Monday 25 June 2012

Genius Maker

Features of Matrix Algebra Software:


The Matrix algebra is a mathematics software for performing algebraic operations on matrix. Assume 2 matrices namely A and B are given. This software facilitates to do operations such as Matrix addition, Matrix subtraction and Matrix multiplication of any order not exceeding 4 x 4. The multiplication support available for both scalar multiplication and vector multiplication. The typical operations, which a user can perform are as given below.
2A  +  5B
23A - 34B
6A   x  5B

Matrix algebra software interface


How to start with Matrix Algebra software ?

  • Open Genius Maker software and click "Matrix algebra" button. It opens the Matrix algebra window as shown above.
  • It automatically shows a mathematical equation in the equation box and numbers in the matrix boxes A and B. These numbers are provided to assist you to quick start Matrix algebra software. You may clear that data by pressing the "Clear data" button and enter a  fresh set of values whenever needed. Similarly you may change the equation also from the top panel.
EXAMPLE - 1
  • Let us take an example.
  • Set the equation as 1A + 2B
  • Define the size of the Matrix-A as 3 x 2
  • You may see that the size of Matrix-A changes accordingly.
  • Click the "Clear data" button of Matrix - A
  • Now enter the values of Matrix - A as below.
    5        6
    3        2
    2        1
  • Define the size of the Matrix-B as 3 x 2
  • You may see that the size of Matrix-B changes accordingly.
  • Click the "Clear data" button of Matrix - B
  • Now enter the values of Matrix - B as below.
    3        5
    1        4
    4        2
  • Click "Evaluate" button on the equation box.
  • You may see that the result appears in the resultant matrix box. 
EXAMPLE - 2
  • Now let us try an example for matrix multiplication.
  • Set the equation as 3A x 4B
  • Let us keep the Matrix - A of the previous example same.
  • Define the size of the Matrix-B as 2 x 4
  • You may see that the size of Matrix-B changes accordingly.
  • Click the "Clear data" button of Matrix - B
  • Now enter the values of Matrix - B as below.
    2        1        5        7
    4        6        3        2
  • Click "Evaluate" button on the equation box.
  • You may see that the result appears in the resultant matrix box as a 3 x 4 matrix.
  • Now you may try with different equations, different matrix sizes and values for matrices. The maximum supported size of a row or a column is 4.

 

Additional Features :

  • Copying a matrix: Whenever you need to copy any matrix to another one, make use of the "copy" and "paste" buttons suitably. For example, if you want to do some operations on the resultant matrix, which is currently displayed, then press the "copy" button on the resultant matrix box and then click "paste" button of either Matrix - A or Matrix - B based on your need. Similarly you can copy any of the 3 matrix to any other 2 matrices. An exception is that you cannot paste a matrix on to the resultant matrix box.

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Marfans syndrome

Marfan syndrome (also called Marfan's syndrome) is a genetic disorder of the connective tissue. People with Marfan's tend to be unusually tall, with long limbs and long, thin fingers.

The syndrome is inherited as a dominant trait, carried by the gene FBN1, which encodes the connective protein fibrillin-1.[1][2] People have a pair of FBN1 genes. Because it is dominant, people who have inherited one affected FBN1 gene from either parent will have Marfan syndrome.

Marfan syndrome has a range of expressions, from mild to severe. The most serious complications are defects of the heart valves and aorta. It may also affect the lungs, the eyes, the dural sac surrounding the spinal cord, the skeleton and the hard palate.

In addition to being a connective protein that forms the structural support for tissues outside the cell, the normal fibrillin-1 protein binds to another protein, transforming growth factor beta (TGF-β).[2] TGF-β has deleterious effects on vascular smooth muscle development and the integrity of the extracellular matrix. Researchers now believe, secondary to mutated fibrillin, excessive TGF-β at the lungs, heart valves, and aorta weakens the tissues and causes the features of Marfan syndrome.[3] Since angiotensin II receptor antagonists (ARBs) also reduce TGF-β, ARBs (losartan, etc.) have been tested in a small sample of young, severely affected Marfan syndrome patients. In some patients, the growth of the aorta was indeed reduced.[4]

Marfan syndrome is named after Antoine Marfan,[5] the French pediatrician who first described the condition in 1896.[6][7] The gene linked to the disease was first identified by Francesco Ramirez in 1991.[8]

Signs and symptoms

The constellation of long limbs, dislocated lenses and the aortic root dilation are generally sufficient to make the diagnosis of Marfan syndrome with reasonable confidence. More than 30 other clinical features are variably associated with the syndrome, most involving the skeleton, skin, and joints. Considerable clinical variability occurs within families carrying the identical mutation.

Skeletal system

Most of the readily visible signs are associated with the skeletal system. Many individuals with Marfan syndrome grow to above-average height. Some have long, slender limbs (dolichostenomelia) with long fingers and toes (arachnodactyly). An individual's arms may be disproportionately long, with thin, weak wrists. In addition to affecting height and limb proportions, Marfan syndrome can produce other skeletal anomalies. Abnormal curvature of the spine (scoliosis), abnormal indentation (pectus excavatum) or protrusion (pectus carinatum) of the sternum are not uncommon. Other signs include abnormal joint flexibility, a high palate, malocclusions, flat feet, hammer toes, stooped shoulders, and unexplained stretch marks on the skin. It can also cause pain in the joints, bones and muscles in some patients. Some people with Marfan have speech disorders resulting from symptomatic high palates and small jaws. Early osteoarthritis may occur.

Eyes

Lens dislocation in Marfan's syndrome; the lens was kidney-shaped and was resting against the ciliary body.
Marfan syndrome can also seriously affect the eyes and vision. Nearsightedness and astigmatism are common, but farsightedness can also result. Subluxation (dislocation) of the crystalline lens in one or both eyes (ectopia lentis) (in 80% of patients) also occurs and may be detected by an ophthalmologist or optometrist using a slit-lamp biomicroscope. In Marfan's the dislocation is typically superotemporal whereas in the similar condition homocystinuria, the dislocation is inferonasal. Sometimes eye problems appear only after the weakening of connective tissue has caused detachment of the retina.[9] Early onset glaucoma can be another related problem.

Cardiovascular system

The most serious signs and symptoms associated with Marfan syndrome involve the cardiovascular system: undue fatigue, shortness of breath, heart palpitations, racing heartbeats, or angina pectoris with pain radiating to the back, shoulder, or arm. Cold arms, hands and feet can also be linked to Marfan's syndrome because of inadequate circulation. A heart murmur, abnormal reading on an ECG, or symptoms of angina can indicate further investigation. The signs of regurgitation from prolapse of the mitral or aortic valves (which control the flow of blood through the heart) result from cystic medial degeneration of the valves, which is commonly associated with Marfan's syndrome (see mitral valve prolapse, aortic regurgitation). However, the major sign that would lead a doctor to consider an underlying condition is a dilated aorta or an aortic aneurysm. Sometimes, no heart problems are apparent until the weakening of the connective tissue (cystic medial degeneration) in the ascending aorta causes an aortic aneurysm or aortic dissection, a surgical emergency. An aortic dissection is most often fatal and presents with pain radiating down the back, giving a tearing sensation.
Because underlying connective tissue abnormalities cause Marfan syndrome, there is an increased incidence of dehiscence of prosthetic mitral valve.[10] Care should be taken to attempt repair of damaged heart valves rather than replacement.
During pregnancy, even in the absence of preconception cardiovascular abnormality, women with Marfan syndrome are at significant risk of aortic dissection, which is often fatal even when rapidly treated. Women with Marfan syndrome, then, should receive a thorough assessment prior to conception, and echocardiography should be performed every six to 10 weeks during pregnancy, to assess the aortic root diameter. For most women, safe vaginal delivery is possible.[11]

Lungs

Marfan syndrome is a risk factor for spontaneous pneumothorax. In spontaneous unilateral pneumothorax, air escapes from a lung and occupies the pleural space between the chest wall and a lung. The lung becomes partially compressed or collapsed. This can cause pain, shortness of breath, cyanosis, and, if not treated, it can cause death. It has also been associated with sleep apnea and idiopathic obstructive lung disease.

Central nervous system

Dural ectasia, the weakening of the connective tissue of the dural sac encasing the spinal cord, though not life-threatening, can reduce the quality of life for an individual. It can be present for a long time without producing any noticeable symptoms. Symptoms that can occur are lower back pain, leg pain, abdominal pain, other neurological symptoms in the lower extremities, or headaches. Such symptoms usually diminish when the individual lies flat on his or her back. These types of symptoms might lead a doctor to order an X-ray of the lower spine. Dural ectasia is usually not visible on an X-ray in the early phases. A worsening of symptoms and the lack of finding any other cause should eventually lead a doctor to order an upright MRI of the lower spine. Dural ectasia that has progressed to the point of causing these symptoms would appear in an upright MRI image as a dilated pouch wearing away at the lumbar vertebrae.[9] Other spinal issues associated with Marfan syndrome include degenerative disk disease, spinal cysts and dysautonomia.

Pathogenesis

Marfan syndrome is caused by mutations in the FBN1 gene on chromosome 15,[12] which encodes the glycoprotein fibrillin-1, a component of the extracellular matrix. Fibrillin-1 protein is essential for the proper formation of the extracellular matrix, including the biogenesis and maintenance of elastic fibers. The extracellular matrix is critical for both the structural integrity of connective tissue, but also serves as a reservoir for growth factors.[13] Elastin fibers are found throughout the body, but are particularly abundant in the aorta, ligaments and the ciliary zonules of the eye; consequently, these areas are among the worst affected.
A transgenic mouse has been created carrying a single copy of a mutant fibrillin-1, a mutation similar to that found in the human gene known to cause Marfan syndrome. This mouse strain recapitulates many of the features of the human disease and promises to provide insights into the pathogenesis of the disease. Reducing the level of normal fibrillin 1 causes a Marfan-related disease in mice.[14]
Transforming growth factor beta (TGFβ) plays an important role in Marfan syndrome. Fibrillin-1 directly binds a latent form of TGFβ, keeping it sequestered and unable to exert its biological activity. The simplest model of Marfan syndrome suggests reduced levels of fibrillin-1 allow TGFβ levels to rise due to inadequate sequestration. Although it is not proven how elevated TGFβ levels are responsible for the specific pathology seen with the disease, an inflammatory reaction releasing proteases that slowly degrade the elastin fibers and other components of the extracellular matrix is known to occur. The importance of the TGFβ pathway was confirmed with the discovery of the similar Loeys-Dietz syndrome involving the TGFβR2 gene on chromosome 3, a receptor protein of TGFβ.[15] Marfan syndrome has often been confused with Loeys-Dietz syndrome, because of the considerable clinical overlap between the two pathologies.[16]