# on 05-Mar-2017 (Sun)

#### Flashcard 1484289084684

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There are the 3 "A" core expressions the are used to protect the attacment relationship, and lead to the 5 different survival styles, What are these 3 core expressions? (each start with the letter A)
Anger, Aggression, Authenticitcy

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#### Flashcard 1484290919692

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1. When core needs are not met by children of rel trauma, what 4 negative experiences (3 start w/D and 1 w/ i) that the adaptive stratagies are trying to help deal with.
2. What are the key parts of self does NARM empahsize to help develp a healthy regulatroy system?
1. Disconnection, Dysregulation, Disorganisation and Issolation.
2. Organized, Coherent, and Functional

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#### Flashcard 1484292754700

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What is the goal of the Pride Based Counter Indenfication?
Pride based counter identifications reflect how we would liek to see ourselves or others see us, the paroix is the more energy a person invest in these defensive the stronger the shame based id becomes.

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#### Flashcard 1484295113996

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What are the 12 steps of the NARM healing cycle?
1. INCREASING AWARENESS OF ADAPTIVE SURVIVAL SYTLES
2. Inquiry into identiy
3. Disidentification from shame and pride based identifications
4. Self hatred self rejection and jugements diminished
5. Reconnection with core needs and capacities
6. Resoriaton of connection and aliveness
7. INCREASING CAPCITY FOR SOMATIC AWARENESS
8. Somatic Mindfulness
9. Discharge of shoke states
10. increasing regulation and presence
11. Increasing contact with the body
12. Greater capacity for self regulations
(Rinse and repeat)

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#### Flashcard 1484296949004

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What is the difference between psychodynamic and esoteric approaches to ego?
What are the pros/cons to these different approaches?
Psychodynamic work to sokidify the sense of identify and strengthen the ego, where as esoteric orientations hold that egow is an illusion and separates us fro Being and keeps us from experiencing teh spaciousness, fulidity, and fullness of our essential nature.
Both perspectives are important, Esoteric approaches address the limitations of what they call Ego, but generally do not incorarate the clinical awareness of the importance of attachement adn developmental trauma in creation of the sense of self.

Brief answer: psychodynmic focus on Strengthen ego vs Esoteric focus on release ego. Psychodynamic supports impact on ego caused by rel trauma while esoteric supports learning how to better regulate and re-wire the adaptive stratagies developed by the truama.

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#### Flashcard 1484298784012

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What is the paradox of change?
The more we try to change ourselves, the more we prevent change from ocurring, on the other hand, the more we allow ourselves to fully experience who we are, the greater the possibility of change.
Brief: More we resist the more we persist.

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#### Flashcard 1484301929740

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Elaborate on the 5 adaptive styles in terms of Survial Adaptions (disclousre) and Stratagy Used to PRotect the Attachement Relationship.
 Core Need Survival Adaption Stratagey USed to Protect The Attach Rel Connection Foreclousing Connection, Disconnect from body and social engagement Children gife up their very sense of existence, discounnect and attempt to become invisible. Attunemet Foreclosing the awareness and expression of personal needs Chidrent give up thier own need in order to focus on the needs of others, particularly the needs of the parents Trust Forclosing trust and healthy interdependence Children give up their quthenticity in order to be who the parents want them to be: best friend, sport star, confidante, etc. Autonomy Foreclosing authentic expression, responding with what they think is expected of them Children give up direct expression of independence in oreder not to feel abandoned or crushed Love-Sexuality Foreclosing love and heart connection, foreclosing sexuality, Forclosing integration of love and sexuality Children try to avoid rejection by perfecting themselves, hoping that they can win love through looks or performance.

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#### Flashcard 1484304026892

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What does each adaptive style develop around to help make sense of the broad spectrum of symptoms often seen in developmental trauam?
Connection: develops around teh need for the conact and the fear of connection
Attunement: Develops around the conflict between having personal needs and the rejection of them.
Trust: develops around both the desire for and the fear of setting limits and expressing independence.
Love-Sexuality: Develops around wanting to love and be loved and the fear of vulnrability. It also develops aroudn the splitting of love and sexuality.

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#### Flashcard 1484505091340

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it is now thought that perhaps a [...] of all eukaryotic proteins can adopt structures that are mostly disordered, fluctuating rapidly between many different conforma- tions.
quarter

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it is now thought that perhaps a quarter of all eukaryotic proteins can adopt structures that are mostly disordered, fluctuating rapidly between many different conforma- tions.

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#### Flashcard 1484506664204

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it is now thought that perhaps a quarter of all eukaryotic proteins can adopt structures that are mostly [...]
disordered, fluctuating rapidly between many different conforma- tions.

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it is now thought that perhaps a quarter of all eukaryotic proteins can adopt structures that are mostly disordered, fluctuating rapidly between many different conforma- tions.

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#### Flashcard 1484508237068

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[...]—an enzyme in tears that dissolves bacterial cell walls—retains its antibacterial activity for a long time because it is stabilized by such cross-linkages.
lysozyme

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lysozyme—an enzyme in tears that dissolves bacterial cell walls—retains its antibacterial activity for a long time because it is stabilized by such cross-linkages.

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#### Flashcard 1484509809932

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lysozyme—an enzyme in tears that [...]—retains its antibacterial activity for a long time because it is stabilized by such cross-linkages.
dissolves bacterial cell walls

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lysozyme—an enzyme in tears that dissolves bacterial cell walls—retains its antibacterial activity for a long time because it is stabilized by such cross-linkages.

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#### Flashcard 1484511382796

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lysozyme—an enzyme in tears that dissolves bacterial cell walls—retains its antibacterial activity for a long time because it is [...]
stabilized by such cross-linkages.

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lysozyme—an enzyme in tears that dissolves bacterial cell walls—retains its antibacterial activity for a long time because it is stabilized by such cross-linkages.

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#### Flashcard 1484512955660

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The use of smaller subunits to build larger structures has several advantages: [...] 2. Both assembly and disassembly can be readily controlled reversible pro- cesses, because the subunits associate through multiple bonds of relatively low energy. 3. Errors in the synthesis of the structure can be more easily avoided, since correction mechanisms can operate during the course of assembly to exclude malformed subunits.
1. A large structure built from one or a few repeating smaller subunits requires only a small amount of genetic information.

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The use of smaller subunits to build larger structures has several advantages: 1. A large structure built from one or a few repeating smaller subunits requires only a small amount of genetic information. 2. Both assembly and disassembly can be readily controlled reversible pro- cesses, because the subunits associate through multiple bonds of relatively low energy. 3. Errors in the sy

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#### Flashcard 1484514528524

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The use of smaller subunits to build larger structures has several advantages: 1. A large structure built from one or a few repeating smaller subunits requires only a small amount of genetic information. [...] 3. Errors in the synthesis of the structure can be more easily avoided, since correction mechanisms can operate during the course of assembly to exclude malformed subunits.
2. Both assembly and disassembly can be readily controlled reversible pro- cesses, because the subunits associate through multiple bonds of relatively low energy.

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The use of smaller subunits to build larger structures has several advantages: 1. A large structure built from one or a few repeating smaller subunits requires only a small amount of genetic information. 2. Both assembly and disassembly can be readily controlled reversible pro- cesses, because the subunits associate through multiple bonds of relatively low energy. 3. Errors in the synthesis of the structure can be more easily avoided, since correction mechanisms can operate during the course of assembly to exclude malformed subunits.</s

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#### Flashcard 1484516101388

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The use of smaller subunits to build larger structures has several advantages: 1. A large structure built from one or a few repeating smaller subunits requires only a small amount of genetic information. 2. Both assembly and disassembly can be readily controlled reversible pro- cesses, because the subunits associate through multiple bonds of relatively low energy. [...]
3. Errors in the synthesis of the structure can be more easily avoided, since correction mechanisms can operate during the course of assembly to exclude malformed subunits.

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eating smaller subunits requires only a small amount of genetic information. 2. Both assembly and disassembly can be readily controlled reversible pro- cesses, because the subunits associate through multiple bonds of relatively low energy. <span>3. Errors in the synthesis of the structure can be more easily avoided, since correction mechanisms can operate during the course of assembly to exclude malformed subunits.<span><body><html>

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#### Flashcard 1484540742924

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These principles are dramatically illustrated in the protein coat or capsid of many simple viruses, which takes the form of a [...]
hollow sphere based on an icosahedron

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These principles are dramatically illustrated in the protein coat or capsid of many simple viruses, which takes the form of a hollow sphere based on an icosahedron

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#### Flashcard 1484542315788

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The first large macromolecular aggregate shown to be capable of self-as- sembly from its component parts was [...]
tobacco mosaic virus (TMV ).

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The first large macromolecular aggregate shown to be capable of self-as- sembly from its component parts was tobacco mosaic virus (TMV ).

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#### Flashcard 1484543888652

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the simplest case, a long core protein or other macromolecule provides a scaffold that determines the extent of the final assembly. This is the mechanism that deter- mines the length of the [...] particle, where the RNA chain provides the core. Similarly, a core protein interacting with actin is thought to determine the length of the thin filaments in muscle.
TMV

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the simplest case, a long core protein or other macromolecule provides a scaffold that determines the extent of the final assembly. This is the mechanism that deter- mines the length of the TMV particle, where the RNA chain provides the core. Similarly, a core protein interacting with actin is thought to determine the length of the thin filaments in muscle.</bo

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#### Flashcard 1484545461516

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the simplest case, a long core protein or other macromolecule provides a scaffold that determines the extent of the final assembly. This is the mechanism that deter- mines the length of the TMV particle, where the RNA chain provides the core. Similarly, a core protein interacting with [...] is thought to determine the length of the thin filaments in muscle.
actin

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er macromolecule provides a scaffold that determines the extent of the final assembly. This is the mechanism that deter- mines the length of the TMV particle, where the RNA chain provides the core. Similarly, a core protein interacting with <span>actin is thought to determine the length of the thin filaments in muscle.<span><body><html>

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#### Flashcard 1484547034380

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Typically, hundreds of monomers will aggregate to form an unbranched fibrous structure that is several micrometers long and [...] in width
5 to 15 nm

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Typically, hundreds of monomers will aggregate to form an unbranched fibrous structure that is several micrometers long and 5 to 15 nm in width

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#### Flashcard 1484548607244

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Typically, hundreds of monomers will aggregate to form an unbranched fibrous structure that is [...] long and 5 to 15 nm in width
several micrometers

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Typically, hundreds of monomers will aggregate to form an unbranched fibrous structure that is several micrometers long and 5 to 15 nm in width

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#### Flashcard 1484550180108

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A surprisingly large fraction of pro- teins have the potential to form [...] structures, because the short segment of the polypeptide chain that forms the spine of the fibril can have a variety of different sequences and follow one of several different paths (Figure 3–32). However, very few proteins will actually form this structure inside cells
amyloid fibril

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A surprisingly large fraction of pro- teins have the potential to form such structures, because the short segment of the polypeptide chain that forms the spine of the fibril can have a variety of different sequences and follow one of several different paths (

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#### Flashcard 1484551752972

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A surprisingly large fraction of pro- teins have the potential to form Amyloid fibril structures, because [...] (Figure 3–32). However, very few proteins will actually form this structure inside cells
the short segment of the polypeptide chain that forms the spine of the fibril can have a variety of different sequences and follow one of several different paths

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A surprisingly large fraction of pro- teins have the potential to form such structures, because the short segment of the polypeptide chain that forms the spine of the fibril can have a variety of different sequences and follow one of several different paths (Figure 3–32). However, very few proteins will actually form this structure inside cells

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#### Flashcard 1484554112268

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A set of closely related diseases—[...] in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP
scra- pie

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular pr

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#### Flashcard 1484555685132

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A set of closely related diseases—scra- pie in sheep, [...] disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP
Creutzfeldt–Jakob

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP</spa

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#### Flashcard 1484557257996

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, [...] in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP
Kuru

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP

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#### Flashcard 1484558830860

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and [...] (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP
bovine spongiform encephalopathy

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP

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#### Flashcard 1484560403724

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a [...]
misfolded, aggregated form of a particular protein called PrP

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A set of closely related diseases—scra- pie in sheep, Creutzfeldt–Jakob disease (CJD) in humans, Kuru in humans, and bovine spongiform encephalopathy (BSE) in cattle—are caused by a misfolded, aggregated form of a particular protein called PrP

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#### Flashcard 1484561976588

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Eukaryotic cells, for example, store many different peptide and protein hormones that they will secrete in specialized “secretory granules,” which package a high concentra- tion of their cargo in dense cores with a regular structure (see Figure 13–65). We now know that these structured cores consist of [...], which in this case have a structure that causes them to dissolve to release soluble cargo after being secreted by exocytosis to the cell exterior
amyloid fibrils

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protein hormones that they will secrete in specialized “secretory granules,” which package a high concentra- tion of their cargo in dense cores with a regular structure (see Figure 13–65). We now know that these structured cores consist of <span>amyloid fibrils, which in this case have a structure that causes them to dissolve to release soluble cargo after being secreted by exocytosis to the cell exterior<span><body><html>

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#### Flashcard 1484563549452

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Eukaryotic cells, for example, store many different peptide and protein hormones that they will secrete in specialized “secretory granules,” which package a high concentra- tion of their cargo in dense cores with a regular structure (see Figure 13–65). We now know that these structured cores consist of amyloid fibrils, which in this case have a structure that causes them [...]
to dissolve to release soluble cargo after being secreted by exocytosis to the cell exterior

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nules,” which package a high concentra- tion of their cargo in dense cores with a regular structure (see Figure 13–65). We now know that these structured cores consist of amyloid fibrils, which in this case have a structure that causes them <span>to dissolve to release soluble cargo after being secreted by exocytosis to the cell exterior<span><body><html>

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#### Flashcard 1484565122316

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When A has [...] then solving a linear equation using the pseudoin v erse provides one of the man y p ossible solutions. Speciﬁcally , it pro vides the solution x = A + y with minimal Euclidean norm || || x 2 among all p ossible solutions
more columns than rows,

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When A has more columns than rows, then solving a linear equation using the pseudoin v erse provides one of the man y p ossible solutions. Speciﬁcally , it pro vides the solution x = A + y with minimal Euclidean norm ||

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When A has more columns than rows, then solving a linear equation using the [...] provides one of the man y p ossible solutions. Speciﬁcally , it pro vides the solution x = A + y with minimal Euclidean norm || || x 2 among all p ossible solutions
pseudoin v erse

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When A has more columns than rows, then solving a linear equation using the pseudoin v erse provides one of the man y p ossible solutions. Speciﬁcally , it pro vides the solution x = A + y with minimal Euclidean norm || || x 2 among all p ossible solutions

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When A has more columns than rows, then solving a linear equation using the pseudoin v erse provides one of the man y p ossible solutions. Speciﬁcally , it pro vides [...]
the solution x = A + y with minimal Euclidean norm ||x||2 among all p ossible solutions

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When A has more columns than rows, then solving a linear equation using the pseudoin v erse provides one of the man y p ossible solutions. Speciﬁcally , it pro vides the solution x = A + y with minimal Euclidean norm ||x|| 2 among all p ossible solutions

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the [...] provides an alternativ e w a y of writing the F rob enius norm of a matrix: || || A F = T r( AA )
trace op erator

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the trace op erator provides an alternativ e w a y of writing the F rob enius norm of a matrix: || || A F = T r( AA )

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the trace op erator provides an alternativ e w a y of writing the [...] of a matrix: || || A F = T r( AA )
F rob enius norm

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the trace op erator provides an alternativ e w a y of writing the F rob enius norm of a matrix: || || A F = T r( AA )

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the trace op erator provides an alternativ e w a y of writing the F rob enius norm of a matrix: ||A||F = [...]
Tr( AAT )

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the trace op erator provides an alternativ e w a y of writing the F rob enius norm of a matrix: ||A|| F = Tr( AA T )

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the trace op erator is in v arian t to the [...]: T r( ) = T r( A A )
transp ose op erator

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the trace op erator is in v arian t to the transp ose op erator: T r( ) = T r( A A )

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the [...] is in v arian t to the transp ose op erator: T r( ) = T r( A A )
trace op erator

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the trace op erator is in v arian t to the transp ose op erator: T r( ) = T r( A A )

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the trace op erator is in v arian t to the transp ose op erator: T r(A) = [...]
T r(AT )

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the trace op erator is in v arian t to the transp ose op erator: T r(A) = T r(A T )

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This inv ariance to cyclic p erm utation holds even if [...] F or example, for A ∈ R m n × and B ∈ R n m × , w e ha v e T r(AB ) = T r( BA)
the resulting pro duct has a diﬀeren t shap e.

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This inv ariance to cyclic p erm utation holds even if the resulting pro duct has a diﬀeren t shap e. F or example, for A ∈ R m n × and B ∈ R n m × , w e ha v e T r(AB ) = T r( BA)

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One simple mac hine learning algorithm, [...] can b e deriv ed using only knowledge of basic linear algebra
principal components analysis or PCA

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One simple mac hine learning algorithm, principal components analysis or PCA can b e deriv ed using only knowledge of basic linear algebra

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Lossy compression means [...]
storing the p oints in a wa y that requires less memory but ma y lose some precision

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Lossy compression means storing the p oints in a wa y that requires less memory but ma y lose some precision

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[...] means storing the p oints in a wa y that requires less memory but ma y lose some precision
Lossy compression

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Lossy compression means storing the p oints in a wa y that requires less memory but ma y lose some precision

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T o k eep the enco ding problem easy , PCA [...]
constrains the colum ns of D to b e orthogonal to eac h other.

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T o k eep the enco ding problem easy , PCA constrains the colum ns of D to b e orthogonal to eac h other.

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There are three p ossible sources of uncertain t y: [...] 2. Incomplete observ ability . Ev en deterministic systems can app ear sto chastic when w e cannot observ e all of the v ariables that drive the b ehavior of the system. F or example, in the Mont y Hall problem, a game sho w con testan t is ask ed to choose b etw een three do ors and wins a prize held b ehind the c hosen do or. T w o do ors lead to a goat while a third leads to a car. The outcome giv en the contestan t’s c hoice is deterministic, but from the con testan t’s p oin t of view, the outcome is uncertain. 3. Incomplete mo deling. When we use a mo del that must discard some of the information we hav e observ ed, the discarded information results in uncertain t y in the mo del’s predictions.
1. Inheren t stochasticit y in the system b eing mo deled. F or example, most in terpretations of quantum mechanics describ e the dynamics of subatomic particles as b eing probabilistic. W e can also create theoretical scenarios that w e p ostulate to ha v e random dynamics, such as a hypothetical card game where w e assume that the cards are truly sh uﬄed in to a random order.

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There are three p ossible sources of uncertain t y: 1. Inheren t stochasticit y in the system b eing mo deled. F or example, most in terpretations of quantum mechanics describ e the dynamics of subatomic particles as b eing probabilistic. W e can also create theoretical scenarios that w e p ostulate to ha v e random dynamics, such as a hypothetical card game where w e assume that the cards are truly sh uﬄed in to a random order. 2. Incomplete observ ability . Ev en deterministic systems can app ear sto chastic when w e cannot observ e all of the v ariables that drive the b ehavior of the system. F or example, i

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There are three p ossible sources of uncertain t y: 1. Inheren t stochasticit y in the system b eing mo deled. F or example, most in terpretations of quantum mechanics describ e the dynamics of subatomic particles as b eing probabilistic. W e can also create theoretical scenarios that w e p ostulate to ha v e random dynamics, such as a hypothetical card game where w e assume that the cards are truly sh uﬄed in to a random order. [...] 3. Incomplete mo deling. When we use a mo del that must discard some of the information we hav e observ ed, the discarded information results in uncertain t y in the mo del’s predictions.
2. Incomplete observ ability . Ev en deterministic systems can app ear sto chastic when w e cannot observ e all of the v ariables that drive the b ehavior of the system. F or example, in the Mont y Hall problem, a game sho w con testan t is ask ed to choose b etw een three do ors and wins a prize held b ehind the c hosen do or. T w o do ors lead to a goat while a third leads to a car. The outcome giv en the contestan t’s c hoice is deterministic, but from the con testan t’s p oin t of view, the outcome is uncertain.

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of subatomic particles as b eing probabilistic. W e can also create theoretical scenarios that w e p ostulate to ha v e random dynamics, such as a hypothetical card game where w e assume that the cards are truly sh uﬄed in to a random order. <span>2. Incomplete observ ability . Ev en deterministic systems can app ear sto chastic when w e cannot observ e all of the v ariables that drive the b ehavior of the system. F or example, in the Mont y Hall problem, a game sho w con testan t is ask ed to choose b etw een three do ors and wins a prize held b ehind the c hosen do or. T w o do ors lead to a goat while a third leads to a car. The outcome giv en the contestan t’s c hoice is deterministic, but from the con testan t’s p oin t of view, the outcome is uncertain. 3. Incomplete mo deling. When we use a mo del that must discard some of the information we hav e observ ed, the discarded information results in uncertain t y in the mo del’s prediction

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There are three p ossible sources of uncertain t y: 1. Inheren t stochasticit y in the system b eing mo deled. F or example, most in terpretations of quantum mechanics describ e the dynamics of subatomic particles as b eing probabilistic. W e can also create theoretical scenarios that w e p ostulate to ha v e random dynamics, such as a hypothetical card game where w e assume that the cards are truly sh uﬄed in to a random order. 2. Incomplete observ ability . Ev en deterministic systems can app ear sto chastic when w e cannot observ e all of the v ariables that drive the b ehavior of the system. F or example, in the Mont y Hall problem, a game sho w con testan t is ask ed to choose b etw een three do ors and wins a prize held b ehind the c hosen do or. T w o do ors lead to a goat while a third leads to a car. The outcome giv en the contestan t’s c hoice is deterministic, but from the con testan t’s p oin t of view, the outcome is uncertain. [...]
3. Incomplete mo deling. When we use a mo del that must discard some of the information we hav e observ ed, the discarded information results in uncertain t y in the mo del’s predictions.

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s and wins a prize held b ehind the c hosen do or. T w o do ors lead to a goat while a third leads to a car. The outcome giv en the contestan t’s c hoice is deterministic, but from the con testan t’s p oin t of view, the outcome is uncertain. <span>3. Incomplete mo deling. When we use a mo del that must discard some of the information we hav e observ ed, the discarded information results in uncertain t y in the mo del’s predictions.<span><body><html>

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A random v ariable is [...]
a v ariable that can take on diﬀerent v alues randomly

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A random v ariable is a v ariable that can take on diﬀerent v alues randomly

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On its o wn, a random v ariable is just [...] it m ust b e coupled with a probability distribution that sp eciﬁes how likely each of these states are.
a description of the states that are p ossible;

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On its o wn, a random v ariable is just a description of the states that are p ossible; it m ust b e coupled with a probability distribution that sp eciﬁes how likely each of these states are.

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On its o wn, a random v ariable is just a description of the states that are p ossible; it m ust b e [...]
coupled with a probability distribution that sp eciﬁes how likely each of these states are.

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On its o wn, a random v ariable is just a description of the states that are p ossible; it m ust b e coupled with a probability distribution that sp eciﬁes how likely each of these states are.

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T o b e a probability mass function on a random v ariable x , a function P m ust satisfy the follo wing prop erties:
• The domain of P [...]
• ∀x ∈ x , 0 ≤ P ( x ) ≤ 1 . An imp ossible ev en t has probabilit y and no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1
$$\sum_{x \in x}P(x) = 1$$ . W e refer to this prop erty as b eing normalized . Without this prop ert y , we could obtain probabilities greater than one by computing the probabilit y of one of man y ev en ts o ccurring.
must b e the set of all p ossible states of x.

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T o b e a probability mass function on a random v ariable x , a function P m ust satisfy the follo wing prop erties: • The domain of P must b e the set of all p ossible states of x. • ∀x ∈ x , 0 ≤ P ( x ) ≤ 1 . An imp ossible ev en t has probabilit y and no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has proba

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T o b e a probability mass function on a random v ariable x , a function P m ust satisfy the follo wing prop erties:
• The domain of P must b e the set of all p ossible states of x.
• ∀x ∈ x , [...]
$$\sum_{x \in x}P(x) = 1$$ . W e refer to this prop erty as b eing normalized . Without this prop ert y , we could obtain probabilities greater than one by computing the probabilit y of one of man y ev en ts o ccurring.
0 ≤ P ( x ) ≤ 1 . An imp ossible ev en t has probabilit y and no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1

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T o b e a probability mass function on a random v ariable x , a function P m ust satisfy the follo wing prop erties: • The domain of P must b e the set of all p ossible states of x. • ∀x ∈ x , 0 ≤ P ( x ) ≤ 1 . An imp ossible ev en t has probabilit y and no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1 • ∑x∈xP(x)=1∑x∈xP(x)=1 . W e refer to this prop erty as b eing normalized . Without this prop ert y , we could obtain probabilities greater than one by computing the probabilit y o

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T o b e a probability mass function on a random v ariable x , a function P m ust satisfy the follo wing prop erties:
• The domain of P must b e the set of all p ossible states of x.
• ∀x ∈ x , 0 ≤ P ( x ) ≤ 1 . An imp ossible ev en t has probabilit y and no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1
$$\sum_{x \in x}P(x) = 1$$ . W e refer to this prop erty as b eing [...] . Without this prop ert y , we could obtain probabilities greater than one by computing the probabilit y of one of man y ev en ts o ccurring.
normalized

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no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1 • ∑x∈xP(x)=1∑x∈xP(x)=1 . W e refer to this prop erty as b eing <span>normalized . Without this prop ert y , we could obtain probabilities greater than one by computing the probabilit y of one of man y ev en ts o ccurring.<span><body><html>

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T o b e a probability mass function on a random v ariable x , a function P m ust satisfy the follo wing prop erties:
• The domain of P must b e the set of all p ossible states of x.
• ∀x ∈ x , 0 ≤ P ( x ) ≤ 1 . An imp ossible ev en t has probabilit y and no state can 0 b e less probable than that. Likewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1
$$\sum_{x \in x}P(x) = 1$$ . W e refer to this prop erty as b eing normalized . Without this prop ert y , we could [...]
obtain probabilities greater than one by computing the probabilit y of one of man y ev en ts o ccurring.

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ewise, an ev en t that is guaran teed to happ en has probabilit y , and no state can ha v e a greater c hance of o ccurring. 1 • ∑x∈xP(x)=1∑x∈xP(x)=1 . W e refer to this prop erty as b eing normalized . Without this prop ert y , we could <span>obtain probabilities greater than one by computing the probabilit y of one of man y ev en ts o ccurring.<span><body><html>

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W e can place a uniform distribution on x —that is, make each of its states equally lik ely—b y setting its probabilit y mass function to [...]
P (x = x i ) = 1/k

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W e can place a uniform distribution on x —that is, make each of its states equally lik ely—b y setting its probabilit y mass function to P (x = x i ) = 1/k

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The probability distribution o v er the subset is kno wn as the [...]
marginal probability distribution.

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The probability distribution o v er the subset is kno wn as the marginal probability distribution.

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The name “[...]” comes from the pro cess of computing marginal probabilities on pap er. When the v alues of P ( x y , ) are written in a grid with diﬀeren t v alues of x in rows and diﬀerent v alues of y in columns, it is natural to sum across a row of the grid, then write P ( x ) in the margin of the pap er just to the righ t of the ro w
marginal probabilit y

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The name “marginal probabilit y” comes from the pro cess of computing marginal probabilities on pap er. When the v alues of P ( x y , ) are written in a grid with diﬀeren t v alues of x in rows and diﬀerent v alues of

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The name “marginal probabilit y” comes from [...]. When the v alues of P ( x y , ) are written in a grid with diﬀeren t v alues of x in rows and diﬀerent v alues of y in columns, it is natural to sum across a row of the grid, then write P ( x ) in the margin of the pap er just to the righ t of the ro w
the pro cess of computing marginal probabilities on pap er

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The name “marginal probabilit y” comes from the pro cess of computing marginal probabilities on pap er. When the v alues of P ( x y , ) are written in a grid with diﬀeren t v alues of x in rows and diﬀerent v alues of y in columns, it is natural to sum across a row of the grid, then writ

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The name “marginal probabilit y” comes from the pro cess of computing marginal probabilities on pap er. When the v alues of P ( x y , ) are written in a grid with diﬀeren t v alues of x in rows and diﬀerent v alues of y in columns, it is natural to [...], then write P ( x ) in the margin of the pap er just to the righ t of the ro w
sum across a row of the grid

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me “marginal probabilit y” comes from the pro cess of computing marginal probabilities on pap er. When the v alues of P ( x y , ) are written in a grid with diﬀeren t v alues of x in rows and diﬀerent v alues of y in columns, it is natural to <span>sum across a row of the grid, then write P ( x ) in the margin of the pap er just to the righ t of the ro w<span><body><html>

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The exp ectation or exp ected v alue of some function f ( x ) with resp ect to a probabilit y distribution P ( x ) is the [...] that f tak es on when x is dra wn from . F or discrete v ariables this can be computed with a summation: P E x ∼ P [ ( )] = f x x P x f x , ( ) ( )
a v erage or mean v alue

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The exp ectation or exp ected v alue of some function f ( x ) with resp ect to a probabilit y distribution P ( x ) is the a v erage or mean v alue that f tak es on when x is dra wn from . F or discrete v ariables this can be computed with a summation: P E x ∼ P [ ( )] = f x x P x f x , ( ) ( )

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The exp ectation or exp ected v alue of some function f ( x ) with resp ect to a probabilit y distribution P ( x ) is the a v erage or mean v alue that f tak es on when x is dra wn from . F or discrete v ariables this can be computed with [...]
a summation: Ex~P[f(x)]=$$\sum_{x} P(x)f(x)$$xP(x)f(x)