Inductive logic programming

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https://en.wikipedia.org/wiki/Inductive_logic_programming 

 

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Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.

• Schema: positive examples + negative examples + background knowledge ⇒ hypothesis.

Inductive logic programming is particularly useful in bioinformatics and natural language processing. Gordon Plotkin and Ehud Shapiro laid the initial theoretical foundation for inductive machine learning in a logical setting. Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples. The term Inductive Logic Programming was first introduced in a paper by Stephen Muggleton in 1991. Muggleton also founded the annual international conference on Inductive Logic Programming, introduced the theoretical ideas of Predicate Invention, Inverse resolution, and Inverse entailment. Muggleton implemented Inverse entailment first in the PROGOL system. The term "inductive" here refers to philosophical (i.e. suggesting a theory to explain observed facts) rather than mathematical (i.e. proving a property for all members of a well-ordered set) induction.

Formal definition

The background knowledge is given as a logic theory B, commonly in the form of Horn clauses used in logic programming. The positive and negative examples are given as a conjunction ${\displaystyle E^{+}}$ and ${\displaystyle E^{-}}$ of unnegated and negated ground literals, respectively. A correct hypothesis h is a logic proposition satisfying the following requirements.

${\displaystyle {\begin{array}{llll}{\text{Necessity:}}&B&\not \models &E^{+}\\{\text{Sufficiency:}}&B\land h&\color {blue}{\models }&E^{+}\\{\text{Weak consistency:}}&B\land h&\not \models &{\textit {false}}\\{\text{Strong consistency:}}&B\land h\land E^{-}&\not \models &{\textit {false}}\end{array}}}$

"Necessity" does not impose a restriction on h, but forbids any generation of a hypothesis as long as the positive facts are explainable without it. "Sufficiency" requires any generated hypothesis h to explain all positive examples ${\displaystyle E^{+}}$. "Weak consistency" forbids generation of any hypothesis h that contradicts the background knowledge B. "Strong consistency" also forbids generation of any hypothesis h that is inconsistent with the negative examples ${\displaystyle E^{-}}$, given the background knowledge B; it implies "Weak consistency"; if no negative examples are given, both requirements coincide. Džeroski  requires only "Sufficiency" (called "Completeness" there) and "Strong consistency".

Example

Assumed family relations in section "Example"

The following well-known example about learning definitions of family relations uses the abbreviations

par: parent, fem: female, dau: daughter, g: George, h: Helen, m: Mary, t: Tom, n: Nancy, and e: Eve.

It starts from the background knowledge (cf. picture)

${\displaystyle {\textit {par}}(h,m)\land {\textit {par}}(h,t)\land {\textit {par}}(g,m)\land {\textit {par}}(t,e)\land {\textit {par}}(n,e)\land {\textit {fem}}(h)\land {\textit {fem}}(m)\land {\textit {fem}}(n)\land {\textit {fem}}(e)}$,

the positive examples

${\displaystyle {\textit {dau}}(m,h)\land {\textit {dau}}(e,t)}$,

and the trivial proposition true to denote the absence of negative examples.

Plotkin's  "relative least general generalization (rlgg)" approach to inductive logic programming shall be used to obtain a suggestion about how to formally define the daughter relation dau.

This approach uses the following steps.

• Relativize each positive example literal with the complete background knowledge:

  ${\displaystyle {\begin{aligned}{\textit {dau}}(m,h)\leftarrow {\textit {par}}(h,m)\land {\textit {par}}(h,t)\land {\textit {par}}(g,m)\land {\textit {par}}(t,e)\land {\textit {par}}(n,e)\land {\textit {fem}}(h)\land {\textit {fem}}(m)\land {\textit {fem}}(n)\land {\textit {fem}}(e)\\{\textit {dau}}(e,t)\leftarrow {\textit {par}}(h,m)\land {\textit {par}}(h,t)\land {\textit {par}}(g,m)\land {\textit {par}}(t,e)\land {\textit {par}}(n,e)\land {\textit {fem}}(h)\land {\textit {fem}}(m)\land {\textit {fem}}(n)\land {\textit {fem}}(e)\end{aligned}}}$,

• Convert into clause normal form:

  ${\displaystyle {\begin{aligned}{\textit {dau}}(m,h)\lor \lnot {\textit {par}}(h,m)\lor \lnot {\textit {par}}(h,t)\lor \lnot {\textit {par}}(g,m)\lor \lnot {\textit {par}}(t,e)\lor \lnot {\textit {par}}(n,e)\lor \lnot {\textit {fem}}(h)\lor \lnot {\textit {fem}}(m)\lor \lnot {\textit {fem}}(n)\lor \lnot {\textit {fem}}(e)\\{\textit {dau}}(e,t)\lor \lnot {\textit {par}}(h,m)\lor \lnot {\textit {par}}(h,t)\lor \lnot {\textit {par}}(g,m)\lor \lnot {\textit {par}}(t,e)\lor \lnot {\textit {par}}(n,e)\lor \lnot {\textit {fem}}(h)\lor \lnot {\textit {fem}}(m)\lor \lnot {\textit {fem}}(n)\lor \lnot {\textit {fem}}(e)\end{aligned}}}$,

• Anti-unify each compatible  pair  of literals:
  • ${\displaystyle {\textit {dau}}(x_{me},x_{ht})}$ from ${\displaystyle {\textit {dau}}(m,h)}$ and ${\displaystyle {\textit {dau}}(e,t)}$,
  • ${\displaystyle \lnot {\textit {par}}(x_{ht},x_{me})}$ from ${\displaystyle \lnot {\textit {par}}(h,m)}$ and ${\displaystyle \lnot {\textit {par}}(t,e)}$,
  • ${\displaystyle \lnot {\textit {fem}}(x_{me})}$ from ${\displaystyle \lnot {\textit {fem}}(m)}$ and ${\displaystyle \lnot {\textit {fem}}(e)}$,
  • ${\displaystyle \lnot {\textit {par}}(g,m)}$ from ${\displaystyle \lnot {\textit {par}}(g,m)}$ and ${\displaystyle \lnot {\textit {par}}(g,m)}$, similar for all other background-knowledge literals
  • ${\displaystyle \lnot {\textit {par}}(x_{gt},x_{me})}$ from ${\displaystyle \lnot {\textit {par}}(g,m)}$ and ${\displaystyle \lnot {\textit {par}}(t,e)}$, and many more negated literals
• Delete all negated literals containing variables that don't occur in a positive literal:
  • after deleting all negated literals containing other variables than ${\displaystyle x_{me},x_{ht}}$, only ${\displaystyle {\textit {dau}}(x_{me},x_{ht})\lor \lnot {\textit {par}}(x_{ht},x_{me})\lor \lnot {\textit {fem}}(x_{me})}$ remains, together with all ground literals from the background knowledge
• Convert clauses back to Horn form:
  • ${\displaystyle {\textit {dau}}(x_{me},x_{ht})\leftarrow {\textit {par}}(x_{ht},x_{me})\land {\textit {fem}}(x_{me})\land ({\text{all background knowledge facts}})}$

The resulting Horn clause is the hypothesis h obtained by the rlgg approach. Ignoring the background knowledge facts, the clause informally reads "${\displaystyle x_{me}}$ is called a daughter of ${\displaystyle x_{ht}}$ if ${\displaystyle x_{ht}}$ is the parent of ${\displaystyle x_{me}}$ and ${\displaystyle x_{me}}$ is female", which is a commonly accepted definition.

Concerning the above requirements, "Necessity" was satisfied because the predicate dau doesn't appear in the background knowledge, which hence cannot imply any property containing this predicate, such as the positive examples are. "Sufficiency" is satisfied by the computed hypothesis h, since it, together with ${\displaystyle {\textit {par}}(h,m)\land {\textit {fem}}(m)}$ from the background knowledge, implies the first positive example ${\displaystyle {\textit {dau}}(m,h)}$, and similarly h and ${\displaystyle {\textit {par}}(t,e)\land {\textit {fem}}(e)}$ from the background knowledge implies the second positive example ${\displaystyle {\textit {dau}}(e,t)}$. "Weak consistency" is satisfied by h, since h holds in the (finite) Herbrand structure described by the background knowledge; similar for "Strong consistency".

The common definition of the grandmother relation, viz. ${\displaystyle {\textit {gra}}(x,z)\leftarrow {\textit {fem}}(x)\land {\textit {par}}(x,y)\land {\textit {par}}(y,z)}$, cannot be learned using the above approach, since the variable y occurs in the clause body only; the corresponding literals would have been deleted in the 4th step of the approach. To overcome this flaw, that step has to be modified such that it can be parametrized with different literal post-selection heuristics. Historically, the GOLEM implementation is based on the rlgg approach.

Inductive Logic Programming system

Inductive Logic Programming system is a program that takes as an input logic theories ${\displaystyle B,E^{+},E^{-}}$ and outputs a correct hypothesis H wrt theories ${\displaystyle B,E^{+},E^{-}}$ An algorithm of an ILP system consists of two parts: hypothesis search and hypothesis selection. First a hypothesis is searched with an inductive logic programming procedure, then a subset of the found hypotheses (in most systems one hypothesis) is chosen by a selection algorithm. A selection algorithm scores each of the found hypotheses and returns the ones with the highest score. An example of score function include minimal compression length where a hypothesis with a lowest Kolmogorov complexity has the highest score and is returned. An ILP system is complete iff for any input logic theories ${\displaystyle B,E^{+},E^{-}}$ any correct hypothesis H wrt to these input theories can be found with its hypothesis search procedure.

Hypothesis search

Modern ILP systems like Progol, Hail  and Imparo  find a hypothesis H using the principle of the inverse entailment for theories B, E, H: ${\displaystyle B\land H\models E\iff B\land \neg E\models \neg H}$. First they construct an intermediate theory F called a bridge theory satisfying the conditions ${\displaystyle B\land \neg E\models F}$ and ${\displaystyle F\models \neg H}$. Then as ${\displaystyle H\models \neg F}$, they generalize the negation of the bridge theory F with the anti-entailment. However, the operation of the anti-entailment since being highly non-deterministic is computationally more expensive. Therefore, an alternative hypothesis search can be conducted using the operation of the inverse subsumption (anti-subsumption) instead which is less non-deterministic than anti-entailment.

Questions of completeness of a hypothesis search procedure of specific ILP system arise. For example, Progol's hypothesis search procedure based on the inverse entailment inference rule is not complete by Yamamoto's example. On the other hand, Imparo is complete by both anti-entailment procedure  and its extended inverse subsumption  procedure.

Implementations

• 1BC and 1BC2: first-order naive Bayesian classifiers:
• ACE (A Combined Engine)
• Aleph
• Atom
• Claudien
• DL-Learner
• DMax
• FastLAS (Fast Learning from Answer Sets)
• FOIL (First Order Inductive Learner)
• Golem
• ILASP (Inductive Learning of Answer Set Programs)
• Imparo
• Inthelex (INcremental THEory Learner from EXamples)
• Lime
• Metagol
• Mio
• MIS (Model Inference System) by Ehud Shapiro
• PROGOL
• RSD
• Warmr (now included in ACE)
• ProGolem

Magnetic field of Mars

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Magnetic_field_of_Mars 

 

Martian Dynamo. The schematic illustration of the ancient dipolar magnetic field of Mars generated by a core dynamo process.

The magnetic field of Mars is the magnetic field generated from Mars' interior. Today, Mars does not have a global magnetic field. However, Mars did power an early dynamo that produced a strong magnetic field 4 billion years ago, comparable to Earth's present surface field. After the early dynamo ceased, a weak late dynamo was reactivated (or persisted up to) ~3.8 billion years ago. The distribution of Martian crustal magnetization is similar to the Martian dichotomy (i.e., the Martian hemispheric topographic dichotomy). Whereas the Martian northern lowlands are largely unmagnetized, the southern hemisphere possesses strong remanent magnetization, showing alternating stripes. Our understanding of the evolution of the magnetic field of Mars is based on the combination of satellite measurements, Martian ground-based magnetic data, paleomagnetic analysis of meteorites, planetary thermal evolution modeling, and magnetohydrodynamic simulations.

Crustal magnetism

Satellite data

Map of Martian crustal magnetism. Cylindrical projection map of crustal magnetism on Mars observed by MGS satellite at 400 km altitude. Colors represent intensities of the median value of the radial magnetic field components contoured over two orders of magnitude variation.

The reconstruction of the Martian global crustal magnetism is mainly based on magnetic field measurements from the Mars Global Surveyor (MGS) magnetic field experiment/electron reflectometer (MAG/ER) and Mars Atmosphere and Volatile Evolution (MAVEN) magnetic-field data. However, these satellites are located at altitudes of 90–6000 km and have spatial resolutions of ≥160 km, so the measured magnetization cannot observe crustal magnetic fields at shorter length scales.

Mars currently does not sustain an active dynamo based on the Mars Global Surveyor (MGS) and Mars Atmosphere and Volatile Evolution (MAVEN) magnetic field measurements. However, the satellite data show that the older(~4.2–4.3 Ga) southern-hemisphere crust records strong remanent magnetization (~22 nT), but the younger northern lowlands have a much weaker or zero remanent magnetization. In contrast, the large basins formed during the Late Heavy Bombardment (LHB) (~ 4.1–3.9 Ga) (e.g., Argyre, Hellas, and Isidis) and volcanic provinces (e.g., Elysium, Olympus Mons, Tharsis Montes, and Alba Patera) lack magnetic signatures, but the younger Noachian and Hesperian volcanoes (e.g., Tyrrhenus Mons and Syrtis Major) have crustal remanence.

Mars lander observation

The Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission measured the crustal field at the Insight landing site located in Elysium Planitia to be ~2 µT. This detailed ground-level data is an order of magnitude higher than satellite-based estimates of ~200 nT at the InSight landing site. The source of this high magnetization is suggested to be Noachian basement (~3.9 Ga) beneath the Early Amazonian and Hesperian flows (~3.6 and 1.5 Ga).

Paleomagnetism

Paleomagnetic evidence

Martian meteorites enable estimates of Mar's paleofield based on the thermal remanent magnetization (or TRM) (i.e., the remanent magnetization acquired when the meteorite cooled below the Curie temperature in the presence of the ambient magnetic field). The thermal remanent magnetization of carbonates in meteorite ALH84001 revealed that the early (4.1–3.9 Ga) Martian magnetic field was ~50 µT, much higher than the modern field, suggesting that a Martian dynamo was present until at least this time. Younger (~1.4 Ga) Martian Nakhlite meteorite Miller Range (MIL) 03346 recorded a paleofield of only ~5 µT. However, given the possible source locations of the Nakhlite meteorite, this paleointensity still suggests that the surface magnetization is stronger than the magnetic fields estimated from satellite measurements. The ~5 µT paleofield of this meteorite can be explained either by a late active dynamo or the field generated from lava flows emplaced in the absence of a late Martian dynamo.

Martian meteorites as paleomagnetic recorders

Martian meteorites contain a wide range of magnetic minerals that can record ancient remanent magnetism, including magnetite, titano-magnetite, pyrrhotite, and hematite. The magnetic mineralogy includes single domain (SD), pseudo single domain (PSD)-like, multi-domain (MD) states. However, only limited Martian meteorites are available to reconstruct the Martian paleofield due to aqueous, thermal, and shock overprints that make many Martian meteorites unsuitable for these studies. Paleomagnetic studies of Martian meteorites are listed in the table below:

Type	Crystallization Age	Shock events	Paleointensity	Sources
Shergottites (Shergotty)	~343 Ma	multiple shock events	2 µT, 0.25–1 µT	shock demagnetization
Shergottites (Tissint)	~600 Ma	multiple shock events	2 µT	remagnetized by impact events
Nakhlite	~1.3–1.4 Ga	-	4 µT	late dynamo ?
Nakhlite	~1.4 Ga	no significant shock event	5 µT	old source rock or late dynamo ?
ALH84001	~4.5 Ga	~4.0 Ga (major impact)	50 µT	active early dynamo
ALH84001	~4.5 Ga	~4.0 Ga (major impact)

Martian dynamo

Timeline of Martian dynamo

Timeline of the Martian dynamo. Grey shading represents possible age constraints (in Ga years) for the early and late dynamo. Stars indicate new age constraints from MAVEN data. [a] Early dynamo before the formation of Hellas, Isidis, and Argyre. [b] The cessation of the early dynamo based on large basin population. [c] The age of ALH84001. [d] Late dynamo after the formation of the major basins.

The exact timing and duration of the Martian dynamo remain unknown, but there are several constraints from satellite observations and paleomagnetic studies. The strong crustal magnetization in the southern hemisphere and the paleomagnetic evidence of ALH84001 indicate that Mars sustained a strong magnetic field between ~4.2–4.3 Ga. The absence of crustal magnetic signatures in the upper lowlands and large impact basins implies dynamo termination prior to the formation of these basins (~4.0–3.9 Ga). Magnetic anomalies from two young volcanoes (e.g., Tyrrhenus Mons, Syrtis Major) may reflect the presence of a Martian magnetic field with possible magnetic reversals during the late Noachian and Hesperian period.

Hemispheric magnetic dichotomy

One unresolved question is why the Martian crustal hemispheric dichotomy correlates to the magnetic dichotomy (and whether the origin of this dichotomy is an exogenic or endogenic process). One exogenic explanation is that the Borealis impact event resulted in thermal demagnetization of an initially magnetized northern hemisphere, but the proposed age of this event (~4.5 Ga) is long before the Martian dynamo termination (~4.0–4.1 Ga). An alternate model suggests that degree-1 mantle convection (i.e., a convective structure in which mantle upwelling dominates in one hemisphere but downwelling takes in the other hemisphere) can produce a single-hemisphere dynamo.

Alternating stripes

One striking feature in Martian crustal magnetism is the long E–W trending alternating stripes on the southern hemisphere (Terra Cimmeria and Terra Sirenum). It has been proposed that these bands are formed by plate tectonic activity similar to the alternating magnetic polarity caused by seafloor crust spreading on Earth or the results of repeated dike intrusions. However, careful selection of the data analysis method is required to interpret these alternating stripes. Using sparse solutions (e.g., L1 regularization) of crustal-field measurements instead of smoothing solutions (e.g., L2 regularization) shows highly magnetized local patches (with the rest of the crust unmagnetized) instead of stripes. These patches might be formed by localized events such as volcanism or heating by impact events, which may not require continuous fields (e.g., intermittent dynamo).

Dynamo mechanisms

The dynamo mechanism of Mars is poorly understood but expected to be similar to the Earth's dynamo mechanism. Thermal convection due to the high thermal gradients in the hot, initial core was likely the primary mechanism for driving a dynamo early in Mars' history. As the mantle and core cooled over time, inner-core crystallization (which would provide latent heat) and chemical convection may have played a major role in driving the dynamo. Following inner-core formation, light elements migrated from the inner-core boundary into the liquid outer core and drove convection by buoyancy. However, even InSight lander data could not confirm the presence of Mars' solid inner core, and we cannot exclude the possibility that there was no core crystallization (only thermal convection without chemical convection). Also, the possibility that magnetic fields may have been generated by a magma ocean cannot be ruled out.

It is also unclear when and by what mechanism the Martian dynamo shut down. Perhaps a change in the cooling rate of the mantle may have caused the cessation of the Martian dynamo. One theory is giant impacts during the early and mid-Noachian periods stopped the dynamo by decreasing global heat flow at the core-mantle boundary.

The seismic measurements from the InSight lander revealed that the Martian outer core is in a liquid state and larger than expected. In one model, a partially crystallized Martian core explains the current state of Mars (i.e., lack of magnetic field despite liquid outer core), and this model predicts that the magnetic field has the potential to be reactivated in the future.

Possible dynamo mechanisms

Dynamo sources	Dynamo mechanisms	Notes
Thermal	Thermal convection	- requires high temperature, high sulfur content - no solid inner core
	Magma ocean	- requires conductive silicate-dominated melts
Thermocompositional	Chemical convection (Top-down crystallization)	- requires low temperature, low thermal expansivity, low sulfur content - possible future dynamo reactivation
	Chemical convection (Bottom-up crystallization or iron snow)	- requires low temperature, high thermal expansivity, high sulfur content - powers dynamo based on the light element partitioning coefficient
Mechanical	Impact events	- reduces global heat flow at the core mantle boundary and stops dynamo

Fetus

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Fetus 

A fetus or foetus (/ˈfiːtəs/; plural fetuses, feti, foetuses, or foeti) is the unborn offspring that develops from an animal embryo. Following embryonic development the fetal stage of development takes place. In human prenatal development, fetal development begins from the ninth week after fertilization (or eleventh week gestational age) and continues until birth. Prenatal development is a continuum, with no clear defining feature distinguishing an embryo from a fetus. However, a fetus is characterized by the presence of all the major body organs, though they will not yet be fully developed and functional and some not yet situated in their final anatomical location.

Etymology

The word fetus (plural fetuses or feti) is related to the Latin fētus ("offspring", "bringing forth", "hatching of young") and the Greek "φυτώ" to plant. The word "fetus" was used by Ovid in Metamorphoses, book 1, line 104.

The predominant British, Irish, and Commonwealth spelling is foetus, which has been in use since at least 1594. The spelling with -oe- arose in Late Latin, in which the distinction between the vowel sounds -oe- and -e- had been lost. This spelling is the most common in most Commonwealth nations, except in the medical literature, where fetus is used. The more classical spelling fetus is used in Canada and the United States. In addition, fetus is now the standard English spelling throughout the world in medical journals. The spelling faetus was also used historically.

Development in humans

Further information: Prenatal development

Weeks 9 to 16 (2 to 3.6 months)

A human fetus, attached to placenta, at three months gestational age.

In humans, the fetal stage starts nine weeks after fertilization. At the start of the fetal stage, the fetus is typically about 30 millimetres (1+1⁄4 in) in length from crown-rump, and weighs about 8 grams. The head makes up nearly half of the size of the fetus. Breathing-like movements of the fetus are necessary for the stimulation of lung development, rather than for obtaining oxygen. The heart, hands, feet, brain and other organs are present, but are only at the beginning of development and have minimal operation.

At this point in development, uncontrolled movements and twitches occur as muscles, the brain, and pathways begin to develop.

Weeks 17 to 25 (3.6 to 6.6 months)

A woman pregnant for the first time (nulliparous) typically feels fetal movements at about 21 weeks, whereas a woman who has given birth before will typically feel movements by 20 weeks. By the end of the fifth month, the fetus is about 20 cm (8 in) long.

Weeks 26 to 38 (6.6 to 8.6 months)

The amount of body fat rapidly increases. Lungs are not fully mature. Neural connections between the sensory cortex and thalamus develop as early as 24 weeks' gestational age, but the first evidence of their function does not occur until around 30 weeks, when minimal consciousness, dreaming, and the ability to feel pain emerges. Bones are fully developed, but are still soft and pliable. Iron, calcium, and phosphorus become more abundant. Fingernails reach the end of the fingertips. The lanugo, or fine hair, begins to disappear, until it is gone except on the upper arms and shoulders. Small breast buds are present on both sexes. Head hair becomes coarse and thicker. Birth is imminent and occurs around the 38th week after fertilization. The fetus is considered full-term between weeks 36 and 40, when it is sufficiently developed for life outside the uterus. It may be 48 to 53 cm (19 to 21 in) in length, when born. Control of movement is limited at birth, and purposeful voluntary movements develop all the way until puberty.

Variation in growth

Further information: Birth weight and Environmental toxicants and fetal development

There is much variation in the growth of the human fetus. When fetal size is less than expected, the condition is known as intrauterine growth restriction (IUGR) also called fetal growth restriction (FGR); factors affecting fetal growth can be maternal, placental, or fetal.

Maternal factors include maternal weight, body mass index, nutritional state, emotional stress, toxin exposure (including tobacco, alcohol, heroin, and other drugs which can also harm the fetus in other ways), and uterine blood flow.

Placental factors include size, microstructure (densities and architecture), umbilical blood flow, transporters and binding proteins, nutrient utilization and nutrient production.

Fetal factors include the fetus genome, nutrient production, and hormone output. Also, female fetuses tend to weigh less than males, at full term.

Fetal growth is often classified as follows: small for gestational age (SGA), appropriate for gestational age (AGA), and large for gestational age (LGA). SGA can result in low birth weight, although premature birth can also result in low birth weight. Low birth weight increases risk for perinatal mortality (death shortly after birth), asphyxia, hypothermia, polycythemia, hypocalcemia, immune dysfunction, neurologic abnormalities, and other long-term health problems. SGA may be associated with growth delay, or it may instead be associated with absolute stunting of growth.

Viability

Main article: Fetal viability

 

Stages in prenatal development, showing viability and point of 50% chance of survival at bottom. Weeks and months numbered by gestation.

Fetal viability refers to a point in fetal development at which the fetus may survive outside the womb. The lower limit of viability is approximately 5+3⁄4 months gestational age and is usually later.

There is no sharp limit of development, age, or weight at which a fetus automatically becomes viable. According to data from 2003 to 2005, survival rates are 20–35% for babies born at 23 weeks of gestation (5+3⁄4 months); 50–70% at 24–25 weeks (6 – 6+1⁄4 months); and >90% at 26–27 weeks (6+1⁄2 – 6+3⁄4 months) and over. It is rare for a baby weighing less than 500 g (1 lb 2 oz) to survive.

When such premature babies are born, the main causes of mortality are that the respiratory system and the central nervous system are not completely differentiated. If given expert postnatal care, some preterm babies weighing less than 500 g (1 lb 2 oz) may survive, and are referred to as extremely low birth weight or immature infants.

Preterm birth is the most common cause of infant mortality, causing almost 30 percent of neonatal deaths. At an occurrence rate of 5% to 18% of all deliveries, it is also more common than postmature birth, which occurs in 3% to 12% of pregnancies.

Circulatory system

Main article: Fetal circulation

Before birth

Diagram of the human fetal circulatory system.

The heart and blood vessels of the circulatory system, form relatively early during embryonic development, but continue to grow and develop in complexity in the growing fetus. A functional circulatory system is a biological necessity, since mammalian tissues can not grow more than a few cell layers thick without an active blood supply. The prenatal circulation of blood is different from postnatal circulation, mainly because the lungs are not in use. The fetus obtains oxygen and nutrients from the mother through the placenta and the umbilical cord.

Blood from the placenta is carried to the fetus by the umbilical vein. About half of this enters the fetal ductus venosus and is carried to the inferior vena cava, while the other half enters the liver proper from the inferior border of the liver. The branch of the umbilical vein that supplies the right lobe of the liver first joins with the portal vein. The blood then moves to the right atrium of the heart. In the fetus, there is an opening between the right and left atrium (the foramen ovale), and most of the blood flows from the right into the left atrium, thus bypassing pulmonary circulation. The majority of blood flow is into the left ventricle from where it is pumped through the aorta into the body. Some of the blood moves from the aorta through the internal iliac arteries to the umbilical arteries, and re-enters the placenta, where carbon dioxide and other waste products from the fetus are taken up and enter the mother's circulation.

Some of the blood from the right atrium does not enter the left atrium, but enters the right ventricle and is pumped into the pulmonary artery. In the fetus, there is a special connection between the pulmonary artery and the aorta, called the ductus arteriosus, which directs most of this blood away from the lungs (which are not being used for respiration at this point as the fetus is suspended in amniotic fluid).

• 

  3D ultrasound of 80-millimetre (3 in) fetus (about 3+1⁄2 months gestational age)

• 

  Fetus at 4+1⁄4 months

• 

  Fetus at 5 months

Postnatal development

Main article: Adaptation to extrauterine life

With the first breath after birth, the system changes suddenly. Pulmonary resistance is reduced dramatically, prompting more blood to move into the pulmonary arteries from the right atrium and ventricle of the heart and less to flow through the foramen ovale into the left atrium. The blood from the lungs travels through the pulmonary veins to the left atrium, producing an increase in pressure that pushes the septum primum against the septum secundum, closing the foramen ovale and completing the separation of the newborn's circulatory system into the standard left and right sides. Thereafter, the foramen ovale is known as the fossa ovalis.

The ductus arteriosus normally closes within one or two days of birth, leaving the ligamentum arteriosum, while the umbilical vein and ductus venosus usually closes within two to five days after birth, leaving, respectively, the liver's ligamentum teres and ligamentum venosus.

Immune system

The placenta functions as a maternal-fetal barrier against the transmission of microbes. When this is insufficient, mother-to-child transmission of infectious diseases can occur.

Maternal IgG antibodies cross the placenta, giving the fetus passive immunity against those diseases for which the mother has antibodies. This transfer of antibodies in humans begins as early as the fifth month (gestational age) and certainly by the sixth month.

Developmental problems

Further information: Environmental toxicants and fetal development and Birth defect

A developing fetus is highly susceptible to anomalies in its growth and metabolism, increasing the risk of birth defects. One area of concern is the lifestyle choices made during pregnancy. Diet is especially important in the early stages of development. Studies show that supplementation of the person's diet with folic acid reduces the risk of spina bifida and other neural tube defects. Another dietary concern is whether breakfast is eaten. Skipping breakfast could lead to extended periods of lower than normal nutrients in the maternal blood, leading to a higher risk of prematurity, or birth defects.

Alcohol consumption may increase the risk of the development of fetal alcohol syndrome, a condition leading to intellectual disability in some infants. Smoking during pregnancy may also lead to miscarriages and low birth weight (2,500 grams (5 pounds 8 ounces). Low birth weight is a concern for medical providers due to the tendency of these infants, described as "premature by weight", to have a higher risk of secondary medical problems.

X-rays are known to have possible adverse effects on the development of the fetus, and the risks need to be weighed against the benefits.

Congenital disorders are acquired before birth. Infants with certain congenital heart defects can survive only as long as the ductus remains open: in such cases the closure of the ductus can be delayed by the administration of prostaglandins to permit sufficient time for the surgical correction of the anomalies. Conversely, in cases of patent ductus arteriosus, where the ductus does not properly close, drugs that inhibit prostaglandin synthesis can be used to encourage its closure, so that surgery can be avoided.

Other heart birth defects include ventricular septal defect, pulmonary atresia, and tetralogy of Fallot.

An abdominal pregnancy can result in the death of the fetus and where this is rarely not resolved it can lead to its formation into a lithopedion.

Fetal pain

Main article: Fetal pain

Fetal pain, its existence and its implications are debated politically and academically. According to the conclusions of a review published in 2005, "Evidence regarding the capacity for fetal pain is limited but indicates that fetal perception of pain is unlikely before the third trimester." However, developmental neurobiologists argue that the establishment of thalamocortical connections (at about 6+1⁄2 months) is an essential event with regard to fetal perception of pain. Nevertheless, the perception of pain involves sensory, emotional and cognitive factors and it is "impossible to know" when pain is experienced, even if it is known when thalamocortical connections are established. Some authors argue that fetal pain is possible from the second half of pregnancy: “The available scientific evidence makes it possible, even probable, that fetal pain perception occurs well before late gestation” wrote KJS Anand in the journal of the IASP.

Whether a fetus has the ability to feel pain and suffering is part of the abortion debate. In the United States, for example, anti-abortion advocates have proposed legislation that would require providers of abortions to inform pregnant women that their fetuses may feel pain during the procedure and that would require each person to accept or decline anesthesia for the fetus.

Legal and social issues

Abortion of a human pregnancy is legal and/or tolerated in most countries, although with gestational time limits that normally prohibit late-term abortions.

Other animals

Further information: Evolution of mammals

 

Fourteen phases of elephant development before birth

A fetus is a stage in the prenatal development of viviparous organisms. This stage lies between embryogenesis and birth. Many vertebrates have fetal stages, ranging from most mammals to many fish. In addition, some invertebrates bear live young, including some species of onychophora and many arthropods.

The fetuses of most mammals are situated similarly to the human fetus within their mothers. However, the anatomy of the area surrounding a fetus is different in litter-bearing animals compared to humans: each fetus of a litter-bearing animal is surrounded by placental tissue and is lodged along one of two long uteri instead of the single uterus found in a human female.

Development at birth varies considerably among animals, and even among mammals. Altricial species are relatively helpless at birth and require considerable parental care and protection. In contrast, precocial animals are born with open eyes, have hair or down, have large brains, and are immediately mobile and somewhat able to flee from, or defend themselves against, predators. Primates are precocial at birth, with the exception of humans.

The duration of gestation in placental mammals varies from 18 days in jumping mice to 23 months in elephants. Generally speaking, fetuses of larger land mammals require longer gestation periods.

Fetal stage of a porpoise

The benefits of a fetal stage means that young are more developed when they are born. Therefore, they may need less parental care and may be better able to fend for themselves. However, carrying fetuses exerts costs on the mother, who must take on extra food to fuel the growth of her offspring, and whose mobility and comfort may be affected (especially toward the end of the fetal stage).

In some instances, the presence of a fetal stage may allow organisms to time the birth of their offspring to a favorable season.