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Saturday, September 9, 2023

Solenoid

From Wikipedia, the free encyclopedia

An illustration of a solenoid
Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines

A solenoid is a type of electromagnet formed by a helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field. The coil can produce a uniform magnetic field in a volume of space when an electric current is passed through it.

André-Marie Ampère coined the term solenoid in 1823, having conceived of the device in 1820.

The helical coil of a solenoid does not necessarily need to revolve around a straight-line axis; for example, William Sturgeon's electromagnet of 1824 consisted of a solenoid bent into a horseshoe shape (similarly to an arc spring).

Solenoids provide magnetic focusing of electrons in vacuums, notably in television camera tubes such as vidicons and image orthicons. Electrons take helical paths within the magnetic field. These solenoids, focus coils, surround nearly the whole length of the tube.

Physics

Infinite continuous solenoid

Figure 1: An infinite solenoid with three arbitrary Ampèrian loops labelled a, b, and c. Integrating over path c demonstrates that the magnetic field inside the solenoid must be radially uniform.

An infinite solenoid has infinite length but finite diameter. "Continuous" means that the solenoid is not formed by discrete finite-width coils but by many infinitely thin coils with no space between them; in this abstraction, the solenoid is often viewed as a cylindrical sheet of conductive material.

The magnetic field inside an infinitely long solenoid is homogeneous and its strength neither depends on the distance from the axis nor on the solenoid's cross-sectional area.

This is a derivation of the magnetic flux density around a solenoid that is long enough so that fringe effects can be ignored. In Figure 1, we immediately know that the flux density vector points in the positive z direction inside the solenoid, and in the negative z direction outside the solenoid. We confirm this by applying the right hand grip rule for the field around a wire. If we wrap our right hand around a wire with the thumb pointing in the direction of the current, the curl of the fingers shows how the field behaves. Since we are dealing with a long solenoid, all of the components of the magnetic field not pointing upwards cancel out by symmetry. Outside, a similar cancellation occurs, and the field is only pointing downwards.

Now consider the imaginary loop c that is located inside the solenoid. By Ampère's law, we know that the line integral of B (the magnetic flux density vector) around this loop is zero, since it encloses no electrical currents (it can be also assumed that the circuital electric field passing through the loop is constant under such conditions: a constant or constantly changing current through the solenoid). We have shown above that the field is pointing upwards inside the solenoid, so the horizontal portions of loop c do not contribute anything to the integral. Thus the integral of the up side 1 is equal to the integral of the down side 2. Since we can arbitrarily change the dimensions of the loop and get the same result, the only physical explanation is that the integrands are actually equal, that is, the magnetic field inside the solenoid is radially uniform. Note, though, that nothing prohibits it from varying longitudinally, which in fact, it does.

A similar argument can be applied to the loop a to conclude that the field outside the solenoid is radially uniform or constant. This last result, which holds strictly true only near the center of the solenoid where the field lines are parallel to its length, is important as it shows that the flux density outside is practically zero since the radii of the field outside the solenoid will tend to infinity. An intuitive argument can also be used to show that the flux density outside the solenoid is actually zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can (see Gauss's law for magnetism). The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form loops. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced. Now recall that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer. Of course, if the solenoid is constructed as a wire spiral (as often done in practice), then it emanates an outside field the same way as a single wire, due to the current flowing overall down the length of the solenoid.

The picture shows how Ampère's law can be applied to the solenoid

Applying Ampère's circuital law to the solenoid (see figure on the right) gives us

where is the magnetic flux density, is the length of the solenoid, is the magnetic constant, the number of turns, and the current. From this we get

This equation is valid for a solenoid in free space, which means the permeability of the magnetic path is the same as permeability of free space, μ0.

If the solenoid is immersed in a material with relative permeability μr, then the field is increased by that amount:

In most solenoids, the solenoid is not immersed in a higher permeability material, but rather some portion of the space around the solenoid has the higher permeability material and some is just air (which behaves much like free space). In that scenario, the full effect of the high permeability material is not seen, but there will be an effective (or apparent) permeability μeff such that 1 ≤ μeff ≤ μr.

The inclusion of a ferromagnetic core, such as iron, increases the magnitude of the magnetic flux density in the solenoid and raises the effective permeability of the magnetic path. This is expressed by the formula

where μeff is the effective or apparent permeability of the core. The effective permeability is a function of the geometric properties of the core and its relative permeability. The terms relative permeability (a property of just the material) and effective permeability (a property of the whole structure) are often confused; they can differ by many orders of magnitude.

For an open magnetic structure, the relationship between the effective permeability and relative permeability is given as follows:

where k is the demagnetization factor of the core.

Finite continuous solenoid

Magnetic field line and density created by a solenoid with surface current density

A finite solenoid is a solenoid with finite length. Continuous means that the solenoid is not formed by discrete coils but by a sheet of conductive material. We assume the current is uniformly distributed on the surface of the solenoid, with a surface current density K; in cylindrical coordinates:

The magnetic field can be found using the vector potential, which for a finite solenoid with radius R and length l in cylindrical coordinates is

Where:

  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Here, , , and are complete elliptic integrals of the first, second, and third kind.

Using:

The magnetic flux density is obtained as

On the symmetry axis, the radial component vanishes, and the axial field component is

Inside the solenoid, far away from the ends (), this tends towards the constant value .

Short solenoid estimate

For the case in which the radius is much larger than the length of the solenoid (), the magnetic flux density through the centre of the solenoid (in the z direction, parallel to the solenoid's length, where the coil is centered at z=0) can be estimated as the flux density of a single circular conductor loop:

Irregular solenoids

Examples of irregular solenoids (a) sparse solenoid, (b) varied pitch solenoid, (c) non-cylindrical solenoid

Within the category of finite solenoids, there are those that are sparsely wound with a single pitch, sparsely wound with varying pitches (varied-pitch solenoid), or those with a varying radius for different loops (non-cylindrical solenoids). They are called irregular solenoids. They have found applications in different areas, such as sparsely wound solenoids for wireless power transfer, varied-pitch solenoids for magnetic resonance imaging (MRI), and non-cylindrical solenoids for other medical devices.

The calculation of the intrinsic inductance and capacitance cannot be done using those for the traditional solenoids, i.e. the tightly wound ones. New calculation methods were proposed for the calculation of intrinsic inductance and capacitance.

Inductance

As shown above, the magnetic flux density within the coil is practically constant and given by

where μ0 is the magnetic constant, the number of turns, the current and the length of the coil. Ignoring end effects, the total magnetic flux through the coil is obtained by multiplying the flux density by the cross-section area :

Combining this with the definition of inductance

the inductance of a solenoid follows as

A table of inductance for short solenoids of various diameter to length ratios has been calculated by Dellinger, Whittmore, and Ould.

This, and the inductance of more complicated shapes, can be derived from Maxwell's equations. For rigid air-core coils, inductance is a function of coil geometry and number of turns, and is independent of current.

Similar analysis applies to a solenoid with a magnetic core, but only if the length of the coil is much greater than the product of the relative permeability of the magnetic core and the diameter. That limits the simple analysis to low-permeability cores, or extremely long thin solenoids. The presence of a core can be taken into account in the above equations by replacing the magnetic constant μ0 with μ or μ0μr, where μ represents permeability and μr relative permeability. Note that since the permeability of ferromagnetic materials changes with applied magnetic flux, the inductance of a coil with a ferromagnetic core will generally vary with current.

Kidney dialysis

From Wikipedia, the free encyclopedia
Kidney dialysis
Patient receiving hemodialysis
Specialtynephrology
ICD-9-CM39.95
MeSHD006435
Schematic of semipermeable membrane during hemodialysis, where blood is red, dialysing fluid is blue, and the membrane is yellow

Kidney dialysis (from Greek διάλυσις, dialysis, 'dissolution'; from διά, dia, 'through', and λύσις, lysis, 'loosening or splitting') is the process of removing excess water, solutes, and toxins from the blood in people whose kidneys can no longer perform these functions naturally. This is referred to as renal replacement therapy. The first successful dialysis was performed in 1943.

Dialysis may need to be initiated when there is a sudden rapid loss of kidney function, known as acute kidney injury (previously called acute renal failure), or when a gradual decline in kidney function, chronic kidney failure, reaches stage 5. Stage 5 chronic renal failure is reached when the glomerular filtration rate is 10–15% of the normal, creatinine clearance is less than 10 mL per minute, and uremia is present.

Dialysis is used as a temporary measure in either acute kidney injury or in those awaiting kidney transplant and as a permanent measure in those for whom a transplant is not indicated or not possible.

In West European countries, Australia, Canada, the United Kingdom, and the United States, dialysis is paid for by the government for those who are eligible.

Background

A hemodialysis machine

The kidneys have an important role in maintaining health. When the person is healthy, the kidneys maintain the body's internal equilibrium of water and minerals (sodium, potassium, chloride, calcium, phosphorus, magnesium, sulphate). The acidic metabolism end-products that the body cannot get rid of via respiration are also excreted through the kidneys. The kidneys also function as a part of the endocrine system, producing erythropoietin, calcitriol and renin. Erythropoietin is involved in the production of red blood cells and calcitriol plays a role in bone formation. Dialysis is an imperfect treatment to replace kidney function because it does not correct the compromised endocrine functions of the kidney. Dialysis treatments replace some of these functions through diffusion (waste removal) and ultrafiltration (fluid removal). Dialysis uses highly purified (also known as "ultrapure") water.

Principle

Dialysis works on the principles of the diffusion of solutes and ultrafiltration of fluid across a semi-permeable membrane. Diffusion is a property of substances in water; substances in water tend to move from an area of high concentration to an area of low concentration. Blood flows by one side of a semi-permeable membrane, and a dialysate, or special dialysis fluid, flows by the opposite side. A semipermeable membrane is a thin layer of material that contains holes of various sizes, or pores. Smaller solutes and fluid pass through the membrane, but the membrane blocks the passage of larger substances (for example, red blood cells and large proteins). This replicates the filtering process that takes place in the kidneys when the blood enters the kidneys and the larger substances are separated from the smaller ones in the glomerulus.

Osmosis, diffusion, ultrafiltration, and dialysis

The two main types of dialysis, hemodialysis and peritoneal dialysis, remove wastes and excess water from the blood in different ways. Hemodialysis removes wastes and water by circulating blood outside the body through an external filter, called a dialyzer, that contains a semipermeable membrane. The blood flows in one direction and the dialysate flows in the opposite. The counter-current flow of the blood and dialysate maximizes the concentration gradient of solutes between the blood and dialysate, which helps to remove more urea and creatinine from the blood. The concentrations of solutes normally found in the urine (for example potassium, phosphorus and urea) are undesirably high in the blood, but low or absent in the dialysis solution, and constant replacement of the dialysate ensures that the concentration of undesired solutes is kept low on this side of the membrane. The dialysis solution has levels of minerals like potassium and calcium that are similar to their natural concentration in healthy blood. For another solute, bicarbonate, dialysis solution level is set at a slightly higher level than in normal blood, to encourage the diffusion of bicarbonate into the blood, to act as a pH buffer to neutralize the metabolic acidosis that is often present in these patients. The levels of the components of dialysate are typically prescribed by a nephrologist according to the needs of the individual patient.

In peritoneal dialysis, wastes and water are removed from the blood inside the body using the peritoneum as a natural semipermeable membrane. Wastes and excess water move from the blood, across the peritoneal membrane and into a special dialysis solution, called dialysate, in the abdominal cavity.

Types

There are three primary and two secondary types of dialysis: hemodialysis (primary), peritoneal dialysis (primary), hemofiltration (primary), hemodiafiltration (secondary) and intestinal dialysis (secondary).

Hemodialysis

In hemodialysis, the patient's blood is pumped through the blood compartment of a dialyzer, exposing it to a partially permeable membrane. The dialyzer is composed of thousands of tiny hollow synthetic fibers. The fiber wall acts as the semipermeable membrane. Blood flows through the fibers, dialysis solution flows around the outside of the fibers, and water and wastes move between these two solutions. The cleansed blood is then returned via the circuit back to the body. Ultrafiltration occurs by increasing the hydrostatic pressure across the dialyzer membrane. This usually is done by applying a negative pressure to the dialysate compartment of the dialyzer. This pressure gradient causes water and dissolved solutes to move from blood to dialysate and allows the removal of several litres of excess fluid during a typical 4-hour treatment. In the United States, hemodialysis treatments are typically given in a dialysis center three times per week (due in the United States to Medicare reimbursement rules); however, as of 2005 over 2,500 people in the United States are dialyzing at home more frequently for various treatment lengths. Studies have demonstrated the clinical benefits of dialyzing 5 to 7 times a week, for 6 to 8 hours. This type of hemodialysis is usually called nocturnal daily hemodialysis and a study has shown it provides a significant improvement in both small and large molecular weight clearance and decreases the need for phosphate binders. These frequent long treatments are often done at home while sleeping, but home dialysis is a flexible modality and schedules can be changed day to day, week to week. In general, studies show that both increased treatment length and frequency are clinically beneficial.

Hemo-dialysis was one of the most common procedures performed in U.S. hospitals in 2011, occurring in 909,000 stays (a rate of 29 stays per 10,000 population).

Peritoneal dialysis

Schematic diagram of peritoneal dialysis

In peritoneal dialysis, a sterile solution containing glucose (called dialysate) is run through a tube into the peritoneal cavity, the abdominal body cavity around the intestine, where the peritoneal membrane acts as a partially permeable membrane.

This exchange is repeated 4–5 times per day; automatic systems can run more frequent exchange cycles overnight. Peritoneal dialysis is less efficient than hemodialysis, but because it is carried out for a longer period of time the net effect in terms of removal of waste products and of salt and water are similar to hemodialysis. Peritoneal dialysis is carried out at home by the patient, often without help. This frees patients from the routine of having to go to a dialysis clinic on a fixed schedule multiple times per week. Peritoneal dialysis can be performed with little to no specialized equipment (other than bags of fresh dialysate).

Hemofiltration

Continuous veno-venous haemofiltration with pre- and post-dilution (CVVH)

Hemofiltration is a similar treatment to hemodialysis, but it makes use of a different principle. The blood is pumped through a dialyzer or "hemofilter" as in dialysis, but no dialysate is used. A pressure gradient is applied; as a result, water moves across the very permeable membrane rapidly, "dragging" along with it many dissolved substances, including ones with large molecular weights, which are not cleared as well by hemodialysis. Salts and water lost from the blood during this process are replaced with a "substitution fluid" that is infused into the extracorporeal circuit during the treatment.

Hemodiafiltration

Hemodiafiltration is a combination between hemodialysis and hemofiltration, thus used to purify the blood from toxins when the kidney is not working normally and also used to treat acute kidney injury (AKI).

Intestinal dialysis

Continuous veno-venous haemodiafiltration (CVVHDF)

In intestinal dialysis, the diet is supplemented with soluble fibres such as acacia fibre, which is digested by bacteria in the colon. This baterial growth increases the amount of nitrogen that is eliminated in fecal waste. An alternative approach utilizes the ingestion of 1 to 1.5 liters of non-absorbable solutions of polyethylene glycol or mannitol every fourth hour.

Indications

The decision to initiate dialysis or hemofiltration in patients with kidney failure depends on several factors. These can be divided into acute or chronic indications.

Depression and kidney failure symptoms can be similar to each other. It's important that there's open communication between a dialysis team and the patient. Open communication will allow giving a better quality of life. Knowing the patients' needs will allow the dialysis team to provide more options like: changes in dialysis type like home dialysis for patients to be able to be more active or changes in eating habits to avoid unnecessary waste products.

Acute indications

Indications for dialysis in a patient with acute kidney injury are summarized with the vowel mnemonic of "AEIOU":

  1. Acidemia from metabolic acidosis in situations in which correction with sodium bicarbonate is impractical or may result in fluid overload.
  2. Electrolyte abnormality, such as severe hyperkalemia, especially when combined with AKI.
  3. Intoxication, that is, acute poisoning with a dialyzable substance. These substances can be represented by the mnemonic SLIME: salicylic acid, lithium, isopropanol, magnesium-containing laxatives and ethylene glycol.
  4. Overload of fluid not expected to respond to treatment with diuretics
  5. Uremia complications, such as pericarditis, encephalopathy, or gastrointestinal bleeding.

Chronic indications

Chronic dialysis may be indicated when a patient has symptomatic kidney failure and low glomerular filtration rate (GFR < 15 mL/min). Between 1996 and 2008, there was a trend to initiate dialysis at progressively higher estimated GFR, eGFR. A review of the evidence shows no benefit or potential harm with early dialysis initiation, which has been defined by start of dialysis at an estimated GFR of greater than 10 ml/min/1.732. Observational data from large registries of dialysis patients suggests that early start of dialysis may be harmful. The most recent published guidelines from Canada, for when to initiate dialysis, recommend an intent to defer dialysis until a patient has definite kidney failure symptoms, which may occur at an estimated GFR of 5–9 ml/min/1.732.

Dialyzable substances

Characteristics

Dialyzable substances—substances removable with dialysis—have these properties:

  1. Low molecular mass
  2. High water solubility
  3. Low protein binding capacity
  4. Prolonged elimination (long half-life)
  5. Small volume of distribution

Substances

Missing dialysis

Given dialysis patients have little or no capacity to filtrate solutes and regulate their fluid volume due to kidney dysfunction, missing dialysis is potentially lethal. These patients can be hyperkalaemic leading to cardiac dysrhythmias and potential cardiac arrest, as well as fluid in the alveoli of their lungs which can impair breathing.

Some medications can be used in the short term to decrease serum potassium and stabilise the cardiac muscle so as to facilitate stabilisation of acute patients in the setting of missed dialysis. Salbutamol and Insulin can decrease serum potassium by up to 1.0mmol/L each by shifting potassium from the extracellular space into the intracellular spaces within skeletal muscle cells, and calcium gluconate is used to stabilise the myocardium in hyperkalaemic patients, in an attempt to reduce the likelihood of lethal arrhythmias arising from a high serum potassium.

Given that dialysis patients have little to no kidney function, Furosemide is generally ineffective in combating pulmonary oedema due to missed dialysis. Instead, patients are often placed on CPAP, BIPAP, or high-flow oxygen to support breathing until they can be dialysed.

Pediatric dialysis

Over the past 20 years, children have benefited from major improvements in both technology and clinical management of dialysis. Morbidity during dialysis sessions has decreased with seizures being exceptional and hypotensive episodes rare. Pain and discomfort have been reduced with the use of chronic internal jugular venous catheters and anesthetic creams for fistula puncture. Non-invasive technologies to assess patient target dry weight and access flow can significantly reduce patient morbidity and health care costs. Mortality in paediatric and young adult patients on chronic hemodialysis is associated with multifactorial markers of nutrition, inflammation, anaemia and dialysis dose, which highlights the importance of multimodal intervention strategies besides adequate hemodialysis treatment as determined by Kt/V alone.

Biocompatible synthetic membranes, specific small size material dialyzers and new low extra-corporeal volume tubing have been developed for young infants. Arterial and venous tubing length is made of minimum length and diameter, a <80 ml to <110 ml volume tubing is designed for pediatric patients and a >130 to <224 ml tubing are for adult patients, regardless of blood pump segment size, which can be of 6.4 mm for normal dialysis or 8.0mm for high flux dialysis in all patients. All dialysis machine manufacturers design their machine to do the pediatric dialysis. In pediatric patients, the pump speed should be kept at low side, according to patient blood output capacity, and the clotting with heparin dose should be carefully monitored. The high flux dialysis (see below) is not recommended for pediatric patients.

In children, hemodialysis must be individualized and viewed as an "integrated therapy" that considers their long-term exposure to chronic renal failure treatment. Dialysis is seen only as a temporary measure for children compared with renal transplantation because this enables the best chance of rehabilitation in terms of educational and psychosocial functioning. Long-term chronic dialysis, however, the highest standards should be applied to these children to preserve their future "cardiovascular life"—which might include more dialysis time and on-line hemodiafiltration online hdf with synthetic high flux membranes with the surface area of 0.2 m2 to 0.8 m2 and blood tubing lines with the low volume yet large blood pump segment of 6.4/8.0 mm, if we are able to improve on the rather restricted concept of small-solute urea dialysis clearance.

Dialysis in different countries

In the United Kingdom

The National Health Service provides dialysis in the United Kingdom. In England, the service is commissioned by NHS England. About 23,000 patients use the service each year. Patient transport services are generally provided without charge, for patients who need to travel to dialysis centres. Cornwall Clinical Commissioning Group proposed to restrict this provision to patients who did not have specific medical or financial reasons in 2018 but changed their minds after a campaign led by Kidney Care UK and decided to fund transport for patients requiring dialysis three times a week for a minimum or six times a month for a minimum of three months.

A UK study found that receiving dialysis at home is less costly than receiving dialysis in hospital. However, many people in the UK prefer to receive dialysis in hospital for various reasons such as providing regular social contact. Encouraging people to have dialysis at home could lead to savings for the NHS, as well as reducing the impact of dialysis on people's social and professional lives.

In the United States

Since 1972, insurance companies in the United States have covered the cost of dialysis and transplants for all citizens. By 2014, more than 460,000 Americans were undergoing treatment, the costs of which amount to six percent of the entire Medicare budget. Kidney disease is the ninth leading cause of death, and the U.S. has one of the highest mortality rates for dialysis care in the industrialized world. The rate of patients getting kidney transplants has been lower than expected. These outcomes have been blamed on a new for-profit dialysis industry responding to government payment policies. A 1999 study concluded that "patients treated in for-profit dialysis facilities have higher mortality rates and are less likely to be placed on the waiting list for a renal transplant than are patients who are treated in not-for-profit facilities", possibly because transplantation removes a constant stream of revenue from the facility. The insurance industry has complained about kickbacks and problematic relationships between charities and providers.

In China

The Government of China provides the funding for dialysis treatment. There is a challenge to reach everyone who needs dialysis treatment because of the unequal distribution of health care resources and dialysis centers. There are 395,121 individuals who receive hemodialysis or peritoneal dialysis in China per year. The percentage of the Chinese population with Chronic Kidney Disease is 10.8%. The Chinese Government is trying to increase the amount of peritoneal dialysis taking place to meet the needs of the nation's individuals with Chronic Kidney Disease.

In Australia

Dialysis is provided without cost to all patients through Medicare, with 75% of all dialysis being administered as haemodialysis to patients three times per week in a dialysis facility. The Northern Territory has the highest incidence rate per population of haemodialysis, with Indigenous Australians having higher rates of Chronic Kidney Disease and lower rates of functional kidney transplants than the broader population. The remote Central Australian town of Alice Springs, despite having a population of approximately 25000, has the largest dialysis unit in the Southern Hemisphere. Many people must move to Alice Springs from remote Indigenous communities to access health services such as haemodialysis, which results in housing shortages, overcrowding, and poor living conditions.

History

Arm hooked up to dialysis tubing.

In 1913, Leonard Rowntree and John Abel of Johns Hopkins Hospital developed the first dialysis system which they successfully tested in animals. A Dutch doctor, Willem Johan Kolff, constructed the first working dialyzer in 1943 during the Nazi occupation of the Netherlands. Due to the scarcity of available resources, Kolff had to improvise and build the initial machine using sausage casings, beverage cans, a washing machine and various other items that were available at the time. Over the following two years (1944–1945), Kolff used his machine to treat 16 patients with acute kidney failure, but the results were unsuccessful. Then, in 1945, a 67-year-old comatose woman regained consciousness following 11 hours of hemodialysis with the dialyzer and lived for another seven years before dying from an unrelated condition. She was the first-ever patient successfully treated with dialysis. Gordon Murray of the University of Toronto independently developed a dialysis machine in 1945. Unlike Kolff's rotating drum, Murray's machine used fixed flat plates, more like modern designs. Like Kolff, Murray's initial success was in patients with acute renal failure. Nils Alwall of Lund University in Sweden modified a similar construction to the Kolff dialysis machine by enclosing it inside a stainless steel canister. This allowed the removal of fluids, by applying a negative pressure to the outside canister, thus making it the first truly practical device for hemodialysis. Alwall treated his first patient in acute kidney failure on 3 September 1946.

Algorithmic information theory

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Algorithmic_information_theory ...