces a local flow - a one parameter group of local diffeomorphisms, sending points along integral curves of the vector field. The local flow of a vector field is u... | milkshake721/2.1M-wiki-STEM |
One-parameter group-Examples-Such one-parameter groups are of basic importance in the theory of Lie groups, for which every element of the associated Lie algebra defines such a homomorphism, the exponential map. In the case of matrix groups it is given by the matrix exponential.
Another important case is seen in functi... | milkshake721/2.1M-wiki-STEM |
One-parameter group-Physics-In physics, one-parameter groups describe dynamical systems. Furthermore, whenever a system of physical laws admits a one-parameter group of differentiable symmetries, then there is a conserved quantity, by Noether's theorem. | milkshake721/2.1M-wiki-STEM |
One-parameter group-Physics-In the study of spacetime the use of the unit hyperbola to calibrate spatio-temporal measurements has become common since Hermann Minkowski discussed it in 1908. The principle of relativity was reduced to arbitrariness of which diameter of the unit hyperbola was used to determine a world-lin... | milkshake721/2.1M-wiki-STEM |
One-parameter group-In GL(n,ℂ)-An important example in the theory of Lie groups arises when G is taken to be GL(n;C) , the group of invertible n×n matrices with complex entries. In that case, a basic result is the following: Theorem: Suppose φ:R→GL(n;C) is a one-parameter group. Then there exists a unique n×n matr... | milkshake721/2.1M-wiki-STEM |
One-parameter group-Topology-A technical complication is that φ(R) as a subspace of G may carry a topology that is coarser than that on R ; this may happen in cases where φ is injective. Think for example of the case where G is a torus T , and φ is constructed by winding a straight line round T at an irrational... | milkshake721/2.1M-wiki-STEM |
One-parameter group-Topology-In that case the induced topology may not be the standard one of the real line. | milkshake721/2.1M-wiki-STEM |
Contourlet-Contourlet-Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The contourlet transform has a fast implementation based on a Laplacian pyramid decomposition followed by directional filterbanks applied on ... | milkshake721/2.1M-wiki-STEM |
Contourlet-Contourlet transform-Introduction and motivation In the field of geometrical image transforms, there are many 1-D transforms designed for detecting or capturing the geometry of image information, such as the Fourier and wavelet transform. However, the ability of 1-D transform processing of the intrinsic geom... | milkshake721/2.1M-wiki-STEM |
Contourlet-Contourlet transform-The contourlet transform is inspired by the human visual system and Curvelet transform which can capture the smoothness of the contour of images with different elongated shapes and in variety of directions. However, it is difficult to sampling on a rectangular grid for Curvelet transform... | milkshake721/2.1M-wiki-STEM |
Contourlet-Contourlet transform-Definition The contourlet transform uses a double filter bank structure to get the smooth contours of images. In this double filter bank, the Laplacian pyramid (LP) is first used to capture the point discontinuities, and then a directional filter bank (DFB) is used to form those point di... | milkshake721/2.1M-wiki-STEM |
Contourlet-Contourlet transform-The properties of discrete contourlet transform If perfect-reconstruction filters are used for both the LP decomposition and DFB, then the discrete contourlet transform can reconstruct the original image perfectly, which means it provides a frame operator.
If orthogonal filters are used ... | milkshake721/2.1M-wiki-STEM |
Contourlet-Contourlet transform-The upper bound for the redundancy ratio of the discrete contourlet transform is 4/3 If the j pyramidal level of LP applies to lj level DFB, the basis images of the contourlet transform have the size of width ≈ 2j and length ≈ 2j+lj−2 When FIR is used, the computational complexity... | milkshake721/2.1M-wiki-STEM |
Contourlet-Nonsubsampled contourlet transform-Motivation and applications The contourlet transform has a number of useful features and qualities, but it also has its flaws. One of the more notable variations of the contourlet transform was developed and proposed by da Cunha, Zhou and Do in 2006. The nonsubsampled conto... | milkshake721/2.1M-wiki-STEM |
Contourlet-Nonsubsampled contourlet transform-Basic concept To retain the directional and multiscale properties of the transform, the Laplacian Pyramid was replaced with a nonsubsampled pyramid structure to retain the multiscale property, and a nonsubsampled directional filter bank for directionality. The first major n... | milkshake721/2.1M-wiki-STEM |
Contourlet-Variations of the contourlet transform-Wavelet-based contourlet transform Although the wavelet transform is not optimal in capturing the 2-D singularities of images, it can take the place of LP decomposition in the double filter bank structure to make the contourlet transform a non-redundant image transform.... | milkshake721/2.1M-wiki-STEM |
Contourlet-Variations of the contourlet transform-The hidden Markov tree (HMT) model for the contourlet transform Based on the study of statistics of contourlet coefficients of natural images, the HMT model for the contourlet transform is proposed. The statistics show that the contourlet coefficients are highly non-Gau... | milkshake721/2.1M-wiki-STEM |
Contourlet-Variations of the contourlet transform-Contourlet transform with sharp frequency localization An alternative or variation of the contourlet transform was proposed by Lu and Do in 2006. This new proposed method was intended as a remedy to fix non-localized basis images in frequency. The issue with the origina... | milkshake721/2.1M-wiki-STEM |
Contourlet-Variations of the contourlet transform-Image enhancement based on nonsubsampled contourlet transform In prior studies the contourlet transform has proven effective in the denoising of images but in this method the researchers developed a method of image enhancement. When enhancing images preservation and the... | milkshake721/2.1M-wiki-STEM |
Contourlet-Applications-Image Denoising Image Enhancement Image Restoration Image Despeckling | milkshake721/2.1M-wiki-STEM |
Maximum-minimums identity-Maximum-minimums identity-In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2n − 1 non-empty subsets of S.
Let S = {x1, x2, ..., xn}. The identity states that max min min min {x1,x2,…,xn}, or conversely min ma... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Cricopharyngeal spasm-Cricopharyngeal spasms occur in the cricopharyngeus muscle of the pharynx. Cricopharyngeal spasm is an uncomfortable but harmless and temporary disorder. | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Signs and symptoms-Sensation of a 'lump' in the back of the throat Throat feels swollen Discomfort - Lump can often feel quite big and pain is occasional Symptoms normally worse in the evening Stress aggravates the symptoms Saliva is difficult to swallow, yet food is easy to swallow - eating, in f... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Signs and symptoms-The symptoms can be mimicked by pushing on the cartilage in the neck, just below the Adam's apple | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Physiology-There are two sphincters in the oesophagus. They are normally contracted and they relax when one swallows so that food can pass through them going to the stomach. They then squeeze closed again to prevent regurgitation of the stomach contents and prevent air from entering the digestive ... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Causes-Causes include stress and anxiety. Other causes are not yet clear.
The condition persists in the autonomic nervous system even when the original stress is relieved. | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Causes-An assumption in psychiatry is that a lack of serotonin can be associated with depression and anxiety. A further assumption is that a low levels of serotonin can causes spasms in the cervical area. A plausible explanation for the cricopharyngeal spasms is a lack of neurotransmitter preventi... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Causes-The condition can appear as a symptom of the generalized anxiety disorder. Early signs are other symptoms like difficulty or inability to eat (loss of appetite, satiety after swallowing minor quantities), headache, dry mouth at night, sleeping issues, tremor, tension in the neck, in the thr... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Causes-The subject heads to cricopharyngeal spasms when, for instance, eating pasty food requiring more throat cleanings, like peanuts, pumpkin seeds and other nuts, becomes painful. Continuous swallowing appears with the spasms as the brain interprets the feeling as something stuck.
The vagus ner... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Diagnosis-These spasms are frequently misunderstood by the patient to be cancer due to the 'lump in the throat' feeling (Globus pharyngis) that is symptomatic of this syndrome. | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Diagnosis-All the anatomic examinations can appear normal despite the condition. The throat endoscopy can objectify that nothing is stuck, that there is no lesion or inflammation. The barium swallow can miss that the sphincter is hypertonic if it does not happen during the examination, or if the s... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Diagnosis-The cricopharyngeal spasms ("feeling that something is stuck") occur in the cricopharyngeal part of the inferior pharyngeal constrictor muscle, at the bottom of the throat. They cause muscle tension on the cricoid cartilage, leading to a globus feeling. Pharyngeal spasms, a more common s... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Diagnosis-The patient complains about the signs and symptoms enumerated above. The pain causes dry deglutition and dry deglutition adds to the pain, triggering a vicious circle. The spams start after dry deglutition, after the meals or randomly during the day. They can start (and stop) brutally. O... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Diagnosis-The cricopharyngeal spasms can be, for instance, formally diagnosed as part of the more general condition. For instance, did the patient recently encounter other symptoms of the generalized anxiety disorder? Does the patient have neurovegetative symptoms? Are there symptoms of dysautonom... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Treatment-The condition is known to be temporary. In some individuals it can disappear by itself without medication. For others, it can stagnate or worsen until appropriate medical care is given.
Since the problem can last, medical specialists are not readily available and potential treatments act... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Treatment-Treatments based on medicines Antispasmodic medicines (immediate benefit) Nifedipine, in small doses (2x 5 mg per day, 10 mg per day in slow release or as much as the blood pressure allows it), can be prescribed in an attempt to provide a first relief, by blocking the esophageal spasms t... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Treatment-Muscle relaxants (benefit obtained on the short-term) Clonazepam (Rivotril), diazepam (Valium) and lorazepam (Ativan) and other benzodiazepines relax the muscles in the throat, slow or halt the contractions. (In some people, benzodiazepines taken on the long term may have addictive prope... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Treatment-Tricyclic anti-depressants (Pamelor etc.), taken in small doses, have been having positive results recently, according to the Cleveland Clinic. | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Treatment-Proton-pump inhibitors, or other medicines acting against reflux, if signs of reflux are found, until they disappear.A typical treatment that can be prescribed starts, for instance, with nidefipine (as long as it brings a relief), a benzodiazepine (one month maximum) that has a myorelaxa... | milkshake721/2.1M-wiki-STEM |
Cricopharyngeal spasm-Treatment-Treatments based on other factors Stress reduction Take notes of what improves and worsens the symptoms.
High stress levels make the spasms more noticeable.
Psychologists provide custom tips and tricks.
Mindfulness, with professionals, or smartphone apps.
Breathing exercises such as card... | milkshake721/2.1M-wiki-STEM |
Number form-Number form-A number form is a mental map of numbers, which automatically and involuntarily appears whenever someone who experiences number-forms thinks of numbers. Numbers are mapped into distinct spatial locations and the mapping may be different across individuals. Number forms were first documented and ... | milkshake721/2.1M-wiki-STEM |
Number form-Neural mechanisms-It has been suggested that number-forms are a result of cross-activation between regions of the parietal lobe that are involved in numerical cognition and angular gyrus for spatial cognition. Since the areas that process numerical and spatial representations are close to each other, this m... | milkshake721/2.1M-wiki-STEM |
Number form-Reaction time research-Reaction time studies have shown that number-form synesthetes are faster to say which of two numbers is larger when the numbers are arranged in a manner consistent with their number-form, suggesting that number forms are automatically evoked. This can be thought of as a spatial Stroop... | milkshake721/2.1M-wiki-STEM |
Number form-Differences with number line-These number forms can be distinguished from the non-conscious mental number lines by the fact that they are conscious, idiosyncratic and stable across the person's lifespan. Although this form of synesthesia has not been as intensively studied as grapheme–color synesthesia, Hub... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Forbidden subgraph problem-In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G , find the maximal number of edges ex (n,G) an n -vertex graph can have such that it does not have a subgraph isomorphic to G . In this context, G is called a fo... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Definitions-The extremal number ex (n,G) is the maximum number of edges in an n -vertex graph containing no subgraph isomorphic to G . Kr is the complete graph on r vertices. T(n,r) is the Turán graph: a complete r -partite graph on n vertices, with vertices distributed between parts... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Upper bounds-Turán's theorem Turán's theorem states that for positive integers n,r satisfying n≥r≥3 , ex {\textstyle \operatorname {ex} (n,K_{r})=\left(1-{\frac {1}{r-1}}\right){\frac {n^{2}}{2}}.} This solves the forbidden subgraph problem for G=Kr . Equality cases for Turán's theorem co... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Upper bounds-Erdős–Stone theorem Erdős–Stone theorem states that for all positive integers n and all graphs G , ex {\textstyle \operatorname {ex} (n,G)=\left(1-{\frac {1}{\chi (G)-1}}+o(1)\right){\binom {n}{2}}.} When G is not bipartite, this gives us a first-order approximation of ex (... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Upper bounds-Progress on the Zarankiewicz problem includes following theorem: Kővári–Sós–Turán theorem. For every pair of positive integers s,t with t≥s≥1 , there exists some constant C (independent of n ) such that ex {\textstyle \operatorname {ex} (n,K_{s,t})\leq Cn^{2-{\frac {1}{s}}}}... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Upper bounds-Theorem (Bondy and Simonovits, 1974). There exists some constant C such that ex {\textstyle \operatorname {ex} (n,C_{2k})\leq Cn^{1+{\frac {1}{k}}}} for every positive integer n and positive integer k≥2 .A powerful lemma in extremal graph theory is dependent random choice. Th... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-There are various techniques used for obtaining the lower bounds. | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-Probabilistic method While this method mostly gives weak bounds, the theory of random graphs is a rapidly developing subject. It is based on the idea that if we take a graph randomly with a sufficiently small density, the graph would contain only a small number of subgraphs of G... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-This method can also be used to find the constructions of a graph for bounds on the girth of the graph. The girth, denoted by g(G) , is the length of the shortest cycle of the graph. Note that for g(G)>2k , the graph must forbid all the cycles with length less than equal to 2k... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-Algebraic constructions For specific cases, improvements have been made by finding algebraic constructions. A common feature for such constructions is that it involves the use of geometry to construct a graph, with vertices representing geometric objects and edges according to th... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-, demonstrates the power of this method. | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-First, suppose that n=p2−1 for some prime p . Consider the polarity graph G with vertices elements of Fp2−{0,0} and edges between vertices (x,y) and (a,b) if and only if ax+by=1 in Fp . This graph is K2,2 -free because a system of two linear equations in Fp cannot have ... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-Proof outline. Like in the previous theorem, we can take n=p3 for prime p and let the vertices of our graph be elements of Fp3 . This time, vertices (a,b,c) and (x,y,z) are connected if and only if (x−a)2+(y−b)2+(z−c)2=u in Fp , for some specifically chosen u . Then this ... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-Randomized Algebraic constructions This technique combines the above two ideas. It uses random polynomial type relations when defining the incidences between vertices, which are in some algebraic set. Using this technique to prove the following theorem. | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Lower bounds-Theorem: For every s≥2 , there exists some t such that ex (n,Ks,t)≥(12−o(1))n1−1s Proof outline: We take the largest prime power q with qs≤n . Due to the prime gaps, we have q=(1−o(1))n1s . Let f∈Fq[x1,x2,⋯,xs,y1,y2,⋯,ys]≤d be a random polynomial in Fq with degree at mos... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Supersaturation-Supersaturation refers to a variant of the forbidden subgraph problem, where we consider when some h -uniform graph G contains many copies of some forbidden subgraph H . Intuitively, one would expect this to once G contains significantly more than ex (n,H) edges. We intr... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Supersaturation-It is true that ex (n,G)(nh) is in fact positive and monotone decreasing, so the limit must therefore exist. As an example, Turán's Theorem gives that π(Kr+1)=1−1r , and the Erdős–Stone theorem gives that π(G)=1−1χ(H)−1 . In particular, for bipartite G , π(G)=0 . Determ... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Supersaturation-Supersaturation Theorem Consider an h -uniform hypergraph H with v vertices. The supersaturation theorem states that for every ϵ>0 , there exists a δ>0 such that if G is a graph on n vertices and at least (π(H)+ϵ)(n2) edges for n sufficiently large, then there are at ... | milkshake721/2.1M-wiki-STEM |
Forbidden subgraph problem-Generalizations-The problem may be generalized for a set of forbidden subgraphs S : find the maximal number of edges in an n -vertex graph which does not have a subgraph isomorphic to any graph from S .There are also hypergraph versions of forbidden subgraph problems that are much more dif... | milkshake721/2.1M-wiki-STEM |
JANUS clinical trial data repository-JANUS clinical trial data repository-Janus clinical trial data repository is a clinical trial data repository (or data warehouse) standard as sanctioned by the U.S. Food and Drug Administration (FDA). It was named for the Roman god Janus (mythology), who had two faces, one that coul... | milkshake721/2.1M-wiki-STEM |
JANUS clinical trial data repository-JANUS clinical trial data repository-The Janus data model is a relational database model, and is based on SDTM as a standard, in terms of many of its basic concepts such as the loading and storing of findings, events, interventions and inclusion data. However, Janus itself is a data... | milkshake721/2.1M-wiki-STEM |
JANUS clinical trial data repository-JANUS clinical trial data repository-The goals of Janus are as follows: To create an integrated data platform for most commercial tools for review, analysis and reporting Reduce the overall cost of existing information gathering and submissions development processes as well as revie... | milkshake721/2.1M-wiki-STEM |
JANUS clinical trial data repository-JANUS clinical trial data repository-Provides central access to standardized data, and provide common data views across collaborative partners.
Support cross-trial analyses for data mining and help detect clinical trends and address clinical hypotheses, and perform more advanced, ro... | milkshake721/2.1M-wiki-STEM |
TTC3P1-TTC3P1-Tetratricopeptide repeat domain 3 pseudogene 1 is a protein that in humans is encoded by the TTC3P1 gene. | milkshake721/2.1M-wiki-STEM |
TTC3P1-Aliases for TTC3P1 Gene-GeneCards Symbol: TTC3P1 2 Tetratricopeptide Repeat Domain 3 Pseudogene 1 2 3 5 RNF105L 2 3 5 TTC3L 3 5 Tetratricopeptide Repeat Domain 3-Like 2 External Ids for TTC3P1 Gene HGNC: 23318 NCBI Entrez Gene: 286495 Ensembl: ENSG00000215105 Previous HGNC Symbols for TTC3P1 Gene TTC3L Previous ... | milkshake721/2.1M-wiki-STEM |
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