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Question: What are the symptoms of alpha thalassemia major?

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Context 1: Thalassaemia minor | definition of Thalassaemia minor by Medical dictionary
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Thalassemia describes a group of inherited disorders characterized by reduced or absent amounts of hemoglobin, the oxygen-carrying protein inside the red blood cells  There are two basic groups of thalassemia disorders: alpha thalassemia and beta thalassemia  These conditions cause varying degrees of anemia, which can range from insignificant to life threatening 
All types of thalassemias are considered quantitative diseases of hemoglobin, because the quantity of hemoglobin produced is reduced or absent  Usual adult hemoglobin is made up of three components: alpha globin, beta globin, and heme  Thalassemias are classified according to the globin that is affected, hence the names alpha and beta thalassemia  Although both classes of thalassemia affect the same protein, the alpha and beta thalassemias are distinct diseases that affect the body in different ways 
Beta thalassemia may be the most best-known type of thalassemia and is also called Cooley's anemia  It is caused by a change in the gene for the beta globin component of hemoglobin  Beta thalassemia causes variable anemia that can range from moderate to severe, depending in part on the exact genetic change underlying the disease  Beta thalassemia can be classified based on clinical symptoms  Beta thalassemia major usually causes severe anemia that can occur within months after birth  If left untreated, severe anemia can result in insufficient growth and development, as well as other common physical complications that can lead to a dramatically decreased life-expectancy  Fortunately, in developed countries beta thalassemia is usually identified by screening in the newborn period, before symptoms have developed  Children who are identified early can be started on ongoing blood transfusion therapy as needed  Although transfusion therapy prevents many of the complications of severe anemia, the body is unable to eliminate the excess iron contained in the transfused blood  Over time, the excess iron deposits in tissues and organs, resulting in damage and organ failure  Another medication must be administered to help the body eliminate the excess iron and prevent iron-over-load complications  Beta thalassemia intermedia describes the disease in individuals who have moderate anemia that only requires blood transfusions intermittently, if at all 
Alpha thalassemia is the result of changes in the genes for the alpha globin component of hemoglobin  There are two main types of alpha thalassemia disease: hemoglobin H disease and alpha thalassemia major  The two diseases are quite different from beta thalassemia as well as from one another  Individuals with hemoglobin H disease can experience events of hemolytic anemia—anemia caused by the rapid breakdown of the red blood cells  These events are thought to be triggered by various environmental causes, such as infection and/or exposure to certain chemicals  Hemoglobin H disease is in most cases milder than beta thalassemia  It does not generally require transfusion therapy  Alpha thalassemia major is a very serious disease that results in severe anemia that begins even before birth  Most affected babies do not survive to be born or die shortly after birth 
The thalassemias are among the most common genetic diseases worldwide  Both alpha and beta thalassemia have been described in individuals of almost every ancestry, but the conditions are more common among certain ethnic groups  Unaffected carriers of all types of thalassemia traits do not experience health problems  In fact, the thalassemia trait is protective against malaria, a disease caused by blood-borne parasites transmitted through mosquito bites  According to a widely accepted theory, most genetic changes—mutations—that cause thalassemia occurred multiple generations ago  Coincidentally, these mutations increased the likelihood that carriers would survive malaria infection  Survivors passed the mutation onto their offspring, and the trait became established throughout areas where malaria is common  As populations migrated, so did the thalassemia traits 
Beta thalassemia trait is seen most commonly in people with the following ancestry: Mediterranean (including North African, and particularly Italian and Greek), Middle Eastern, Indian, African, Chinese, and Southeast Asian (including Vietnamese, Laotian, Thai, Singaporean, Filipino, Cambodian, Malaysian, Burmese, and Indonesian)  Alpha-thalassemia trait is seen with increased frequency in the same ethnic groups  However, there are different types of alpha thalassemia traits within these populations  The frequency of hemoglobin H disease and alpha thalassemia major depends on the type of alpha thalassemia trait  The populations in which alpha thalassemia diseases are most common include Southeast Asians and Chinese (particularly Southern Chinese) 
It is difficult to obtain accurate prevalence figures for various types of thalassemia within different populations  This difficulty arises due to testing limitations in determining exact genetic diagnoses, as well as the fact that many studies have focused on small, biased hospital populations 
Two studies reflect prevalence figures that can be helpful counseling families and determining who to screen for beta thalassemia  Between the years of 1990 and 1996, the State of California screened more than 3 1 million infants born in the state for beta thalassemia  Approximately 1 in 114,000 infants had beta thalassemia major, with prevalence rates being highest among Asian Indians (about one in 4,000), Southeast Asians (about one in 10,000), and Middle Easterners (about one in 7,000)  Another type of beta thalassemia disease, E/beta thalassemia, was represented in approximately one in 110,000 births, all of which occurred in families of Southeast Asian ancestry  Among Southeast Asians, the prevalence of E/beta thalassemia was approximately one in 2,600 births  This is in keeping with the observation that hemoglobin E trait carrier rates are relatively high within the Southeast Asian population: 16% in a study of 768 immigrants to California, and up to 25% in some specific Southeast Asian populations such as Cambodians  While these California studies address some of the limitations of earlier population studies, the pattern observed in California is expected to be different in other areas of the United States and the world  For example, Italians are underrepresented in this population when compared to the population of the East Coast of the United States 
Determining prevalence figures for alpha thalassemia is even more difficult due to increased limitations in diagnostic testing  All types of alpha thalassemia disease are most common among people of Southeast Asian and Chinese descent, for reasons that become clearer with an understanding of the underlying genetics of alpha thalassemia  One study of 500 pregnant women in Northern Thailand estimated a frequency of one in 500 pregnancies affected by alpha thalassemia major, for example  Prevalence of alpha thalassemia disease is significantly lower in the United States primarily because of immigration patterns; although at least one state, California, has observed growing hemoglobin H disease incidence rates that are high enough to justify universal newborn screening for the condition 
Humans normally make several types of the oxygen-carrying protein hemoglobin  An individual's stage in development determines whether he or she makes primarily embryonic, fetal, or adult hemoglobins  All types of hemoglobin are made of three components: heme, alpha (or alpha-like) globin, and beta (or beta-like) globin  All types of thalassemia are caused by changes in either the alpha- or beta-globin gene  These changes cause little or no globin to be produced  The thalassemias are, therefore, considered quantitative hemoglobin diseases  All types of thalassemias are recessively inherited, meaning that a genetic change must be inherited from both the mother and the father  The severity of the disease is influenced by the exact thalassemia mutations inherited, as well as other genetic and environmental factors  There are rare exceptions, notably with beta thalassemia, where globin gene mutations exhibit a dominant pattern of inheritance in which only one gene needs to be altered in order to see disease expression  Scientists continue to study the causes  For instance, a new mutation for alpha-thalassemia was discovered for the first time among Iranian patients in 2004 
BETA-THALASSEMIA  Most individuals have two normal copies of the beta globin gene, which is located on chromosome 11 and makes the beta globin component of normal adult hemoglobin, hemoglobin A  There are approximately 100 genetic mutations that have been described that cause beta thalassemia, designated as either beta0 or beta + mutations  No beta globin is produced with a beta0 mutation, and only a small fraction of the normal amount of beta globin is produced with a beta + mutation 
When an individual has one normal beta globin gene and one with a beta thalassemia mutation, he or she is said to carry the beta thalassemia trait  Beta thalassemia trait, like other hemoglobin traits, is protective against malaria infection  Trait status is generally thought not to cause health problems, although some women with beta thalassemia trait may have an increased tendency toward anemia during pregnancy 
When two members of a couple carry the beta thalassemia trait, there is a 25% chance that each of their children will inherit beta thalassemia disease by inheriting two beta thalassemia mutations, one from each parent  The clinical severity of the beta thalassemia disease—whether an individual has beta thalassemia intermedia or beta thalassemia major—will depend largely on whether the mutations inherited are beta0 thalassemia or beta + thalassemia mutations  Two beta0 mutations generally lead to beta thalassemia major, and two beta+ thalassemia mutations generally lead to beta thalassemia intermedia  Inheritance of one beta0 and one beta + thalassemia mutation tends to be less predictable 
Although relatively uncommon, there are other thalassemia-like mutations that can affect the beta globin gene  Hemoglobin E is the result of a substitution of a single nucleotide  This change results in a structurally altered hemoglobin that is produced in decreased amounts  Therefore, hemoglobin E is unique in that it is both a quantitative (i e  thalassemia-like) and qualitative trait  When co-inherited with a beta thalassemia trait, it causes a disease that is almost indistinguishable from beta thalassemia disease  Large deletions around and including the beta globin gene can lead to delta/beta thalassemia or hereditary persistence of fetal hemoglobin (HPFH)  Interestingly, delta/beta thalassemia trait behaves very similarly to beta thalassemia trait in its clinical manifestations  However, HPFH trait does not tend to cause hemoglobin disease when co-inherited with a second thalassemia or other beta globin mutation 
ALPHA-THALASSEMIA  Most individuals have four normal copies of the alpha globin gene, two copies on each chromosome 16  These genes make the alpha globin component of normal adult hemoglobin, which is called hemoglobin A  Alpha globin is also a component of fetal hemoglobin and the other major adult hemoglobin called hemoglobin A2  Mutations of the alpha globin genes are usually deletions of the gene, resulting in absent production of alpha globin  Since there are four genes (instead of the usual two) to consider when looking at alpha globin gene inheritance, there are several alpha globin types that are possible 
Absence of one alpha globin gene leads to a condition known as silent alpha thalassemia trait  This condition causes no health problems and can be detected only by special genetic testing  Alpha thalassemia trait occurs when two alpha globin genes are missing  This can occur in two ways  The genes may be deleted from the same chromosome, causing the 'cis' type of alpha thalassemia trait  Alternately, they may be deleted from different chromosomes, causing the 'trans' type of alpha thalassemia trait  In both instances, there are no associated health problems, although the trait status may be detected by more routine blood screening 
Hemoglobin H disease results from the deletion of three alpha globin genes, such that there is only one functioning gene  Typically, this can occur when one parent carries the silent alpha thalassemia trait, and the other parent carries the 'cis' type of the alpha thalassemia trait  In this situation, there is a 25% chance for hemoglobin H disease in each of such a couple's children 
Hemoglobin H disease-like symptoms can also be a part of a unique condition called alpha thalassemia mental retardation syndrome  Alpha thalassemia mental retardation syndrome can be caused by a deletion of a significant amount of chromosome 16, affecting the alpha globin genes  This is usually not inherited, but rather occurs sporadically in the affected individual  Affected individuals have mild hemoglobin H disease, mild-to-moderate mental retardation, and characteristic facial features  This syndrome can also occur as a sex-linked form in which a mutation is inherited in a particular gene on the X-chromosome  This gene influences alpha globin production, as well as various other developmental processes  Individuals affected with this form of the syndrome tend to have more severe mental retardation, delayed development, nearly absent speech, characteristic facial features, and genital-urinary abnormalities  The remaining discussion will focus only on aspects of hemoglobin H disease 
Alpha thalassemia major results from the deletion of all four alpha globin genes, such that there are no functioning alpha globin genes  This can occur when both parents carry the 'cis' type of the alpha thalassemia trait  In this situation, there is a 25% chance for alpha thalassemia major in each of such a couple's children 
Beta thalassemia major is characterized by severe anemia that can begin months after birth  In the United States and other developed countries beta thalassemia is identified and treated early and effectively  Therefore, the following discussion of symptoms applies primarily to affected individuals in the past and unfortunately in some underdeveloped countries now  If untreated, beta thalassemia major can lead to severe lethargy, paleness, and delays in growth and development  The body attempts to compensate by producing more blood, which is made inside the bones in the marrow  However, this is ineffective without the needed genetic instructions to make enough functioning hemoglobin  Instead, obvious bone expansion and changes occur that cause characteristic facial and other changes in appearance, as well as increased risk of fractures  Severe anemia taxes other organs in the body—such as the heart, spleen, and liver—which must work harder than usual  This can lead to heart failure, as well as enlargement and other problems of the liver and spleen  When untreated, beta thalassemia major generally results in childhood death, usually due to heart failure  In 2004, the first known heart attack associated with beta thalassemia major was reported  Fortunately, in developed countries diagnosis is usually made early, often before symptoms have begun  This allows for treatment with blood transfusion therapy, which can prevent most of the complications of the severe anemia caused by beta thalassemia major  Individuals with beta thalassemia intermedia have a more moderate anemia that may only require treatment with transfusion intermittently, such as when infections occur and stress the body  As a person with beta thalassemia intermedia gets older, however, the need for blood transfusions may increase to the point that they are required on a regular basis  When this occurs their disease becomes more similar to beta thalassemia major  Other genetic and environmental factors can influence the course of the disease as well  For example, co-inheritance of one or two alpha thalassemia mutations can tend to ameliorate some of the symptoms of beta thalassemia disease, which result in part from an imbalance in the amount of alpha- and beta-globin present in the red blood cells 
Hemoglobin h disease
Absence of three alpha globin genes causes an imbalance of alpha and beta globin proteins in the red blood cells  The excess beta globin proteins tend to come together to form hemoglobin H, which is unable to release oxygen to the tissues  In addition, hemoglobin H tends to precipitate out in the cells, causing damage to the red blood cell membrane  When affected individuals are exposed to certain drugs and chemicals known to make the membrane more fragile, the cells are thought to become vulnerable to breakdown in large numbers, a complication called hemolytic anemia  Fever and infection are also considered to be triggers of hemolytic anemia in hemoglobin H disease  This can result in fatigue, paleness, and a yellow discoloration of the skin and whites of eyes called jaundice  Usually, the anemia is mild enough not to require treatment  Severe anemia events may require blood transfusion, however, and are usually accompanied by such other symptoms as dark feces or urine and abdominal or back pain  These events are uncommon in hemoglobin H disease, although they occur more frequently in a more serious type of hemoglobin H disease called hemoglobin H/Constant Spring disease  Individuals effected with this type of hemoglobin H disease are also more likely to have enlargement of and other problems with the spleen 
Alpha thalassemia major
Because alpha globin is a necessary component of all major hemoglobins and some minor hemoglobins, absence of all functioning alpha globin genes leads to serious medical consequences that begin even before birth  Affected fetuses develop severe anemia as early as the first trimester of pregnancy  The placenta, heart, liver, spleen, and adrenal glands may all become enlarged  Fluid can begin collecting throughout the body as early as the start of the second trimester, causing damage to developing tissues and organs  Growth retardation is also common  Affected fetuses usually miscarry or die shortly after birth  In addition, women carrying affected fetuses are at increased risk of developing complications of pregnancy and delivery  Up to 80% of such women develop toxemia, a disturbance of metabolism that can potentially lead to convulsions and coma  Other maternal complications include premature delivery and increased rates of delivery by cesarean section, as well as hemorrhage after delivery 
Thalassemia may be suspected if an individual shows signs that are suggestive of the disease  In all cases, however, laboratory diagnosis is essential to confirm the exact diagnosis and to allow for the provision of accurate genetic counseling about recurrence risks and testing options for parents and affected individuals  Screening is likewise recommended to determine trait status for individuals of high-risk ethnic groups 
The following tests are used to screen for thalassemia disease and/or trait:
hemoglobin electrophoresis with quantitative hemoglobin A2 and hemoglobin F
free erythrocyte-protoporphyrin (or ferritin or other studies of serum iron levels)
A complete blood count will identify low levels of hemoglobin, small red blood cells, and other red blood cell abnormalities that are characteristic of a thalassemia diagnosis  Since thalassemia trait can sometimes be difficult to distinguish from iron deficiency, tests to evaluate iron levels are important  A hemoglobin electrophoresis is a test that can help identify the types and quantities of hemoglobin made by an individual  This test uses an electric field applied across a slab of gel-like material  Hemoglobins migrate through this gel at various rates and to specific locations, depending on their size, shape, and electrical charge  Isoelectric focusing and high-performance liquid chromatography (HPLC) use similar principles to separate hemoglobins and can be used instead of or in various combinations with hemoglobin electrophoresis to determine the types and quantities of hemoglobin present  Hemoglobin electrophoresis results are usually within the normal range for all types of alpha thalassemia  However, hemoglobin A2 levels and sometimes hemoglobin F levels are elevated when beta thalassemia disease or trait is present  Hemoglobin electrophoresis can also detect structurally abnormal hemoglobins that may be co-inherited with a thalassemia trait to cause thalassemia disease (i e , hemoglobin E) or other types of hemoglobin disease (i e , sickle hemoglobin)  Sometimes DNA testing is needed in addition to the above screening tests  This can be performed to help confirm the diagnosis and establish the exact genetic type of thalassemia 
Diagnosis of thalassemia can occur under various circumstances and at various ages  Several states offer thalassemia screening as part of the usual battery of blood tests done for newborns  This allows for early identification and treatment  Thalassemia can be identified before birth through the use of prenatal diagnosis  Chorionic villus sampling (CVS) can be offered as early as 10 weeks of pregnancy and involves removing a sample of the placenta made by the baby and testing the cells  CVS carries a risk of causing a miscarriage that is between 0 5%-1%  Amniocentesis is generally offered between 15 and 22 weeks of pregnancy, but can sometimes be offered earlier  Two to three tablespoons of the fluid surrounding the baby is removed  This fluid contains fetal cells that can be tested  The risk of miscarriage associated with amniocentesis ranges from 0 33-0 5%  Pregnant woman and couples may choose prenatal testing in order to prepare for the birth of a baby that may have thalassemia  Alternately, knowing the diagnosis during pregnancy allows for the option of pregnancy termination  Preimplantation genetic diagnosis (PGD) is a relatively new technique that involves in-vitro fertilization followed by genetic testing of one cell from each developing embryo  Only the embryos unaffected by sickle cell disease are transferred back into the uterus  PGD is currently available on a research basis only and is relatively expensive 
Individuals with beta thalassemia major receive regular blood transfusions, usually on a monthly basis  This helps prevent severe anemia and allows for more normal growth and development  Transfusion therapy does have limitations, however  Individuals can develop reactions to certain proteins in the blood—called a transfusion reaction  This can make locating appropriately matched donor blood more difficult  Although blood supplies in the United States are very safe, particularly relative to the past and to other areas of the world, there remains an increased risk of exposure to such blood-borne infections as hepatitis  Additionally, the body is not able to get rid of the excess iron that accompanies each transfusion  An additional medication called desferoxamine is administered, usually five nights per week over a period of several hours, using an automatic pump that can be used during sleep or taken anywhere the person goes  This medication is able to bind to the excess iron, which can then be eliminated through urine  If desferoxamine is not used regularly or is unavailable, iron overload can develop and cause tissue damage and organ damage and failure  The heart, liver, and endocrine organs are particularly vulnerable  Desferoxamine itself may rarely produce allergic or toxic side effects, including hearing damage  Signs of desferoxamine toxicity are screened for and generally develop in individuals who overuse the medication when body iron levels are sufficiently low  Overall, however, transfusion and desferoxamine therapy have increased the life expectancy of individuals with the most severe types of beta thalassemia major to the 4th or 5th decade  This can be expected to improve with time and increased developments in treatment, as well as for those with more mild forms of the disease 
New treatments offer additional options for some individuals with beta thalassemia major  There are various medications that target the production of red blood cells (i e  erythropoeitin) or fetal hemoglobin (i e  hydroxyurea and butyrate)  Their effectiveness in ameliorating the severity of beta thalassemia is currently being investigated  Another promising new treatment is bone marrow transplantation, in which the bone marrow of an affected individual is replaced with the bone marrow of an unaffected donor  If successful, this treatment can provide a cure  However, there is an approximately 10-15% chance the procedure could be unsuccessful (i e  the thalassemia returns); result in complications (i e  graft-versus-host disease); or result in death  The risk for specific individuals depends on current health status, age, and other factors  Because of the risks involved and the fact that beta thalassemia is a treatable condition, transplant physicians require a brother or sister donor who has an identically matched tissue type, called HLA type  HLA type refers to the unique set of proteins present on each individual's cells, which allows the immune system to recognize "self" from "foreign " HLA type is genetically determined, so there is a 25% chance for two siblings to be a match  Transplant physicians and researchers are also investigating ways to improve the safety and effectiveness of bone marrow transplantation  Using newborn sibling umbilical cord blood—the blood from the placenta that is otherwise discarded after birth but contains cells that can go on to make bone marrow—seems to provide a safer and perhaps more effective source of donor cells  Donors and recipients may not have to be perfect HLA matches for a successful transplant using cord blood cells  Trials are also underway to determine the effectiveness of "partial transplants," in which a safer transplant procedure is used to replace only a percentage of the affected individual's bone marrow  Other possible treatments on the horizon may include gene therapy techniques aimed at increasing the amount of normal hemoglobin the body is able to make 
Hemoglobin H disease is a relatively mild form of thalassemia that may go unrecognized  It is not generally considered a condition that will reduce one's life expectancy  Education is an important part of managing the health of an individual with hemoglobin H disease  It is important to be able to recognize the signs of severe anemia that require medical attention  It is also important to be aware of the medications, chemicals, and other exposures to avoid due to the theoretical risk they pose of causing a severe anemia event  When severe anemia occurs, it is treated with blood transfusion therapy  For individuals with hemoglobin H disease, this is rarely required  For those with the hemoglobin H/Constant Spring form of the disease, the need for transfusions may be intermittent or ongoing, perhaps on a monthly basis and requiring desferoxamine treatment  Individuals with this more severe form of the disease may also have an increased chance of requiring removal of an enlarged and/or overactive spleen 
Anemia — A blood condition in which the level of hemoglobin or the number of red blood cells falls below normal values  Common symptoms include paleness, fatigue, and shortness of breath 
Bilirubin — A yellow pigment that is the end result of hemoglobin breakdown  This pigment is metabolized in the liver and excreted from the body through the bile  Bloodstream levels are normally low; however, extensive red cell destruction leads to excessive bilirubin formation and jaundice 
Bone marrow — A spongy tissue located in the hollow centers of certain bones, such as the skull and hip bones  Bone marrow is the site of blood cell generation 
Bone marrow transplantation — A medical procedure used to treat some diseases that arise from defective blood cell formation in the bone marrow  Healthy bone marrow is extracted from a donor to replace the marrow in an ailing individual  Proteins on the surface of bone marrow cells must be identical or very closely matched between a donor and the recipient 
Desferoxamine — The primary drug used in iron chelation therapy  It aids in counteracting the life-threatening buildup of iron in the body associated with long-term blood transfusions 
Globin — One of the component protein molecules found in hemoglobin  Normal adult hemoglobin has a pair each of alpha-globin and beta-globin molecules 
Heme — The iron-containing molecule in hemoglobin that serves as the site for oxygen binding 
Hemoglobin — Protein-iron compound in the blood that carries oxygen to the cells and carries carbon dioxide away from the cells 
Hemoglobin A — Normal adult hemoglobin that contains a heme molecule, two alpha-globin molecules, and two beta-globin molecules 
Hemoglobin electrophoresis — A laboratory test that separates molecules based on their size, shape, or electrical charge 
Hepatomegaly — An abnormally large liver 
HLA type — Refers to the unique set of proteins called human leukocyte antigens  These proteins are present on each individual's cell and allow the immune system to recognize 'self' from 'foreign'  HLA type is particularly important in organ and tissue transplantation 
Hydroxyurea — A drug that has been shown to induce production of fetal hemoglobin  Fetal hemoglobin has a pair of gamma-globin molecules in place of the typical beta-globins of adult hemoglobin  Higher-than-normal levels of fetal hemoglobin can ameliorate some of the symptoms of thalassemia 
Iron overload — A side effect of frequent blood transfusions in which the body accumulates abnormally high levels of iron  Iron deposits can form in organs, particularly the heart, and cause life-threatening damage 
Jaundice — Yellowing of the skin or eyes due to excess of bilirubin in the blood 
Mutation — A permanent change in the genetic material that may alter a trait or characteristic of an individual, or manifest as disease, and can be transmitted to offspring 
Placenta — The organ responsible for oxygen and nutrition exchange between a pregnant mother and her developing baby 
Red blood cell — Hemoglobin-containing blood cells that transport oxygen from the lungs to tissues  In the tissues, the red blood cells exchange their oxygen for carbon dioxide, which is brought back to the lungs to be exhaled 
Screening — Process through which carriers of a trait may be identified within a population 
Splenomegaly — Enlargement of the spleen 
Because alpha thalassemia major is most often a condition that is fatal in the prenatal or newborn period, treatment has previously been focused on identifying affected pregnancies in order to provide appropriate management to reduce potential maternal complications  Pregnancy termination provides one form of management  Increased prenatal surveillance and early treatment of maternal complications is an approach that is appropriate for mothers who wish to continue their pregnancy with the knowledge that the baby will most likely not survive  In recent years, there have been a handful of infants with this condition who have survived long-term  Most of these infants received experimental treatment including transfusions before birth, early delivery, and even bone marrow transplantation before birth, although the latter procedure has not yet been successful  For those infants that survive to delivery, there seems to be an increased risk of developmental problems and physical effects, particularly heart and genital malformations  Otherwise, their medical outlook is similar to a child with beta thalassemia major, with the important exception that ongoing, life-long blood transfusions begin right at birth 
As discussed above, the prognosis for individuals with the most serious types of thalassemia has improved drastically in the last several years following recent medical advances in transfusion, chemo-, and transplantation therapy  Advances continue and promise to improve the life expectancy and quality of life further for affected individuals 
"First Known Heart Attack Associated With Beta-thalassemia Major Reported " Heart Disease Weekly February 22, 2004: 10 
"Novel Alpha-thalassemia Mutations Identified " Hematology Week January 26, 2004: 19 
Children's Blood Foundation  333 East 38th St , Room 830, New York, NY 10016-2745  (212) 297-4336  cfg@nyh med cornell edu 
Cooley's Anemia Foundation, Inc  129-09 26th Ave  #203, Flushing, NY 11354  (800) 522-7222 or (718) 321-2873  http://www thalassemia org 
March of Dimes Birth Defects Foundation  1275 Mamaroneck Ave , White Plains, NY 10605  (888) 663-4637  resourcecenter@modimes org  http://www modimes org 
National Heart, Lung, and Blood Institute  PO Box 30105, Bethseda, MD 20824-0105  (301) 592-8573  nhlbiinfo@rover nhlbi nih gov  http://www nhlbi nih gov 
National Organization for Rare Disorders (NORD)  PO Box 8923, New Fairfield, CT 06812-8923  (203) 746-6518 or (800) 999-6673  Fax: (203) 746-6481  http://www rarediseases org 
Bojanowski J  "Alpha Thalassemia Major: The Possibility of Long-Term Survival " Pamphlet from the Northern California Comprehensive Thalassemia Center  (1999) 
Children's Hospital Oakland, Northern California Comprehensive Thalassemia Center website  http://www thalassemia com 
Cooley's Anemia Foundation, Inc  website  http://www thalassemia org/gohome html 
Joint Center for Sickle Cell and Thalassemic Disorders website  http://cancer mgh harvard edu/medOnc/sickle htm 
[thal″ah-se´me-ah]
a heterogeneous group of hereditary hemolytic anemias marked by a decreased rate of synthesis of one or more hemoglobin polypeptide chains, classified according to the chain involved (α, β, δ); the two major categories are α- and β-thalassemia 
α-thalassemia (alpha-thalassemia) that caused by diminished synthesis of alpha chains of hemoglobin  The homozygous form is incompatible with life, the stillborn infant displaying severe hydrops fetalis  The heterozygous form may be asymptomatic or marked by mild anemia 
β-thalassemia (beta-thalassemia) that caused by diminished synthesis of beta chains of hemoglobin  The homozygous form is called t  major and the heterozygous form is called t  minor 
thalassemia ma´jor the homozygous form of β-thalassemia, in which hemoglobin A is completely absent; it appears in the newborn period and is marked by hemolytic, hypochromic, microcytic anemia; hepatosplenomegaly; skeletal deformation; mongoloid facies; and cardiac enlargement 
thalassemia mi´nor the heterozygous form of β-thalassemia; it is usually asymptomatic, but there may be mild anemia 
sickle cell–thalassemia a hereditary anemia involving simultaneous heterozygosity for hemoglobin S and thalassemia 
thal·as·se·mi·a
, thalassanemia (thal'ă-sē'mē-ă, thă-las-ă-nē'mē-ă),
Any of a group of inherited disorders of hemoglobin metabolism in which there is impaired synthesis of one or more of the polypeptide chains of globin; several genetic types exist, and the corresponding clinical picture may vary from barely detectable hematologic abnormality to severe and fatal anemia 
[G  thalassa, the sea, + haima, blood]
/thal·as·se·mia/ (thal″ah-se´me-ah) a heterogeneous group of hereditary hemolytic anemias marked by a decreased rate of synthesis of one or more hemoglobin polypeptide chains, classified according to the chain involved (α, β, δ); the two major categories are α- and β-thalassemia 
α-thalassemia that caused by diminished synthesis of alpha chains of hemoglobin  The homozygous form is incompatible with life, the stillborn infant displaying severe hydrops fetalis  The heterozygous form may be asymptomatic or marked by mild anemia 
β-thalassemia that caused by diminished synthesis of beta chains of hemoglobin  The homozygous form is called t  major and the heterozygous form is called t  minor 
thalassemia ma´jor the homozygous form of &#x03B2;, in which hemoglobin A is completely absent; it appears in the newborn period and is marked by hemolytic, hypochromic, microcytic anemia, hepatosplenomegaly, skeletal deformation, mongoloid facies, and cardiac enlargement 
thalassemia mi´nor the heterozygous form of &#x03B2;, usually asymptomatic, although there is sometimes mild anemia 
(thăl′ə-sē′mē-ə)
An inherited form of anemia occurring chiefly among people of Mediterranean descent, caused by faulty synthesis of part of the hemoglobin molecule  Also called Mediterranean anemia 
thal′as·se′mic adj 
[thal′əsē′mē·ə]
Etymology: Gk, thalassa, sea, a + haima, without blood
production and hemolytic anemia characterized by microcytic, hypochromic red blood cells  Thalassemia is caused by inherited deficiency of alpha- or beta-globin synthesis  See also hemochromatosis, hemosiderosis 
Beta thalassemia, clinical thalassemia, Cooley's anemia, Mediterranean anemia, thalassemia major Hematology A group of genetic diseases by underproduction of hemoglobin due to mutations in the beta globin gene, which is more common in Mediterraneans Heredity Parents are carriers–heterozygotes; one in 4 children is homozygous for the mutation and thus has full-blown disease Clinical See Anemia  Cf Sickle cell anemia 
α-thalassemia
Hemoglobin Barts Hematology An inherited condition caused by a defect in the synthesis of the Hb α chain; Hb Barts hemoglobinopathy is characterized by the presence of 4 gamma chains; it is more common in southeast Asians; the most severe form of alpha thalassemia causes stillbirth due to hydrops fetalis Heredity Parents are carriers–heterozygotes; one in 4 children is homozygous for the mutation and thus has full-blown disease Clinical Pallor, fatiguability, FTT, fever, infections, diarrhea Management Transfusions
Thalassemia major Hematology A hemoglobinopathy caused by a defect in the synthesis of Hb β chain Clinical Pallor, fatigability, FTT, fever due to infections, diarrhea, bone deformities, hepatosplenomegaly Management Transfusions, but iron overload can damage the heart, liver, and endocrine systems, ergo iron chelation–early use of deferiprone, deferoxamine ↓ transfusion-related iron overload and may protect against DM, cardiac disease, early death
δ-thalassemia
Hematology A condition characterized by a defect of Hb A2–α2δ2; because Hb A2 comprises only 3% of the circulating Hb, even its complete absence; δ-thalassemia has little clinical or hematologic impact
γ-thalassemia
Hematology A condition characterized by a defect of gamma–γ Hb chains found in Hb F–α2γ2; because Hb F is present primarily in the fetus and newborns, it is rarely seen outside of the neonatal period, but may cause transient neonatal hemolytic anemia 
, thalassanemia (thal'ă-sē'mē-ă, -ă-să-nē'mē-ă)
Any of a group of inherited disorders of hemoglobin metabolism in which there is impaired synthesis of one or more of the polypeptide chains of globin; several genetic types exist, and the corresponding clinical picture may vary from barely detectable hematologic abnormality to severe and fatal anemia  People of Mediterranean, extraction are more often affected than others by this type of anemia 
Synonym(s): thalassaemia, thalassanaemia 
Any of a group of inherited disorders of hemoglobin metabolism with impaired synthesis of one or more polypeptide chains of globin; several genetic types exist 
<a href="https://medical-dictionary thefreedictionary com/Thalassaemia+minor">thalassemia</a>
Barts hemoglobin
beta hemoglobinopathy
beta-delta thalassemia
beta-thalassaemia
Bite Cell
black gallstone
I know of a couple, totally unrelated and unbeknownst to them, who are silent carriers of Thalassaemia minor 
Pakistan: Genetic factor: All in the genes
But, unfortunately, when one person with thalassaemia minor carrier happens to marry another with the same diagnosis, there is a strong possibility that their child would be thalassaemia major, as happened in the case of Taneja 
' My life depends upon a monthly blood transfusion '
0] thalassaemia demonstrates variable severity, ranging from a condition similar to [beta] thalassaemia minor to something approaching thalassaemia major 
A retrospective review of homozygous haemoglobin E patients
Thal, Alan P 
thalame
thalamencephalic
thalamencephalon
thalamic
thalamic fasciculus
thalamic nucleus
thalamic pain syndrome
thalamic peduncle
thalamic radiation
thalamo-
thalamocoele
thalamocortical
thalamocortical fibers
thalamogeniculate artery
thalamolenticular
thalamoperforating artery
thalamostriate radiation
thalamotuberal artery
Thalassaemia minor
thalassaemiaor Cooley's disease
thalassemic facies
thalasso-
Thalassobacter
Thalassobacter utilis
thalassoplankton
thalassoposia
thalidomide neuropathy
Thalidomider
thallium poisoning
Thalarctos
THALAS
Thalasaemia
Thalassaemia Association of Malaysia
thalassaemia major
Thalassaemias
thalassaemic
thalassanaemia
Thalassemia Action Group
Thalassemia Clinical Research Network
thalassemia syndrome
Context 2: Paper Info

Title: Generalized Pole-Residue Method for Dynamic Analysis of Nonlinear Systems based on Volterra Series
Publish Date: March 7, 2023
Author List: Qianying Cao (from State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology), Anteng Chang (from College of Engineering, Ocean University of China), Junfeng Du (from College of Engineering, Ocean University of China), Lin Lu (from State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology)

Figure

Fig  1: Procedure to compute the response by a combination of Volterra series and Laguerre polynomials
Fig  2: Linear frequency response function: (a) Modulus of H 1 (ω), (b) phase angle of H 1 (ω)
Fig  6: Comparison of h 1 (t) based on the analytical and reconstructed by Laguerre polynomials
Fig  11: Response for Case 1: (a) comparison between the proposed method and Runge-Kutta method, (b) contribution of the three components
Fig  18: Comparison of original excitations and reconstructed results: (a) Case 1, (b) Case 2 (c) Case 3
Fig  19: Response to irregular excitation for Case 1: (a) comparison between the proposed method and Runge-Kutta method, (b) contribution of the three components
Fig  23: Input-output dataset used to identify Volterra series: (a) input excitation, (b) output response
Fig  26: Comparison of responses between the predicted and numerical results: (a) response to regular excitation, (b) response to irregular excitation
Parameter values of the irregular excitation

abstract

Dynamic systems characterized by second-order nonlinear ordinary differential equations appear in many fields of physics and engineering  To solve these kinds of problems, time-consuming stepby-step numerical integration methods and convolution methods based on Volterra series in the time domain have been widely used 
In contrast, this work develops an efficient generalized pole-residue method based on the Volterra series performed in the Laplace domain  The proposed method involves two steps: (1) the Volterra kernels are decoupled in terms of Laguerre polynomials, and (2) the partial response related to a single Laguerre polynomial is obtained analytically in terms of the pole-residue method 
Compared to the traditional pole-residue method for a linear system, one of the novelties of the pole-residue method in this paper is how to deal with the higher-order poles and their corresponding coefficients  Because the proposed method derives an explicit, continuous response function of time, it is much more efficient than traditional numerical methods 
Unlike the traditional Laplace domain method, the proposed method is applicable to arbitrary irregular excitations  Because the natural response, forced response and cross response are naturally obtained in the solution procedure, meaningful mathematical and physical insights are gained  In numerical studies, systems with a known equation of motion and an unknown equation of motion are investigated 
For each system, regular excitations and complex irregular excitations with different parameters are studied  Numerical studies validate the good accuracy and high efficiency of the proposed method by comparing it with the fourth-order Runge-Kutta method 

Introduction

Most real dynamic systems, as encountered in mechanical and civil engineering, are inherently nonlinear and include geometric nonlinearities, nonlinear constitutive relations in material or nonlinear resistances, etc    Nonlinear problems are attracting increasing attention from engineers and scientists 
This work focuses on solving nonlinear system vibration problems, i e , computing transient responses of nonlinear oscillators under arbitrary irregular excitations based on a combination of a pole-residue operation and Volterra series  Because Volterra series are single-valued, the scope of the present study is restricted to nonlinear behaviours without bifurcations  
To analyse nonlinear vibration problems, researchers have performed extensive studies and developed various mathematical methods  Popular methods include step-by-step numerical integration methods in the time domain, such as the Runge-Kutta method  This kind of method not only requires a small time-step resolution for obtaining high-precision solutions but also is prone to numerical instability  
For a long response with small time steps, the time domain methods are very costly in computational time  Volterra series is another widely used method, which is the extension of the Duhamel integral for linear systems   Volterra series can reproduce many nonlinear phenomena, but they are very complex due to higher-dimensional convolution integrals  
Since 1980's, significant progress has been made in the general area of the Volterra series  The reader is referred to Ref  for a quite thorough literature review on the relevant topics  After 2017, most papers focus on Volterra series identification  De Paula and Marques proposed a method for the identification of Volterra kernels, which was based on time-delay neural networks 
Son and Kim presented a method for a direct estimation of the Volterra kernel coefficients  Dalla Libera et al  introduced two new kernels for Volterra series identification  Peng et al  used the measured response to identify the kernel function and performed the nonlinear structural damage detection  Only a few papers concentrated on simplifying the computation of convolution integrals 
Traditional methods for computing convolution integrals involved in the Volterra series have been performed in three distinct domains: time, frequency and Laplace  The time domain method based on Volterra series refers to discrete time convolution methods, which also suffer computational cost problems  
Both the frequency domain method and the Laplace domain method based on the Volterra series consist of three steps: (1) Volterra series are transformed into an algebraic equation in the frequency domain or Laplace domain; the algebraic equation is solved by purely algebraic manipulations; and (3) the solution in Step ( ) is transformed back to the time domain 
Many researchers have used the frequency domain method to compute the responses of nonlinear systems  Billings et al  developed a new method for identifying the generalized frequency response function (GFRF) of nonlinear systems and then predicted the nonlinear response based on these GFRFs  Carassale et al  introduced a frequency domain approach for nonlinear bridge aerodynamics and aeroelasticity 
Ho et al  computed an output frequency domain function of a nonlinear damped duffing system modelled by a Volterra series under a sinusoidal input  Kim et al  identified the higher order frequency response functions by using the nonlinear autoregressive with exogenous input technique and the harmonic probing method 
This type of frequency domain method is much more efficient than the time domain method due to the fast Fourier transform algorithm  However, the frequency domain method not only is limited by frequency resolutions but also suffers from leakage problems due to the use of discrete Fourier transforms  In addition, the frequency domain method calculates only a steady-state response 
A natural response generated by initial conditions and a cross response caused by interactions between a system and an excitation are ignored  In contrast, the Laplace domain method can calculate all response components because initial conditions are considered in the computational procedure  However, it has been restricted to analytical operations for simple excitations, such as sinusoidal excitations and exponential excitations  
The proposed method falls into the category of the Volterra series method computed in the Laplace domain  Unlike the traditional Laplace domain method, the proposed method is applicable to arbitrary irregular excitations  Because the proposed method follows a similar path as a pole-residue method for linear systems , the proposed method to solve nonlinear system vibration problems is called the generalized pole-residue method 
The main concept of the pole-residue method developed by Hu et al  was that the poles and residues of the response could be easily obtained from those of the input and system transfer function to obtain the closed-form response solution of linear systems  This method included three steps: (1) writing the system transfer function into pole-residue form; (2) writing the excitation into pole-residue form by the Prony-SS method; (3) computing the poles and residues of the response by an algebraic operation based on those from system and excitation 
Compared to Hu et al  , which was regarded as an efficient tool to compute responses of linear systems, the generalized pole-residue method in this paper is introduced to compute responses of nonlinear systems  The proposed method involves two steps: (1) the Volterra kernels are decoupled in terms of Laguerre polynomials, and (2) the partial response related to a single Laguerre polynomial is obtained analytically in terms of the pole-residue method 
Compared to the traditional pole-residue method for a linear system, one of the novelties of the generalized pole-residue method is how to deal with the higher-order poles and their corresponding coefficients  Similar to the Taylor series, the Volterra series representation is an infinite series, and convergence conditions are needed to assure that the representation is meaningful 
Because the proposed method is based on the Volterra series, only the system with convergent Volterra series representation can be treated by the proposed method  The paper is organized as follows  In Section 2, the nonlinear response is modelled by a Volterra series, and Volterra kernel functions are decoupled by Laguerre polynomials 
Then, the pole-residue method for computing explicit responses is developed in Section 3  Numerical studies and discussions are given in Section 4  Finally, the conclusions are drawn in Section 5 

Response calculation based on Volterra series

A nonlinear oscillator, whose governing equation of motion is given by where z(t, y, ẏ) represents an arbitrary nonlinear term; m, c, and k are the mass, damping and linear stiffness, respectively; y(t), ẏ(t) and ÿ(t) are the displacement, velocity and acceleration, respectively; and f (t) is the time-dependent excitation 
If the energy of excitation f (t) is limited, the nonlinear response under zero initial conditions (i e , zero displacement and zero velocity) can be represented by the Volterra series : where N is the order of Volterra series and In Eq  3, h 1 (τ ) is called the first-order Volterra kernel function, which represents the linear behaviour of the system; h n (τ 1 ,      
, τ n ) for n > 1 are the higher-order Volterra kernel functions, which describe the nonlinear behaviour of the system  The complete formulation of y(t) includes infinite series where the labour of calculating the n th term increases quickly with the growth of n  Fortunately, the response accuracy may be ensured by the first several order Volterra series 
This is proved here in numerical studies  The commonly known Laguerre polynomials are represented as : where p i is the order of the Laguerre polynomials and a i is the damping rate  The Laguerre polynomials satisfy the orthogonal relationship expressed as: By using Laguerre polynomials, the Volterra kernel function h n (t 1 ,      
, t n ) in Eq  3 can be decoupled as follows : where the coefficient is computed resorting to the orthogonal relationship in Eq  5: Substituting Eq  6 into Eq  3 yields       The above operation that uses the Laguerre polynomials to decouple Volterra higher order kernel functions has been well-developed 
The reader is referred to Refs  for details about the adopted technique  After decoupling Volterra higher order kernel functions in time, one can regroup Eq  8 into:       By denoting Eq  9 becomes The above procedure to compute the nonlinear response by a combination of Volterra series and Laguerre polynomials is schematically shown in Fig   
Volterra kernel functions h n (t 1 ,       , t n ) can be obtained by either an equation of motion or measured input-output signals  To derive a closedform solution of the response, we must obtain a closed-form solution of x i (t) first  In the following presentation, a closed-form solution of the aforementioned x i (t) and y n (t) is derived by using the pole-residue method 
3  Pole-residue method for calculating x i (t) and y n (t) Performing the Laplace transform of x i (t) in Eq  10 yields where in which Eq  13 includes a single pole and several higher-order poles  For k = 0, −a i is a single pole, and b p i (0) is a corresponding coefficient, namely, the residue  For k > 0, −a i are higher-order poles, and b p i (k) are corresponding coefficients 
For an irregular excitation signal f (t) of a finite duration of T , it can always be approximated into a pole-residue form by using the complex exponential signal decomposition method-Prony-SS : where N ℓ is the number of components; α ℓ and λ ℓ are constant coefficients, which either are real numbers or occur in complex conjugate pairs 
We define λ ℓ = −δ ℓ + iΩ ℓ , where Ω ℓ is the excitation frequency and δ ℓ is the damping factor of the ℓ th component  We denote α ℓ = A ℓ e iθ ℓ , where A ℓ is the amplitude and θ ℓ is the sinusoidal initial phase in radians  Taking the Laplace transform of Eq  15 yields Note that the concept of the Prony-SS method is similar to that of a principal component method 
A smooth excitation usually requires just several terms to achieve a good approximation  For high irregular loadings, including more terms would achieve a better approximation  Substituting Eqs  13 and 16 into Eq  12 yields Expressing xi (s) in its pole-residue form yields where λ ℓ are simple poles, and the corresponding residues are easily obtained by
and −a i are higher-order poles, and the corresponding coefficients are firstly derived as: By taking the inverse Laplace transform of Eq  18, a closed-form solution is obtained: Substituting Eqs  11 and 21 into Eq  2 yields Theoretically speaking, the proposed method for deriving the closed-form solution of the nonlinear response is applicable to any order of the Volterra series 
For practical engineering, usually only the first several order responses dominate  By setting up N = 2, Eq  22 can be simplified into three components: where the natural response, which is only related to system poles, is given by and the cross response, which is related to both system poles and excitation poles, is given by
and the forced response, which is related only to excitation poles, is given by The first term in Eq  26 is the first-order forced response governed by the excitation frequency, i e , the imaginary part of the pole λ ℓ   The second term corresponds to the second-order nonlinear forced response, which includes the sum frequency and difference frequency responses governed by λ ℓ + λ j  
Eq  26 straightforwardly offers visible information about the possible nonlinear vibrations by the cooperation of excitation frequencies  Particularly, consider a sinusoidal excitation f (t) = sin ω r t, which can be expressed as f (t) = γe λt + γ * e λ * t , where γ = −0 5i and λ = iω r   Substituting these values into Eq 
26, the second term of Eq  26 is simplified as where the first term is the difference frequency response, and the second term is the sum frequency response 

Numerical studies

In practical engineering, some systems have an accurate equation of motion  Additionally, some systems have difficulty constructing their equations of motion because of complex nonlinear dynamic behaviours and uncertain system parameters  In this article, a system with a known equation of motion is called a known system, and a system with an unknown equation of motion is called an unknown system for simplicity 
In this section, two numerical studies are presented  The first study verifies the proposed method using a known nonlinear oscillator, and the second study demonstrates the applicability of the proposed method to an unknown system  Throughout the numerical studies, the unit system is the metre-kilogramme-second (MKS) system; for conciseness, explicit units for quantities are omitted 

A known nonlinear system

This study chooses a nonlinear oscillator written as: where mass m = 1, damping c = 1, linear stiffness k 1 = 10, quadratic stiffness k 2 = 20 and cubic stiffness k 3 = 20  It is a case that has been studied in a previously published article   The linear natural frequency of the system ω 0 = k 1 /m = 3 16 and the damping ratio ζ = c/(2mω 0 ) = 15 8% 
This kind of oscillator occurs in many engineering problems, such as a model of fluid resonance in a narrow gap between large vessels 



ground_truth: Severe anemia that begins even before birth.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What does the paper aim to solve?

Read the following text and answer briefly.

Context 2:  In the model, k 1 y represents the linear restoring force of the fluid, and k 2 y 2 and k 3 y 3 are respectively the quadratic and cubic nonlinear restoring forces of the fluid 

Volterra kernel functions

Generally, the first several order responses dominate the total response of a system  Hence, the order of the Volterra series in Eq  22 is chosen to be 3, namely, N = 3  For computing the first three order responses from Eq  22, the first three order Volterra kernel functions need to be known  Since Volterra kernel functions and corresponding frequency response functions are related by a specific Fourier transform pair, we can first write the first three orders of frequency response functions directly from Eq  28 
Then, Volterra kernel functions are obtained by the inverse Fourier transform  Based on the harmonic probing algorithm , the linear frequency response function (LFRF) H 1 (ω), the quadratic frequency response function (QFRF) H 2 (ω 1 , ω 2 ) and the cubic frequency response function (CFRF) H 3 (ω 1 , ω 2 , ω 3 ) are analytically given by:
and Figures show H 1 (ω), H 2 (ω 1 , ω 2 ) and H 3 (ω 1 , ω 2 , ω 3 ), respectively, which agree well with those reported in Ref    As expected, the modulus of H 1 (ω) in Fig  peaks near the linear natural frequency ω 0 , and the phase angle decreases monotonically from 0 to -π with increasing frequency 
Figure shows the sum frequency QFRF, where the energy converges along the line of ω 1 +ω 2 ≈ ω 0   Therefore, when the sum frequency of a two-tone excitation equals the linear resonant frequency, the second-order response may reach its maximum  Additionally, those pairs of excitations in line ω 1 + ω 2 ≈ ω 0 may produce non-negligible vibration magnitudes due to second-order nonlinear effects 
For the difference frequency QFRF in Fig  (b), the energy converges along two main lines, i e , ω 1 ≈ ω 0 and ω 2 ≈ ω 0   Figures show moduli of H 3 (ω, ω, ω) and H 3 (ω, ω, −ω), which are diagonal terms of the sum frequency CFRF and the difference frequency CFRF, respectively  While the modulus of H 3 (ω, ω, ω) peaks near ω ≈ ω 0 /3 and ω 0 , that of H 3 (ω, ω, −ω) peaks near ω ≈ ω 0 with a small hump around ω ≈ ω 0 /2 
Values at ω ≈ ω 0 /3 and ω 0 /2 may be magnified by higher-order stiffness terms in Eq  28  By performing the inverse fast Fourier transform to Eqs  29-31, the corresponding linear impulse response function h 1 (t), quadratic impulse response function h 2 (t 1 , t 2 ) and cubic impulse response function h 3 (t 1 , t 2 , t 3 ) are obtained 
Here, h 1 (t) and h 2 (t 1 , t 2 ) are plotted in Figs  , respectively, and h 3 (t, t, t) is shown in Fig    In the numerical implementation, Eqs  29-31 have been utilized with the frequency interval ∆ω = 0 1, number of frequency components N n = 1025, and cut-off frequencies 102 4 and −102 4  For decoupling Volterra kernel functions by using Laguerre polynomials, the damping rate and number of Laguerre polynomials for each order Volterra kernel function need to be determined (see Eqs  4 and 6) 
In this example, we set a 1 = a 2 = a 3 = 2 and R 1 = R 2 = R 3 = 24 because coefficients c p 1    pn become very small when R n > 24, n = 1, 2, 3  According to Eq  7, the coefficients of the first three order Volterra kernel functions are calculated, which are shown in Figs  9 and 10  For convenience, Fig  plots only c p 1 p 2 p 3 for p 3 = 0 
With the increase of the order of Laguerre polynomials, coefficients in Figs  9 and 10 gradually decrease, which illustrates how the first several orders of Laguerre polynomials dominate all orders of the Volterra kernel function  With the known Laguerre polynomials and corresponding coefficients, Volterra kernel functions are reconstructed by Eq  6 
For comparison, reconstructed Volterra kernel functions are also plotted in Figs    The reconstructed results agree well with the analytical values, which verifies the accuracy of the decomposition 

Sinusoidal excitation

From Eq  28, we consider a sinusoidal excitation where A and Ω are the amplitude and the frequency, respectively  Five cases of A and Ω are shown in Table   Excitation frequencies in Cases 1 and 2 are larger than the linear natural frequency (ω 0 ≈ 3 16), those in Case 3 are very close to ω 0 , and those in Cases 4 and 5 are smaller than ω 0  
All cases have same amplitudes  The poles of a sinusoidal excitation are λ 1,2 = ±iΩ, and the residues are α 1,2 = ∓iA/2  Numerical values of excitation poles and residues for different cases are listed in Table   Table : Parameter values, poles and residues of the sinusoidal excitation Substituting poles and residues of the excitation, as well as those of the system into Eqs 
20 and 19, response coefficients β p i ,k corresponding to system poles −a i and response coefficients γ p i ,ℓ corresponding to excitation poles λ ℓ are calculated, respectively  According to Eq  22, the first three orders of responses for each case in Table are calculated  Figures )-15(a) show the comparison of responses obtained by the proposed method and the fourth-order Runge-Kutta method with ∆t = 10 −4  
For Cases 1 and 2, the first-order responses agree well with the total responses obtained by the Runge-Kutta method, and the higher-order responses only slightly improve the transient parts  For Cases 3-5, the sum of the first three orders of responses is in good agreement with the Runge-Kutta solution 
When the response nonlinearity increases, higher-order responses need to be considered  In other words, the proposed method can accurately compute the nonlinear responses by choosing a small number N of Volterra series terms  Figures )-15(b) show the contributions of the three response components for the five cases 
In each case, the first-order response is the most dominant component, and the contributions of secondand third-order responses are much less than those of the first-order response  Especially for Cases 1 and 2, whose excitation frequencies are far from the linear natural frequency, second-and thirdorder responses are close to zero 
This may be because the QFRF and CFRF approach zero when the frequency is larger than 4 rad/s (see Figs  )  Furthermore, the mean values of the first-order responses are approximately zero, and those of the second-order responses are always smaller than zero, which are the difference frequency components in Eq  27 
Moreover, it is clearly observed that second-order responses for Cases 3-5 exhibit a periodic oscillation with a period near half of that for the first-order response, which is excited by the sum frequency component of the excitation (see second part of Eq  27)  Compared with steady-state solutions of first-and second-order responses, those of third-order responses in Cases 3-5 are no longer single regular motions 
By performing the FFT, frequency spectra of these three third-order responses are shown in Fig    We find that these three third-order responses are all dominated by their own fundamental harmonic component and the third harmonic (triple frequency) component  Figure shows the computational time to calculate the response of the oscillator for Case 1 by the proposed method, the fourth-order Runge-Kutta method and the convolution method 
The proposed method, which has an explicit solution, is much more efficient in computational time than the latter two methods, which need small time steps to obtain high-precision solutions  In particular, the efficiency of the proposed method increases with the length of the response time  Computation time (sec )
t=0 02s Convolution, t=0 02s Convolution, t=0 001s Runge-Kutta, t=0 001s Fig  : Comparison of computation efficiency of the proposed method, the fourth-fifth order Runge-Kutta method and the convolution method regular loading in Case 1

Irregular excitation

In Eq  28, considering an irregular excitation consisting of several cosine functions where N f is the number of cosine components; A n , Ω n and θ n are the amplitude, frequency and phase angle of the n th component, respectively  Table lists three cases of these parameters  In each case, the amplitudes of all components are the same, and phase angles θ n uniformly distributed between 0 and 2π are randomly generated 
To decompose the excitation into a pole-residue form, the Prony-SS method is used, whose concept is similar to that of a principal component method  The readers are referred to Ref  for details  The chosen rank of each case is also shown in Table   Figure shows the comparison of original excitations and reconstructed results of these three cases, which all have excellent agreement 
show the results computed by the fourth-order Runge-Kutta method  In all cases, the sums of the first three orders of responses agree well with those obtained by the Runge-Kutta method  The contributions of the first three orders of responses for each case are plotted in Figs  )-21(b)  Similarly, the system vibration is dominated by the first-order response 
However, the contributions of second-and third-order significantly grow with increasing excitation magnitude and frequency number  Furthermore, when the magnitude of the nonlinear response becomes large, sharp troughs are present  This phenomenon may be induced by the nonlinear stiffness  While the first-order response fails to capture these troughs, the higher-order responses successfully capture these troughs 
Figure plots the computational time to calculate the response of the oscillator for the irregular loading in Case 1 by the proposed method and the fourth-fifth order Runge-Kutta method, respectively  While the fourth-fifth order Runge-Kutta method is more efficient under a small response length, the proposed method becomes much more efficient when the response length is larger than about 130 s 
In addition, the proposed method obtains the explicit response solution, so one can directly obtain the response value at a specific time t p instead of integrating from 0 to t p for traditional numerical methods  Computation time (sec ) Proposed, t=0 02s Runge-Kutta, t=0 001s Fig  : Comparison of computation efficiency of the method and the fourth-fifth order Runge-Kutta method for irregular loading in Case 1

An unknown nonlinear

To check the applicability of the proposed method to an unknown nonlinear system, a known input excitation and its corresponding response are used to identify its Volterra kernel functions  When the Volterra kernel functions are known, we can follow the procedure in Section 4 1 to predict system responses 
In this study, the input excitation is white noise with a constant power spectrum S 0 = 0 001, and the corresponding response is obtained by solving Eq  28 by the fourth-order Runge-Kutta method, which is shown in Fig    From Section 4 1, we determine that the sum of the first two orders of responses agrees well with the total response 
In this study, the order of Volterra series N is chosen to be 2, damping rates of Laguerre polynomials are a 1 = a 2 = 2, and numbers of Laguerre polynomials are R 1 = R 2 = 24  To estimate the first two orders of Volterra kernel functions, a matrix equation is constructed using excitation data and response data 
By using the least square method to solve this matrix equation, coefficients c p 1 and c p 1 p 2 in Eq  8 are identified  Figure plots c p 1 and c p 1 p 2 , respectively, which have good agreement with the exact results in Fig    Then, the first two order Volterra kernel functions are constructed by Eq  6 
Compared with the exact results in Figs  , the identified Volterra kernel functions in Fig  completely agree well with the exact solutions  Note that the white noise excitation, which can excite more frequency components of the response, is chosen to obtain good Volterra kernel functions  A regular excitation f (t) = sin(πt) and an irregular excitation f (t) = N f n=1 A n cos(Ω n t + θ n ) with A n = 0 3 and Ω n varying from 0 to 40 with equal interval 1 are chosen as input excitations 
The predicted responses, along with results obtained by the fourth-order Runge-Kutta method, are shown in Fig    In both cases, the proposed method accurately predicts system responses  As presented in Eq  23, a nonlinear response is the sum of three terms: natural response y s (t), forced response y f (t) and cross response y c (t) 
These individual terms, as well as their sum to two excitations, are shown in Figs  27 and 28, respectively  As shown in Figs  and 28, both first-and second-order responses include the natural response y s (t) and the forced response y f (t), but the cross response y c (t) only exists in second-order responses 
When t becomes larger, both y s (t) and y c (t) diminish due to the presence of system damping, and the total response is entirely governed by y f (t)  Moreover, we notice some features at t = 0 for these components, including y s (0) = −y f (0) for the first-order response and y s (0) + y f (0) = −y c (0) for the second-order response, which are due to imposed zero initial conditions 

Conclusions

Considering arbitrary irregular excitations, an efficient generalized pole-residue method to compute the nonlinear dynamic response modelled by the Volterra series was developed  A core of the proposed method was obtaining poles and corresponding coefficients of Volterra kernel functions, then those of each order response modelled by each order Volterra series 
Once the poles and corresponding coefficients of Volterra kernel functions and excitations were both available, the remaining derivation could follow a similar pole-residue method that had been developed for ordinary linear oscillators  To obtain the poles and corresponding coefficients of Volterra kernel functions, two steps were included: (1) using Laguerre polynomials to decouple higher-order Volterra kernel functions with respect to time and (2) obtaining poles and corresponding coefficients of Laguerre polynomials in the Laplace domain 
Because the proposed method gave an explicit, continuous response function of time, it was much more efficient than traditional numerical methods  Moreover, many meaningful physical and mathematical insights were gained because not only each order response but also the natural response, the forced response and the cross response of each order were obtained in the solution procedure 
To demonstrate that the proposed method was not only suitable for a system with a known equation of motion but also applicable to a system with an unknown equation of motion, two numerical studies were conducted  For each study, regular excitations and complex irregular excitations with different parameters were investigated 
The efficiency of the proposed method was verified by the fourth-order Runge-Kutta method  This paper only computes the response under zero initial conditions  The response under non-zero initial conditions will be investigated in our future work 
Context 3: KSTP (1500 AM; SKOR North) is a commercial AM radio station licensed to Saint Paul, Minnesota  It is the flagship AM radio station of Hubbard Broadcasting, which also owns several other television and radio stations across the United States   KSTP has a sports radio format and is the ESPN Radio Network affiliate for Minneapolis-St  Paul   The radio studios are  on University Avenue in Minneapolis, shared with sister stations KSTP-FM, KSTP-TV, KTMY, and KSTC-TV  On weekdays, KSTP airs local sports shows from 9 a m  to 9 p m  and carries ESPN programming weekday mornings, late nights and weekends  Some KSTP shows are simulcast on other sports radio stations in the region 

KSTP runs the maximum power for AM stations, 50,000 watts   It shares clear-channel, Class A status on 1500 AM with WFED in Washington, D C   KSTP broadcasts a directional signal at night, using a three-tower array, with its transmitter on U S  Route 61 at Beam Avenue in Maplewood   Programming is also heard on 250 watt FM translator K235BP at 94 9 MHz in Bemidji 

History

WAMD and KFOY
KSTP's start in 1928 was the product of a merger between two pioneering Twin Cities stations: WAMD ("Where All Minneapolis Dances") in Minneapolis, first licensed on February 16, 1925 to Stanley E  Hubbard, and KFOY in St  Paul, first licensed on March 12, 1924 to the Beacon Radio Service in St  Paul 

Following a few test transmissions, WAMD made its formal debut broadcast on February 22, 1925  (In later interviews Stanley Hubbard traced WAMD's start to April 1924 ) It was located at the Marigold Dance Garden, and featured nightly "Midnight Frolics" broadcasts by the ballroom's orchestra  It is claimed that WAMD was the first radio station to be completely supported by running paid advertisements  Effective June 15, 1927, WAMD was assigned to 1330 kHz 

On November 11, 1927 WAMD's transmitter site at Oxboro Heath on Lyndale Avenue South burned down, two weeks after the station had been sold to the National Battery Company  An initial arrangement was made to carry WAMD's programs over WRHM (now WWTC), transmitting on WAMD's 1330 kHz frequency  Beginning on November 24, 1927 the WAMD broadcasts, still on 1330 kHz, were shifted to KFOY's facility in St  Paul  (At this time KFOY was assigned to 1050 kHz)  The next day it was announced that National Battery had purchased KFOY, and as of December 1, 1927 both KFOY and WAMD were reassigned to 1350 kHz  WAMD continued making regular broadcasts until the end of March 1928, while KFOY, although it continued to be licensed for a few more months on a time-sharing basis with WAMD, ceased operations at this point 

National Battery Company
In mid-December 1927, the National Battery Company announced it had received permission from the Federal Radio Commission (FRC) to build a new station, with the call letters KSTP, operating from a transmitter site to be constructed three miles south of Wescott  The next month it was reported that the new station, still under construction, had been assigned to 1360 kHz  KSTP made its debut broadcast on March 29, 1928  Although technically it was a separate station from WAMD and KFOY, both of which were formally deleted on April 30, 1928, overall KSTP was treated as the direct successor to a consolidated WAMD and KFOY 

Hubbard became the merged station's general manager, acquiring controlling interest in 1941  A month after the merger, KSTP became an affiliate for the NBC Red Network   It remained with NBC for 46 years  On November 11, 1928, under the provisions of the FRC's General Order 40, KSTP was assigned to a "high-powered regional" frequency of 1460 kHz  The only other station assigned to this frequency was WTFF in Mount Vernon Hills, Virginia (later WJSV, now WFED, Washington, D C )  On February 7, 1933, the FRC authorized KSTP to increase its daytime power to 25 KW  In 1938 and 1939 KSTP also operated a high-fidelity AM "experimental audio broadcasting station" Apex station, W9XUP, originally on 25,950 kHz and later on 26,150 kHz  In 1941, as part of the implementation of the North American Regional Broadcasting Agreement, KSTP was assigned to its current "clear channel" frequency of 1500 kHz, with the provision that it and WJSV, as "Class I-B" stations, had to maintain directional antennas at night in order to mutually protect each other from interference  An FM station, KSTP-FM, was founded in 1946 but shut down in 1952 

Hubbard reportedly acquired an RCA TV camera in 1939, and started experimenting with television broadcasts   But World War II put a hold on the development of television   In 1948, with the war over, KSTP-TV became the first television station in Minnesota   With KSTP 1500 already associated with NBC Radio, KSTP-TV became an NBC Television Network affiliate   From 1946 to 1952, KSTP also had an FM counterpart



ground_truth: The paper aims to solve nonlinear system vibration problems efficiently.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When did KSTP switch to a sports radio format?

Read the following text and answer briefly.

Context 3:   KSTP-FM 102 1 was only on the air four years   There were few radios equipped to receive FM signals in that era, and management decided to discontinue FM broadcasts 

MOR and Top 40
As network programming moved from radio to television, KSTP programmed a full service Middle of the Road (MOR) radio format, in the shadow of its chief competitor, CBS Radio affiliate 830 WCCO  In 1965, a new FM station, reviving the KSTP-FM call sign, was put on the air, largely simulcasting the AM station   But by the late 1960s, KSTP-FM began a separate format of beautiful music   KSTP was the radio home of the Minnesota Vikings football team from 1970 to 1975  

In 1973, KSTP broke away from its longtime adult MOR sound and became one of four area stations at the time to program a Top 40 format  "15 KSTP, The Music Station" competed with Top 40 AM rivals WDGY, KDWB and later, WYOO  The competition would eventually shake itself out, with outrageous rocker WYOO dropping out after being sold in 1976, and then the staid WDGY switching to country music the following year   As for uptempo hits station 15 KSTP, it went from a tight Top 40 format to leaning adult rock in 1978, to leaning adult contemporary in 1979, to evolving into adult contemporary/talk by 1980   In 1982, it officially shifted to talk   Most Top 40 rock music, by this time, had moved to the FM band 

Past Personalities

Notable hosts who have been on KSTP include John Hines, Jesse Ventura, Larry Carolla, Tom Barnard, Big Al Davis, Don Vogel, John MacDougall, Griff, Mike Edwards, Geoff Charles, Joe Soucheray, James Lileks, Leigh Kamman, Barbara Carlson, Peter Thiele, Tom Mischke, Jason Lewis, Chuck Knapp, Machine Gun Kelly, Charle Bush, Mark O'Connell and Paul Brand  These broadcasters were supported by producers such as Bruce Huff, Rob Pendleton, Alison Brown, Jean Bjorgen, David Elvin (who Vogel dubbed the "Steven Spielberg of Talk Radio"), Mitch Berg and others 

The station has, for the most part, emphasized local hosts over the years   But in 1988, KSTP was one of Rush Limbaugh's first affiliates when his conservative talk show was rolled out for national syndication   (Clear Channel-owned KTLK-FM took over rights to Limbaugh's show in January 2006)  Other syndicated hosts previously heard on KSTP include Sean Hannity, Bruce Williams, Larry King, and Owen Spann 

Sports Radio
KSTP switched to Sports Radio on February 15, 2010   As the station had to wait for ESPN's contract with rival KFAN and its sister station KFXN to expire, it did not become an ESPN Radio affiliate until April 12, the same day that the Minnesota Twins were scheduled to play the first game in their new ball park, Target Field, against the Boston Red Sox   As a result Coast to Coast AM and Live on Sunday Night, it's Bill Cunningham were retained during this period   One ESPN Radio network program, The Herd with Colin Cowherd, was picked up by KSTP immediately following the format change 

In 2018, the station was approved for an FM translator on 94 1 FM, broadcasting from a transmitter atop the IDS Center in downtown Minneapolis  The two-watt signal threw most of its power to the west, preventing interference to low powered FM stations on the same channel including WFNU-LP in St  Paul  With only two watts of power, however, the signal was limited to the immediate downtown area surrounding the IDS Center   It later acquired a 250 watt translator, K235BP at 94 9 MHz   The original translator was discontinued 

On January 15, 2019, KSTP rebranded as "SKOR North" (a reference to the Vikings team song/chant, "Skol, Vikings"), with local programming between 12 noon and 7 pm  About a year later, in May of 2020, KSTP suspended most of its local programming and laid off nearly all of its local staff  Station management cited the economic toll of the coronavirus for the changes  Sports broadcasting continues, primarily composed of ESPN radio network broadcasts 

Sports Teams

KSTP-AM served as the radio flagship for the Minnesota Vikings football team from 1970 to 1975 

On August 1, 2006, the station announced that it would be the new flagship station for the Minnesota Twins baseball team, effective with the start of the 2007 season  The Twins had been on rival WCCO since arriving in Minnesota in 1961   KSTP served as the flagship for the Twins until the end of the 2012 season, when games moved to 96 3 KTWN-FM (now KMWA)   The Twins have since returned to WCCO 830 

The switch to a fairly weak FM station caused dissent among some listeners, particularly in communities that had trouble picking up KSTP 1500   Although KSTP is the state's second most powerful AM station, it must operate directionally at night, delivering a reduced signal to parts of the market  WCCO, by comparison, offers a signal with a wider coverage area during the day than KSTP does, with WCCO's non-directional 50,000 watt signal  In response, the Twins have expanded the number of affiliates 

On March 9, 2011, KSTP announced it would be the new flagship for the University of Minnesota Golden Gophers men's and women's basketball and men's ice hockey, ending a 68-year run on WCCO  The rights have since moved to KFXN-FM, which already aired Gopher football 

On March 2, 2017, KSTP announced it would be the first radio broadcaster for Minnesota United FC   The move brings live soccer action to 1500 AM 

Previous logos

References

External links
KSTP website

FCC History Cards for KSTP (covering 1928-1980)
Radiotapes com Historic Minneapolis/St  Paul airchecks dating back to 1924 including KSTP and other Twin Cities radio stations 
Rick Burnett's TwinCitiesRadioAirchecks com has additional airchecks of KSTP and other Twin Cities radio stations from the '60s and '70s, including Chuck Knapp's 2nd show on KSTP 

Hubbard Broadcasting
ESPN Radio stations
Peabody Award winners
Radio stations in Minneapolis–Saint Paul
Radio stations established in 1925
1925 establishments in Minnesota
Minnesota Kicks
Sports radio stations in the United States
Clear-channel radio stations



ground_truth: KSTP switched to a sports radio format on February 15, 2010.